Finite Group Databasebeta

← #17898868

Subgroups — #17898868

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542081C211yesmaximal, characteristic
2#14537797C218yesmaximal, complemented
3#14537777C218yesmaximal, complemented
4#14537725C211yesmaximal, characteristic, complemented
5#14537503C211yesmaximal, characteristic, complemented
6#14537501C211yesmaximal, characteristic, complemented
7#14537480C212yesmaximal, complemented
8#14537477C212yesmaximal, complemented
9#14537434C212yesmaximal, complemented
10#14537416C211yesmaximal, characteristic, complemented
11#14537211C212yesmaximal, complemented
12C2×#97×D17C211yesmaximal, characteristic, complemented
13C17×#2961C211yesmaximal, characteristic, complemented
14C2×#10587593C2212yes—
15C2×#10587587C2212yes—
16C22×C8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18#11763364C412yes—
19#11763360C412yes—
20#11763359C2211yescharacteristic
21#11763346C2214yes—
22#11763345C414yes—
23#11763344C414yes—
24#11763322C414yes—
25#11763321C2212yes—
26C4×#63256C2214yes—
27#11763277C2212yes—
28C2×C42×D17C2211yescharacteristic
29#11762940C2218yescomplemented
30#11762882C2218yes—
31#11762882C2218yescomplemented
32#11762879C2218yes—
33#11762879C2218yescomplemented
34C8×D68C2218yes—
35#11762874C2218yes—
36#11762869C2218yescomplemented
37#11762865C2214yes—
38#11762865C2218yescomplemented
39#11762861C2214yes—
40#11762836C2212yes—
41#11762833C2211yescharacteristic
42#11762777C2212yes—
43#11762775C2212yes—
44#11762772C2212yes—
45#11762766C2214yescomplemented
46#11762765C2212yes—
47#11762763C2214yescomplemented
48M16×Dic17C2212yes—
49C4×#63218C2214yescomplemented
50C2×#10587474C2211yescharacteristic
51C2×#10587486C2211yescharacteristic
52C2×#10587486C2211yescharacteristic
53#97×D17C2214yes—
54#97×D17C2214yes—
55#97×D17C2214yescomplemented
56C17×#533C2211yescharacteristic
57C17×#446C2218yescomplemented
58C17×#424C2212yes—
59C17×#423C2211yescharacteristic
60C17×#405C2212yes—
61C2×C17×#97C2211yescharacteristic
62C2×#63256C2×C414yes—
63C2×#63252C2312yes—
64C22×C4×D17C2×C412yes—
65C22×C4×D17C2311yescharacteristic
66C2×M16×C17C2312yes—
67C22×C8×C17C2311yescharacteristic
68C22×C8×C17C2311yescharacteristic
69C17×C4⋊Q8C2×C412yes—
70C17×#125C2×C412yes—
71C17×C22⋊Q8C2×C414yes—
72C4×Q8×C17C2314yes—
73C17×#117C2312yes—
74C2×C42×C17C2311yescharacteristic
75#10587633C2×C414yes—
76#10587632C2×C414yes—
77Q8×Dic17C2×C414yes—
78#10587616C2×C414yes—
79C2×C4×Dic17C2×C412yes—
80C2×C4×Dic17C2311yescharacteristic
81C2×#63223C2312yes—
82C22×#3622C2311yescharacteristic
83C22×#3622C2311yescharacteristic
84#10587593—28no—
85#10587587—28no—
86C2×#63218C2314yes—
87C2×#63218C2314yes—
88C2×C8×D17—24no—
89C2×C8×D17—24no—
90C2×C8×D17C2314yes—
91C2×C8×D17C2314yes—
92C2×C8×D17C2314yes—
93C2×C8×D17C2314yes—
94#10587584C2×C418yes—
95#10587583C2×C414yes—
96#10587581C2×C414yes—
97#10587581C2×C414yes—
98#10587580C2×C418yes—
99#10587579C2×C414yes—
100#10587579C2×C418yes—
101#10587579C2×C414yes—
102#10587578C2×C414yes—
103#10587578C2×C418yes—
104#10587576C2×C414yes—
105#10587573C2×C414yes—
106#10587572C2×C414yes—
107#10587568C2×C414yes—
108#10587567C2×C418yes—
109#10587561C2×C412yes—
110#10587560C2×C411yescharacteristic
