Finite Group Databasebeta

← #17198554

Subgroups — #17198554

Order 4352.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763391C211yesmaximal, characteristic
2#14531974C211yesmaximal, characteristic, complemented
3#14531936C211yesmaximal, characteristic, complemented
4#14531927C211yesmaximal, characteristic, complemented
5#14531922C211yesmaximal, characteristic, complemented
6#14531915C211yesmaximal, characteristic, complemented
7#14531897C211yesmaximal, characteristic, complemented
8#14531826C211yesmaximal, characteristic, complemented
9#14531818C211yesmaximal, characteristic, complemented
10#14531782C211yesmaximal, characteristic, complemented
11#14531772C211yesmaximal, characteristic, complemented
12#14531761C211yesmaximal, characteristic, complemented
13#14531730C211yesmaximal, characteristic, complemented
14#14531718C211yesmaximal, characteristic, complemented
15#14531632C211yesmaximal, characteristic, complemented
16#14531627C211yesmaximal, characteristic, complemented
17#14531595C211yesmaximal, characteristic, complemented
18#14531593C211yesmaximal, characteristic, complemented
19#14531561C211yesmaximal, characteristic, complemented
20#14531538C211yesmaximal, characteristic, complemented
21#14531496C211yesmaximal, characteristic, complemented
22#14531482C211yesmaximal, characteristic, complemented
23#14531474C211yesmaximal, characteristic, complemented
24#14531465C211yesmaximal, characteristic, complemented
25#14531447C211yesmaximal, characteristic, complemented
26#14531440C211yesmaximal, characteristic, complemented
27#14531418C211yesmaximal, characteristic, complemented
28#14531338C211yesmaximal, characteristic, complemented
29C4×#10587571C211yesmaximal, characteristic, complemented
30#14531247C211yesmaximal, characteristic, complemented
31C17×#2364C211yesmaximal, characteristic, complemented
32#11763391C4116yescomplemented
33C2×#10587584C2211yescharacteristic
34C2×#10587565C2211yescharacteristic
35C2×#10587622C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587615C2211yescharacteristic
38C2×#10587621C2211yescharacteristic
39C2×#10587582C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587624C2211yescharacteristic
42C2×#10587623C2211yescharacteristic
43C2×#10587623C2211yescharacteristic
44C2×C4×Dic34C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C2×#10587612C2211yescharacteristic, complemented
51C2×#10587578C2211yescharacteristic
52C2×#10587558C2211yescharacteristic
53C2×#10587563C2211yescharacteristic, complemented
54C22×#63227C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57#11762714C2211yescharacteristic, complemented
58#11762713C2211yescharacteristic, complemented
59#11762713C2211yescharacteristic, complemented
60#11762712C2211yescharacteristic
61#11762712C2211yescharacteristic
62#11762712C2211yescharacteristic, complemented
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762708C2211yescharacteristic, complemented
70#11762707C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762706C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic, complemented
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic, complemented
81#11762701C2211yescharacteristic
82#11762701C2211yescharacteristic
83#11762701C2211yescharacteristic
84#11762701C2211yescharacteristic
85#11762701C2211yescharacteristic
86#11762700C2211yescharacteristic
87#11762700C2211yescharacteristic
88#11762700C2211yescharacteristic
89#11762699C2211yescharacteristic
90#11762698C2211yescharacteristic
91#11762698C2211yescharacteristic
92#11762698C2211yescharacteristic
93#11762698C2211yescharacteristic
94#11762698C2211yescharacteristic
95#11762698C2211yescharacteristic
96#11762698C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic
99#11762697C2211yescharacteristic
