Finite Group Databasebeta

← #17201315

Subgroups — #17201315

Order 4352.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534970C211yesmaximal, characteristic, complemented
2#14534950C211yesmaximal, characteristic
3#14534943C211yesmaximal, characteristic
4#14534883C211yesmaximal, characteristic, complemented
5#14534883C211yesmaximal, characteristic, complemented
6#14534880C211yesmaximal, characteristic, complemented
7#14534876C211yesmaximal, characteristic, complemented
8#14534868C211yesmaximal, characteristic
9#14534861C211yesmaximal, characteristic
10#14534808C211yesmaximal, characteristic
11#14534805C211yesmaximal, characteristic
12#14534699C211yesmaximal, characteristic
13#14534694C211yesmaximal, characteristic
14#14534666C211yesmaximal, characteristic, complemented
15#14534663C211yesmaximal, characteristic, complemented
16#14532088C211yesmaximal, characteristic, complemented
17#14532088C211yesmaximal, characteristic, complemented
18#14532088C211yesmaximal, characteristic, complemented
19#14532083C211yesmaximal, characteristic
20#14532083C211yesmaximal, characteristic
21#14532074C211yesmaximal, characteristic, complemented
22#14532061C211yesmaximal, characteristic
23#14532055C211yesmaximal, characteristic
24#14531343C211yesmaximal, characteristic, complemented
25#14531339C211yesmaximal, characteristic, complemented
26#14531334C211yesmaximal, characteristic
27#14531332C211yesmaximal, characteristic
28#14531276C211yesmaximal, characteristic
29#14531259C211yesmaximal, characteristic, complemented
30C4×#10587573C211yesmaximal, characteristic, complemented
31C17×#2666C211yesmaximal, characteristic, complemented
32C2×#10587584C2211yescharacteristic
33C2×#10587562C2211yescharacteristic
34C2×#10587556C2211yescharacteristic
35C2×#10587576C2211yescharacteristic
36C2×Q8×Dic17C2211yescharacteristic
37C2×C4×Dic34C2211yescharacteristic
38C2×#10587573C2211yescharacteristic
39C2×#10587573C2211yescharacteristic
40C2×#10587578C2211yescharacteristic
41C17⋊#401C2211yescharacteristic
42C17⋊#401C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762751C2211yescharacteristic
46#11762751C2211yescharacteristic
47#11762751C2211yescharacteristic
48#11762751C2211yescharacteristic
49#11762749C2211yescharacteristic
50#11762749C2211yescharacteristic
51#11762749C2211yescharacteristic
52#11762749C2211yescharacteristic
53#11762749C2211yescharacteristic
54#11762748C2211yescharacteristic
55#11762748C2211yescharacteristic
56#11762748C2211yescharacteristic
57#11762748C2211yescharacteristic
58#11762747C2211yescharacteristic
59#11762747C2211yescharacteristic
60#11762747C2211yescharacteristic
61#11762746C2211yescharacteristic
62#11762744C2211yescharacteristic
63#11762742C2211yescharacteristic
64#11762742C2211yescharacteristic
65#11762742C2211yescharacteristic
66#11762742C2211yescharacteristic
67#11762742C2211yescharacteristic
68#11762742C2211yescharacteristic
69#11762741C2211yescharacteristic
70#11762741C2211yescharacteristic
71#11762741C2211yescharacteristic
72#11762741C2211yescharacteristic
73#11762741C2211yescharacteristic
74#11762741C2211yescharacteristic
75#11762739C2211yescharacteristic
76#11762739C2211yescharacteristic
77#11762739C2211yescharacteristic
78#11762739C2211yescharacteristic
79#11762738C2211yescharacteristic
80#11762738C2211yescharacteristic
81#11762736C2211yescharacteristic
82#11762736C2211yescharacteristic
83#11762735C2211yescharacteristic
84#11762735C2211yescharacteristic
85#11762731C2211yescharacteristic
86#11762731C2211yescharacteristic
87#11762731C2211yescharacteristic
88#11762731C2211yescharacteristic
