Finite Group Databasebeta

← #17199734

Subgroups — #17199734

Order 4352.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763448C211yesmaximal, characteristic
2#14531931C211yesmaximal, characteristic, complemented
3#14531927C211yesmaximal, characteristic, complemented
4#14531922C211yesmaximal, characteristic, complemented
5#14531921C211yesmaximal, characteristic, complemented
6#14531856C211yesmaximal, characteristic, complemented
7#14531826C211yesmaximal, characteristic, complemented
8#14531823C211yesmaximal, characteristic, complemented
9#14531806C211yesmaximal, characteristic, complemented
10#14531795C211yesmaximal, characteristic, complemented
11#14531752C211yesmaximal, characteristic, complemented
12#14531707C211yesmaximal, characteristic, complemented
13#14531627C211yesmaximal, characteristic, complemented
14#14531626C211yesmaximal, characteristic, complemented
15#14531623C211yesmaximal, characteristic, complemented
16#14531602C211yesmaximal, characteristic, complemented
17#14531580C211yesmaximal, characteristic, complemented
18#14531571C211yesmaximal, characteristic, complemented
19#14531547C211yesmaximal, characteristic, complemented
20#14531474C211yesmaximal, characteristic, complemented
21#14531465C211yesmaximal, characteristic, complemented
22#14531447C211yesmaximal, characteristic, complemented
23#14531440C211yesmaximal, characteristic, complemented
24#14531379C211yesmaximal, characteristic, complemented
25#14531378C211yesmaximal, characteristic, complemented
26#14531371C211yesmaximal, characteristic, complemented
27#14531363C211yesmaximal, characteristic, complemented
28#14531325C211yesmaximal, characteristic, complemented
29#14531247C211yesmaximal, characteristic, complemented
30#14531244C211yesmaximal, characteristic, complemented
31C17×#2333C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34#11763448C4116yescomplemented
35C2×#10587571C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587621C2211yescharacteristic
38C2×#10587582C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587623C2211yescharacteristic
42C2×#10587623C2211yescharacteristic
43C2×C4×Dic34C2211yescharacteristic, complemented
44C2×#10587573C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic, complemented
46C2×C4×C22⋊D17C2211yescharacteristic
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic, complemented
49C2×#10587567C2211yescharacteristic
50C2×#10587567C2211yescharacteristic
51C2×#10587612C2211yescharacteristic, complemented
52C2×#10587578C2211yescharacteristic
53C2×#10587558C2211yescharacteristic
54C2×#10587558C2211yescharacteristic, complemented
55C2×#10587563C2211yescharacteristic, complemented
56C22×#63225C2211yescharacteristic, complemented
57C22×#63227C2211yescharacteristic
58C22×#63227C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61#11762713C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762712C2211yescharacteristic
64#11762712C2211yescharacteristic, complemented
65#11762712C2211yescharacteristic, complemented
66#11762711C2211yescharacteristic
67#11762710C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic
71#11762709C2211yescharacteristic
72#11762709C2211yescharacteristic
73#11762709C2211yescharacteristic
74#11762709C2211yescharacteristic
75#11762709C2211yescharacteristic
76#11762709C2211yescharacteristic, complemented
77#11762709C2211yescharacteristic, complemented
78#11762709C2211yescharacteristic, complemented
79#11762708C2211yescharacteristic, complemented
80#11762706C2211yescharacteristic, complemented
81#11762706C2211yescharacteristic, complemented