100#11762697C2211yescharacteristic, complemented
101#11762697C2211yescharacteristic, complemented
102#11762697C2211yescharacteristic, complemented
103#11762697C2211yescharacteristic, complemented
104#11762697C2211yescharacteristic, complemented
105#11762696C2211yescharacteristic, complemented
106#11762694C2211yescharacteristic, complemented
107#11762693C2211yescharacteristic, complemented
108#11762693C2211yescharacteristic, complemented
109#11762692C2211yescharacteristic, complemented
110#11762691C2211yescharacteristic, complemented
111#11762691C2211yescharacteristic, complemented
112#11762691C2211yescharacteristic, complemented
113#11762691C2211yescharacteristic, complemented
114#11762690C2211yescharacteristic, complemented
115#11762689C2211yescharacteristic
116#11762689C2211yescharacteristic, complemented
117#11762688C2211yescharacteristic
118#11762688C2211yescharacteristic
119#11762688C2211yescharacteristic
120#11762688C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762686C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762683C2211yescharacteristic
126#11762683C2211yescharacteristic
127#11762682C2211yescharacteristic
128#11762682C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762682C2211yescharacteristic, complemented
131#11762682C2211yescharacteristic, complemented
132#11762682C2211yescharacteristic, complemented
133#11762681C2211yescharacteristic
134#11762681C2211yescharacteristic, complemented
135#11762680C2211yescharacteristic
136#11762680C2211yescharacteristic
137#11762678C2211yescharacteristic, complemented
138#11762676C2211yescharacteristic, complemented
139#11762676C2211yescharacteristic, complemented
140#11762673C2211yescharacteristic, complemented
141#11762671C2211yescharacteristic
142#11762671C2211yescharacteristic
143#11762668C2211yescharacteristic
144#11762668C2211yescharacteristic
145#11762667C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic, complemented
147#11762664C2211yescharacteristic
148#11762664C2211yescharacteristic
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×#63225C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154#11762660C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic
163C4×#63227C2211yescharacteristic
164C4×#63227C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic
170#11762655C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C4×C22⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×Dic34C2311yescharacteristic
209C17×#121C2×C418yescomplemented
210C4×D4×C17—42no—
211C4×D4×C17—42no—
212C2×C4⋊C4×C17C2311yescharacteristic
213C2×C4⋊C4×C17C2311yescharacteristic
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C22⋊C4×C17C2311yescharacteristic
217C2×C22⋊C4×C17C2311yescharacteristic
218C2×C22⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C42×C17C2311yescharacteristic
226C2×C42×C17C2311yescharacteristic
227C2×C42×C17C2311yescharacteristic
228C2×C42×C17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245#10587625C2×C418yescomplemented
246#10587624C2×C418yescomplemented
247#10587623C2×C418yescomplemented
248#10587623C2×C418yescomplemented
249#10587622C2×C418yescomplemented
250#10587621C2×C418yescomplemented
251D4×Dic17—42no—
252#10587615C2×C418yescomplemented
253C4×C22⋊D17—42no—
254C4×C22⋊D17—42no—
255C4×C22⋊D17C2×C418yescomplemented
256C2×#63227—42no—
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
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
277#10587612—42no—
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319#10587584C2×C418yescomplemented
320#10587582C2×C418yescomplemented
321#10587578—42no—
322#10587571C2×C418yescomplemented
323#10587567C2×C418yescomplemented
324C22⋊C4×D17—42no—
325C22⋊C4×D17C2×C418yescomplemented