89#11762731C2211yescharacteristic
90#11762731C2211yescharacteristic
91#11762730C2211yescharacteristic
92#11762730C2211yescharacteristic
93#11762730C2211yescharacteristic
94#11762728C2211yescharacteristic
95#11762722C2211yescharacteristic
96#11762720C2211yescharacteristic
97#11762716C2211yescharacteristic
98#11762707C2211yescharacteristic
99#11762707C2211yescharacteristic
100#11762705C2211yescharacteristic
101#11762705C2211yescharacteristic
102#11762705C2211yescharacteristic
103#11762701C2211yescharacteristic
104#11762701C2211yescharacteristic
105#11762700C2211yescharacteristic
106#11762700C2211yescharacteristic
107#11762699C2211yescharacteristic
108#11762699C2211yescharacteristic
109#11762698C2211yescharacteristic
110#11762698C2211yescharacteristic
111#11762698C2211yescharacteristic
112#11762698C2211yescharacteristic
113#11762696C2211yescharacteristic
114#11762695C2211yescharacteristic
115#11762694C2211yescharacteristic
116#11762694C2211yescharacteristic
117#11762694C2211yescharacteristic
118#11762694C2211yescharacteristic
119#11762694C2211yescharacteristic
120#11762694C2211yescharacteristic
121#11762692C2211yescharacteristic
122#11762692C2211yescharacteristic
123#11762692C2211yescharacteristic
124#11762691C2211yescharacteristic
125#11762691C2211yescharacteristic
126#11762691C2211yescharacteristic
127#11762691C2211yescharacteristic
128#11762691C2211yescharacteristic
129#11762691C2211yescharacteristic
130#11762691C2211yescharacteristic
131#11762690C2211yescharacteristic
132#11762690C2211yescharacteristic
133#11762676C2211yescharacteristic
134#11762674C2211yescharacteristic
135C4⋊C4×Dic17C2211yescharacteristic
136C4⋊C4×Dic17C2211yescharacteristic
137C4⋊C4×Dic17C2211yescharacteristic
138C4⋊C4×Dic17C2211yescharacteristic
139C4⋊C4×Dic17C2211yescharacteristic
140C4⋊C4×Dic17C2211yescharacteristic
141C4⋊C4×Dic17C2211yescharacteristic
142C4⋊C4×Dic17C2211yescharacteristic
143C4⋊C4×Dic17C2211yescharacteristic
144C4⋊C4×Dic17C2211yescharacteristic
145C4⋊C4×Dic17C2211yescharacteristic
146C4⋊C4×Dic17C2211yescharacteristic
147C4×#63225C2211yescharacteristic
148C4×#63225C2211yescharacteristic
149#11762660C2211yescharacteristic
150#11762660C2211yescharacteristic
151#11762660C2211yescharacteristic
152#11762660C2211yescharacteristic
153#11762660C2211yescharacteristic
154#11762660C2211yescharacteristic
155#11762660C2211yescharacteristic
156#11762660C2211yescharacteristic
157#11762660C2211yescharacteristic
158#11762660C2211yescharacteristic
159#11762660C2211yescharacteristic
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762654C2211yescharacteristic
167#11762654C2211yescharacteristic
168#11762654C2211yescharacteristic
169C42×Dic17C2211yescharacteristic
170C42×Dic17C2211yescharacteristic
171C42×Dic17C2211yescharacteristic
172C17×#400C2211yescharacteristic
173C17×#400C2211yescharacteristic
174C17×#398C2211yescharacteristic
175C17×#398C2211yescharacteristic
176C17×#398C2211yescharacteristic
177C17×#398C2211yescharacteristic
178C17×#395C2211yescharacteristic
179C17×#395C2211yescharacteristic
180C17×#391C2211yescharacteristic
181C17×#389C2211yescharacteristic
182C17×#387C2211yescharacteristic
183C17×#387C2211yescharacteristic
184C17×#383C2211yescharacteristic
185C17×#382C2211yescharacteristic
186C4×C4⋊C4×C17C2211yescharacteristic
187C22×Q8×C17C2311yescharacteristic
188C22×C4×D17C2311yescharacteristic
189C22×Dic34C2311yescharacteristic
190C2×C4⋊C4×C17C2311yescharacteristic
191C2×C4⋊C4×C17C2311yescharacteristic
192C2×C4⋊C4×C17C2311yescharacteristic
193C2×C4⋊C4×C17C2311yescharacteristic
194C2×C4⋊C4×C17C2311yescharacteristic