82#11762706C2211yescharacteristic, complemented
83#11762706C2211yescharacteristic, complemented
84#11762704C2211yescharacteristic, complemented
85#11762703C2211yescharacteristic, complemented
86#11762703C2211yescharacteristic, complemented
87#11762703C2211yescharacteristic, complemented
88#11762702C2211yescharacteristic, complemented
89#11762702C2211yescharacteristic, complemented
90#11762701C2211yescharacteristic
91#11762701C2211yescharacteristic
92#11762701C2211yescharacteristic
93#11762701C2211yescharacteristic, complemented
94#11762701C2211yescharacteristic, complemented
95#11762700C2211yescharacteristic
96#11762700C2211yescharacteristic
97#11762700C2211yescharacteristic
98#11762700C2211yescharacteristic, complemented
99#11762700C2211yescharacteristic, complemented
100#11762700C2211yescharacteristic, complemented
101#11762699C2211yescharacteristic
102#11762699C2211yescharacteristic, complemented
103#11762698C2211yescharacteristic
104#11762698C2211yescharacteristic
105#11762698C2211yescharacteristic
106#11762698C2211yescharacteristic
107#11762698C2211yescharacteristic
108#11762698C2211yescharacteristic, complemented
109#11762698C2211yescharacteristic, complemented
110#11762698C2211yescharacteristic, complemented
111#11762698C2211yescharacteristic, complemented
112#11762697C2211yescharacteristic, complemented
113#11762697C2211yescharacteristic, complemented
114#11762697C2211yescharacteristic, complemented
115#11762697C2211yescharacteristic, complemented
116#11762697C2211yescharacteristic, complemented
117#11762693C2211yescharacteristic, complemented
118#11762691C2211yescharacteristic, complemented
119#11762691C2211yescharacteristic, complemented
120#11762690C2211yescharacteristic, complemented
121#11762689C2211yescharacteristic
122#11762689C2211yescharacteristic, complemented
123#11762688C2211yescharacteristic
124#11762688C2211yescharacteristic, complemented
125#11762687C2211yescharacteristic
126#11762687C2211yescharacteristic
127#11762686C2211yescharacteristic
128#11762686C2211yescharacteristic, complemented
129#11762686C2211yescharacteristic, complemented
130#11762685C2211yescharacteristic, complemented
131#11762683C2211yescharacteristic, complemented
132#11762683C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762682C2211yescharacteristic, complemented
135#11762682C2211yescharacteristic, complemented
136#11762681C2211yescharacteristic, complemented
137#11762673C2211yescharacteristic, complemented
138#11762671C2211yescharacteristic, complemented
139#11762668C2211yescharacteristic
140#11762668C2211yescharacteristic, complemented
141#11762668C2211yescharacteristic, complemented
142#11762667C2211yescharacteristic, complemented
143#11762667C2211yescharacteristic, complemented
144#11762667C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic, complemented
146#11762666C2211yescharacteristic, complemented
147#11762664C2211yescharacteristic
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150#11762664C2211yescharacteristic
151#11762664C2211yescharacteristic
152#11762664C2211yescharacteristic
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157#11762660C2211yescharacteristic, complemented
158#11762660C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C22⋊C4×Dic17C2211yescharacteristic, complemented
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C4×#63227C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic, complemented
171#11762656C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#390C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic, complemented