326#10587565C2×C418yescomplemented
327#10587563—42no—
328#10587558—42no—
329C4×Dic34—42no—
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
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
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C24×C17C2411yescharacteristic
373C23×D17—41no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17C22×C414yes—
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17C22×C414yes—
389C2×D4×C17C22×C414yes—
390C2×D4×C17C22×C414yes—
391C22×C4×C17—22no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17C22×C414yes—
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17C22×C414yes—
427C2×C22⋊D17C22×C414yes—
428C2×C22⋊D17C22×C414yes—
429C2×C22⋊D17C22×C414yes—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17C22×C414yes—
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C2×C4×D17—22no—
454C2×C4×D17—41no—
455C2×C4×D17—41no—
456C2×C4×D17—41no—
457C2×C4×D17—41no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17C22×C414yes—
464C2×C4×D17C22×C414yes—
465C2×Dic34—41no—
466C2×Dic34—41no—
467C2×Dic34C22×C414yes—
468C4⋊C4×C17—22no—
469C4⋊C4×C17—41no—
470C4⋊C4×C17C22×C414yes—
471C22⋊C4×C17—22no—
472C22⋊C4×C17—22no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17—41no—
477C22⋊C4×C17—41no—
478C22⋊C4×C17—41no—
479C22⋊C4×C17C22×C414yes—
480C22⋊C4×C17C22×C414yes—
481C42×C17—22no—
482C42×C17—41no—
483C42×C17—41no—
484C42×C17—41no—
485C22⋊Dic17—22no—
486C22⋊Dic17—22no—
487C22⋊Dic17—41no—
488C22⋊Dic17—41no—
489C22⋊Dic17—41no—
490C22⋊Dic17—41no—
491C22⋊Dic17—41no—
492C22⋊Dic17—41no—
493C22⋊Dic17—41no—
494C22⋊Dic17—41no—
495C22⋊Dic17C22×C414yes—
496C22⋊Dic17C22×C414yes—
497C22⋊Dic17C22×C414yes—
498C22⋊Dic17C22×C414yes—
499C22⋊Dic17C22×C414yes—
500C22⋊Dic17C22×C414yes—
501#63227—22no—
502#63227—22no—
503#63227—22no—
504#63227—41no—
505#63227—41no—
506#63227—41no—
507#63227—41no—
508#63227—41no—
509#63227—41no—
510#63227—41no—
511#63227—41no—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227C22×C414yes—
516#63227C22×C414yes—
517#63227C22×C414yes—
518#63227C22×C414yes—
519#63227C22×C414yes—
520#63227C22×C414yes—
521C4⋊Dic17—22no—
522C4⋊Dic17—41no—
523C4⋊Dic17—41no—
524C4⋊Dic17—41no—
525C4⋊Dic17C22×C414yes—
526#63225—22no—
527#63225—41no—
528#63225—41no—
529#63225—41no—
530#63225—41no—
531#63225—41no—
532#63225—41no—
533#63225—41no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225—41no—
540#63225C22×C414yes—
541#63225C22×C414yes—
542#63225C22×C414yes—
543#63225C22×C414yes—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—41no—
549C4×Dic17—41no—
550C4×Dic17—41no—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17C22×C414yes—
561C4×Dic17C22×C414yes—
562#34446—171nomaximal, Sylow
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17C23×C412yes—
582C23×C17C23×C412yes—
583C23×C17C23×C412yes—
584C23×C17C2511yescharacteristic
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—44no—
598C22×D17—44no—
599C22×D17—44no—
600C22×D17—82no—
601C22×D17—82no—
602C22×D17—82no—
603C22×D17—82no—
604C22×D17C23×C412yes—
605C22×D17C23×C412yes—
606D4×C17—44no—
607D4×C17—44no—
608D4×C17—44no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—44no—
641C2×C4×C17—82no—
642C2×C4×C17—82no—
643C2×C4×C17—82no—
644C2×C4×C17—82no—
645C2×C4×C17C23×C412yes—
646C2×C4×C17C23×C412yes—
647C2×C4×C17C23×C412yes—
648C2×C4×C17C23×C412yes—
649C2×C4×C17H(5,𝔽2)12yes—
650C22⋊D17—44no—
651C22⋊D17—44no—
652C22⋊D17—44no—
653C22⋊D17—44no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—44no—
690C2×Dic17—82no—
691C2×Dic17—82no—
692C2×Dic17C23×C412yes—
693C2×Dic17C23×C412yes—
694C2×Dic17C23×C412yes—
695C2×Dic17C23×C412yes—
696C2×Dic17C23×C412yes—
697C2×Dic17C23×C412yes—
698C2×Dic17H(5,𝔽2)12yes—
699C4×D17—44no—
700C4×D17—44no—
701C4×D17—82no—
702C4×D17—82no—