195C2×C4⋊C4×C17C2311yescharacteristic
196C2×C4⋊C4×C17C2311yescharacteristic
197C2×C4⋊C4×C17C2311yescharacteristic
198C2×C4⋊C4×C17C2311yescharacteristic
199C2×C4⋊C4×C17C2311yescharacteristic
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C42×C17C2311yescharacteristic
204C2×C42×C17C2311yescharacteristic
205C2×C42×C17C2311yescharacteristic
206Q8×Dic17—24no—
207C2×#63227C2311yescharacteristic
208C2×#63227C2311yescharacteristic
209C2×#63227C2311yescharacteristic
210C2×#63227C2311yescharacteristic
211C2×#63227C2311yescharacteristic
212C2×#63227C2311yescharacteristic
213C2×#63227C2311yescharacteristic
214C2×#63227C2311yescharacteristic
215C2×#63227C2311yescharacteristic
216C2×#63227C2311yescharacteristic
217C2×#63227C2311yescharacteristic
218C2×#63227C2311yescharacteristic
219C2×#63227C2311yescharacteristic
220C2×#63227C2311yescharacteristic
221C2×C4⋊Dic17C2311yescharacteristic
222C2×C4⋊Dic17C2311yescharacteristic
223C2×C4⋊Dic17C2311yescharacteristic
224C2×C4⋊Dic17C2311yescharacteristic
225C2×C4⋊Dic17C2311yescharacteristic
226C2×C4⋊Dic17C2311yescharacteristic
227C2×C4⋊Dic17C2311yescharacteristic
228C2×C4⋊Dic17C2311yescharacteristic
229C2×C4⋊Dic17C2311yescharacteristic
230C2×C4⋊Dic17C2311yescharacteristic
231C2×C4⋊Dic17C2311yescharacteristic
232C2×C4⋊Dic17C2311yescharacteristic
233C2×C4⋊Dic17C2311yescharacteristic
234C2×C4⋊Dic17C2311yescharacteristic
235C2×C4⋊Dic17C2311yescharacteristic
236C2×#63225C2311yescharacteristic
237C2×#63225C2311yescharacteristic
238C2×#63225C2311yescharacteristic
239C2×#63225C2311yescharacteristic
240C2×#63225C2311yescharacteristic
241C2×#63225C2311yescharacteristic
242C2×#63225C2311yescharacteristic
243C2×#63225C2311yescharacteristic
244C2×#63225C2311yescharacteristic
245C2×#63225C2311yescharacteristic
246C2×#63225C2311yescharacteristic
247C2×#63225C2311yescharacteristic
248C2×#63225C2311yescharacteristic
249C2×#63225C2311yescharacteristic
250C2×#63225C2311yescharacteristic
251C2×#63225C2311yescharacteristic
252C2×#63225C2311yescharacteristic
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×C4×Dic17C2311yescharacteristic
257C2×C4×Dic17C2311yescharacteristic
258C2×C4×Dic17C2311yescharacteristic
259C2×C4×Dic17C2311yescharacteristic
260C2×C4×Dic17C2311yescharacteristic
261C2×C4×Dic17C2311yescharacteristic
262C2×C4×Dic17C2311yescharacteristic
263C2×C4×Dic17C2311yescharacteristic
264C2×C4×Dic17C2311yescharacteristic
265C2×C4×Dic17C2311yescharacteristic
266C2×C4×Dic17C2311yescharacteristic
267C2×C4×Dic17C2311yescharacteristic
268C2×C4×Dic17C2311yescharacteristic
269C2×C4×Dic17C2311yescharacteristic
270C2×C4×Dic17C2311yescharacteristic
271C2×C4×Dic17C2311yescharacteristic
272C2×C4×Dic17C2311yescharacteristic
273C2×C4×Dic17C2311yescharacteristic
274C2×C4×Dic17C2311yescharacteristic
275C2×C4×Dic17C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279#10587584—24no—
280#10587578—24no—
281#10587576—24no—
282#10587573—24no—
283#10587573—24no—
284#10587562—24no—
285#10587556—24no—
286C4×Dic34—24no—
287C17×#95C2311yescharacteristic
288C17×#95C2311yescharacteristic
289C17×#95C2311yescharacteristic
290C17×#95C2311yescharacteristic
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301C17×#95C2311yescharacteristic
302C17×#95C2311yescharacteristic
303C17×#95C2311yescharacteristic
304C17×#95C2311yescharacteristic
305#10587502C2311yescharacteristic
306#10587502C2311yescharacteristic
307#10587502C2311yescharacteristic
308#10587502C2311yescharacteristic
309#10587502C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351C23×D17C2411yescharacteristic
