Finite Group Databasebeta

← #28400358

Subgroups — #28400358

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299151C211yesmaximal, characteristic, complemented
2#41×Dic113C211yesmaximal, characteristic
3#20298907C211yesmaximal, characteristic, complemented
4#20298903C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298891C211yesmaximal, characteristic, complemented
8#20298886C211yesmaximal, characteristic, complemented
9#20298881C211yesmaximal, characteristic, complemented
10#20298876C211yesmaximal, characteristic, complemented
11#20298636C211yesmaximal, characteristic, complemented
12#20298634C211yesmaximal, characteristic, complemented
13C2×#16813551C211yesmaximal, characteristic, complemented
14#20298594C211yesmaximal, characteristic
15#416×C113C211yesmaximal, characteristic
16C22×#11744751C2211yescharacteristic
17#16813621C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813613C2211yescharacteristic
20#16813613C2211yescharacteristic
21#16813599—21no—
22#16813599—21no—
23Q8×Dic113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25C4×Dic226—21no—
26C4×Dic226—21no—
27D4×Dic113—21no—
28D4×Dic113—21no—
29D4×Dic113C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813581—21no—
32#16813581C2211yescharacteristic
33#16813581C2211yescharacteristic
34C2×C4×Dic113—21no—
35C2×C4×Dic113C2211yescharacteristic
36#16813556C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813551C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813543C2211yescharacteristic
51#16813543C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C22×Dic113—21no—
62C22×Dic113—21no—
63C22×Dic113D411yescharacteristic
64C22×Dic113D411yescharacteristic
65C2×#11744751—22no—
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C4×Dic113—21no—
85C4×Dic113—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113D411yescharacteristic
89C4×Dic113D411yescharacteristic
90C4×Dic113C2311yescharacteristic
91C4×Dic113C2311yescharacteristic
92#41×C113—22no—
93#41×C113Q814yescomplemented
94C2×Q8×C113C2311yescharacteristic
95C2×D4×C113—21no—
96C2×D4×C113C2311yescharacteristic
97C22×C4×C113—21no—
98C22×C4×C113C2311yescharacteristic
99C2×C8×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C42×C113—21no—
106C23×C113—21no—
107C23×C113C2×D411yescharacteristic
108Q8×C113—21no—
109Q8×C113C2×Q812yes—
110D4×C113—24no—
111D4×C113—21no—
112D4×C113C2×Q812yes—
113C2×C4×C113—21no—
114C2×C4×C113—24no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×Q812yes—
119C2×C4×C113#4112yes—
120C2×C4×C113C2411yescharacteristic
121C2×Dic113—22no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—41no—
127C2×Dic113—42no—
128C2×Dic113—42no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133Dic226—42no—
134Dic226—42no—
135C8×C113—21no—
136C8×C113—21no—
137#11744751—21no—
138#11744751—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113—22no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113C22⋊Q812yes—
145C22×C113C22×D411yescharacteristic
146C4×C113—22no—
147C4×C113—41no—
148C4×C113—41no—
149C4×C113C22⋊Q812yes—
150C4×C113C22×Q811yescharacteristic
151C4×C113C2×#4111yescharacteristic
152Dic113—21no—
153Dic113—21no—
154Dic113—21no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158Dic113—41no—
159Dic113#13512yes—
160C2×C113—22no—
161C2×C113—42no—
162C2×C113C2×C22⋊Q811yescharacteristic
163C2×C113C2×#13511yescharacteristic
164C2×C113#57511yescharacteristic
165#3076—1131nomaximal, Sylow
166C113#307611yescharacteristic, complemented, Sylow
