Finite Group Databasebeta

← #28402382

Subgroups — #28402382

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299248C211yesmaximal, characteristic, complemented
2#20299232C211yesmaximal, characteristic, complemented
3#20298943C211yesmaximal, characteristic, complemented
4#20298913C211yesmaximal, characteristic, complemented
5#20298909C211yesmaximal, characteristic, complemented
6#20298877C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298791C211yesmaximal, characteristic, complemented
9#20298731C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11#20298678C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13C2×#16813544C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#466×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268632C2211yescharacteristic, complemented
22C2×C8×D113C2211yescharacteristic, complemented
23#16813621C2211yescharacteristic, complemented
24#16813618C2211yescharacteristic
25#16813604—21no—
26#16813603—21no—
27#16813599—21no—
28#16813597C2211yescharacteristic
29#16813595—21no—
30#16813593C2211yescharacteristic, complemented
31#16813592—21no—
32#16813590—21no—
33D4×Dic113C2211yescharacteristic, complemented
34#16813584C2211yescharacteristic
35C4×C22⋊D113C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813544C2211yescharacteristic
42#16813544C2211yescharacteristic
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic, complemented
54#121×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic, complemented
56#107×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61#14268646—44no—
62C2×Dic226—21no—
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—41no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74D4×D113—22no—
75D4×D113—41no—
76D4×D113—44no—
77C22×Dic113—21no—
78C22×Dic113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113C2311yescharacteristic
82#14268632—22no—
83#14268632—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C8×D113—41no—
87C4⋊Dic113—21no—
88C4⋊Dic113C2311yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268626D411yescharacteristic
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113D411yescharacteristic
96#14268624—21no—
97#14268624—21no—
98#14268624D411yescharacteristic
99C4×Dic113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105D8×C113—41no—
106C2×C8×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—42no—
121C22×D113—42no—
122C22×D113—81no—
123C22×D113—81no—
124C22×D113C2×D411yescharacteristic
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—42no—
130D4×C113—42no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—81no—
141C22⋊D113D814yescomplemented
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—42no—
145C2×Dic113—42no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151D452—21no—
152D452—42no—
153D452—42no—
154D452#4112yescomplemented
155C4×D113—21no—
156C4×D113—21no—
157C4×D113—42no—
158C4×D113—42no—
159Dic226—42no—
160C8×C113—21no—
161C8×C113—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113C2×D812yes—
173C22×C113C22×D411yescharacteristic
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—22no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—84no—
183C2×D113—84no—
184C2×D113C2×D812yes—
185C4×C113—21no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113C2×#4111yescharacteristic
189C4×C113H(5,𝔽2)11yescharacteristic
190Dic113—21no—
191Dic113—21no—
192Dic113—41no—
193Dic113—41no—
194Dic113C2×D812yes—
195C2×C113—22no—
196C2×C113—81no—
197C2×C113—81no—
198C2×C113#54611yescharacteristic
199C2×C113C22×D811yescharacteristic
200C2×C113#57711yescharacteristic
201D113—22no—
202D113—42no—
203D113—81no—
204#3294—1131nomaximal, Sylow
205C113#329411yescharacteristic, complemented, Sylow
206#547—1131no—
207D42—1131no—
208#486—1131no—
209#480—1131no—
210#480—1131no—
211#474—1131no—
212#466—1131no—
213#466D11311yescharacteristic, complemented
214#459—1131no—
215#447—1131no—
216#447—1131no—
217C4×D8—1131no—
218C8×D4—1131no—
219C2×#102—1131no—
220C2×#102—1131no—
221C2×#41—2261no—
222C22×D4—1131no—
223C22×D4—1131no—
224C22×D4—2261no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×D8C2×D11311yescharacteristic, complemented
228C22×C8—1131no—
229C22×C8C2×D11311yescharacteristic, complemented
230C4⋊Q8—1131no—
231#127—1131no—
232#123—2261no—
233#123—2261no—
234C22⋊Q8—2261no—