352C2×Q8×C17—22no—
353C2×Q8×C17—41no—
354C2×Q8×C17—41no—
355C22×C4×C17C2411yescharacteristic
356C22×C4×C17C2411yescharacteristic
357C22×C4×C17C2411yescharacteristic
358C22×C4×C17C2411yescharacteristic
359C22×C4×C17C2411yescharacteristic
360C22×C4×C17C2411yescharacteristic
361C22×C4×C17C2411yescharacteristic
362C22×C4×C17C2411yescharacteristic
363C22×C4×C17C2411yescharacteristic
364C22×C4×C17C2411yescharacteristic
365C22×C4×C17C2411yescharacteristic
366C22×C4×C17C2411yescharacteristic
367C22×C4×C17C2411yescharacteristic
368C22×C4×C17C2411yescharacteristic
369C22×C4×C17C2411yescharacteristic
370C22×Dic17C2411yescharacteristic
371C22×Dic17C2411yescharacteristic
372C22×Dic17C2411yescharacteristic
373C22×Dic17C2411yescharacteristic
374C22×Dic17C2411yescharacteristic
375C22×Dic17C2411yescharacteristic
376C22×Dic17C2411yescharacteristic
377C22×Dic17C2411yescharacteristic
378C22×Dic17C2411yescharacteristic
379C22×Dic17C2411yescharacteristic
380C22×Dic17C2411yescharacteristic
381C22×Dic17C2411yescharacteristic
382C22×Dic17C2411yescharacteristic
383C22×Dic17C2411yescharacteristic
384C22×Dic17C2411yescharacteristic
385C2×C4×D17—22no—
386C2×C4×D17—22no—
387C2×C4×D17—22no—
388C2×Dic34—22no—
389C2×Dic34—22no—
390C2×Dic34—22no—
391C4⋊C4×C17—22no—
392C4⋊C4×C17—22no—
393C4⋊C4×C17—22no—
394C4⋊C4×C17—22no—
395C4⋊C4×C17—22no—
396C4⋊C4×C17—41no—
397C4⋊C4×C17—41no—
398C4⋊C4×C17—41no—
399C4⋊C4×C17—41no—
400C4⋊C4×C17—41no—
401C4⋊C4×C17—41no—
402C4⋊C4×C17—41no—
403C4⋊C4×C17—41no—
404C42×C17—41no—
405C42×C17—41no—
406C42×C17#4114yes—
407#63227—22no—
408#63227—22no—
409#63227—22no—
410#63227—22no—
411#63227—22no—
412#63227—22no—
413#63227—22no—
414#63227—22no—
415#63227—41no—
416#63227—41no—
417#63227—41no—
418#63227—41no—
419#63227—41no—
420#63227—41no—
421C4⋊Dic17—22no—
422C4⋊Dic17—22no—
423C4⋊Dic17—22no—
424C4⋊Dic17—22no—
425C4⋊Dic17—22no—
426C4⋊Dic17—22no—
427C4⋊Dic17—22no—
428C4⋊Dic17—22no—
429C4⋊Dic17—22no—
430C4⋊Dic17—22no—
431C4⋊Dic17—22no—
432C4⋊Dic17—41no—
433C4⋊Dic17—41no—
434C4⋊Dic17—41no—
435C4⋊Dic17—41no—
436#63225—22no—
437#63225—22no—
438#63225—22no—
439#63225—22no—
440#63225—22no—
441#63225—22no—
442#63225—22no—
443#63225—22no—
444#63225—22no—
445#63225—22no—
446#63225—22no—
447#63225—22no—
448#63225—22no—
449#63225—22no—
450#63225—22no—
451#63225—22no—
452#63225—41no—
453#63225—41no—
454#63225—41no—
455#63225—41no—
456C4×Dic17—22no—
457C4×Dic17—22no—
458C4×Dic17—22no—
459C4×Dic17—22no—
460C4×Dic17—22no—
461C4×Dic17—22no—
462C4×Dic17—22no—
463C4×Dic17—22no—
464C4×Dic17—22no—
465C4×Dic17—22no—
466C4×Dic17—22no—
467C4×Dic17—22no—
468C4×Dic17—22no—
469C4×Dic17—22no—
470C4×Dic17—22no—
471C4×Dic17—22no—
472C4×Dic17—22no—
473C4×Dic17—41no—
474C4×Dic17—41no—
475C4×Dic17—41no—
476C4×Dic17—41no—
477C4×Dic17#4114yes—
478C4×Dic17#4114yes—
479#34604—171nomaximal, Sylow
480C23×C17C2511yescharacteristic
481C22×D17—21no—
482C22×D17—21no—
483C22×D17—21no—
484C22×D17—21no—
485C22×D17—21no—
486C22×D17—21no—
487C22×D17—21no—
488Q8×C17—44no—
489C2×C4×C17—21no—
490C2×C4×C17—21no—
491C2×C4×C17—21no—
492C2×C4×C17—21no—
493C2×C4×C17—21no—
494C2×C4×C17—21no—
495C2×C4×C17—21no—
496C2×C4×C17—21no—
497C2×C4×C17—21no—
498C2×C4×C17—21no—
499C2×C4×C17—21no—
500C2×C4×C17—21no—
501C2×C4×C17—21no—
502C2×C4×C17—21no—
503C2×C4×C17—21no—
504C2×C4×C17—21no—
505C2×C4×C17—21no—
506C2×C4×C17—21no—
507C2×C4×C17—21no—
508C2×C4×C17—21no—
509C2×C4×C17—21no—
510C2×C4×C17—21no—
511C2×C4×C17—21no—
512C2×C4×C17—21no—
513C2×C4×C17—21no—
514C2×C4×C17—21no—
515C2×C4×C17—21no—
516C2×C4×C17—21no—
517C2×C4×C17—21no—
518C2×C4×C17—21no—
519C2×C4×C17—21no—