703Dic34—44no—
704C2×#538—171no—
705#2383—171no—
706#2377—171no—
707#2376—171no—
708#2375—171no—
709#2374—171no—
710#2373—171no—
711#2364D1711yescharacteristic, complemented
712#2363—171no—
713#2363—171no—
714#2359—171no—
715#2359—171no—
716#2358—171no—
717#2354—171no—
718#2353—171no—
719#2342—171no—
720#2342—171no—
721#2337—171no—
722#2337—171no—
723#2334—171no—
724#2332—171no—
725#2326—171no—
726#2325—171no—
727#2324—171no—
728#2323—171no—
729#2321—171no—
730#2321—171no—
731#2318—171no—
732C4×#126—171no—
733C4×#124—171no—
734#2293—171no—
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—41no—
745C22×C17—41no—
746C22×C17—41no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17—41no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17C24×C411yescharacteristic
757C22×C17C2×H(5,𝔽2)11yescharacteristic
758C22×C17C2×H(5,𝔽2)11yescharacteristic
759C22×C17#58511yescharacteristic
760C22×C17#58511yescharacteristic
761C22×C17#58511yescharacteristic
762C22×C17#58511yescharacteristic
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—22no—
766C2×D17—22no—
767C2×D17—22no—
768C2×D17—22no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17—41no—
772C2×D17—41no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—88no—
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—22no—
783C4×C17—41no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
787C4×C17—41no—
788C4×C17—41no—
789C4×C17—41no—
790Dic17—22no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—22no—
795Dic17—22no—
796Dic17—22no—
797Dic17—41no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804#538—1716no—
805C2×#126—171no—
806C2×#126—171no—
807C2×#124—171no—
808C2×#124—171no—
809C2×#123—171no—
810C2×#123—171no—
811C2×C22⋊Q8—171no—
812C2×#121—171no—
813C2×#121—171no—
814C2×#121C2×D1711yescharacteristic
815C2×#120—171no—
816C2×#120—171no—
817C2×C4×Q8—171no—
818C2×C4×D4—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4C2×D1711yescharacteristic
824C2×C4×D4C2×D1711yescharacteristic, complemented
825C2×#117—171no—
826C2×#117—171no—
827C2×#117—171no—
828C2×#117—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4—171no—
831C22×C22⋊C4—171no—
832#391—171no—
833#391—171no—
834#391—171no—
835#390—171no—
836#390—171no—
837#390—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390—171no—
842#390—171no—
843#390—171no—
844#389—171no—
845#389—171no—
846#389—171no—
847#389—171no—
848#389—171no—
849#389—171no—
850#388—171no—
851#388—171no—
852#388—171no—
853#388—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388C2×D1711yescharacteristic
881#388C2×D1711yescharacteristic, complemented
882#387—171no—
883#387—171no—
884#387—171no—
885#387—171no—
886#387—171no—
887#387—171no—
888#387—171no—
889#387—171no—
890#387—171no—
891#387—171no—
892#387C2×D1711yescharacteristic, complemented
893#387C2×D1711yescharacteristic, complemented
894#386—171no—
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386—171no—
904#386C2×D1711yescharacteristic
905#386C2×D1711yescharacteristic
906#386C2×D1711yescharacteristic
907#386C2×D1711yescharacteristic, complemented
908#385—171no—
909#385—171no—
910#385—171no—
911#385—171no—
912#385—171no—
913#385—171no—
914#385—171no—
915#385—171no—
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#384—171no—
921#383—171no—
922#383—171no—
923#382—171no—
924#381—171no—
925#381—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#379—171no—
931#379—171no—
932C4×C4⋊C4—171no—
933C4×C4⋊C4—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C22⋊C4—171no—
941C4×C22⋊C4—171no—
942C4×C22⋊C4—171no—
943C4×C22⋊C4—171no—
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4C2×D1711yescharacteristic
954C4×C22⋊C4C2×D1711yescharacteristic, complemented
955C4×C22⋊C4C2×D1711yescharacteristic, complemented