167#533—1131no—
168C4×#41—1131no—
169#479—1131no—
170#479—1131no—
171#478—1131no—
172#478—1131no—
173#477—1131no—
174#476—1131no—
175#475—1131no—
176#474—1131no—
177#427—1131no—
178#427—1131no—
179C2×C4⋊C8—1131no—
180#416—1131no—
181#416D11311yescharacteristic
182C2×#41C2×D11311yescharacteristic
183C22×C8—1131no—
184C22×C8C2×D11311yescharacteristic
185C4⋊Q8—1131no—
186C4⋊Q8—1131no—
187#125—1131no—
188#125—1131no—
189C22⋊Q8—2261no—
190C22⋊Q8—2261no—
191C4×Q8—1131no—
192C4×Q8—1131no—
193C4×Q8—2261no—
194C4×Q8—2261no—
195C4×D4—1131no—
196C4×D4—1131no—
197C4×D4—2261no—
198C4×D4—2261no—
199#117—1131no—
200#117—1131no—
201#117—2261no—
202#117C2×D11311yescharacteristic
203C2×C42—1131no—
204C2×C42—2261no—
205#107—1131no—
206#107—1131no—
207#107—1131no—
208#107—1131no—
209#106—1131no—
210#106—1131no—
211#106—1131no—
212#106—1131no—
213C4⋊C8—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216C4⋊C8—1131no—
217#103—1131no—
218#103—1131no—
219#103C2×D11311yescharacteristic
220#103C2×D11311yescharacteristic
221#102—1131no—
222#102—1131no—
223#102C2×D11311yescharacteristic
224#102C2×D11311yescharacteristic
225#41—22no—
226#41Dic22614yescomplemented
227C2×Q8—2261no—
228C2×Q8—2261no—
229C2×Q8C22×D11311yescharacteristic
230C2×D4—21no—
231C2×D4C22×D11311yescharacteristic
232C22×C4—21no—
233C22×C4—1131no—
234C22×C4—1131no—
235C22×C4—2261no—
236C22×C4—2261no—
237C22×C4C22×D11311yescharacteristic
238C2×C8—22no—
239C2×C8—1131no—
240C2×C8—1131no—
241C2×C8—2262no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C42—21no—
264C42—1131no—
265C42—1131no—
266C42—1131no—
267C42—1131no—
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C42—2261no—
272C23—21no—
273C23D4×D11311yescharacteristic
274Q8—21no—
275Q8—4522no—
276Q8—4522no—
277Q8C2×Dic22612yes—
278D4—24no—
279D4—21no—
280D4C2×Dic22612yes—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—1131no—
286C2×C4—1131no—
287C2×C4—1131no—
288C2×C4—1131no—
289C2×C4—4522no—
290C2×C4—4522no—
291C2×C4—4521no—
292C2×C4—2262no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4D4×D11311yescharacteristic
298C2×C4C2×Dic22612yes—
299C2×C4#1426864612yes—
300C2×C4C23×D11311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2261no—
304C8—2261no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22#1681359912yes—
311C22C2×D4×D11311yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—1132no—
316C4—4521no—
317C4—4521no—
318C4—4521no—
319C4—4521no—
320C4—2261no—
321C4—2261no—
322C4—2261no—
323C4#1681359912yes—
324C4C22×Dic22611yescharacteristic
325C4C2×#1426864611yescharacteristic
326C2—22no—
327C2—42no—
328C2C2×#1681359911yescharacteristic
329C2#135×D11311yescharacteristic
330C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#416D113
hypocenterC113#3076
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20299151C2semidirect
3. #20298907C2semidirect
4. #20298903C2semidirect
5. #20298900C2semidirect
6. #20298896C2semidirect
7. #20298891C2semidirect
8. #20298886C2semidirect
9. #20298881C2semidirect
10. #20298876C2semidirect
11. #20298636C2semidirect
12. #20298634C2semidirect
13. C2×#16813551C2semidirect
93. #41×C113Q8semidirect
166. C113#3076semidirect
226. #41Dic226semidirect

Maximal subgroups

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

subgroupindex
#202991512
#41×Dic1132
#202989072
#202989032
#202989002
#202988962
#202988912
#202988862
#202988812
#202988762
#202986362
#202986342
C2×#168135512
#202985942
#416×C1132
#3076113