235#121—1131no—
236#121—1131no—
237#121—2261no—
238#121C2×D11311yescharacteristic
239#121C2×D11311yescharacteristic, complemented
240#120—2261no—
241#120—2261no—
242C4×D4—1131no—
243C4×D4—1131no—
244C4×D4—1131no—
245C2×C4⋊C4—1131no—
246C2×C4⋊C4—1131no—
247#107—1131no—
248#107—1131no—
249#107C2×D11311yescharacteristic, complemented
250C4⋊C8—1131no—
251#102—1131no—
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259#102C2×D11311yescharacteristic, complemented
260#102C2×D11311yescharacteristic, complemented
261C22⋊C8—1131no—
262C22⋊C8—1131no—
263C4×C8—1131no—
264C24—2261no—
265C24—2261no—
266#41—4524no—
267C2×Q8—2261no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—1131no—
271C2×D4—1131no—
272C2×D4—1131no—
273C2×D4—4521no—
274C2×D4—4524no—
275C2×D4—4521no—
276C2×D4—2262no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2262no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—1131no—
287C22×C4—2261no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4C22×D11311yescharacteristic
292D8—41no—
293D8—4521no—
294D8—2262no—
295C2×C8—41no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—4521no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—1131no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4C22×D11311yescharacteristic
308C4⋊C4C22×D11311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—1131no—
312C22⋊C4—1131no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—1131no—
318C23—21no—
319C23—21no—
320C23—1131no—
321C23—9041no—
322C23—9041no—
323C23—4522no—
324C23—4522no—
325C23—4522no—
326C23—4522no—
327C23—2261no—
328C23—2261no—
329C23D4×D11311yescharacteristic
330Q8—4522no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—1134no—
338D4—1132no—
339D4—9041no—
340D4—4522no—
341D4—4522no—
342D4—4522no—
343D4—4522no—
344D4—4522no—
345D4—2261no—
346D4—2261no—
347D4—2261no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—1131no—
353C2×C4—1131no—
354C2×C4—1131no—
355C2×C4—4522no—
356C2×C4—4522no—
357C2×C4—4522no—
358C2×C4—4522no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4D4×D11311yescharacteristic
364C2×C4C23×D11311yescharacteristic
365C8—21no—
366C8—21no—
367C8—2261no—
368C8—2261no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—1132no—
378C22—9044no—
379C22—9044no—
380C22—4521no—
381C22—4521no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22—2262no—
386C22—2261no—
387C22—2261no—
388C22D8×D11312yes—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—1132no—
394C4—4521no—
395C4—4521no—
396C4—2261no—
397C4—2261no—
398C4#41×D11311yescharacteristic
399C4#1681366711yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—9041no—
404C2—4522no—
405C2—2262no—
406C2#2029923711yescharacteristic
407C2C2×D8×D11311yescharacteristic
408C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3294
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20299248C2semidirect
2. #20299232C2semidirect
3. #20298943C2semidirect
4. #20298913C2semidirect
5. #20298909C2semidirect
6. #20298877C2semidirect
7. #20298833C2semidirect
8. #20298791C2semidirect
9. #20298731C2semidirect
10. #20298730C2semidirect
11. #20298678C2semidirect
12. C8×C22⋊D113C2semidirect
13. C2×#16813544C2semidirect
14. #102×D113C2semidirect
15. #466×C113C2semidirect
21. C2×#14268632C22semidirect
22. C2×C8×D113C22semidirect
23. #16813621C22semidirect
30. #16813593C22semidirect
33. D4×Dic113C22semidirect
36. C2×C4⋊Dic113C22semidirect
37. C4⋊C4×D113C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813551C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
46. #16813543C22semidirect
48. #16813542C22semidirect
49. C22⋊#11744751C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
52. C2×D8×C113C22semidirect
53. C22×C8×C113C22semidirect
55. #121×C113C22semidirect
56. #107×C113C22semidirect
57. #102×C113C22semidirect
58. #102×C113C22semidirect
141. C22⋊D113D8semidirect
154. D452#41semidirect
205. C113#3294semidirect
213. #466D113semidirect
227. C2×D8C2×D113semidirect
229. C22×C8C2×D113semidirect
239. #121C2×D113semidirect
249. #107C2×D113semidirect
259. #102C2×D113semidirect
260. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992482
#202992322
#202989432
#202989132
#202989092
#202988772
#202988332
#202987912
#202987312
#202987302
#202986782
C8×C22⋊D1132
C2×#168135442
#102×D1132
#466×C1132
#3294113