184C17×#381C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C2×#63254—42no—
206C2×#63254—42no—
207C2×#63254C2×C418yescomplemented
208C2×D4×D17—42no—
209C2×D4×D17—42no—
210C2×D4×D17C2×C418yescomplemented
211C22×D68C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×Dic34C2311yescharacteristic
218C17×#121C2×C418yescomplemented
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251#10587625C2×C418yes—
252#10587623C2×C418yescomplemented
253#10587623C2×C418yescomplemented
254#10587621C2×C418yescomplemented
255D4×Dic17—42no—
256C4×C22⋊D17—42no—
257C4×C22⋊D17—42no—
258C4×C22⋊D17C2×C418yescomplemented
259C2×#63227—42no—
260C2×#63227C2×C418yescomplemented
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290#10587612—42no—
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×#63225—42no—
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330#10587582C2×C418yescomplemented
331#10587580C2×C418yescomplemented
332#10587578—42no—
333#10587573—42no—
334#10587571C2×C418yescomplemented
335#10587570C2×C418yescomplemented
336#10587567—42no—
337#10587567C2×C418yescomplemented
338C22⋊C4×D17—42no—
339C22⋊C4×D17C2×C418yescomplemented
340#10587563—42no—
341#10587558—42no—
342#10587558—42no—
343C4×Dic34—42no—
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17—41no—
391C23×D17C22×C414yes—
392C23×D17C22×C414yes—
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C2×D4×C17—41no—
397C2×D4×C17—41no—
398C2×D4×C17—41no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17C22×C414yes—
403C2×D4×C17C22×C414yes—
404C2×D4×C17C22×C414yes—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17C22×C414yes—
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17C22×C414yes—
437C2×C22⋊D17C22×C414yes—
438C2×C22⋊D17C22×C414yes—
439C2×C22⋊D17C22×C414yes—
440C2×C22⋊D17C22×C414yes—
441C22×Dic17—22no—
442C22×Dic17—22no—
443C22×Dic17—22no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17C22×C414yes—
452C22×Dic17C22×C414yes—
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466#63254—416no—
467D4×D17—416no—
468C2×D68—41no—
469C2×D68—41no—
470C2×D68C22×C414yes—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17C22×C414yes—
484C2×C4×D17C22×C414yes—
485C2×C4×D17C22×C414yes—
486C2×Dic34—22no—
487C2×Dic34—22no—
488C2×Dic34C22×C414yes—
489C4⋊C4×C17—41no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17C22×C414yes—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17C22×C414yes—
503C22⋊C4×C17C22×C414yes—
504C42×C17—41no—
505C42×C17—41no—
506C42×C17—41no—
507C42×C17—41no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17C22×C414yes—
519C22⋊Dic17C22×C414yes—
520C22⋊Dic17C22×C414yes—
521#63227—22no—
522#63227—22no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227C22×C414yes—
544#63227C22×C414yes—
545#63227C22×C414yes—
546#63227C22×C414yes—
547#63227C22×C414yes—
548#63227C22×C414yes—
549#63227C22×C414yes—
550C4⋊Dic17—22no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554#63225—22no—
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—22no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225C22×C414yes—
569#63225C22×C414yes—
570#63225C22×C414yes—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17—41no—
587C4×Dic17C22×C414yes—
588#34495—171nomaximal, Sylow
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17C23×C412yes—
608C23×C17C23×C412yes—
609C23×C17C23×C412yes—
610C23×C17C2511yescharacteristic
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—44no—
630C22×D17—44no—
631C22×D17—44no—
632C22×D17—44no—
633C22×D17—44no—
634C22×D17—44no—
635C22×D17—82no—
636C22×D17—82no—
637C22×D17—82no—
