Finite Group Databasebeta

← #28402121

Subgroups — #28402121

Order 14464.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813650C211yesmaximal, characteristic, complemented
2C2×#16813643C211yesmaximal, characteristic, complemented
3#20299266C211yesmaximal, characteristic, complemented
4#20299239C211yesmaximal, characteristic, complemented
5#20298984C211yesmaximal, characteristic, complemented
6#20298835C211yesmaximal, characteristic, complemented
7#20298823C211yesmaximal, characteristic, complemented
8#20298792C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298744C211yesmaximal, characteristic, complemented
12#20298731C211yesmaximal, characteristic, complemented
13#20298697C211yesmaximal, characteristic, complemented
14#20298667C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268646C2211yescharacteristic, complemented
19C22×D452C2211yescharacteristic
20#16813650—24no—
21#16813643—24no—
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268636C2211yescharacteristic
25C2×#14268634C2211yescharacteristic, complemented
26C2×D904C2211yescharacteristic
27C2×D904C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C2×#14268632C2211yescharacteristic
30C2×C8×D113C2211yescharacteristic, complemented
31#16813618—21no—
32#16813618C2211yescharacteristic, complemented
33#16813611C2211yescharacteristic
34#16813607—21no—
35#16813597—21no—
36#16813597C2211yescharacteristic
37#16813597C2211yescharacteristic, complemented
38#16813595—21no—
39#16813594—21no—
40#16813592—21no—
41#16813587C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic
43C4×C22⋊D113C2211yescharacteristic
44#16813582—21no—
45C22⋊C4×D113—21no—
46#16813551C2211yescharacteristic, complemented
47#16813545C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813542C2211yescharacteristic, complemented
51C22⋊#11744751C2211yescharacteristic
52#16813534C2211yescharacteristic, complemented
53#16813532C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×M16×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#107×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64#14268647—22no—
65#14268647—41no—
66#14268646—22no—
67#14268646—41no—
68C2×Dic226C2311yescharacteristic
69C2×D452—22no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452—21no—
73C2×D452—21no—
74C2×D452—41no—
75C2×D452C2311yescharacteristic
76C2×D452C2311yescharacteristic
77C2×D452C2311yescharacteristic
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81C2×C22⋊D113—21no—
82C2×C22⋊D113D411yescharacteristic
83C22×Dic113—21no—
84C2×C4×D113—21no—
85C2×C4×D113—21no—
86C2×C4×D113—21no—
87C2×C4×D113C2311yescharacteristic
88#14268637—22no—
89#14268636—22no—
90#14268636D414yescomplemented
91#14268634—41no—
92D904—22no—
93D904—22no—
94#14268632—22no—
95#14268632—41no—
96C2×#11744751C2311yescharacteristic
97C2×#11744751C2311yescharacteristic
98C8×D113—22no—
99#14268626—21no—
100#14268626D411yescharacteristic
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108C4×Dic113—21no—
109C4×Dic113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114SD16×C113—22no—
115M16×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—81no—
131C22×D113C2×D411yescharacteristic
132Q8×C113—21no—
133Q8×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—81no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C22⋊D113—41no—
145C22⋊D113—42no—
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—81no—
149C2×Dic113—21no—
150C2×Dic113—42no—
151C2×Dic113C2×D411yescharacteristic
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154D452—21no—
155D452—21no—
156D452—21no—
157D452—21no—
158D452—21no—
159D452—42no—
160D452—42no—
161D452—81no—
162D452—81no—
163D452C2×D412yes—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—42no—
167C4×D113—42no—
168C4×D113—81no—
169Dic226—21no—
170Dic226C2×D412yes—
171C8×C113—21no—
172C8×C113C2×D412yes—
173#11744751—21no—
174#11744751—21no—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—22no—
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—84no—
195C4×C113—21no—
196C4×C113—41no—
197C4×C113—41no—
198C4×C113—41no—
199C4×C113C22×D411yescharacteristic
200C4×C113H(5,𝔽2)11yescharacteristic
201Dic113—22no—
202Dic113—21no—
203Dic113—21no—
204Dic113—21no—
205C2×C113—41no—
206C2×C113—81no—
207C2×C113D4211yescharacteristic
208C2×C113#57511yescharacteristic
209C2×C113#57611yescharacteristic
210D113—41no—
211D113—42no—
212D113—81no—
213D113—81no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550—1131no—
219#546—1131no—
220#496—1131no—
221#468D11311yescharacteristic, complemented
