Finite Group Databasebeta

← #28403134

Subgroups — #28403134

Order 14464.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic
2#20298997C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298926C211yesmaximal, characteristic, complemented
5#20298922C211yesmaximal, characteristic, complemented
6#20298916C211yesmaximal, characteristic, complemented
7#20298905C211yesmaximal, characteristic, complemented
8#20298895C211yesmaximal, characteristic, complemented
9#20298846C211yesmaximal, characteristic, complemented
10#20298846C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298641C211yesmaximal, characteristic, complemented
14#20298638C211yesmaximal, characteristic, complemented
15#552×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19#16813617—21no—
20#16813614C2211yescharacteristic
21#16813604—21no—
22#16813596C2211yescharacteristic
23#16813596C2211yescharacteristic
24#16813594—21no—
25C4×D452C2211yescharacteristic
26#16813582—21no—
27#16813581C2211yescharacteristic
28C2×C4⋊Dic113C2211yescharacteristic
29#16813555C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813553C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813553C2211yescharacteristic
37#16813553C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113—21no—
50#125×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53C22⋊Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56#117×C113—21no—
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C2×C4×D113—21no—
64#14268634—22no—
65#14268631—22no—
66#14268631—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C4⋊Dic113—21no—
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77C22⋊Dic113—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81C4×Dic113—21no—
82C2×Q8×C113C2311yescharacteristic
83C2×D4×C113D411yescharacteristic
84C22×C4×C113—21no—
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—21no—
88C4⋊C4×C113—21no—
89C4⋊C4×C113—21no—
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113D411yescharacteristic
94C4⋊C4×C113C2311yescharacteristic
95C4⋊C4×C113C2311yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C22⋊C4×C113—21no—
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113D411yescharacteristic
101C22⋊C4×C113D411yescharacteristic
102C42×C113—21no—
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113C2×D411yescharacteristic
106C23×C113C2×D411yescharacteristic
107C22×D113—21no—
108Q8×C113—21no—
109Q8×C113—21no—
110D4×C113—41no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—42no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—42no—
126C22⋊D113—81no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—81no—
131D452—21no—
132D452—21no—
133C4×D113—81no—
134#11744751—21no—
135#11744751—21no—
136#11744751—21no—
137#11744751#4112yes—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113C22×D411yescharacteristic
145C2×D113—41no—
146C2×D113—41no—
147C2×D113—41no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113C2×#4111yescharacteristic
157C4×C1132−1+411yescharacteristic
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—41no—
162C2×C113—41no—
163C2×C113#54711yescharacteristic
164C2×C113#57511yescharacteristic
165C2×C113#57711yescharacteristic
166D113—81no—
167#3351—1131nomaximal, Sylow
168C113#335111yescharacteristic, complemented, Sylow
169#553—1131no—
170#552D11311yescharacteristic, complemented
171#499—1131no—
172#485—1131no—
173#483—1131no—
174#482—1131no—
175#481—1131no—
176#479—1131no—
177#478—1131no—
178#468—1131no—
179#468—1131no—
180C4×SD16—1131no—
181#436—1131no—
182#428—1131no—
183#428—1131no—
184C2×SD16—1131no—
185C2×M16—1131no—
186C2×M16—1131no—
187#126—21no—
188#126—2261no—
189#125—21no—
190#125—1131no—
191#125C2×D11311yescharacteristic
192#123—21no—
193#123—2261no—
194C22⋊Q8C2×D11311yescharacteristic
195C22⋊Q8C2×D11311yescharacteristic
196#121—1131no—
197#121—1131no—
198#121—2261no—
199C4×Q8C2×D11311yescharacteristic
200C4×D4—1131no—
201C4×D4—2261no—
202C4×D4C2×D11311yescharacteristic
203#117—21no—
204#117—1131no—
205#117C2×D11311yescharacteristic
206C2×C4⋊C4—1131no—
207C2×C4⋊C4C2×D11311yescharacteristic
208#107—1131no—
209#107—1131no—
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214#106—1131no—
215#106—1131no—
216#106—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#102—1131no—
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226C4×C8—1131no—
227C2×Q8C22×D11311yescharacteristic
228C2×D4—1131no—
229C2×D4—2261no—
230C2×D4—2261no—
231C2×D4C22⋊D11311yescharacteristic
232C22×C4—21no—
233C22×C4—2261no—
234C22×C4—2261no—
235C22×C4C22×D11311yescharacteristic
236C22×C4C22×D11311yescharacteristic
237SD16—2262no—
238M16—2262no—
239M16—2262no—
240C2×C8—1131no—
241C2×C8—1131no—
242C2×C8—1131no—
243C2×C8—1131no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4C22⋊D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4C22⋊D11311yescharacteristic
268C22⋊C4C22⋊D11311yescharacteristic
269C42—21no—
270C42—21no—
271C42—2261no—
272C42C22×D11311yescharacteristic
273C23—2261no—
274C23C2×C22⋊D11311yescharacteristic
275C23C2×C22⋊D11311yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—41no—
279D4—9041no—
280D4—4522no—
281D4—2261no—
282D4—2261no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—9041no—
293C2×C4—9041no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4C2×C22⋊D11311yescharacteristic
298C2×C4C2×C22⋊D11311yescharacteristic
299C2×C4C2×C22⋊D11311yescharacteristic
300C2×C4C2×C22⋊D11311yescharacteristic
301C2×C4C23×D11311yescharacteristic
302C8—1132no—
303C8—2261no—
304C8—2261no—
305C8—2261no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—4521no—
313C22—4521no—
314C22—4521no—
315C22C22×C22⋊D11311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4#41×D11311yescharacteristic
328C4#1681366911yescharacteristic
329C2—41no—
330C2—41no—
331C2—9041no—
332C2#2029924711yescharacteristic
333C2#2029939611yescharacteristic
334C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#552×C113C2
socleC22×C113C22×D4
prime radical#20299294C2
hypercenter#552D113
hypocenterC113#3351
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #20298997C2semidirect
3. #20298936C2semidirect
4. #20298926C2semidirect
5. #20298922C2semidirect
6. #20298916C2semidirect
7. #20298905C2semidirect
8. #20298895C2semidirect
9. #20298846C2semidirect
10. #20298846C2semidirect
11. C4×#14268634C2semidirect
12. #20298676C2semidirect
13. #20298641C2semidirect
14. #20298638C2semidirect
15. #552×C113C2semidirect
168. C113#3351semidirect
170. #552D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202989972
#202989362
#202989262
#202989222
#202989162
#202989052
#202988952
#202988462
C4×#142686342
#202986762
#202986412
#202986382
#552×C1132
#3351113