638C22×D17—82no—
639C22×D17—82no—
640C22×D17—82no—
641C22×D17—82no—
642C22×D17—82no—
643C22×D17C23×C412yes—
644C22×D17C23×C412yes—
645C22×D17C23×C412yes—
646D4×C17—44no—
647D4×C17—44no—
648D4×C17—44no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—44no—
682C2×C4×C17—82no—
683C2×C4×C17—82no—
684C2×C4×C17C23×C412yes—
685C2×C4×C17C23×C412yes—
686C2×C4×C17C23×C412yes—
687C2×C4×C17C23×C412yes—
688C22⋊D17—28no—
689C22⋊D17—28no—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—44no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—28no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—44no—
726C2×Dic17—82no—
727C2×Dic17—82no—
728C2×Dic17C23×C412yes—
729C2×Dic17C23×C412yes—
730C2×Dic17C23×C412yes—
731C2×Dic17C23×C412yes—
732C2×Dic17C23×C412yes—
733C2×Dic17H(5,𝔽2)12yes—
734C2×Dic17H(5,𝔽2)12yes—
735C2×Dic17H(5,𝔽2)12yes—
736D68—44no—
737C4×D17—28no—
738C4×D17—44no—
739C4×D17—44no—
740C4×D17—82no—
741C4×D17—82no—
742Dic34—28no—
743C2×#546—171no—
744#2376—171no—
745#2376—171no—
746#2375—171no—
747#2375—171no—
748#2367—171no—
749#2363—171no—
750#2363—171no—
751#2362—171no—
752#2361—171no—
753#2357—171no—
754#2352—171no—
755#2342—171no—
756#2342—171no—
757#2341—171no—
758D4×C22⋊C4—171no—
759#2335—171no—
760#2335—171no—
761#2333—171no—
762#2333D1711yescharacteristic, complemented
763#2324—171no—
764#2323—171no—
765#2321—171no—
766#2321—171no—
767#2312—171no—
768#2312—171no—
769#2311—171no—
770#2309—171no—
771C4×#124—171no—
772#2293—171no—
773#2293—171no—
774C22×C17—22no—
775C22×C17—22no—
776C22×C17—22no—
777C22×C17—22no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17C24×C411yescharacteristic
796C22×C17C2×H(5,𝔽2)11yescharacteristic
797C22×C17C2×H(5,𝔽2)11yescharacteristic
798C22×C17C2×H(5,𝔽2)11yescharacteristic
799C22×C17#58511yescharacteristic
800C22×C17#58511yescharacteristic
801C22×C17#58511yescharacteristic
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—41no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—88no—
824C2×D17—88no—
825C4×C17—22no—
826C4×C17—22no—
827C4×C17—22no—
828C4×C17—22no—
829C4×C17—41no—
830C4×C17—41no—
831C4×C17—41no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837Dic17—22no—
838Dic17—22no—
839Dic17—22no—
840Dic17—22no—
841Dic17—22no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845Dic17—41no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17#51814yes—
850C22×#41—171no—
851C23×D4—171no—
852#546—1716no—
853C2×#124—171no—
854C2×#123—171no—
855C2×#123—171no—
856C2×C22⋊Q8—171no—
857C2×#121—171no—
858C2×#121—171no—
859C2×#121C2×D1711yescharacteristic
860C2×#120—171no—
861C2×#120—171no—
862C2×C4×Q8—171no—
863C2×C4×Q8—171no—
864C2×C4×D4—171no—
865C2×C4×D4—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×#117—171no—
871C2×#117—171no—
872C2×#117—171no—
873C2×#117—171no—
874C2×#117—171no—
875C22×C4⋊C4—171no—
876C22×C22⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C22⋊C4—171no—
879C22×C22⋊C4—171no—
880#391—171no—
881#391—171no—
882#390—171no—
883#390—171no—
884#390—171no—
885#390—171no—
886#390—171no—
887#390—171no—
888#390—171no—
889#390—171no—
890#390—171no—
891#390—171no—
892#390—171no—
893#390—171no—
894#390—171no—
895#390—171no—
896#390—171no—
897#390—171no—
898#390C2×D1711yescharacteristic
899#390C2×D1711yescharacteristic, complemented
900#389—171no—
901#389—171no—
902#389—171no—
903#389—171no—
904#389—171no—
905#389—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388—171no—
922#388—171no—
923#388—171no—
924#388—171no—
925#388—171no—
926#388—171no—
927#388—171no—
928#388—171no—
929#388—171no—
930#388—171no—
931#388—171no—
