Finite Group Databasebeta

← #17198701

Subgroups — #17198701

Order 4352.

2314 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×#11763392C211yesmaximal, characteristic
2#14531973C211yesmaximal, characteristic, complemented
3#14531951C211yesmaximal, characteristic, complemented
4#14531928C211yesmaximal, characteristic, complemented
5#14531922C211yesmaximal, characteristic, complemented
6#14531910C211yesmaximal, characteristic, complemented
7#14531904C211yesmaximal, characteristic, complemented
8#14531897C211yesmaximal, characteristic, complemented
9#14531892C211yesmaximal, characteristic, complemented
10#14531856C211yesmaximal, characteristic, complemented
11#14531814C211yesmaximal, characteristic, complemented
12#14531772C211yesmaximal, characteristic, complemented
13#14531767C211yesmaximal, characteristic, complemented
14#14531733C211yesmaximal, characteristic, complemented
15#14531636C211yesmaximal, characteristic, complemented
16#14531626C211yesmaximal, characteristic, complemented
17#14531594C211yesmaximal, characteristic, complemented
18#14531580C211yesmaximal, characteristic, complemented
19#14531550C211yesmaximal, characteristic, complemented
20#14531544C211yesmaximal, characteristic, complemented
21#14531495C211yesmaximal, characteristic, complemented
22#14531487C211yesmaximal, characteristic, complemented
23#14531474C211yesmaximal, characteristic, complemented
24#14531473C211yesmaximal, characteristic, complemented
25#14531446C211yesmaximal, characteristic, complemented
26#14531437C211yesmaximal, characteristic, complemented
27#14531424C211yesmaximal, characteristic, complemented
28#14531305C211yesmaximal, characteristic, complemented
29C4×#10587570C211yesmaximal, characteristic, complemented
30#14531230C211yesmaximal, characteristic, complemented
31C17×#2353C211yesmaximal, characteristic, complemented
32#11763392C4116yescomplemented
33C2×#10587584C2211yescharacteristic
34C2×#10587562C2211yescharacteristic
35C2×#10587561C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587564C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587623C2211yescharacteristic
45C2×C4×Dic34C2211yescharacteristic, complemented
46C2×C4×D68C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic, complemented
52C2×#10587612C2211yescharacteristic
53C2×#10587612C2211yescharacteristic, complemented
54C2×#10587563C2211yescharacteristic
55C22×#63227C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic, complemented
59#11762715C2211yescharacteristic, complemented
60#11762713C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762712C2211yescharacteristic
63#11762712C2211yescharacteristic
64#11762711C2211yescharacteristic
65#11762710C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762706C2211yescharacteristic, complemented
75#11762705C2211yescharacteristic, complemented
76#11762704C2211yescharacteristic, complemented
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic, complemented
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic
84#11762702C2211yescharacteristic, complemented
85#11762702C2211yescharacteristic, complemented
86#11762701C2211yescharacteristic
87#11762701C2211yescharacteristic
88#11762701C2211yescharacteristic
89#11762701C2211yescharacteristic
90#11762701C2211yescharacteristic
91#11762701C2211yescharacteristic
92#11762701C2211yescharacteristic
93#11762701C2211yescharacteristic, complemented
94#11762701C2211yescharacteristic, complemented
95#11762701C2211yescharacteristic, complemented
96#11762700C2211yescharacteristic
97#11762700C2211yescharacteristic
98#11762700C2211yescharacteristic
99#11762699C2211yescharacteristic
100#11762698C2211yescharacteristic
101#11762698C2211yescharacteristic
102#11762698C2211yescharacteristic
103#11762698C2211yescharacteristic
104#11762698C2211yescharacteristic
105#11762698C2211yescharacteristic, complemented
