Finite Group Databasebeta

← #28400150

Subgroups — #28400150

Order 14464.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813643C211yesmaximal, characteristic, complemented
2C22×C8×D113C211yesmaximal, characteristic, complemented
3#20299111C211yesmaximal, characteristic, complemented
4#20299108C211yesmaximal, characteristic, complemented
5#20298838C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298832C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic, complemented
10#20298827C211yesmaximal, characteristic, complemented
11#20298824C211yesmaximal, characteristic, complemented
12#20298633C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19#16813643—24no—
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268636C2211yescharacteristic, complemented
22C2×#14268632C2211yescharacteristic, complemented
23C22×#11744751C2211yescharacteristic
24C2×C8×D113—24no—
25C2×C8×D113C2211yescharacteristic
26C2×C8×D113C2211yescharacteristic
27C2×C8×D113C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813607—21no—
30#16813604—21no—
31#16813602C2211yescharacteristic
32#16813601C2211yescharacteristic
33#16813598C2211yescharacteristic
34#16813597C2211yescharacteristic
35#16813596C2211yescharacteristic
36#16813593C2211yescharacteristic
37#16813592—21no—
38#16813590—21no—
39D4×Dic113—21no—
40#16813584—21no—
41#16813582—21no—
42#16813582—21no—
43#16813580C2211yescharacteristic
44#16813580C2211yescharacteristic
45#16813555C2211yescharacteristic, complemented
46#16813555C2211yescharacteristic, complemented
47#16813554C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52#16813543C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C22×C8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113D411yescharacteristic
62#14268648—22no—
63#14268648—22no—
64#14268646—22no—
65#14268646—22no—
66C2×Dic226C2311yescharacteristic
67C2×D452—21no—
68C2×D452—21no—
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C22×Dic113—21no—
74C22×Dic113D411yescharacteristic
75C2×C4×D113—22no—
76C2×C4×D113—22no—
77C2×C4×D113—21no—
78C2×C4×D113D411yescharacteristic
79C2×C4×D113D411yescharacteristic
80C2×C4×D113C2311yescharacteristic
81C2×C4×D113C2311yescharacteristic
82#14268637—22no—
83#14268636—22no—
84#14268632—22no—
85C2×#11744751—22no—
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C8×D113—22no—
89C8×D113—22no—
90C8×D113—22no—
91C8×D113D414yescomplemented
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94C4⋊Dic113C2311yescharacteristic
95#14268626—21no—
96#14268626—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105C4×Dic113—21no—
106C4×Dic113—21no—
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113—21no—
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111SD16×C113—22no—
112C2×C8×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113—21no—
116C4⋊C4×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C23×C113—21no—
121C23×C113C2×D411yescharacteristic
122C22×D113—22no—
123C22×D113—22no—
124C22×D113—22no—
125C22×D113—21no—
126C22×D113C2×D411yescharacteristic
127C22×D113C2×D411yescharacteristic
128Q8×C113—21no—
129Q8×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—42no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2411yescharacteristic
140C22⋊D113—42no—
141C22⋊D113—42no—
142C22⋊D113—42no—
143C2×Dic113—22no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—42no—
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150D452—21no—
151D452—21no—
152D452—42no—
153D452—42no—
154C4×D113—22no—
155C4×D113—21no—
156C4×D113—21no—
157C4×D113—22no—
158C4×D113—42no—
159C4×D113C2×D412yes—
160C4×D113#4112yes—
161Dic226—21no—
162Dic226—21no—
163C8×C113—21no—
164C8×C113C2×D412yes—
165#11744751—21no—
166#11744751C2×D412yes—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113#13512yescomplemented
173C22×C113C22×D411yescharacteristic
174C2×D113—28no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113#12112yes—
183C2×D113#13512yescomplemented
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113C22×D411yescharacteristic
189C4×C113C2×#4111yescharacteristic
190Dic113—21no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194Dic113#12112yes—
195C2×C113—22no—
196C2×C113—81no—
197C2×C113C2×#12111yescharacteristic
198C2×C113C2×#13511yescharacteristic
199C2×C113C2×#13511yescharacteristic
200D113—22no—
201D113—22no—
202D113—81no—
203#3050—1131nomaximal, Sylow
204C113#305011yescharacteristic, complemented, Sylow
205C2×#135—1131no—
206C23×C8—1131no—
207#525—1131no—
208#525—1131no—
209#467—1131no—
210#467—1131no—
211#466—1131no—
212#466—1131no—
213#465—1131no—
214#465—1131no—
215#465—1131no—
216#465D11311yescharacteristic, complemented
217#427—1131no—
218#416—1131no—