111C4×D68C2318yes—
112C4×D68C2314yes—
113#10587558C2314yes—
114C42×D17C2×C412yes—
115C42×D17C2×C412yes—
116C42×D17C2312yes—
117C42×D17C2312yes—
118C42×D17C2314yes—
119#10587555C2×C411yescharacteristic
120C17×C4⋊C8C2314yes—
121C17×C4⋊C8C2318yes—
122C17×#97C2314yes—
123C17×#97C2314yes—
124C4×C8×C17C2314yes—
125#10587491C2318yes—
126#10587491C2318yes—
127#10587491C2318yes—
128#10587486C2312yes—
129#10587486C2312yes—
130#10587486C2312yes—
131#10587486C2312yes—
132#10587486C2314yes—
133C8×Dic17C2314yes—
134C4⋊#3622C2314yes—
135C4⋊#3622C2318yes—
136#10587474C2314yes—
137#10587474C2314yes—
138C4×#3622C2314yes—
139C23×D17C22×C411yescharacteristic
140C2×Q8×C17C22×C414yes—
141C22×C4×C17C22×C412yes—
142C22×C4×C17C2411yescharacteristic
143C2×C22⋊D17C22×C414yes—
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C412yes—
146#63256—48no—
147#63252—24no—
148#63252—24no—
149C2×D68C22×C412yes—
150C2×D68C22×C418yes—
151C2×D68C22×C414yes—
152C2×C4×D17—22no—
153C2×C4×D17—22no—
154C2×C4×D17—44no—
155C2×C4×D17C22×C412yes—
156C2×C4×D17C22×C412yes—
157C2×C4×D17C22×C412yes—
158C2×C4×D17C22×C412yes—
159C2×C4×D17C22×C412yes—
160C2×C4×D17C22×C418yes—
161C2×C4×D17C2412yes—
162C2×C4×D17C2414yes—
163C2×Dic34C22×C412yes—
164M16×C17—24no—
165C2×C8×C17—22no—
166C2×C8×C17#4114yescomplemented
167C2×C8×C17C2412yes—
168C2×C8×C17C2414yes—
169C2×C8×C17C2412yes—
170C4⋊C4×C17C22×C418yes—
171C4⋊C4×C17C22×C414yes—
172C4⋊C4×C17C22×C414yes—
173C22⋊C4×C17C22×C414yes—
174C42×C17C22×C411yescharacteristic
175C42×C17C22×C411yescharacteristic
176C42×C17C2414yes—
177C42×C17C2412yes—
178#63227C22×C418yes—
179#63227C22×C418yes—
180#63227C22×C418yes—
181#63227C22×C418yes—
182C4⋊Dic17C22×C414yes—
183C4⋊Dic17C22×C418yes—
184#63225C22×C418yes—
185C4×Dic17C22×C412yes—
186C4×Dic17C22×C412yes—
187C4×Dic17C22×C412yes—
188C4×Dic17C22×C412yes—
189C4×Dic17C22×C412yes—
190C4×Dic17C22×C418yes—
191C4×Dic17C2411yescharacteristic
192C4×Dic17C2411yescharacteristic
193#63223—24no—
194C2×#3622—22no—
195C2×#3622#4114yescomplemented
196C2×#3622C2414yes—
197C2×#3622C2412yes—
198C2×#3622C2412yes—
199#63218—28no—
200#63218—28no—
201C8×D17—28no—
202C8×D17—28no—
203C8×D17—28no—
204C8×D17—28no—
205#60207—171nomaximal, Sylow
206C23×C17C23×C411yescharacteristic
207C22×D17—22no—
208C22×D17—24no—
209C22×D17C23×C414yes—
210C22×D17C23×C412yes—
211Q8×C17—44no—
212C2×C4×C17—42no—
213C2×C4×C17C23×C412yes—
214C2×C4×C17C23×C412yes—
215C2×C4×C17C23×C418yes—
216C2×C4×C17C23×C411yescharacteristic
217C2×C4×C17C2×#4112yes—
218C2×C4×C17C2×#4112yes—
219C2×C4×C17C2511yescharacteristic
220C22⋊D17—28no—
221C2×Dic17—22no—
222C2×Dic17—42no—
223C2×Dic17C23×C414yes—
224C2×Dic17C23×C412yes—
225C2×Dic17C23×C412yes—
226C2×Dic17C23×C412yes—
227D68—216no—
228D68—24no—
229D68—44no—
230C4×D17—24no—
231C4×D17—24no—
232C4×D17—24no—
233C4×D17—22no—
234C4×D17—22no—
235C4×D17—24no—
236C4×D17—24no—
237C4×D17—42no—
238C4×D17—42no—
239C4×D17—48no—
240Dic34—24no—
241C8×C17—22no—
242C8×C17—24no—
243C8×C17C2×#4114yes—
244#3622—22no—
245#3622—24no—
246#3622C2×#4114yes—
247#3444—171no—
248#2970—178no—
249#2968—178no—
250#2961—171no—
251#2961D1711yescharacteristic, complemented
252#2932—171no—
253#2932—171no—