932#388—171no—
933#388—171no—
934#388—171no—
935#388—171no—
936#388—171no—
937#388—171no—
938#388C2×D1711yescharacteristic, complemented
939#388C2×D1711yescharacteristic, complemented
940#387—171no—
941#387—171no—
942#387—171no—
943#387—171no—
944#387C2×D1711yescharacteristic, complemented
945#387C2×D1711yescharacteristic, complemented
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#386—171no—
955#386—171no—
956#386C2×D1711yescharacteristic
957#386C2×D1711yescharacteristic, complemented
958#386C2×D1711yescharacteristic, complemented
959#386C2×D1711yescharacteristic, complemented
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#382—171no—
967#381—171no—
968#381C2×D1711yescharacteristic, complemented
969#380—171no—
970#380—171no—
971#380—171no—
972#380—171no—
973#380—171no—
974#380—171no—
975#380—171no—
976#380—171no—
977#379—171no—
978#379—171no—
979#379—171no—
980#379—171no—
981#379—171no—
982#379—171no—
983C4×C4⋊C4—171no—
984C4×C4⋊C4—171no—
985C4×C4⋊C4—171no—
986C4×C4⋊C4—171no—
987C4×C4⋊C4—171no—
988C4×C4⋊C4—171no—
989C4×C22⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4—171no—
1002C4×C22⋊C4C2×D1711yescharacteristic, complemented
1003C4×C22⋊C4C2×D1711yescharacteristic, complemented
1004C4×C22⋊C4C2×D1711yescharacteristic, complemented
1005C43—171no—
1006C2×C17—42no—
1007C2×C17—42no—
1008C2×C17—42no—
1009C2×C17C2×#51811yescharacteristic
1010C2×C17#342811yescharacteristic
1011C2×C17C4×H(5,𝔽2)11yescharacteristic
1012C2×C17#354611yescharacteristic
1013C2×C17#355111yescharacteristic
1014C2×C17#355811yescharacteristic
1015C2×C17#356211yescharacteristic
1016D17—42no—
1017D17—42no—
1018D17—42no—
1019C25—171no—
1020C25—171no—
1021C2×#41—178no—
1022C2×#41—682no—
1023C2×#41—682no—
1024C22×Q8—171no—
1025C22×D4—171no—
1026C22×D4—171no—
1027C22×D4—171no—
1028C22×D4—171no—
1029C22×D4—171no—
1030C22×D4—178no—
1031C22×D4—171no—
1032C22×D4—682no—
1033C22×D4—682no—
1034C22×D4C22×D1711yescharacteristic
1035C22×D4C22×D1711yescharacteristic
1036C22×D4C22×D1711yescharacteristic
1037C23×C4—171no—
1038C23×C4—171no—
1039C23×C4—171no—
1040C23×C4—171no—
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4C22×D1711yescharacteristic
1047C23×C4C22×D1711yescharacteristic
1048C23×C4C22×D1711yescharacteristic
1049#124—178no—
1050#123—178no—
1051#123—178no—
1052C22⋊Q8—178no—
1053#121—178no—
1054#121—178no—
1055#121C4×D1718yescomplemented
1056#120—178no—
1057#120—178no—
1058C4×Q8—682no—
1059C4×Q8—682no—
1060C4×D4—178no—
1061C4×D4—178no—
1062C4×D4—682no—
1063C4×D4—682no—
1064C4×D4—682no—
1065C4×D4—682no—
1066#117—682no—
1067#117—682no—
1068#117—682no—
1069#117—682no—
1070#117—682no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—682no—
1093C2×C4⋊C4C22×D1711yescharacteristic
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C4⋊C4C22×D1711yescharacteristic
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—178no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—178no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—682no—
1141C2×C22⋊C4—682no—
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C22⋊C4C22×D1711yescharacteristic
1149C2×C22⋊C4C22×D1711yescharacteristic
1150C2×C22⋊C4C22×D1711yescharacteristic
1151C2×C22⋊C4C22×D1711yescharacteristic
1152C2×C22⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4C22×D1711yescharacteristic
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42—171no—
1163C2×C42—171no—
1164C2×C42—171no—
1165C2×C42—171no—
1166C2×C42—171no—
1167C2×C42—171no—
1168C2×C42—171no—
1169C2×C42—171no—
1170C2×C42—171no—
1171C2×C42C22×D1711yescharacteristic