219#416—1131no—
220C2×#41—1131no—
221C2×#41—1131no—
222C23×C4—1131no—
223#135—2264no—
224C2×Q16—1131no—
225C2×SD16—1131no—
226C2×SD16C2×D11311yescharacteristic, complemented
227C2×D8—1131no—
228C22×C8—1131no—
229C22×C8—1131no—
230C22×C8—1131no—
231C22×C8—1131no—
232C22×C8—1131no—
233C22×C8—2264no—
234C22×C8C2×D11311yescharacteristic
235#123—2261no—
236#123—2261no—
237C22⋊Q8—1131no—
238C22⋊Q8—1131no—
239C22⋊Q8—1131no—
240C22⋊Q8C2×D11311yescharacteristic
241#121—1131no—
242#121—1131no—
243#121—1131no—
244#121C2×D11311yescharacteristic
245#120—2261no—
246#120—2261no—
247C4×D4—2261no—
248C4×D4—2261no—
249C4×D4—2261no—
250C4×D4—2261no—
251#117—1131no—
252#117—1131no—
253#107—1131no—
254#107—1131no—
255#106—1131no—
256#106C2×D11311yescharacteristic, complemented
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103C2×D11311yescharacteristic, complemented
261#102—1131no—
262#102—1131no—
263#102—1131no—
264#102C2×D11311yescharacteristic, complemented
265C24—1131no—
266#41—2262no—
267#41—2262no—
268#41—2262no—
269#41—2262no—
270C2×Q8—1131no—
271C2×Q8C22×D11311yescharacteristic
272C2×D4—21no—
273C2×D4—1131no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4C22×D11311yescharacteristic
280C22×C4—1131no—
281C22×C4—1131no—
282C22×C4—1131no—
283C22×C4—1131no—
284C22×C4—1131no—
285C22×C4—2261no—
286C22×C4—2262no—
287C22×C4—2262no—
288C22×C4—2261no—
289C22×C4C22×D11311yescharacteristic
290Q16—2262no—
291SD16—22no—
292SD16—2262no—
293D8—2262no—
294C2×C8—22no—
295C2×C8—1131no—
296C2×C8—1134no—
297C2×C8—1131no—
298C2×C8—2262no—
299C2×C8—2262no—
300C2×C8—2262no—
301C2×C8—2262no—
302C2×C8C22×D11311yescharacteristic
303C2×C8C22×D11311yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—1131no—
306C4⋊C4—1131no—
307C4⋊C4—2261no—
308C4⋊C4—2261no—
309C4⋊C4—2261no—
310C4⋊C4C22×D11311yescharacteristic
311C4⋊C4C22×D11311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C42—2261no—
323C42—2261no—
324C23—21no—
325C23—1131no—
326C23—1131no—
327C23—2262no—
328C23—2262no—
329C23—2261no—
330C23—2262no—
331C23D4×D11311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—2261no—
335Q8—2261no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—4522no—
340D4—4522no—
341D4—4522no—
342D4—4522no—
343D4—4522no—
344D4—2261no—
345D4—2261no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—1131no—
352C2×C4—1132no—
353C2×C4—1132no—
354C2×C4—1131no—
355C2×C4—4522no—
356C2×C4—4522no—
357C2×C4—2262no—
358C2×C4—2262no—
359C2×C4—2262no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4D4×D11311yescharacteristic
366C2×C4C23×D11311yescharacteristic
367C8—21no—
368C8—1132no—
369C8—2261no—
370C8D4×D11312yes—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—1132no—
377C22—1132no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—2268no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22#1681364312yescomplemented
387C22C2×D4×D11311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—1132no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4—2261no—
397C4C2×D4×D11311yescharacteristic
398C4#41×D11311yescharacteristic
399C2—22no—
400C2—81no—
401C2—9041no—
402C2—2262no—
403C2—2262no—
404C2#121×D11311yescharacteristic
405C2#135×D11311yescharacteristic
406C2C2×#1681364311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
hypercenter#465D113
hypocenterC113#3050
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×#16813643C2semidirect
2. C22×C8×D113C2semidirect
3. #20299111C2semidirect
4. #20299108C2semidirect
5. #20298838C2semidirect
6. #20298837C2semidirect
7. #20298833C2semidirect
8. #20298832C2semidirect
9. #20298828C2semidirect
10. #20298827C2semidirect
11. #20298824C2semidirect
12. #20298633C2semidirect
13. #20298593C2semidirect
14. #20298591C2semidirect
15. #465×C113C2semidirect
20. C2×#14268637C22semidirect
21. C2×#14268636C22semidirect
22. C2×#14268632C22semidirect
45. #16813555C22semidirect
46. #16813555C22semidirect
47. #16813554C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
51. #16813544C22semidirect
52. #16813543C22semidirect
53. #16813542C22semidirect
54. C2×SD16×C113C22semidirect
58. #106×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
91. C8×D113D4semidirect
172. C22×C113#135semidirect
183. C2×D113#135semidirect
204. C113#3050semidirect
216. #465D113semidirect
226. C2×SD16C2×D113semidirect
256. #106C2×D113semidirect
260. #103C2×D113semidirect
264. #102C2×D113semidirect
386. C22#16813643semidirect

Maximal subgroups

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

subgroupindex
C2×#168136432
C22×C8×D1132
#202991112
#202991082
#202988382
#202988372
#202988332
#202988322
#202988282
#202988272
#202988242
#202986332
#202985932
#202985912
#465×C1132
#3050113