254#2929—172no—
255#2929—172no—
256#2923—172no—
257#2920—171no—
258#2875—172no—
259C22×#97—171no—
260C22×C17—22no—
261C22×C17C4×#4112yes—
262C22×C17C24×C411yescharacteristic
263C2×D17—28no—
264C2×D17—22no—
265C2×D17—22no—
266C2×D17—24no—
267C2×D17—28no—
268C2×D17#56814yes—
269C4×C17—22no—
270C4×C17—22no—
271C4×C17—28no—
272C4×C17C4×#4112yes—
273C4×C17C22×#4111yescharacteristic
274C4×C17C22×#4111yescharacteristic
275Dic17—24no—
276Dic17—22no—
277Dic17—22no—
278Dic17—22no—
279C2×#131—172no—
280C2×#131—172no—
281C23×C8—171no—
282C23×C8—171no—
283#533—172no—
284#533C2×D1711yescharacteristic
285#532—172no—
286#532—171no—
287#529—174no—
288#529—174no—
289#529—174no—
290#525—174no—
291#525—172no—
292C4×#41—174no—
293C4×#41—172no—
294C22×C42—171no—
295#446—178no—
296#446C2×D1718yescomplemented
297#435—178no—
298#435—178no—
299#435—178no—
300#435—178no—
301C8×D4—178no—
302C8×D4—178no—
303#433—178no—
304#432—174no—
305#432—178no—
306#431—174no—
307#424—172no—
308#424C2×D1712yes—
309#423—171no—
310#423C2×D1711yescharacteristic
311#408—172no—
312#408—172no—
313#407—172no—
314#405—172no—
315#405—174no—
316#405—174no—
317#405C2×D1712yes—
318C4×M16—172no—
319C4×M16—174no—
320C2×#97—171no—
321C2×#97—171no—
322C2×#97—171no—
323C2×#97—174no—
324C2×#97—174no—
325C2×#97—174no—
326C2×#97C2×D1711yescharacteristic
327C2×C17—22no—
328C2×C17C2×C4×#4111yescharacteristic
329C2×C17C2×#56812yes—
330D17—24no—
331D17—44no—
332C2×#41—174no—
333C2×#41—172no—
334C23×C4—171no—
335C23×C4—172no—
336#131—348no—
337#131—348no—
338C2×M16—172no—
339C2×M16—174no—
340C2×M16—174no—
341C2×M16C22×D1712yes—
342C22×C8—171no—
343C22×C8—171no—
344C22×C8—174no—
345C22×C8—174no—
346C22×C8—174no—
347C22×C8—174no—
348C22×C8—344no—
349C22×C8—344no—
350C22×C8C22×D1711yescharacteristic
351C22×C8C22×D1711yescharacteristic
352C4⋊Q8—171no—
353C4⋊Q8C4×D1712yes—
354#127—171no—
355#126—178no—
356#125—174no—
357#125C4×D1712yes—
358#124—174no—
359#124—172no—
360#123—178no—
361#123—174no—
362C22⋊Q8—174no—
363C22⋊Q8—174no—
364C22⋊Q8C4×D1714yes—
365#121—174no—
366#121—174no—
367#121—174no—
368#120—174no—
369C4×Q8—174no—
370C4×Q8—174no—
371C4×Q8C22×D1714yes—
372C4×D4—178no—
373C4×D4—174no—
374C4×D4—174no—
375C4×D4—178no—
376C4×D4—178no—
377C4×D4—174no—
378#117—174no—
379#117—178no—
380#117—174no—
381#117C22×D1712yes—
382C2×C42—172no—
383C2×C42—171no—
384C2×C42—172no—
385C2×C42—172no—
386C2×C42—174no—
387C2×C42—172no—
388C2×C42—172no—
389C2×C42C22×D1711yescharacteristic
390C4⋊C8—174no—
391C4⋊C8—178no—
392C4⋊C8C22×D1714yes—
393C4⋊C8C22×D1718yes—
394C22⋊C8—178no—
395C22⋊C8—178no—
396C22⋊C8—178no—
397#97—172no—
398#97—172no—
399#97—172no—
400#97—172no—
401#97—174no—
402#97—174no—
403#97—174no—
404#97C22×D1714yes—
405#97C22×D1714yes—
406C4×C8—174no—
407C4×C8—174no—
408C4×C8C22×D1714yes—
409C17#6020711yescharacteristic, complemented, Sylow
410C24—171no—
411#41—344no—
412#41—344no—
413#41—688no—
414C2×Q8—172no—
415C2×Q8C2×C4×D1714yes—
416C2×D4—174no—
417C2×D4—178no—
418C2×D4—172no—
419C2×D4—174no—
420C22×C4—171no—
421C22×C4—172no—
422C22×C4—172no—
423C22×C4—172no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—174no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—178no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—684no—
