Finite Group Databasebeta

← #28400186

Subgroups — #28400186

Order 14464.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C22×#14268630C211yesmaximal, characteristic, complemented
3#20299111C211yesmaximal, characteristic, complemented
4#121×D113C211yesmaximal, characteristic, complemented
5#20298852C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298834C211yesmaximal, characteristic, complemented
10#20298832C211yesmaximal, characteristic, complemented
11#20298829C211yesmaximal, characteristic, complemented
12#20298637C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic, complemented
14#20298598C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113—21no—
18C2×D4×D113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20#16813649—24no—
21C2×#14268634C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic, complemented
23C2×#14268632C2211yescharacteristic, complemented
24C2×#14268630—24no—
25C2×#14268630C2211yescharacteristic
26C2×#14268630C2211yescharacteristic
27C2×#14268630C2211yescharacteristic, complemented
28C2×#14268630C2211yescharacteristic, complemented
29C22×#11744751C2211yescharacteristic, complemented
30#16813607—21no—
31#16813598C2211yescharacteristic, complemented
32#16813597C2211yescharacteristic
33#16813597C2211yescharacteristic, complemented
34#16813596C2211yescharacteristic
35#16813596C2211yescharacteristic, complemented
36#16813595—21no—
37#16813594—21no—
38#16813593C2211yescharacteristic
39#16813592—21no—
40#16813584—21no—
41#16813582—21no—
42#16813580C2211yescharacteristic
43C4⋊C4×D113C2211yescharacteristic
44C22⋊C4×D113—21no—
45#16813556C2211yescharacteristic, complemented
46#16813555C2211yescharacteristic, complemented
47#16813553C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813542C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C22×C8×C113C2211yescharacteristic, complemented
56C22⋊Q8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113D411yescharacteristic
63#14268648—22no—
64#14268648—22no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74D4×D113—22no—
75D4×D113—22no—
76D4×D113—44no—
77C22×Dic113D411yescharacteristic
78C2×C4×D113—22no—
79C2×C4×D113—22no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113D411yescharacteristic
83C2×C4×D113D411yescharacteristic
84C2×C4×D113C2311yescharacteristic
85C2×C4×D113C2311yescharacteristic
86#14268634—22no—
87D904—22no—
88#14268632—22no—
89#14268630—22no—
90#14268630—22no—
91#14268630—22no—
92#14268630D414yescomplemented
93C2×#11744751—22no—
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C4⋊Dic113C2311yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98#14268626—21no—
99#14268626—21no—
100C22⋊Dic113—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107C4×Dic113—21no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113—21no—
110C2×D4×C113C2311yescharacteristic
111C22×C4×C113C2311yescharacteristic
112SD16×C113—22no—
113C2×C8×C113—22no—
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113—21no—
117C4⋊C4×C113C2311yescharacteristic
118C4⋊C4×C113C2311yescharacteristic
119C22⋊C4×C113—21no—
120C22⋊C4×C113—21no—
121C23×C113—21no—
122C23×C113C2×D411yescharacteristic
123C22×D113—22no—
124C22×D113—22no—
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—41no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113C2×D411yescharacteristic
132C22×D113C2×D411yescharacteristic
133Q8×C113—21no—
134Q8×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—42no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2411yescharacteristic
145C22⋊D113—42no—
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C2×Dic113—22no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154D452—21no—
155D452—21no—
156D452—21no—
157D452—21no—
158D452—42no—
159D452—42no—
160D452—42no—
161C4×D113—22no—
162C4×D113—21no—
163C4×D113—21no—
164C4×D113—22no—
165C4×D113—42no—
166C4×D113—42no—
167C4×D113C2×D412yes—
168C4×D113#4112yes—
169C8×C113—21no—
170C8×C113C2×D412yescomplemented
171#11744751—21no—
172#11744751C2×D412yescomplemented
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113AGL(1,ℤ/8)12yescomplemented
179C22×C113C22×D411yescharacteristic
180C2×D113—21no—
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—44no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—84no—
193C2×D113#12112yes—
194C4×C113—21no—
195C4×C113—41no—
196C4×C113—41no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113C2×#4111yescharacteristic
200Dic113—21no—
201Dic113—41no—
202Dic113—41no—
203Dic113#12112yes—
204C2×C113—22no—
205C2×C113—81no—
206C2×C113C2×#12111yescharacteristic
207C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C113#57511yescharacteristic
209D113—22no—
210D113—41no—
211D113—81no—
212D113—81no—
213#3055—1131nomaximal, Sylow
214C113#305511yescharacteristic, complemented, Sylow
215C2×AGL(1,ℤ/8)—1131no—
216C22×M16—1131no—
217#525—1131no—
218C2×#121—1131no—
219#469—1131no—
220#469—1131no—
221#468—1131no—
222#468—1131no—
223#466—1131no—
224#466—1131no—
225#465—1131no—
226#465D11311yescharacteristic, complemented
227#428—1131no—
228#418—1131no—
229#417—1131no—
230C2×#41—1131no—
231C22×D4—1131no—
232C22×D4—2261no—