106#11762697C2211yescharacteristic, complemented
107#11762696C2211yescharacteristic, complemented
108#11762696C2211yescharacteristic, complemented
109#11762696C2211yescharacteristic, complemented
110#11762696C2211yescharacteristic, complemented
111#11762694C2211yescharacteristic, complemented
112#11762694C2211yescharacteristic, complemented
113#11762693C2211yescharacteristic, complemented
114#11762691C2211yescharacteristic, complemented
115#11762691C2211yescharacteristic, complemented
116#11762690C2211yescharacteristic, complemented
117#11762688C2211yescharacteristic
118#11762688C2211yescharacteristic
119#11762688C2211yescharacteristic, complemented
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762687C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic, complemented
129#11762683C2211yescharacteristic
130#11762683C2211yescharacteristic
131#11762683C2211yescharacteristic
132#11762683C2211yescharacteristic
133#11762683C2211yescharacteristic
134#11762683C2211yescharacteristic
135#11762683C2211yescharacteristic
136#11762683C2211yescharacteristic, complemented
137#11762683C2211yescharacteristic, complemented
138#11762683C2211yescharacteristic, complemented
139#11762682C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic
141#11762679C2211yescharacteristic, complemented
142#11762671C2211yescharacteristic, complemented
143#11762670C2211yescharacteristic
144#11762669C2211yescharacteristic
145#11762669C2211yescharacteristic, complemented
146#11762668C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4×#63225C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×C4⋊Dic17C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157#11762660C2211yescharacteristic, complemented
158#11762660C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic
160C4×#63227C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic
170#11762656C2211yescharacteristic, complemented
171#11762655C2211yescharacteristic, complemented
172#11762654C2211yescharacteristic, complemented
173C2×C4×D4×C17C2211yescharacteristic
174C17×#388C2211yescharacteristic
175C17×#388C2211yescharacteristic
176C17×#387C2211yescharacteristic, complemented
177C17×#387C2211yescharacteristic, complemented
178C17×#386C2211yescharacteristic
179C17×#386C2211yescharacteristic
180C17×#383C2211yescharacteristic, complemented
181C17×#381C2211yescharacteristic
182C17×#380C2211yescharacteristic, complemented
183C4×C22⋊C4×C17C2211yescharacteristic
184C4×C22⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C17×#376C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C22×D68C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×C4×D17C2311yescharacteristic
202C22×C4×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×Dic34C2311yescharacteristic
209C4×D4×C17C2×C418yescomplemented
210C2×C4⋊C4×C17C2311yescharacteristic
211C2×C4⋊C4×C17C2311yescharacteristic
212C2×C4⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊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×C42×C17C2311yescharacteristic
222C2×C42×C17C2311yescharacteristic
223C2×C42×C17C2311yescharacteristic
224C2×C42×C17C2311yescharacteristic
225C2×C42×C17C2311yescharacteristic
226C2×C22⋊Dic17C2311yescharacteristic
227C2×C22⋊Dic17C2311yescharacteristic
228C2×C22⋊Dic17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236#10587625C2×C418yescomplemented
237#10587623C2×C418yescomplemented
238#10587616C2×C418yescomplemented
239#10587615C2×C418yescomplemented
240C4×C22⋊D17—42no—
241C4×C22⋊D17—42no—
242C4×C22⋊D17—42no—
243C4×C22⋊D17C2×C418yescomplemented
244C2×#63227C2×C418yescomplemented
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
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
273#10587612—42no—
274#10587612—42no—
275C2×C4⋊Dic17C2311yescharacteristic
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
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×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