1172C2×C42C22×D1711yescharacteristic
1173C2×C42C22×D1711yescharacteristic
1174C2×C42C22×D1711yescharacteristic
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202#95C22×D1711yescharacteristic
1203#95C22×D1711yescharacteristic
1204#95C22×D1711yescharacteristic
1205#95C22×D1711yescharacteristic
1206#95C22×D1711yescharacteristic
1207C17#3449511yescharacteristic, complemented, Sylow
1208C24—171no—
1209C24—171no—
1210C24—171no—
1211C24—174no—
1212C24—174no—
1213C24—681no—
1214C24—681no—
1215C24—681no—
1216C24—681no—
1217C24—681no—
1218C24—681no—
1219C24—681no—
1220C24—681no—
1221C24—681no—
1222C24—681no—
1223C24—681no—
1224C24—681no—
1225C24C23×D1711yescharacteristic
1226C24C23×D1711yescharacteristic
1227C24C23×D1711yescharacteristic
1228#41—6816no—
1229C2×Q8—174no—
1230C2×Q8—342no—
1231C2×Q8—342no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—174no—
1239C2×D4—174no—
1240C2×D4—174no—
1241C2×D4—174no—
1242C2×D4—174no—
1243C2×D4—174no—
1244C2×D4—342no—
1245C2×D4—342no—
1246C2×D4—342no—
1247C2×D4—342no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—6816no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4C2×C4×D1714yes—
1258C2×D4C2×C4×D1714yes—
1259C2×D4C2×C4×D1714yes—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—171no—
1269C22×C4—174no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—174no—
1276C22×C4—174no—
1277C22×C4—174no—
1278C22×C4—174no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—171no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—342no—
1287C22×C4—342no—
1288C22×C4—342no—
1289C22×C4—342no—
1290C22×C4—342no—
1291C22×C4—342no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4—681no—
1298C22×C4—681no—
1299C22×C4—681no—
1300C22×C4—681no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4C2×C4×D1714yes—
1309C22×C4C23×D1711yescharacteristic
1310C22×C4C23×D1711yescharacteristic
1311C22×C4C23×D1711yescharacteristic
1312C22×C4C23×D1711yescharacteristic
1313C22×C4C23×D1711yescharacteristic
1314C22×C4C23×D1711yescharacteristic
1315C22×C4C23×D1711yescharacteristic
1316C22×C4C23×D1711yescharacteristic
1317C22×C4C23×D1711yescharacteristic
1318C22×C4C23×D1711yescharacteristic
1319C22×C4C23×D1711yescharacteristic
1320C22×C4C23×D1711yescharacteristic
1321C4⋊C4—41no—
1322C4⋊C4—41no—
1323C4⋊C4—174no—
1324C4⋊C4—174no—
1325C4⋊C4—174no—
1326C4⋊C4—342no—
1327C4⋊C4—342no—
1328C4⋊C4—342no—
1329C4⋊C4—342no—
1330C4⋊C4—342no—
1331C4⋊C4—342no—
1332C4⋊C4—681no—
1333C4⋊C4—681no—
1334C4⋊C4—681no—
1335C4⋊C4—681no—
1336C4⋊C4—681no—
1337C4⋊C4—681no—
1338C4⋊C4—681no—
1339C4⋊C4—681no—
1340C4⋊C4—681no—
1341C4⋊C4—681no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4C2×C4×D1714yes—
1345C22⋊C4—41no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
1355C22⋊C4—174no—
1356C22⋊C4—174no—
1357C22⋊C4—174no—
1358C22⋊C4—174no—
1359C22⋊C4—174no—
1360C22⋊C4—174no—
1361C22⋊C4—174no—
1362C22⋊C4—174no—
1363C22⋊C4—174no—
1364C22⋊C4—174no—
1365C22⋊C4—342no—
1366C22⋊C4—342no—
1367C22⋊C4—342no—
1368C22⋊C4—342no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4—681no—
1394C22⋊C4—681no—
1395C22⋊C4—681no—
1396C22⋊C4—681no—
1397C22⋊C4C2×C4×D1714yes—
1398C22⋊C4C2×C4×D1714yes—
1399C42—41no—
1400C42—41no—
1401C42—41no—
1402C42—41no—
1403C42—174no—
1404C42—342no—
1405C42—342no—
1406C42—342no—
1407C42—342no—
1408C42—342no—
1409C42—681no—
1410C42—681no—
1411C42—681no—
1412C42—681no—
1413C42—681no—
1414C42—681no—
1415C42—681no—
1416C42—681no—
1417C42—681no—
1418C42—681no—
1419C42—681no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—172no—
1439C23—172no—
1440C23—172no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