433C22×C4C2×C4×D1712yes—
434C22×C4C23×D1711yescharacteristic
435M16—24no—
436M16—348no—
437M16—344no—
438M16—348no—
439C2×C8—22no—
440C2×C8—174no—
441C2×C8—172no—
442C2×C8—174no—
443C2×C8—172no—
444C2×C8—348no—
445C2×C8—348no—
446C2×C8—342no—
447C2×C8—348no—
448C2×C8—348no—
449C2×C8#6325614yescomplemented
450C2×C8C23×D1714yes—
451C2×C8C23×D1712yes—
452C2×C8C23×D1712yes—
453C4⋊C4—174no—
454C4⋊C4—178no—
455C4⋊C4—178no—
456C4⋊C4C2×C4×D1714yes—
457C4⋊C4C2×C4×D1718yes—
458C4⋊C4C2×C4×D1714yes—
459C22⋊C4—178no—
460C22⋊C4—178no—
461C22⋊C4—178no—
462C22⋊C4—178no—
463C22⋊C4C2×C4×D1714yes—
464C42—172no—
465C42—172no—
466C42—172no—
467C42—172no—
468C42—172no—
469C42—178no—
470C42—171no—
471C42—171no—
472C42C2×C4×D1711yescharacteristic
473C42C2×C4×D1711yescharacteristic
474C42C23×D1714yes—
475C42C23×D1712yes—
476C23—172no—
477C23—174no—
478C23—344no—
479C23—342no—
480C23C22×C4×D1711yescharacteristic
481Q8—44no—
482Q8—344no—
483D4—3416no—
484D4—348no—
485D4—344no—
486D4—684no—
487C2×C4—42no—
488C2×C4—172no—
489C2×C4—172no—
490C2×C4—172no—
491C2×C4—174no—
492C2×C4—344no—
493C2×C4—344no—
494C2×C4—342no—
495C2×C4—344no—
496C2×C4—342no—
497C2×C4—344no—
498C2×C4—342no—
499C2×C4—344no—
500C2×C4—682no—
501C2×C4—682no—
502C2×C4—688no—
503C2×C4—682no—
504C2×C4C22×C4×D1712yes—
505C2×C4C22×C4×D1712yes—
506C2×C4C22×C4×D1718yes—
507C2×C4C22×C4×D1711yescharacteristic
508C2×C4C2×#6325612yes—
509C2×C4#41×D1712yes—
510C2×C4C24×D1711yescharacteristic
511C8—22no—
512C8—24no—
513C8—174no—
514C8—342no—
515C8—344no—
516C8C2×#6325614yes—
517C22—22no—
518C22—174no—
519C22—348no—
520C22—342no—
521C22—342no—
522C22—348no—
523C22—344no—
524C22C4×#6325612yes—
525C22C23×C4×D1711yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—342no—
530C4—342no—
531C4—342no—
532C4—344no—
533C4C4×#6325612yes—
534C4C2×#41×D1711yescharacteristic
535C4C22×#6325611yescharacteristic
536C2—22no—
537C2—344no—
538C2—684no—
539C2C2×C4×#6325611yescharacteristic
540C2D17×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2961C2
prime radical#14542081C2
cosocleC2×C4×C17C25
hypercenter#2961D17
hypocenterC17#60207
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #14537797C2semidirect
3. #14537777C2semidirect
4. #14537725C2semidirect
5. #14537503C2semidirect
6. #14537501C2semidirect
7. #14537480C2semidirect
8. #14537477C2semidirect
9. #14537434C2semidirect
10. #14537416C2semidirect
11. #14537211C2semidirect
12. C2×#97×D17C2semidirect
13. C17×#2961C2semidirect
29. #11762940C22semidirect
31. #11762882C22semidirect
33. #11762879C22semidirect
36. #11762869C22semidirect
38. #11762865C22semidirect
45. #11762766C22semidirect
47. #11762763C22semidirect
49. C4×#63218C22semidirect
55. #97×D17C22semidirect
57. C17×#446C22semidirect
166. C2×C8×C17#41semidirect
195. C2×#3622#41semidirect
251. #2961D17semidirect
296. #446C2×D17semidirect
409. C17#60207semidirect
449. C2×C8#63256semidirect

Maximal subgroups

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

subgroupindex
#145420812
#145377972
#145377772
#145377252
#145375032
#145375012
#145374802
#145374772
#145374342
#145374162
#145372112
C2×#97×D172
C17×#29612
#6020717