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
315#10587584C2×C418yescomplemented
316#10587580C2×C418yescomplemented
317#10587579—42no—
318#10587571C2×C418yescomplemented
319#10587570C2×C418yescomplemented
320#10587568C2×C418yescomplemented
321C22⋊C4×D17—42no—
322C22⋊C4×D17—42no—
323#10587564C2×C418yescomplemented
324#10587563—42no—
325#10587562C2×C418yescomplemented
326#10587561C2×C418yescomplemented
327C4×D68—42no—
328C42×D17—42no—
329C4×Dic34—42no—
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
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
372C23×D17—41no—
373C23×D17—41no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17C22×C414yes—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17C22×C414yes—
385C22×C4×C17—22no—
386C22×C4×C17—41no—
387C22×C4×C17—41no—
388C22×C4×C17—41no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17C22×C414yes—
396C22×C4×C17C22×C414yes—
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17C22×C414yes—
419C2×C22⋊D17C22×C414yes—
420C2×C22⋊D17C22×C414yes—
421C2×C22⋊D17C22×C414yes—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17C22×C414yes—
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C2×D68—41no—
439C2×D68—41no—
440C2×D68—41no—
441C2×D68—41no—
442C2×D68C22×C414yes—
443C2×D68C22×C414yes—
444C2×C4×D17—22no—
445C2×C4×D17—22no—
446C2×C4×D17—22no—
447C2×C4×D17—22no—
448C2×C4×D17—41no—
449C2×C4×D17—41no—
450C2×C4×D17—41no—
451C2×C4×D17—41no—
452C2×C4×D17—41no—
453C2×C4×D17—41no—
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×D17—41no—
464C2×C4×D17C22×C414yes—
465C2×Dic34—41no—
466C2×Dic34—41no—
467C2×Dic34C22×C414yes—
468C4⋊C4×C17—41no—
469C4⋊C4×C17—41no—
470C4⋊C4×C17C22×C414yes—
471C22⋊C4×C17—22no—
472C22⋊C4×C17—41no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17—41no—
477C22⋊C4×C17C22×C414yes—
478C22⋊C4×C17C22×C414yes—
479C42×C17—22no—
480C42×C17—41no—
481C42×C17—41no—
482C42×C17—41no—
483C42×C17C22×C414yes—
484C22⋊Dic17—22no—
485C22⋊Dic17—22no—
486C22⋊Dic17—41no—
487C22⋊Dic17—41no—
488C22⋊Dic17—41no—
489C22⋊Dic17—41no—
490C22⋊Dic17—41no—
491C22⋊Dic17—41no—
492C22⋊Dic17C22×C414yes—
493C22⋊Dic17C22×C414yes—
494#63227—22no—
495#63227—22no—
496#63227—41no—
497#63227—41no—
498#63227—41no—
499#63227—41no—
500#63227—41no—
501#63227—41no—
502#63227—41no—
503#63227—41no—
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#63227C22×C414yes—
513#63227C22×C414yes—
514#63227C22×C414yes—
515#63227C22×C414yes—
516#63227C22×C414yes—
517#63227C22×C414yes—
518#63227C22×C414yes—
519#63227C22×C414yes—
520#63227C22×C414yes—
521#63227C22×C414yes—
522C4⋊Dic17—22no—
523C4⋊Dic17—41no—
524C4⋊Dic17—41no—
525C4⋊Dic17—41no—
526C4⋊Dic17—41no—
527C4⋊Dic17—41no—
528C4⋊Dic17—41no—
529C4⋊Dic17—41no—
530C4⋊Dic17C22×C414yes—
531#63225—22no—
532#63225—22no—
533#63225—41no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225—41no—
540#63225—41no—
541#63225C22×C414yes—
542#63225C22×C414yes—
543#63225C22×C414yes—
544#63225C22×C414yes—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—22no—
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×Dic17—41no—
561C4×Dic17C22×C414yes—
562#34451—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×C17C23×C412yes—
576C23×C17C23×C412yes—
577C23×C17C2511yescharacteristic
578C22×D17—21no—
579C22×D17—21no—
580C22×D17—21no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—21no—
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—44no—
597C22×D17—44no—
598C22×D17—44no—
599C22×D17—82no—
600C22×D17—82no—
601C22×D17—82no—
602C22×D17—82no—
603C22×D17C23×C412yes—
604C22×D17C23×C412yes—
605C22×D17C23×C412yes—
606D4×C17—44no—
607C2×C4×C17—21no—
608C2×C4×C17—21no—
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—44no—
642C2×C4×C17—82no—
643C2×C4×C17—82no—
644C2×C4×C17C23×C412yes—
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—44no—