956#376—171no—
957C2×#95—171no—
958C2×#95C2×D1711yescharacteristic, complemented
959C43—171no—
960C2×C17—42no—
961C2×C17—42no—
962C2×C17—42no—
963C2×C17#342811yescharacteristic
964C2×C17C4×H(5,𝔽2)11yescharacteristic
965C2×C17C4×H(5,𝔽2)11yescharacteristic
966C2×C17#354511yescharacteristic
967C2×C17#354611yescharacteristic
968C2×C17#356011yescharacteristic
969C2×C17#356611yescharacteristic
970D17—42no—
971D17—42no—
972C25—171no—
973C22×Q8—171no—
974C22×D4—171no—
975C22×D4—171no—
976C22×D4—171no—
977C22×D4—171no—
978C22×D4C22×D1711yescharacteristic
979C22×D4C22×D1711yescharacteristic
980C22×D4C22×D1711yescharacteristic
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—171no—
986C23×C4—171no—
987C23×C4—171no—
988C23×C4C22×D1711yescharacteristic
989C23×C4C22×D1711yescharacteristic
990C23×C4C22×D1711yescharacteristic
991C23×C4C22×D1711yescharacteristic
992C23×C4C22×D1711yescharacteristic
993#126—178no—
994#126—178no—
995#124—178no—
996#124—178no—
997#123—178no—
998#123—178no—
999C22⋊Q8—178no—
1000#121—178no—
1001#121—178no—
1002#121C4×D1718yescomplemented
1003#120—178no—
1004#120—178no—
1005C4×Q8—682no—
1006C4×D4—42no—
1007C4×D4—42no—
1008C4×D4—178no—
1009C4×D4—178no—
1010C4×D4—682no—
1011C4×D4—682no—
1012C4×D4—682no—
1013#117—682no—
1014#117—682no—
1015#117—682no—
1016#117—682no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—171no—
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C4⋊C4C22×D1711yescharacteristic
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—178no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—682no—
1081C2×C22⋊C4—682no—
1082C2×C22⋊C4C22×D1711yescharacteristic
1083C2×C22⋊C4C22×D1711yescharacteristic
1084C2×C22⋊C4C22×D1711yescharacteristic
1085C2×C22⋊C4C22×D1711yescharacteristic
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4C22×D1711yescharacteristic
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—171no—
1107C2×C42—171no—
1108C2×C42—171no—
1109C2×C42—171no—
1110C2×C42C22×D1711yescharacteristic
1111C2×C42C22×D1711yescharacteristic
1112C2×C42C22×D1711yescharacteristic
1113C2×C42C22×D1711yescharacteristic
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95C22×D1711yescharacteristic
1145#95C22×D1711yescharacteristic
1146#95C22×D1711yescharacteristic
1147#95C22×D1711yescharacteristic
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154C17#3444611yescharacteristic, complemented, Sylow
1155C24—171no—
1156C24—171no—
1157C24—174no—
1158C24—681no—
1159C24—681no—
1160C24—681no—
1161C24—681no—
1162C24—681no—
1163C24—681no—
1164C24C23×D1711yescharacteristic
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—174no—
1177C2×D4—174no—
1178C2×D4—174no—
1179C2×D4—174no—
1180C2×D4—681no—
1181C2×D4—681no—
1182C2×D4—681no—
1183C2×D4—681no—
1184C2×D4—681no—
1185C2×D4—681no—
1186C2×D4—681no—
1187C2×D4—681no—
1188C2×D4C2×C4×D1714yes—
1189C2×D4C2×C4×D1714yes—
1190C2×D4C2×C4×D1714yes—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—41no—
1200C22×C4—41no—
1201C22×C4—41no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—41no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—174no—
1213C22×C4—174no—
1214C22×C4—174no—
1215C22×C4—171no—
1216C22×C4—171no—
1217C22×C4—171no—
1218C22×C4—171no—
1219C22×C4—171no—
1220C22×C4—171no—
1221C22×C4—171no—
1222C22×C4—342no—
1223C22×C4—342no—
1224C22×C4—681no—
1225C22×C4—681no—
1226C22×C4—681no—
1227C22×C4—681no—
1228C22×C4—681no—
1229C22×C4—681no—
1230C22×C4—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4C2×C4×D1714yes—
1241C22×C4C23×D1711yescharacteristic
1242C22×C4C23×D1711yescharacteristic
1243C22×C4C23×D1711yescharacteristic
1244C22×C4C23×D1711yescharacteristic
1245C22×C4C23×D1711yescharacteristic
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C4⋊C4—22no—