520C2×C4×C17—21no—
521C2×C4×C17—21no—
522C2×C4×C17—21no—
523C2×C4×C17—21no—
524C2×C4×C17—21no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17C2×#4112yes—
530C2×C4×C17C2×#4112yes—
531C2×C4×C17C2×#4112yes—
532C2×C4×C17C2×#4112yes—
533C2×C4×C17C2×#4112yes—
534C2×Dic17—21no—
535C2×Dic17—21no—
536C2×Dic17—21no—
537C2×Dic17—21no—
538C2×Dic17—21no—
539C2×Dic17—21no—
540C2×Dic17—21no—
541C2×Dic17—21no—
542C2×Dic17—21no—
543C2×Dic17—21no—
544C2×Dic17—21no—
545C2×Dic17—21no—
546C2×Dic17—21no—
547C2×Dic17—21no—
548C2×Dic17—21no—
549C2×Dic17—21no—
550C2×Dic17—21no—
551C2×Dic17—21no—
552C2×Dic17—21no—
553C2×Dic17—21no—
554C2×Dic17—21no—
555C2×Dic17—21no—
556C2×Dic17—21no—
557C2×Dic17—21no—
558C2×Dic17—21no—
559C2×Dic17—21no—
560C2×Dic17—21no—
561C2×Dic17—21no—
562C2×Dic17—21no—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—21no—
569C2×Dic17—21no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17C2×#4112yes—
574C2×Dic17C2×#4112yes—
575C2×Dic17C2×#4112yes—
576C2×Dic17C2×#4112yes—
577C2×Dic172−1+412yes—
578C2×Dic172−1+412yes—
579C4×D17—44no—
580Dic34—28no—
581#2666—171no—
582#2666D1711yescharacteristic, complemented
583#2664—171no—
584#2664—171no—
585#2655—171no—
586#2655—171no—
587#2655—171no—
588#2655—171no—
589#2654—171no—
590#2654—171no—
591#2650—171no—
592#2650—171no—
593#2637—171no—
594#2637—171no—
595#2634—171no—
596#2634—171no—
597#2402—171no—
598#2402—171no—
599#2402—171no—
600#2401—171no—
601#2401—171no—
602#2399—171no—
603#2396—171no—
604#2396—171no—
605C4×#125—171no—
606C4×#125—171no—
607C4×#126—171no—
608C4×#126—171no—
609#2298—171no—
610#2295—171no—
611C42×Q8—171no—
612C22×C17C22×#4111yescharacteristic
613C22×C17C22×#4111yescharacteristic
614C22×C17C22×#4111yescharacteristic
615C22×C17C2×2−1+411yescharacteristic
616C22×C17C2×2−1+411yescharacteristic
617C22×C17#58511yescharacteristic
618C22×C17#58511yescharacteristic
619C2×D17—41no—
620C2×D17—41no—
621C2×D17—41no—
622C2×D17—41no—
623C2×D17—41no—
624C2×D17—41no—
625C2×D17—41no—
626C4×C17—22no—
627C4×C17—22no—
628C4×C17—22no—
629C4×C17—22no—
630C4×C17—22no—
631C4×C17—41no—
632C4×C17—41no—
633C4×C17—41no—
634C4×C17—41no—
635C4×C17—41no—
636C4×C17—41no—
637C4×C17—41no—
638C4×C17—41no—
639C4×C17—41no—
640C4×C17—41no—
641Dic17—22no—
642Dic17—22no—
643Dic17—22no—
644Dic17—41no—
645Dic17—41no—
646Dic17—41no—
647Dic17—41no—
648Dic17—41no—
649Dic17—41no—
650Dic17—41no—
651Dic17—41no—
652Dic17—41no—
653Dic17—41no—
654Dic17—41no—
655Dic17#54114yes—
656C2×#126—171no—
657C2×#126—171no—
658C2×#125—171no—
659C2×#125—171no—
660C2×C4×Q8—171no—
661C2×C4×Q8—171no—
662C2×C4×Q8—171no—
663C2×C4×Q8—171no—
664C2×#117—171no—
665#401—171no—
666#401—171no—
667#400—171no—
668#400—171no—
669#400—171no—
670#400—171no—
671#400—171no—
672#400—171no—
673#400—171no—
674#400—171no—
675#400—171no—
676#400—171no—
677#400—171no—
678#400—171no—
679#400—171no—
680#400—171no—
681#400—171no—
682#400—171no—
683#400—171no—
684#400—171no—
685#400C2×D1711yescharacteristic
686#400C2×D1711yescharacteristic
687#399—171no—
688#399—171no—
689#398—171no—
690#398—171no—
691#398—171no—
692#398—171no—
693#398—171no—
694#398—171no—
695#398—171no—
696#398—171no—
697#398—171no—
698#398—171no—
699#398—171no—
700#398—171no—
701#398—171no—
702#398—171no—
703#398—171no—
704#398—171no—
705#398C2×D1711yescharacteristic
706#398C2×D1711yescharacteristic
707#398C2×D1711yescharacteristic
708#398C2×D1711yescharacteristic
709#397—171no—
710#397—171no—
711#397—171no—
712#397—171no—
713#397—171no—
714#397—171no—
715#396—171no—
716#396—171no—
717#396—171no—
718#396—171no—
719#396—171no—
720#396—171no—
