Finite Group Databasebeta

← #28402875

Subgroups — #28402875

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299249C211yesmaximal, characteristic, complemented
2#20299247C211yesmaximal, characteristic, complemented
3#20298947C211yesmaximal, characteristic, complemented
4#20298933C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298844C211yesmaximal, characteristic, complemented
9#20298802C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298678C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#417×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×#14268646C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268630C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813607—21no—
25#16813605—21no—
26#16813605—21no—
27#16813603—21no—
28#16813601C2211yescharacteristic
29#16813600—21no—
30#16813598C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813596C2211yescharacteristic
33#16813594—21no—
34D4×Dic113C2211yescharacteristic
35#16813584C2211yescharacteristic
36C4×C22⋊D113C2211yescharacteristic
37C2×#14268626—21no—
38C4⋊C4×D113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268647—44no—
60#14268646—22no—
61#14268646—41no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C22×Dic113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268636—41no—
75#14268634—41no—
76#14268632—22no—
77#14268630—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97C4×Dic113C2311yescharacteristic
98#41×C113—22no—
99#41×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C22×C4×C113—21no—
105C22×C4×C113C2311yescharacteristic
106M16×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113—21no—
110C4⋊C4×C113C2311yescharacteristic
111C4⋊C4×C113C2311yescharacteristic
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113—21no—
118D4×C113—21no—
119D4×C113—42no—
120D4×C113#4112yescomplemented
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—42no—
127C2×C4×C113—42no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—22no—
131C22⋊D113—42no—
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—42no—
137C2×Dic113—42no—
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—21no—
142D452—21no—
143D452—42no—
144C4×D113—21no—
145C4×D113—21no—
146C4×D113—42no—
147C4×D113—42no—
148Dic226—21no—
149Dic226—21no—
150Dic226—42no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—22no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113C2×#4111yescharacteristic
173C4×C113H(5,𝔽2)11yescharacteristic
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179Dic113AGL(1,ℤ/8)12yes—
180C2×C113—41no—
181C2×C113—42no—
182C2×C113#54611yescharacteristic
183C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C113#57811yescharacteristic
185D113—41no—
186D113—81no—
187#3330—1131nomaximal, Sylow
188C113#333011yescharacteristic, complemented, Sylow
189#547—1131no—
190#547—1131no—
191#487—1131no—
192#484—1131no—
193#484—1131no—
194#474—1131no—
195#468—1131no—
196#468—1131no—
197#461—1131no—
198#449—1131no—
199#449—1131no—
200C4×D8—1131no—
201#436—1131no—
202#417—1131no—
203#417D11311yescharacteristic, complemented
204C2×#41—1131no—
205C2×#41—2261no—
206C2×#41C2×D11311yescharacteristic
207C2×SD16—1131no—
208C2×SD16—1131no—
209C2×D8—1131no—
210C2×M16—1131no—
211C2×M16C2×D11311yescharacteristic
212C4⋊Q8—1131no—
213C4⋊Q8—1131no—
214#123—2261no—
215#123—2261no—
216#123—2261no—
217#123—2261no—
218C22⋊Q8—1131no—
219C22⋊Q8—1131no—
220C22⋊Q8—2261no—
221#121—1131no—
222#121—1131no—
223#121—2261no—
224C4×D4—1131no—
225C4×D4—1131no—
226C4×D4—1131no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—2261no—
229C2×C4⋊C4C2×D11311yescharacteristic
230#107—1131no—
231#107—1131no—
232#107—1131no—
233C4⋊C8—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103—1131no—
238#103C2×D11311yescharacteristic
239#103C2×D11311yescharacteristic
240#102—1131no—
241#102—1131no—
242#102C2×D11311yescharacteristic
243#102C2×D11311yescharacteristic
244C22⋊C8—1131no—
245C22⋊C8—1131no—
246C4×C8—1131no—
247#41—22no—
248#41—41no—
249#41—4524no—
250#41—4521no—
251#41—2262no—
252C2×Q8—1131no—
253C2×Q8—2261no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—21no—
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4—2261no—
261C2×D4C22×D11311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1131no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4C22×D11311yescharacteristic
270SD16—4521no—
271SD16—4521no—
272D8—2262no—
273M16—41no—
274M16—4521no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8C22×D11311yescharacteristic
278C2×C8C22×D11311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—1131no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4C22×D11311yescharacteristic
290C4⋊C4C22×D11311yescharacteristic
291C22⋊C4—1131no—
292C22⋊C4—1131no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C42—1131no—
300C23—21no—
301C23—1131no—
302C23—2261no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—4522no—
307Q8—2261no—
308Q8—2261no—
309D4—21no—
310D4—42no—
311D4—4522no—
312D4—4522no—
313D4—4522no—
314D4—2262no—
315D4—2261no—
316D4—2261no—
317D4#1426864712yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—1131no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—4522no—
329C2×C4—4522no—
330C2×C4—4522no—
331C2×C4—4522no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4D4×D11311yescharacteristic
338C2×C4C23×D11311yescharacteristic
339C8—21no—
340C8—21no—
341C8—2261no—
342C8—2261no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—4521no—
350C22—4521no—
351C22—4521no—
352C22—2261no—
353C22—2261no—
354C22—2261no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1132no—
361C4—4521no—
362C4—4521no—
363C4—4521no—
364C4—2261no—
365C4—2261no—
366C4C2×#1426864711yescharacteristic
367C4#1681366711yescharacteristic
368C2—41no—
369C2—42no—
370C2—9041no—
371C2—4521no—
372C2#2029923811yescharacteristic
373C2AGL(1,ℤ/8)×D11311yescharacteristic
374C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
hypercenter#417D113
hypocenterC113#3330
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #20299249C2semidirect
2. #20299247C2semidirect
3. #20298947C2semidirect
4. #20298933C2semidirect
5. #20298932C2semidirect
6. #20298876C2semidirect
7. #20298847C2semidirect
8. #20298844C2semidirect
9. #20298802C2semidirect
10. #20298744C2semidirect
11. #20298743C2semidirect
12. #20298678C2semidirect
13. #20298674C2semidirect
14. #20298596C2semidirect
15. #417×C113C2semidirect
120. D4×C113#41semidirect
188. C113#3330semidirect
203. #417D113semidirect
317. D4#14268647semidirect

Maximal subgroups

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

subgroupindex
#202992492
#202992472
#202989472
#202989332
#202989322
#202988762
#202988472
#202988442
#202988022
#202987442
#202987432
#202986782
#202986742
#202985962
#417×C1132
#3330113