1254C4⋊C4—41no—
1255C4⋊C4—174no—
1256C4⋊C4—174no—
1257C4⋊C4—174no—
1258C4⋊C4—174no—
1259C4⋊C4—174no—
1260C4⋊C4—342no—
1261C4⋊C4—342no—
1262C4⋊C4—681no—
1263C4⋊C4—681no—
1264C4⋊C4—681no—
1265C4⋊C4—681no—
1266C4⋊C4—681no—
1267C4⋊C4—681no—
1268C4⋊C4—681no—
1269C4⋊C4—681no—
1270C4⋊C4—681no—
1271C4⋊C4—681no—
1272C4⋊C4—681no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4C2×C4×D1714yes—
1279C22⋊C4—22no—
1280C22⋊C4—22no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—174no—
1288C22⋊C4—174no—
1289C22⋊C4—174no—
1290C22⋊C4—174no—
1291C22⋊C4—174no—
1292C22⋊C4—174no—
1293C22⋊C4—174no—
1294C22⋊C4—174no—
1295C22⋊C4—174no—
1296C22⋊C4—174no—
1297C22⋊C4—174no—
1298C22⋊C4—174no—
1299C22⋊C4—342no—
1300C22⋊C4—342no—
1301C22⋊C4—342no—
1302C22⋊C4—342no—
1303C22⋊C4—342no—
1304C22⋊C4—681no—
1305C22⋊C4—681no—
1306C22⋊C4—681no—
1307C22⋊C4—681no—
1308C22⋊C4—681no—
1309C22⋊C4—681no—
1310C22⋊C4—681no—
1311C22⋊C4—681no—
1312C22⋊C4—681no—
1313C22⋊C4—681no—
1314C22⋊C4—681no—
1315C22⋊C4—681no—
1316C22⋊C4—681no—
1317C22⋊C4—681no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4—681no—
1322C22⋊C4—681no—
1323C22⋊C4C2×C4×D1714yes—
1324C22⋊C4C2×C4×D1714yes—
1325C42—22no—
1326C42—41no—
1327C42—41no—
1328C42—41no—
1329C42—174no—
1330C42—174no—
1331C42—342no—
1332C42—342no—
1333C42—342no—
1334C42—342no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—172no—
1366C23—172no—
1367C23—341no—
1368C23—341no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—341no—
1374C23—341no—
1375C23—341no—
1376C23—341no—
1377C23—341no—
1378C23—341no—
1379C23—684no—
1380C23—684no—
1381C23—684no—
1382C23—1362no—
1383C23—1362no—
1384C23—1362no—
1385C23—1362no—
1386C23C22×C4×D1712yes—
1387C23C22×C4×D1712yes—
1388C23C22×C4×D1712yes—
1389C23C24×D1711yescharacteristic
1390Q8—684no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—684no—
1395D4—684no—
1396D4—684no—
1397D4—684no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—44no—
1430C2×C4—82no—
1431C2×C4—82no—
1432C2×C4—82no—
1433C2×C4—82no—
1434C2×C4—172no—
1435C2×C4—172no—
1436C2×C4—172no—
1437C2×C4—172no—
1438C2×C4—172no—
1439C2×C4—172no—
1440C2×C4—172no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—684no—
1477C2×C4—684no—
1478C2×C4—684no—
1479C2×C4—1362no—
1480C2×C4—1362no—
1481C2×C4—1362no—
1482C2×C4—1362no—
1483C2×C4C22×C4×D1712yes—
1484C2×C4C22×C4×D1712yes—
1485C2×C4C22×C4×D1712yes—
1486C2×C4C22×C4×D1712yes—
1487C2×C4#1058769112yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—342no—
1510C22—342no—
1511C22—342no—
1512C22—342no—
1513C22—342no—
1514C22—342no—
1515C22—681no—
1516C22—681no—
1517C22—681no—
1518C22—681no—
1519C22—681no—
1520C22—681no—
1521C22—681no—
1522C22—681no—
1523C22—1368no—
1524C22C23×C4×D1711yescharacteristic
1525C22H(5,𝔽2)×D1711yescharacteristic
1526C22C2×#1058769111yescharacteristic
1527C22#1176364411yescharacteristic
1528C22#1176364511yescharacteristic
1529C22#1176364511yescharacteristic
1530C22#1176364511yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—41no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—342no—
1544C4—342no—
1545C4—342no—
1546C4—342no—
1547C4—342no—
1548C4—342no—
1549C4—342no—
1550C4—681no—
1551C4—681no—
1552C4—681no—
1553C4—681no—
1554C4—681no—
1555C4—681no—
1556C4—681no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—682no—
1561C2—682no—
1562C2#1454198311yescharacteristic
1563C2#1454198811yescharacteristic
1564C2C4×#1058769111yescharacteristic
1565C2#1454313111yescharacteristic
1566C2#1454314811yescharacteristic
1567C2#1454332311yescharacteristic
1568C2#1454346111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2364C2
socle, cosocleC23×C17C25
prime radicalC2×#11763391C2
hypercenter#2364D17
hypocenterC17#34446
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. #14531974C2semidirect