688C2×Dic17C23×C412yes—
689C2×Dic17C23×C412yes—
690C2×Dic17C23×C412yes—
691C2×Dic17C23×C412yes—
692C2×Dic17C23×C412yes—
693C2×Dic17H(5,𝔽2)12yes—
694D68—44no—
695D68—44no—
696C4×D17—44no—
697C4×D17—44no—
698C4×D17—44no—
699C4×D17—82no—
700C4×D17—82no—
701C4×D17—82no—
702C4×D17—82no—
703Dic34—44no—
704C2×#538—171no—
705#2383—171no—
706#2378—171no—
707#2376—171no—
708#2375—171no—
709#2373—171no—
710#2373—171no—
711#2373—171no—
712#2372—171no—
713#2367—171no—
714#2362—171no—
715#2359—171no—
716#2358—171no—
717#2354—171no—
718#2353D1711yescharacteristic, complemented
719#2342—171no—
720#2342—171no—
721#2337—171no—
722#2335—171no—
723#2333—171no—
724#2333—171no—
725#2326—171no—
726#2325—171no—
727#2324—171no—
728#2324—171no—
729#2321—171no—
730#2321—171no—
731#2319—171no—
732C4×#123—171no—
733C4×#121—171no—
734#2290—171no—
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—41no—
742C22×C17—41no—
743C22×C17—41no—
744C22×C17—41no—
745C22×C17—41no—
746C22×C17—41no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17C24×C411yescharacteristic
750C22×C17C2×H(5,𝔽2)11yescharacteristic
751C22×C17C2×H(5,𝔽2)11yescharacteristic
752C22×C17#58511yescharacteristic
753C22×C17#58511yescharacteristic
754C22×C17#58511yescharacteristic
755C22×C17#58511yescharacteristic
756C2×D17—22no—
757C2×D17—22no—
758C2×D17—22no—
759C2×D17—22no—
760C2×D17—22no—
761C2×D17—22no—
762C2×D17—22no—
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—41no—
766C2×D17—41no—
767C2×D17—41no—
768C2×D17—41no—
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—22no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
787C4×C17—41no—
788C4×C17—41no—
789C4×C17—41no—
790C4×C17—41no—
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×#121—171no—
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×D4—171no—
824C2×C4×D4C2×D1711yescharacteristic
825C2×#117—171no—
826C2×#117—171no—
827C2×#117—171no—
828C22×C22⋊C4—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4—171no—
831C22×C42—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
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#386—171no—
905#386—171no—
906#386C2×D1711yescharacteristic
907#386C2×D1711yescharacteristic
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#383C2×D1711yescharacteristic, complemented
922#381—171no—
923#381—171no—
924#381C2×D1711yescharacteristic
925#380—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380C2×D1711yescharacteristic, complemented
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×C4⋊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—
957#376—171no—
958#376C2×D1711yescharacteristic, complemented
959C2×#95C2×D1711yescharacteristic, complemented
960C2×C17—42no—
961C2×C17—42no—
962C2×C17#342811yescharacteristic
963C2×C17C4×H(5,𝔽2)11yescharacteristic
964C2×C17C4×H(5,𝔽2)11yescharacteristic
965C2×C17#353311yescharacteristic
966C2×C17#354211yescharacteristic
967C2×C17#355111yescharacteristic
968C2×C17#356811yescharacteristic
969D17—42no—
970D17—42no—
971D17—42no—
972C25—171no—
973C22×Q8—171no—
974C22×D4—171no—
975C22×D4—171no—
976C22×D4—171no—
977C22×D4—171no—
978C22×D4—171no—
979C22×D4—171no—
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×C4—171no—
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#121—178no—
1003#120—178no—
1004#120—178no—
1005C4×Q8—682no—
1006C4×D4—178no—
1007C4×D4—682no—
1008C4×D4—682no—
1009C4×D4—682no—
1010C4×D4—682no—
1011C4×D4—682no—
1012C4×D4C4×D1718yescomplemented
1013#117—682no—
1014#117—682no—
1015#117—682no—
1016C2×C4⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C22⋊C4—171no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—178no—
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—171no—
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—171no—
1081C2×C22⋊C4—682no—
1082C2×C22⋊C4—682no—
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×C42—171no—