721#395—171no—
722#395—171no—
723#395—171no—
724#395—171no—
725#395C2×D1711yescharacteristic
726#395C2×D1711yescharacteristic
727#393—171no—
728#393—171no—
729#391—171no—
730#391C2×D1711yescharacteristic
731#389—171no—
732#389—171no—
733#389—171no—
734#389—171no—
735#389—171no—
736#389C2×D1711yescharacteristic
737#388—171no—
738#388—171no—
739#388—171no—
740#388—171no—
741#388—171no—
742#388—171no—
743#388—171no—
744#388—171no—
745#388—171no—
746#388—171no—
747#387—171no—
748#387—171no—
749#387—171no—
750#387—171no—
751#387—171no—
752#387—171no—
753#387—171no—
754#387—171no—
755#387—171no—
756#387—171no—
757#387—171no—
758#387—171no—
759#387—171no—
760#387—171no—
761#387—171no—
762#387—171no—
763#387—171no—
764#387—171no—
765#387—171no—
766#387—171no—
767#387C2×D1711yescharacteristic
768#387C2×D1711yescharacteristic
769#383—171no—
770#383C2×D1711yescharacteristic
771#382—171no—
772#382C2×D1711yescharacteristic
773C4×C4⋊C4—171no—
774C4×C4⋊C4—171no—
775C4×C4⋊C4—171no—
776C4×C4⋊C4—171no—
777C4×C4⋊C4—171no—
778C4×C4⋊C4—171no—
779C4×C4⋊C4—171no—
780C4×C4⋊C4—171no—
781C4×C4⋊C4—171no—
782C4×C4⋊C4—171no—
783C4×C4⋊C4—171no—
784C4×C4⋊C4—171no—
785C4×C4⋊C4—171no—
786C4×C4⋊C4—171no—
787C4×C4⋊C4—171no—
788C4×C4⋊C4—171no—
789C4×C4⋊C4—171no—
790C4×C4⋊C4—171no—
791C4×C4⋊C4—171no—
792C4×C4⋊C4—171no—
793C4×C4⋊C4—171no—
794C4×C4⋊C4—171no—
795C4×C4⋊C4—171no—
796C4×C4⋊C4—171no—
797C4×C4⋊C4—171no—
798C4×C4⋊C4C2×D1711yescharacteristic
799C4×C22⋊C4—171no—
800C4×C22⋊C4—171no—
801C4×C22⋊C4—171no—
802C4×C22⋊C4—171no—
803C4×C22⋊C4—171no—
804C4×C22⋊C4—171no—
805#376—171no—
806#376—171no—
807#376—171no—
808C43—171no—
809C43—171no—
810C43—171no—
811C2×C17#344411yescharacteristic
812C2×C17C2×#54111yescharacteristic
813C2×C17#345511yescharacteristic
814C2×C17#346111yescharacteristic
815C2×C17#346111yescharacteristic
816C2×C17#346111yescharacteristic
817C2×C17#346111yescharacteristic
818D17—81no—
819C22×Q8—171no—
820C22×Q8C22×D1711yescharacteristic
821C23×C4—171no—
822#126—344no—
823#126—344no—
824#125—344no—
825#125—344no—
826C4×Q8—344no—
827C4×Q8—344no—
828C4×Q8—344no—
829C4×Q8—344no—
830#117—344no—
831C2×C4⋊C4—171no—
832C2×C4⋊C4—171no—
833C2×C4⋊C4—171no—
834C2×C4⋊C4—171no—
835C2×C4⋊C4—171no—
836C2×C4⋊C4—171no—
837C2×C4⋊C4—171no—
838C2×C4⋊C4—171no—
839C2×C4⋊C4—171no—
840C2×C4⋊C4—171no—
841C2×C4⋊C4—171no—
842C2×C4⋊C4—171no—
843C2×C4⋊C4—171no—
844C2×C4⋊C4—171no—
845C2×C4⋊C4—171no—
846C2×C4⋊C4—171no—
847C2×C4⋊C4—171no—
848C2×C4⋊C4—171no—
849C2×C4⋊C4—171no—
850C2×C4⋊C4—171no—
851C2×C4⋊C4—171no—
852C2×C4⋊C4—171no—
853C2×C4⋊C4—171no—
854C2×C4⋊C4—171no—
855C2×C4⋊C4—171no—
856C2×C4⋊C4—171no—
857C2×C4⋊C4—171no—
858C2×C4⋊C4—171no—
859C2×C4⋊C4—171no—
860C2×C4⋊C4—171no—
861C2×C4⋊C4—171no—
862C2×C4⋊C4—171no—
863C2×C4⋊C4—171no—
864C2×C4⋊C4—171no—
865C2×C4⋊C4—171no—
866C2×C4⋊C4C22×D1711yescharacteristic
867C2×C4⋊C4C22×D1711yescharacteristic
868C2×C4⋊C4C22×D1711yescharacteristic
869C2×C4⋊C4C22×D1711yescharacteristic
870C2×C4⋊C4C22×D1711yescharacteristic
871C2×C4⋊C4C22×D1711yescharacteristic
872C2×C4⋊C4C22×D1711yescharacteristic
873C2×C4⋊C4C22×D1711yescharacteristic
874C2×C4⋊C4C22×D1711yescharacteristic
875C2×C4⋊C4C22×D1711yescharacteristic
876C2×C4⋊C4C22×D1711yescharacteristic
877C2×C4⋊C4C22×D1711yescharacteristic
878C2×C4⋊C4C22×D1711yescharacteristic
879C2×C22⋊C4—171no—
880C2×C22⋊C4—171no—
881C2×C22⋊C4—171no—
882C2×C22⋊C4—171no—
883C2×C22⋊C4—171no—
884C2×C22⋊C4—171no—
885C2×C22⋊C4—171no—
886C2×C22⋊C4—171no—
887C2×C22⋊C4—171no—
888C2×C22⋊C4—171no—
889C2×C22⋊C4—171no—
890C2×C22⋊C4—171no—
891C2×C22⋊C4—171no—
892C2×C22⋊C4—171no—
893C2×C42—171no—