3. #14531936C2semidirect
4. #14531927C2semidirect
5. #14531922C2semidirect
6. #14531915C2semidirect
7. #14531897C2semidirect
8. #14531826C2semidirect
9. #14531818C2semidirect
10. #14531782C2semidirect
11. #14531772C2semidirect
12. #14531761C2semidirect
13. #14531730C2semidirect
14. #14531718C2semidirect
15. #14531632C2semidirect
16. #14531627C2semidirect
17. #14531595C2semidirect
18. #14531593C2semidirect
19. #14531561C2semidirect
20. #14531538C2semidirect
21. #14531496C2semidirect
22. #14531482C2semidirect
23. #14531474C2semidirect
24. #14531465C2semidirect
25. #14531447C2semidirect
26. #14531440C2semidirect
27. #14531418C2semidirect
28. #14531338C2semidirect
29. C4×#10587571C2semidirect
30. #14531247C2semidirect
31. C17×#2364C2semidirect
32. #11763391C4semidirect
44. C2×C4×Dic34C22semidirect
50. C2×#10587612C22semidirect
53. C2×#10587563C22semidirect
57. #11762714C22semidirect
58. #11762713C22semidirect
59. #11762713C22semidirect
62. #11762712C22semidirect
69. #11762708C22semidirect
70. #11762707C22semidirect
71. #11762706C22semidirect
72. #11762706C22semidirect
73. #11762706C22semidirect
74. #11762706C22semidirect
78. #11762703C22semidirect
80. #11762702C22semidirect
100. #11762697C22semidirect
101. #11762697C22semidirect
102. #11762697C22semidirect
103. #11762697C22semidirect
104. #11762697C22semidirect
105. #11762696C22semidirect
106. #11762694C22semidirect
107. #11762693C22semidirect
108. #11762693C22semidirect
109. #11762692C22semidirect
110. #11762691C22semidirect
111. #11762691C22semidirect
112. #11762691C22semidirect
113. #11762691C22semidirect
114. #11762690C22semidirect
116. #11762689C22semidirect
130. #11762682C22semidirect
131. #11762682C22semidirect
132. #11762682C22semidirect
134. #11762681C22semidirect
137. #11762678C22semidirect
138. #11762676C22semidirect
139. #11762676C22semidirect
140. #11762673C22semidirect
145. #11762667C22semidirect
146. #11762667C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. C4×#63225C22semidirect
152. C4×#63225C22semidirect
153. #11762660C22semidirect
154. #11762660C22semidirect
155. #11762660C22semidirect
156. #11762660C22semidirect
160. C22⋊C4×Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. C4×C22⋊Dic17C22semidirect
167. C4×C22⋊Dic17C22semidirect
170. #11762655C22semidirect
171. C2×#10587502C22semidirect
172. C42×Dic17C22semidirect
175. C2×C4×D4×C17C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
183. C17×#386C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C2×C17×#95C22semidirect
209. C17×#121C2×C4semidirect
245. #10587625C2×C4semidirect
246. #10587624C2×C4semidirect
247. #10587623C2×C4semidirect
248. #10587623C2×C4semidirect
249. #10587622C2×C4semidirect
250. #10587621C2×C4semidirect
252. #10587615C2×C4semidirect
255. C4×C22⋊D17C2×C4semidirect
319. #10587584C2×C4semidirect
320. #10587582C2×C4semidirect
322. #10587571C2×C4semidirect
323. #10587567C2×C4semidirect
325. C22⋊C4×D17C2×C4semidirect
326. #10587565C2×C4semidirect
711. #2364D17semidirect
824. C2×C4×D4C2×D17semidirect
881. #388C2×D17semidirect
892. #387C2×D17semidirect
893. #387C2×D17semidirect
907. #386C2×D17semidirect
954. C4×C22⋊C4C2×D17semidirect
955. C4×C22⋊C4C2×D17semidirect
958. C2×#95C2×D17semidirect
1002. #121C4×D17semidirect
1154. C17#34446semidirect

Maximal subgroups

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

subgroupindex
C2×#117633912
#145319742
#145319362
#145319272
#145319222
#145319152
#145318972
#145318262
#145318182
#145317822
#145317722
#145317612
#145317302
#145317182
#145316322
#145316272
#145315952
#145315932
#145315612
#145315382
#145314962
#145314822
#145314742
#145314652
#145314472
#145314402
#145314182
#145313382
C4×#105875712
#145312472
C17×#23642
#3444617