1445C23—341no—
1446C23—341no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—684no—
1460C23—684no—
1461C23—684no—
1462C23—684no—
1463C23—684no—
1464C23—684no—
1465C23—1362no—
1466C23—1362no—
1467C23—1362no—
1468C23—1362no—
1469C23—1362no—
1470C23—1362no—
1471C23—1362no—
1472C23—1362no—
1473C23C22×C4×D1712yes—
1474C23C22×C4×D1712yes—
1475C23C22×C4×D1712yes—
1476C23C24×D1711yescharacteristic
1477Q8—348no—
1478D4—44no—
1479D4—44no—
1480D4—44no—
1481D4—348no—
1482D4—348no—
1483D4—684no—
1484D4—684no—
1485D4—684no—
1486D4—684no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—44no—
1520C2×C4—82no—
1521C2×C4—82no—
1522C2×C4—172no—
1523C2×C4—172no—
1524C2×C4—172no—
1525C2×C4—172no—
1526C2×C4—172no—
1527C2×C4—172no—
1528C2×C4—172no—
1529C2×C4—172no—
1530C2×C4—348no—
1531C2×C4—348no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—684no—
1564C2×C4—684no—
1565C2×C4—684no—
1566C2×C4—1362no—
1567C2×C4—1362no—
1568C2×C4—1362no—
1569C2×C4—1362no—
1570C2×C4C22×C4×D1712yes—
1571C2×C4C22×C4×D1712yes—
1572C2×C4C22×C4×D1712yes—
1573C2×C4C22×C4×D1712yes—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—342no—
1596C22—342no—
1597C22—342no—
1598C22—342no—
1599C22—342no—
1600C22—342no—
1601C22—342no—
1602C22—342no—
1603C22—342no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—681no—
1608C22—681no—
1609C22—681no—
1610C22—681no—
1611C22—681no—
1612C22—681no—
1613C22—681no—
1614C22—681no—
1615C22—681no—
1616C22—1368no—
1617C22—1368no—
1618C22C23×C4×D1711yescharacteristic
1619C22H(5,𝔽2)×D1711yescharacteristic
1620C22H(5,𝔽2)×D1711yescharacteristic
1621C22H(5,𝔽2)×D1711yescharacteristic
1622C22#1176364411yescharacteristic
1623C22#1176364511yescharacteristic
1624C22#1176364511yescharacteristic
1625C4—22no—
1626C4—22no—
1627C4—22no—
1628C4—22no—
1629C4—41no—
1630C4—41no—
1631C4—41no—
1632C4—41no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—174no—
1638C4—342no—
1639C4—342no—
1640C4—342no—
1641C4—342no—
1642C4—342no—
1643C4—681no—
1644C4—681no—
1645C4—681no—
1646C4—681no—
1647C4—681no—
1648C4—681no—
1649C4—681no—
1650C2—42no—
1651C2—42no—
1652C2—42no—
1653C2—682no—
1654C2—682no—
1655C2—682no—
1656C2D17×#51811yescharacteristic
1657C2#1454198311yescharacteristic
1658C2#1454198811yescharacteristic
1659C2#1454314911yescharacteristic
1660C2#1454320511yescharacteristic
1661C2#1454329511yescharacteristic
1662C2#1454336311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2333C2
socle, cosocleC23×C17C25
prime radicalC2×#11763448C2
hypercenter#2333D17
hypocenterC17#34495
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2333

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531931C2semidirect
3. #14531927C2semidirect
4. #14531922C2semidirect
5. #14531921C2semidirect
6. #14531856C2semidirect
7. #14531826C2semidirect
8. #14531823C2semidirect
9. #14531806C2semidirect
10. #14531795C2semidirect
11. #14531752C2semidirect
12. #14531707C2semidirect
13. #14531627C2semidirect
14. #14531626C2semidirect
15. #14531623C2semidirect
16. #14531602C2semidirect
17. #14531580C2semidirect
18. #14531571C2semidirect
19. #14531547C2semidirect
20. #14531474C2semidirect
21. #14531465C2semidirect
22. #14531447C2semidirect
23. #14531440C2semidirect
24. #14531379C2semidirect
25. #14531378C2semidirect
26. #14531371C2semidirect
27. #14531363C2semidirect
28. #14531325C2semidirect
29. #14531247C2semidirect
30. #14531244C2semidirect
31. C17×#2333C2semidirect
34. #11763448C4semidirect
43. C2×C4×Dic34C22semidirect
44. C2×#10587573C22semidirect
45. C2×D4×Dic17C22semidirect
48. C2×C4×C22⋊D17C22semidirect