894C2×C42—171no—
895C2×C42—171no—
896C2×C42—171no—
897C2×C42—171no—
898C2×C42—171no—
899C2×C42—171no—
900C2×C42—171no—
901C2×C42—171no—
902C2×C42—171no—
903C2×C42—171no—
904C2×C42—171no—
905C2×C42—171no—
906C2×C42—171no—
907C2×C42—171no—
908C2×C42—171no—
909C2×C42—171no—
910C2×C42—171no—
911C2×C42—171no—
912C2×C42—171no—
913C2×C42—171no—
914C2×C42—171no—
915C2×C42—171no—
916C2×C42C22×D1711yescharacteristic
917C2×C42C22×D1711yescharacteristic
918C2×C42C22×D1711yescharacteristic
919#95—171no—
920#95—171no—
921#95—171no—
922#95—171no—
923#95—171no—
924#95—171no—
925#95—171no—
926#95—171no—
927#95—171no—
928#95—171no—
929#95—171no—
930#95—171no—
931#95—171no—
932#95—171no—
933#95—171no—
934#95—171no—
935#95—171no—
936#95—171no—
937#95—171no—
938#95—171no—
939#95—171no—
940#95—171no—
941#95—171no—
942#95—171no—
943#95—171no—
944#95—171no—
945#95—171no—
946#95—171no—
947#95—171no—
948#95—171no—
949#95—171no—
950#95—171no—
951#95—171no—
952#95—171no—
953#95—171no—
954#95—171no—
955#95—171no—
956#95—171no—
957#95—171no—
958#95—171no—
959#95—171no—
960#95—171no—
961#95—171no—
962#95—171no—
963#95—171no—
964#95—171no—
965#95C22×D1711yescharacteristic
966#95C22×D1711yescharacteristic
967#95C22×D1711yescharacteristic
968#95C22×D1711yescharacteristic
969#95C22×D1711yescharacteristic
970#95C22×D1711yescharacteristic
971#95C22×D1711yescharacteristic
972#95C22×D1711yescharacteristic
973#95C22×D1711yescharacteristic
974#95C22×D1711yescharacteristic
975#95C22×D1711yescharacteristic
976#95C22×D1711yescharacteristic
977#95C22×D1711yescharacteristic
978#95C22×D1711yescharacteristic
979#95C22×D1711yescharacteristic
980#95C22×D1711yescharacteristic
981#95C22×D1711yescharacteristic
982#95C22×D1711yescharacteristic
983C17#3460411yescharacteristic, complemented, Sylow
984C24—171no—
985C2×Q8—22no—
986C2×Q8—41no—
987C2×Q8—41no—
988C2×Q8—342no—
989C2×Q8—342no—
990C2×Q8—342no—
991C22×C4—171no—
992C22×C4—171no—
993C22×C4—171no—
994C22×C4—171no—
995C22×C4—171no—
996C22×C4—171no—
997C22×C4—171no—
998C22×C4—171no—
999C22×C4—171no—
1000C22×C4—171no—
1001C22×C4—171no—
1002C22×C4—171no—
1003C22×C4—171no—
1004C22×C4—171no—
1005C22×C4—171no—
1006C22×C4—342no—
1007C22×C4—342no—
1008C22×C4—342no—
1009C22×C4C23×D1711yescharacteristic
1010C22×C4C23×D1711yescharacteristic
1011C22×C4C23×D1711yescharacteristic
1012C22×C4C23×D1711yescharacteristic
1013C22×C4C23×D1711yescharacteristic
1014C22×C4C23×D1711yescharacteristic
1015C22×C4C23×D1711yescharacteristic
1016C22×C4C23×D1711yescharacteristic
1017C22×C4C23×D1711yescharacteristic
1018C22×C4C23×D1711yescharacteristic
1019C22×C4C23×D1711yescharacteristic
1020C22×C4C23×D1711yescharacteristic
1021C22×C4C23×D1711yescharacteristic
1022C22×C4C23×D1711yescharacteristic
1023C22×C4C23×D1711yescharacteristic
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—342no—
1038C4⋊C4—342no—
1039C4⋊C4—342no—
1040C4⋊C4—342no—
1041C4⋊C4—342no—
1042C4⋊C4—342no—
1043C4⋊C4—342no—
1044C4⋊C4—342no—
1045C4⋊C4—342no—
1046C4⋊C4—342no—
1047C4⋊C4—342no—
1048C4⋊C4—342no—
1049C4⋊C4—342no—
1050C4⋊C4—342no—
1051C4⋊C4—342no—
1052C4⋊C4—342no—
1053C4⋊C4—342no—
1054C4⋊C4—342no—
1055C4⋊C4—342no—
1056C4⋊C4—342no—
1057C4⋊C4—342no—
1058C4⋊C4—342no—
1059C4⋊C4—342no—
1060C4⋊C4—342no—
1061C4⋊C4—342no—
1062C4⋊C4—342no—
1063C4⋊C4—342no—
1064C4⋊C4—681no—
1065C4⋊C4—681no—
1066C4⋊C4—681no—
1067C4⋊C4—681no—
1068C4⋊C4—681no—
1069C4⋊C4—681no—
1070C4⋊C4—681no—
1071C4⋊C4—681no—
1072C22⋊C4—342no—
1073C22⋊C4—342no—
1074C22⋊C4—342no—
1075C22⋊C4—342no—
1076C22⋊C4—342no—
1077C22⋊C4—342no—
1078C22⋊C4—342no—
1079C22⋊C4—342no—
1080C22⋊C4—681no—
