Finite Group Databasebeta

← #28402498

Subgroups — #28402498

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299311C211yesmaximal, characteristic, complemented
2#20299247C211yesmaximal, characteristic, complemented
3#20298947C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298830C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298802C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298678C211yesmaximal, characteristic, complemented
13C8×C22⋊D113C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813610—21no—
24#16813608—21no—
25#16813605—21no—
26#16813603—21no—
27#16813601C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813597C2211yescharacteristic
30#16813596C2211yescharacteristic
31#16813595—21no—
32#16813594—21no—
33D4×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic
35C4×C22⋊D113C2211yescharacteristic
36#16813580C2211yescharacteristic
37#16813579—21no—
38C2×#14268626—21no—
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113D411yescharacteristic
68C22×Dic113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268636—41no—
73#14268634—41no—
74#14268632—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—41no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—42no—
119D4×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—42no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—22no—
129C22⋊D113—42no—
130C22⋊D113—81no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—42no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—81no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—42no—
145Dic226—21no—
146Dic226—21no—
147Dic226—81no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—22no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113#13512yes—
177C2×C113—41no—
178C2×C113—42no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—81no—
184#3303—1131nomaximal, Sylow
185C113#330311yescharacteristic, complemented, Sylow
186#555—1131no—
187#547—1131no—
188#487—1131no—
189#485—1131no—
190#485—1131no—
191#476—1131no—
192#465—1131no—
193#465—1131no—
194#461—1131no—
195#449—1131no—
196#449—1131no—
197C4×D8—1131no—
198C8×D4—1131no—
199#416—1131no—
200#416D11311yescharacteristic, complemented
201C2×#41—1131no—
202C2×#41C2×D11311yescharacteristic
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C22×C8—1131no—
207C22×C8C2×D11311yescharacteristic
208C4⋊Q8—1131no—
209C4⋊Q8—1131no—
210#124—2261no—
211#124—2261no—
212#123—2261no—
213#123—2261no—
214C22⋊Q8—1131no—
215C22⋊Q8—1131no—
216#121—1131no—
217#121—1131no—
218#121—2261no—
219#121—2261no—
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223#117—1131no—
224#117—2261no—
225#117C2×D11311yescharacteristic
226C2×C4⋊C4—2261no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102C2×D11311yescharacteristic
240#102C2×D11311yescharacteristic
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C4×C8—1131no—
244#41—22no—
245#41—41no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8—2261no—
250C2×Q8C22×D11311yescharacteristic
251C2×D4—21no—
252C2×D4—1131no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4C22×D11311yescharacteristic
264SD16—4521no—
265SD16—4521no—
266D8—2262no—
267C2×C8—41no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—4521no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—21no—
294C42—1131no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23—2261no—
299C23D4×D11311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—9041no—
303Q8—2261no—
304Q8—2261no—
305D4—21no—
306D4—42no—
307D4—9041no—
308D4—9041no—
309D4—4522no—
310D4—2262no—
311D4—2261no—
312D4—2261no—
313D4#1426864712yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—4522no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—2261no—
347C22—2261no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1132no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—2261no—
359C4—2261no—
360C4C2×#1426864711yescharacteristic
361C4#1681366711yescharacteristic
362C2—41no—
363C2—42no—
364C2—9041no—
365C2—4521no—
366C2#2029923811yescharacteristic
367C2#135×D11311yescharacteristic
368C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
hypercenter#416D113
hypocenterC113#3303
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20299311C2semidirect
2. #20299247C2semidirect
3. #20298947C2semidirect
4. #20298939C2semidirect
5. #20298937C2semidirect
6. #20298886C2semidirect
7. #20298830C2semidirect
8. #20298827C2semidirect
9. #20298802C2semidirect
10. #20298744C2semidirect
11. #20298743C2semidirect
12. #20298678C2semidirect
13. C8×C22⋊D113C2semidirect
14. #20298591C2semidirect
15. #416×C113C2semidirect
185. C113#3303semidirect
200. #416D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202992472
#202989472
#202989392
#202989372
#202988862
#202988302
#202988272
#202988022
#202987442
#202987432
#202986782
C8×C22⋊D1132
#202985912
#416×C1132
#3303113