Finite Group Databasebeta

← #28401287

Subgroups — #28401287

Order 14464.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299150C211yesmaximal, characteristic, complemented
2#20299143C211yesmaximal, characteristic
3#20299002C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298947C211yesmaximal, characteristic, complemented
6#20298943C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298844C211yesmaximal, characteristic, complemented
9#20298842C211yesmaximal, characteristic, complemented
10#20298701C211yesmaximal, characteristic, complemented
11#20298699C211yesmaximal, characteristic, complemented
12#20298697C211yesmaximal, characteristic, complemented
13#20298695C211yesmaximal, characteristic, complemented
14M16×Dic113C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268631C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813620C2211yescharacteristic
24#16813618C2211yescharacteristic
25#16813612—21no—
26#16813608—21no—
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813596C2211yescharacteristic
30#16813594—21no—
31Q8×Dic113C2211yescharacteristic
32#16813587—21no—
33#16813587C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813582—21no—
37#16813578—21no—
38C2×C4×Dic113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813532C2211yescharacteristic
49#16813532C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C22×Dic113—21no—
68C22×Dic113D411yescharacteristic
69C22×Dic113D411yescharacteristic
70C2×C4×D113—21no—
71#14268636—22no—
72#14268635—22no—
73#14268634—22no—
74#14268631—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113D411yescharacteristic
93C4×Dic113D411yescharacteristic
94C4×Dic113C2311yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100SD16×C113—22no—
101M16×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C23×C113—21no—
110C23×C113C2×D411yescharacteristic
111C22×D113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—42no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—42no—
125C22⋊D113—42no—
126C22⋊D113—42no—
127C2×Dic113—22no—
128C2×Dic113—22no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—21no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—42no—
143Dic226—42no—
144C8×C113—21no—
145C8×C113#4112yescomplemented
146#11744751—21no—
147#11744751#4112yescomplemented
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C4×C113—21no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C113C2×#4111yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169Dic113AGL(1,ℤ/8)12yes—
170Dic113#13712yes—
171C2×C113—41no—
172C2×C113—81no—
173C2×C113#53211yescharacteristic
174C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C113C2×#13711yescharacteristic
176D113—81no—
177#3182—1131nomaximal, Sylow
178C113#318211yescharacteristic, complemented, Sylow
179#533—1131no—
180#532—1131no—
181#500—1131no—
182#492—1131no—
183#487—1131no—
184#486—1131no—
185#468—1131no—
186#468—1131no—
187#468—1131no—
188#468D11311yescharacteristic, complemented
189#440—1131no—
190#440—1131no—
191#440—1131no—
192#440—1131no—
193C4×M16—1131no—
194C2×#41—2261no—
195C2×SD16—1131no—
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16C2×D11311yescharacteristic
199C2×M16—1131no—
200C2×M16C2×D11311yescharacteristic
201C4⋊Q8—1131no—
202C4⋊Q8—1131no—
203C4⋊Q8—1131no—
204#127—1131no—
205#125—2261no—
206#124—2261no—
207C22⋊Q8—1131no—
208C22⋊Q8—2261no—
209C22⋊Q8C2×D11311yescharacteristic
210#121—1131no—
211#121—2261no—
212#121C2×D11311yescharacteristic
213C4×Q8—1131no—
214C4×Q8—1131no—
215C4×Q8—2261no—
216C4×D4—1131no—
217C4×D4—1131no—
218C4×D4—2261no—
219#117—2261no—
220C2×C42—1131no—
221#107—1131no—
222#107—1131no—
223#107—1131no—
224#107C2×D11311yescharacteristic
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103C2×D11311yescharacteristic
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102C2×D11311yescharacteristic
233#97—1131no—
234#97—1131no—
235C4×C8—1131no—
236C4×C8—1131no—
237#41—4524no—
238C2×Q8—1131no—
239C2×Q8—2261no—
240C2×Q8—2261no—
241C2×Q8C22×D11311yescharacteristic
242C2×D4—21no—
243C2×D4—1131no—
244C2×D4—2261no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4C22×D11311yescharacteristic
248C22×C4—1131no—
249C22×C4—1131no—
250C22×C4—2261no—
251C22×C4—2261no—
252C22×C4C22×D11311yescharacteristic
253SD16—22no—
254SD16—2262no—
255SD16—2262no—
256SD16—2262no—
257M16—22no—
258M16—2262no—
259C2×C8—1131no—
260C2×C8—1131no—
261C2×C8C22×D11311yescharacteristic
262C2×C8C22×D11311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22×D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C42—1131no—
282C42—1131no—
283C42—1131no—
284C42—1131no—
285C42—2261no—
286C42—2261no—
287C23—21no—
288C23—2261no—
289C23D4×D11311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—4522no—
293Q8—4522no—
294Q8—2261no—
295Q8—2261no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—4522no—
300D4—4522no—
301D4—4522no—
302D4—2261no—
303D4—2261no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—4522no—
314C2×C4—4522no—
315C2×C4—2262no—
316C2×C4—2262no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4D4×D11311yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C8—21no—
323C8—1132no—
324C8—2261no—
325C8#1426864612yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1132no—
341C4—1132no—
342C4—4521no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4—2261no—
347C4#41×D11311yescharacteristic
348C4C2×#1426864611yescharacteristic
349C2—41no—
350C2—81no—
351C2—9041no—
352C2#2029914311yescharacteristic
353C2AGL(1,ℤ/8)×D11311yescharacteristic
354C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
prime radical#20299143C2
hypercenter#468D113
hypocenterC113#3182
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #20299150C2semidirect
3. #20299002C2semidirect
4. #20298969C2semidirect
5. #20298947C2semidirect
6. #20298943C2semidirect
7. #20298846C2semidirect
8. #20298844C2semidirect
9. #20298842C2semidirect
10. #20298701C2semidirect
11. #20298699C2semidirect
12. #20298697C2semidirect
13. #20298695C2semidirect
14. M16×Dic113C2semidirect
15. #468×C113C2semidirect
145. C8×C113#41semidirect
147. #11744751#41semidirect
178. C113#3182semidirect
188. #468D113semidirect
325. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202991502
#202991432
#202990022
#202989692
#202989472
#202989432
#202988462
#202988442
#202988422
#202987012
#202986992
#202986972
#202986952
M16×Dic1132
#468×C1132
#3182113