51. C2×#10587612C22semidirect
54. C2×#10587558C22semidirect
55. C2×#10587563C22semidirect
56. C22×#63225C22semidirect
61. #11762713C22semidirect
62. #11762713C22semidirect
64. #11762712C22semidirect
65. #11762712C22semidirect
76. #11762709C22semidirect
77. #11762709C22semidirect
78. #11762709C22semidirect
79. #11762708C22semidirect
80. #11762706C22semidirect
81. #11762706C22semidirect
82. #11762706C22semidirect
83. #11762706C22semidirect
84. #11762704C22semidirect
85. #11762703C22semidirect
86. #11762703C22semidirect
87. #11762703C22semidirect
88. #11762702C22semidirect
89. #11762702C22semidirect
93. #11762701C22semidirect
94. #11762701C22semidirect
98. #11762700C22semidirect
99. #11762700C22semidirect
100. #11762700C22semidirect
102. #11762699C22semidirect
108. #11762698C22semidirect
109. #11762698C22semidirect
110. #11762698C22semidirect
111. #11762698C22semidirect
112. #11762697C22semidirect
113. #11762697C22semidirect
114. #11762697C22semidirect
115. #11762697C22semidirect
116. #11762697C22semidirect
117. #11762693C22semidirect
118. #11762691C22semidirect
119. #11762691C22semidirect
120. #11762690C22semidirect
122. #11762689C22semidirect
124. #11762688C22semidirect
128. #11762686C22semidirect
129. #11762686C22semidirect
130. #11762685C22semidirect
131. #11762683C22semidirect
132. #11762683C22semidirect
133. #11762683C22semidirect
134. #11762682C22semidirect
135. #11762682C22semidirect
136. #11762681C22semidirect
137. #11762673C22semidirect
138. #11762671C22semidirect
140. #11762668C22semidirect
141. #11762668C22semidirect
142. #11762667C22semidirect
143. #11762667C22semidirect
144. #11762667C22semidirect
145. #11762667C22semidirect
146. #11762666C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
156. #11762660C22semidirect
157. #11762660C22semidirect
158. #11762660C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C22⋊C4×Dic17C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C4×#63227C22semidirect
165. C4×#63227C22semidirect
166. C4×C22⋊Dic17C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762656C22semidirect
171. #11762656C22semidirect
172. C42×Dic17C22semidirect
175. C17×#390C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
181. C17×#386C22semidirect
182. C17×#386C22semidirect
183. C17×#386C22semidirect
184. C17×#381C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
207. C2×#63254C2×C4semidirect
210. C2×D4×D17C2×C4semidirect
218. C17×#121C2×C4semidirect
252. #10587623C2×C4semidirect
253. #10587623C2×C4semidirect
254. #10587621C2×C4semidirect
258. C4×C22⋊D17C2×C4semidirect
260. C2×#63227C2×C4semidirect
330. #10587582C2×C4semidirect
331. #10587580C2×C4semidirect
334. #10587571C2×C4semidirect
335. #10587570C2×C4semidirect
337. #10587567C2×C4semidirect
339. C22⋊C4×D17C2×C4semidirect
762. #2333D17semidirect
899. #390C2×D17semidirect
938. #388C2×D17semidirect
939. #388C2×D17semidirect
944. #387C2×D17semidirect
945. #387C2×D17semidirect
957. #386C2×D17semidirect
958. #386C2×D17semidirect
959. #386C2×D17semidirect
968. #381C2×D17semidirect
1002. C4×C22⋊C4C2×D17semidirect
1003. C4×C22⋊C4C2×D17semidirect
1004. C4×C22⋊C4C2×D17semidirect
1055. #121C4×D17semidirect
1207. C17#34495semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117634482
#145319312
#145319272
#145319222
#145319212
#145318562
#145318262
#145318232
#145318062
#145317952
#145317522
#145317072
#145316272
#145316262
#145316232
#145316022
#145315802
#145315712
#145315472
#145314742
#145314652
#145314472
#145314402
#145313792
#145313782
#145313712
#145313632
#145313252
#145312472
#145312442
C17×#23332
#3449517