1081C22⋊C4—681no—
1082C22⋊C4—681no—
1083C22⋊C4—681no—
1084C22⋊C4—681no—
1085C22⋊C4—681no—
1086C42—41no—
1087C42—41no—
1088C42—174no—
1089C42—174no—
1090C42—342no—
1091C42—342no—
1092C42—342no—
1093C42—342no—
1094C42—342no—
1095C42—342no—
1096C42—342no—
1097C42—342no—
1098C42—342no—
1099C42—342no—
1100C42—342no—
1101C42—342no—
1102C42—342no—
1103C42—342no—
1104C42—342no—
1105C42—342no—
1106C42—342no—
1107C42—681no—
1108C42—681no—
1109C42—681no—
1110C42—681no—
1111C42#6325614yes—
1112C23—341no—
1113C23—341no—
1114C23—341no—
1115C23—341no—
1116C23—341no—
1117C23—341no—
1118C23—341no—
1119C23C24×D1711yescharacteristic
1120Q8—44no—
1121Q8—348no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—172no—
1163C2×C4—172no—
1164C2×C4—172no—
1165C2×C4—172no—
1166C2×C4—172no—
1167C2×C4—172no—
1168C2×C4—341no—
1169C2×C4—341no—
1170C2×C4—341no—
1171C2×C4—341no—
1172C2×C4—341no—
1173C2×C4—341no—
1174C2×C4—341no—
1175C2×C4—341no—
1176C2×C4—341no—
1177C2×C4—341no—
1178C2×C4—341no—
1179C2×C4—341no—
1180C2×C4—341no—
1181C2×C4—341no—
1182C2×C4—341no—
1183C2×C4—341no—
1184C2×C4—341no—
1185C2×C4—341no—
1186C2×C4—341no—
1187C2×C4—341no—
1188C2×C4—341no—
1189C2×C4—341no—
1190C2×C4—341no—
1191C2×C4—341no—
1192C2×C4—341no—
1193C2×C4—341no—
1194C2×C4—341no—
1195C2×C4—341no—
1196C2×C4—341no—
1197C2×C4—341no—
1198C2×C4—341no—
1199C2×C4—341no—
1200C2×C4—341no—
1201C2×C4—341no—
1202C2×C4—341no—
1203C2×C4—341no—
1204C2×C4—341no—
1205C2×C4—341no—
1206C2×C4—341no—
1207C2×C4—684no—
1208C2×C4C2×#6325612yes—
1209C2×C4C2×#6325612yes—
1210C2×C4C2×#6325612yes—
1211C2×C4#41×D1712yes—
1212C2×C4#41×D1712yes—
1213C22—681no—
1214C22—681no—
1215C22—681no—
1216C22—681no—
1217C22—681no—
1218C22—681no—
1219C22—681no—
1220C22C2×#41×D1711yescharacteristic
1221C22C2×#41×D1711yescharacteristic
1222C22C22×#6325611yescharacteristic
1223C222−1+4×D1711yescharacteristic
1224C222−1+4×D1711yescharacteristic
1225C22#1176364411yescharacteristic
1226C22#1176364411yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—174no—
1243C4—342no—
1244C4—342no—
1245C4—342no—
1246C4—681no—
1247C4—681no—
1248C4—681no—
1249C4—681no—
1250C4—681no—
1251C4—681no—
1252C4—681no—
1253C4—681no—
1254C4—681no—
1255C4—681no—
1256C4—681no—
1257C2—1361no—
1258C2#1454208111yescharacteristic
1259C2D17×#54111yescharacteristic
1260C2#1454216611yescharacteristic
1261C2#1454221011yescharacteristic
1262C2#1454221411yescharacteristic
1263C2#1454221811yescharacteristic
1264C2#1454221811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2666C2
prime radicalC23×D17C24
hypercenter#2666D17
hypocenterC17#34604
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2666

Complements

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

NH ≅ G/Ntype
1. #14534970C2semidirect
4. #14534883C2semidirect
5. #14534883C2semidirect
6. #14534880C2semidirect
7. #14534876C2semidirect
14. #14534666C2semidirect
15. #14534663C2semidirect
16. #14532088C2semidirect
17. #14532088C2semidirect
18. #14532088C2semidirect
21. #14532074C2semidirect
24. #14531343C2semidirect
25. #14531339C2semidirect
29. #14531259C2semidirect
30. C4×#10587573C2semidirect
31. C17×#2666C2semidirect
582. #2666D17semidirect
983. C17#34604semidirect

Maximal subgroups

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

subgroupindex
#145349702
#145349502
#145349432
#145348832
#145348802
#145348762
#145348682
#145348612
#145348082
#145348052
#145346992
#145346942
#145346662
#145346632
#145320882
#145320832
#145320742
#145320612
#145320552
#145313432
#145313392
#145313342
#145313322
#145312762
#145312592
C4×#105875732
C17×#26662
#3460417