233C23×C4—1131no—
234AGL(1,ℤ/8)—2264no—
235C2×SD16—1131no—
236C2×SD16C2×D11311yescharacteristic, complemented
237C2×D8—1131no—
238C2×D8—1131no—
239C2×M16—1131no—
240C2×M16—1131no—
241C2×M16—1131no—
242C2×M16—1131no—
243C2×M16—2264no—
244C22×C8—1131no—
245C22×C8C2×D11311yescharacteristic, complemented
246#123—2261no—
247C22⋊Q8—1131no—
248C22⋊Q8C2×D11311yescharacteristic, complemented
249#121—1131no—
250#121—1131no—
251#121—1131no—
252#121—1131no—
253#121—1131no—
254#121—2261no—
255#121—2261no—
256#121C2×D11311yescharacteristic
257#120—2261no—
258C4×D4—2261no—
259C4×D4—2261no—
260#117—1131no—
261C2×C4⋊C4—1131no—
262C2×C22⋊C4—2261no—
263#107—1131no—
264#107—1131no—
265#106—1131no—
266#106C2×D11311yescharacteristic, complemented
267#103—1131no—
268#103C2×D11311yescharacteristic, complemented
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273#102—1131no—
274#102C2×D11311yescharacteristic, complemented
275C24—1131no—
276C24—2261no—
277#41—2262no—
278#41—2262no—
279C2×Q8C22×D11311yescharacteristic
280C2×D4—21no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—4524no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2262no—
288C2×D4—2262no—
289C2×D4—2261no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4C22×D11311yescharacteristic
294C22×C4—1131no—
295C22×C4—1131no—
296C22×C4—1131no—
297C22×C4—1131no—
298C22×C4—1131no—
299C22×C4—2261no—
300C22×C4—2262no—
301C22×C4—2262no—
302C22×C4—2261no—
303C22×C4C22×D11311yescharacteristic
304SD16—22no—
305SD16—2262no—
306D8—2262no—
307D8—2262no—
308M16—1134no—
309M16—2262no—
310M16—2262no—
311M16—2262no—
312C2×C8—22no—
313C2×C8—1131no—
314C2×C8—1131no—
315C2×C8—2262no—
316C2×C8C22×D11311yescharacteristic
317C2×C8C22×D11311yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—1131no—
320C4⋊C4—1131no—
321C4⋊C4—2261no—
322C4⋊C4—2261no—
323C4⋊C4C22×D11311yescharacteristic
324C4⋊C4C22×D11311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C42—2261no—
335C23—21no—
336C23—1131no—
337C23—1131no—
338C23—4521no—
339C23—4522no—
340C23—4522no—
341C23—4522no—
342C23—2262no—
343C23—2261no—
344C23—2261no—
345C23—2262no—
346C23D4×D11311yescharacteristic
347Q8—21no—
348Q8—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—4522no—
353D4—4522no—
354D4—4522no—
355D4—4522no—
356D4—4522no—
357D4—4522no—
358D4—4522no—
359D4—2261no—
360D4—2261no—
361D4—2261no—
362D4—2261no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—1131no—
369C2×C4—1132no—
370C2×C4—1132no—
371C2×C4—1131no—
372C2×C4—4522no—
373C2×C4—4522no—
374C2×C4—2262no—
375C2×C4—2262no—
376C2×C4—2262no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4D4×D11311yescharacteristic
382C2×C4C23×D11311yescharacteristic
383C8—21no—
384C8—1132no—
385C8—2261no—
386C8D4×D11312yescomplemented
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—1132no—
393C22—9044no—
394C22—4524no—
395C22—4521no—
396C22—4521no—
397C22—4521no—
398C22—4521no—
399C22—4521no—
400C22—4521no—
401C22—2261no—
402C22—2261no—
403C22—2261no—
404C22—2261no—
405C22—2261no—
406C22#1681364912yescomplemented
407C22C2×D4×D11311yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—1132no—
413C4—4521no—
414C4—4521no—
415C4—2261no—
416C4C2×D4×D11311yescharacteristic
417C4#41×D11311yescharacteristic
418C2—22no—
419C2—81no—
420C2—9041no—
421C2—9041no—
422C2—4521no—
423C2—2262no—
424C2#121×D11311yescharacteristic
425C2C2×#1681364911yescharacteristic
426C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
hypercenter#465D113
hypocenterC113#3055
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C22×#14268630C2semidirect
3. #20299111C2semidirect
4. #121×D113C2semidirect
5. #20298852C2semidirect
6. #20298850C2semidirect
7. #20298847C2semidirect
8. #20298841C2semidirect
9. #20298834C2semidirect
10. #20298832C2semidirect
11. #20298829C2semidirect
12. #20298637C2semidirect
13. #20298601C2semidirect
14. #20298598C2semidirect
15. #465×C113C2semidirect
21. C2×#14268634C22semidirect
22. C2×D904C22semidirect
23. C2×#14268632C22semidirect
27. C2×#14268630C22semidirect
28. C2×#14268630C22semidirect
29. C22×#11744751C22semidirect
31. #16813598C22semidirect
33. #16813597C22semidirect
35. #16813596C22semidirect
45. #16813556C22semidirect
46. #16813555C22semidirect
47. #16813553C22semidirect
48. #16813546C22semidirect
49. #16813544C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813542C22semidirect
53. #16813542C22semidirect
54. C2×SD16×C113C22semidirect
55. C22×C8×C113C22semidirect
56. C22⋊Q8×C113C22semidirect
58. #106×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
92. #14268630D4semidirect
170. C8×C113C2×D4semidirect
172. #11744751C2×D4semidirect
178. C22×C113AGL(1,ℤ/8)semidirect
214. C113#3055semidirect
226. #465D113semidirect
236. C2×SD16C2×D113semidirect
245. C22×C8C2×D113semidirect
248. C22⋊Q8C2×D113semidirect
266. #106C2×D113semidirect
268. #103C2×D113semidirect
274. #102C2×D113semidirect
386. C8D4×D113semidirect
406. C22#16813649semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C22×#142686302
#202991112
#121×D1132
#202988522
#202988502
#202988472
#202988412
#202988342
#202988322
#202988292
#202986372
#202986012
#202985982
#465×C1132
#3055113