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—682no—
1109C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1141#95C22×D1711yescharacteristic
1142#95C22×D1711yescharacteristic
1143#95C22×D1711yescharacteristic
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#3445111yescharacteristic, complemented, Sylow
1155C24—171no—
1156C24—171no—
1157C24—171no—
1158C24—174no—
1159C24—681no—
1160C24—681no—
1161C24—681no—
1162C24—681no—
1163C24—681no—
1164C24—681no—
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—174no—
1173C2×D4—174no—
1174C2×D4—174no—
1175C2×D4—174no—
1176C2×D4—174no—
1177C2×D4—174no—
1178C2×D4—681no—
1179C2×D4—681no—
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×D4—681no—
1189C2×D4—681no—
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—171no—
1202C22×C4—171no—
1203C22×C4—171no—
1204C22×C4—171no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—174no—
1208C22×C4—174no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—171no—
1213C22×C4—171no—
1214C22×C4—171no—
1215C22×C4—171no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—342no—
1219C22×C4—342no—
1220C22×C4—681no—
1221C22×C4—681no—
1222C22×C4—681no—
1223C22×C4—681no—
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×C4C2×C4×D1714yes—
1239C22×C4C2×C4×D1714yes—
1240C22×C4C23×D1711yescharacteristic
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—41no—
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—342no—
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—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—174no—
1286C22⋊C4—174no—
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—342no—
1298C22⋊C4—342no—
1299C22⋊C4—342no—
1300C22⋊C4—342no—
1301C22⋊C4—681no—
1302C22⋊C4—681no—
1303C22⋊C4—681no—
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—342no—
1331C42—342no—
1332C42—342no—
1333C42—342no—
1334C42—681no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42C2×C4×D1714yes—
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—172no—
1360C23—172no—
1361C23—172no—
1362C23—341no—
1363C23—341no—
1364C23—341no—
1365C23—341no—
1366C23—341no—
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—341no—
1380C23—684no—
1381C23—684no—
1382C23—684no—
1383C23—1362no—
1384C23—1362no—
1385C23—1362no—
1386C23—1362no—
1387C23C22×C4×D1712yes—
1388C23C22×C4×D1712yes—
1389C23C24×D1711yescharacteristic
1390Q8—684no—
1391D4—44no—
1392D4—684no—
1393D4—684no—
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—21no—
1430C2×C4—21no—
1431C2×C4—44no—
1432C2×C4—44no—
1433C2×C4—82no—
1434C2×C4—82no—
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—684no—
1475C2×C4—684no—
1476C2×C4—684no—
1477C2×C4—684no—
1478C2×C4—1362no—
1479C2×C4—1362no—
1480C2×C4—1362no—
1481C2×C4—1362no—
1482C2×C4C22×C4×D1712yes—
1483C2×C4C22×C4×D1712yes—
1484C2×C4C22×C4×D1712yes—
1485C2×C4C22×C4×D1712yes—
1486C2×C4C22×C4×D1712yes—
1487C2×C4#1058769612yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—41no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—342no—
1503C22—342no—
1504C22—342no—
1505C22—342no—
1506C22—342no—
1507C22—342no—
1508C22—342no—
1509C22—342no—
1510C22—342no—
1511C22—681no—
1512C22—681no—
1513C22—681no—
1514C22—681no—
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×#1058769611yescharacteristic
1527C22#1176364411yescharacteristic
1528C22#1176364511yescharacteristic
1529C22#1176364511yescharacteristic
1530C22#1176364511yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
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—682no—
1560C2—682no—
1561C2—682no—
1562C2#1454198511yescharacteristic
1563C2#1454198811yescharacteristic
1564C2C4×#1058769611yescharacteristic
1565C2#1454294211yescharacteristic
1566C2#1454309311yescharacteristic
1567C2#1454321011yescharacteristic
1568C2#1454347511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2353C2
socle, cosocleC23×C17C25