222#466—1131no—
223#464—1131no—
224#459—1131no—
225#452—1131no—
226#449—1131no—
227#449—1131no—
228#447—1131no—
229#440—1131no—
230#435—1131no—
231C2×#41—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235AGL(1,ℤ/8)—2264no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16C2×D11311yescharacteristic, complemented
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8—1131no—
245C2×D8—1131no—
246C2×M16C2×D11311yescharacteristic
247C22×C8—1131no—
248#127—1131no—
249#127—2261no—
250#124—1131no—
251#123—2261no—
252C22⋊Q8C2×D11311yescharacteristic
253#121—1131no—
254#121—1131no—
255#121—2261no—
256#121—2261no—
257#121—2261no—
258#121C2×D11311yescharacteristic
259#120—2261no—
260C4×Q8—1131no—
261C4×D4—1131no—
262C4×D4—1131no—
263C4×D4—2261no—
264C2×C22⋊C4—2261no—
265#107C2×D11311yescharacteristic, complemented
266C4⋊C8—1131no—
267#103—1131no—
268#103C2×D11311yescharacteristic, complemented
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102C2×D11311yescharacteristic, complemented
273C22⋊C8—1131no—
274C22⋊C8—1131no—
275#97—1131no—
276C24—2261no—
277#41—4521no—
278#41—4521no—
279#41—4521no—
280#41—2262no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—21no—
286C2×D4—1131no—
287C2×D4—1131no—
288C2×D4—1131no—
289C2×D4—1131no—
290C2×D4—4521no—
291C2×D4—2262no—
292C2×D4—2261no—
293C2×D4—2261no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2261no—
300C2×D4C22×D11311yescharacteristic
301C22×C4—1131no—
302C22×C4—2261no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4C22×D11311yescharacteristic
307Q16—2262no—
308SD16—22no—
309SD16—1134no—
310SD16—4521no—
311SD16—2262no—
312D8—4521no—
313D8—2262no—
314D8—2262no—
315D8—2262no—
316M16—22no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4C22×D11311yescharacteristic
326C4⋊C4C22×D11311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—1131no—
330C22⋊C4—1131no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C42—1131no—
337C42—2261no—
338C23—21no—
339C23—1131no—
340C23—9041no—
341C23—4522no—
342C23—4522no—
343C23—2261no—
344C23—2261no—
345C23—2261no—
346C23D4×D11311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—1132no—
350Q8—2261no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—1132no—
355D4—9041no—
356D4—9041no—
357D4—9041no—
358D4—4522no—
359D4—4522no—
360D4—4522no—
361D4—4521no—
362D4—4522no—
363D4—4522no—
364D4—2261no—
365D4—2261no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—1131no—
375C2×C4—1131no—
376C2×C4—1131no—
377C2×C4—9041no—
378C2×C4—4522no—
379C2×C4—4522no—
380C2×C4—4522no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4D4×D11311yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—21no—
387C8—2261no—
388C8—2261no—
389C8D4×D11312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—9044no—
397C22—4521no—
398C22—4521no—
399C22—4521no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—2261no—
406C22—2261no—
407C22—2262no—
408C22—2261no—
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—2261no—
415C4—2261no—
416C4—2261no—
417C4—2262no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366811yescharacteristic
420C2—41no—
421C2—81no—
422C2—9041no—
423C2—9041no—
424C2—4522no—
425C2—4521no—
426C2#2029923211yescharacteristic
427C2#2029939711yescharacteristic
428C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
hypercenter#468D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×#16813643C2semidirect
3. #20299266C2semidirect
4. #20299239C2semidirect
5. #20298984C2semidirect
6. #20298835C2semidirect
7. #20298823C2semidirect
8. #20298792C2semidirect
9. #20298758C2semidirect
10. #20298746C2semidirect
11. #20298744C2semidirect
12. #20298731C2semidirect
13. #20298697C2semidirect
14. #20298667C2semidirect
15. #468×C113C2semidirect
18. C2×#14268646C22semidirect
22. C2×#14268637C22semidirect
25. C2×#14268634C22semidirect
30. C2×C8×D113C22semidirect
32. #16813618C22semidirect
37. #16813597C22semidirect
41. #16813587C22semidirect
46. #16813551C22semidirect
47. #16813545C22semidirect
50. #16813542C22semidirect
52. #16813534C22semidirect
53. #16813532C22semidirect
54. C2×SD16×C113C22semidirect
58. #107×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
90. #14268636D4semidirect
215. C113#3268semidirect
221. #468D113semidirect
241. C2×SD16C2×D113semidirect
265. #107C2×D113semidirect
268. #103C2×D113semidirect
272. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×#168136432
#202992662
#202992392
#202989842
#202988352
#202988232
#202987922
#202987582
#202987462
#202987442
#202987312
#202986972
#202986672
#468×C1132
#3268113