prime radicalC2×#11763392C2
hypercenter#2353D17
hypocenterC17#34451
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #14531973C2semidirect
3. #14531951C2semidirect
4. #14531928C2semidirect
5. #14531922C2semidirect
6. #14531910C2semidirect
7. #14531904C2semidirect
8. #14531897C2semidirect
9. #14531892C2semidirect
10. #14531856C2semidirect
11. #14531814C2semidirect
12. #14531772C2semidirect
13. #14531767C2semidirect
14. #14531733C2semidirect
15. #14531636C2semidirect
16. #14531626C2semidirect
17. #14531594C2semidirect
18. #14531580C2semidirect
19. #14531550C2semidirect
20. #14531544C2semidirect
21. #14531495C2semidirect
22. #14531487C2semidirect
23. #14531474C2semidirect
24. #14531473C2semidirect
25. #14531446C2semidirect
26. #14531437C2semidirect
27. #14531424C2semidirect
28. #14531305C2semidirect
29. C4×#10587570C2semidirect
30. #14531230C2semidirect
31. C17×#2353C2semidirect
32. #11763392C4semidirect
45. C2×C4×Dic34C22semidirect
51. C2×C4×C22⋊D17C22semidirect
53. C2×#10587612C22semidirect
58. C2×C42×D17C22semidirect
59. #11762715C22semidirect
60. #11762713C22semidirect
61. #11762713C22semidirect
70. #11762709C22semidirect
71. #11762706C22semidirect
72. #11762706C22semidirect
73. #11762706C22semidirect
74. #11762706C22semidirect
75. #11762705C22semidirect
76. #11762704C22semidirect
81. #11762703C22semidirect
84. #11762702C22semidirect
85. #11762702C22semidirect
93. #11762701C22semidirect
94. #11762701C22semidirect
95. #11762701C22semidirect
105. #11762698C22semidirect
106. #11762697C22semidirect
107. #11762696C22semidirect
108. #11762696C22semidirect
109. #11762696C22semidirect
110. #11762696C22semidirect
111. #11762694C22semidirect
112. #11762694C22semidirect
113. #11762693C22semidirect
114. #11762691C22semidirect
115. #11762691C22semidirect
116. #11762690C22semidirect
119. #11762688C22semidirect
128. #11762685C22semidirect
136. #11762683C22semidirect
137. #11762683C22semidirect
138. #11762683C22semidirect
139. #11762682C22semidirect
141. #11762679C22semidirect
142. #11762671C22semidirect
145. #11762669C22semidirect
146. #11762668C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4×#63225C22semidirect
154. C4×#63225C22semidirect
155. C4×C4⋊Dic17C22semidirect
156. #11762660C22semidirect
157. #11762660C22semidirect
158. #11762660C22semidirect
163. C4×#63227C22semidirect
164. C4×C22⋊Dic17C22semidirect
170. #11762656C22semidirect
171. #11762655C22semidirect
172. #11762654C22semidirect
176. C17×#387C22semidirect
177. C17×#387C22semidirect
180. C17×#383C22semidirect
182. C17×#380C22semidirect
184. C4×C22⋊C4×C17C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C17×#376C22semidirect
187. C2×C17×#95C22semidirect
209. C4×D4×C17C2×C4semidirect
236. #10587625C2×C4semidirect
237. #10587623C2×C4semidirect
238. #10587616C2×C4semidirect
239. #10587615C2×C4semidirect
243. C4×C22⋊D17C2×C4semidirect
244. C2×#63227C2×C4semidirect
315. #10587584C2×C4semidirect
316. #10587580C2×C4semidirect
318. #10587571C2×C4semidirect
319. #10587570C2×C4semidirect
320. #10587568C2×C4semidirect
323. #10587564C2×C4semidirect
325. #10587562C2×C4semidirect
326. #10587561C2×C4semidirect
718. #2353D17semidirect
892. #387C2×D17semidirect
893. #387C2×D17semidirect
921. #383C2×D17semidirect
929. #380C2×D17semidirect
954. C4×C22⋊C4C2×D17semidirect
955. C4×C22⋊C4C2×D17semidirect
958. #376C2×D17semidirect
959. C2×#95C2×D17semidirect
1012. C4×D4C4×D17semidirect
1154. C17#34451semidirect

Maximal subgroups

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

subgroupindex
C2×#117633922
#145319732
#145319512
#145319282
#145319222
#145319102
#145319042
#145318972
#145318922
#145318562
#145318142
#145317722
#145317672
#145317332
#145316362
#145316262
#145315942
#145315802
#145315502
#145315442
#145314952
#145314872
#145314742
#145314732
#145314462
#145314372
#145314242
#145313052
C4×#105875702
#145312302
C17×#23532
#3445117