Finite Group Databasebeta

← #28400413

Subgroups — #28400413

Order 14464.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299228C211yesmaximal, characteristic
2#20299074C211yesmaximal, characteristic
3#20298908C211yesmaximal, characteristic, complemented
4#20298903C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298893C211yesmaximal, characteristic, complemented
7#20298892C211yesmaximal, characteristic, complemented
8#20298884C211yesmaximal, characteristic, complemented
9#20298881C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic
11#20298633C211yesmaximal, characteristic
12#20298623C211yesmaximal, characteristic
13#20298605C211yesmaximal, characteristic
14#103×D113C211yesmaximal, characteristic
15#479×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813621—21no—
21#16813621C2211yescharacteristic
22#16813613C2211yescharacteristic
23#16813612—21no—
24#16813602—21no—
25#16813600—21no—
26Q8×Dic113C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226C2211yescharacteristic
29#16813587—21no—
30#16813587C2211yescharacteristic
31#16813580—21no—
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34#16813579—21no—
35#16813579C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813545C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113Q814yescomplemented
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268630—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C8×D113—22no—
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85#14268624—21no—
86#14268624—21no—
87#14268624D411yescharacteristic
88#14268624D411yescharacteristic
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C42×C113—21no—
105C42×C113C2311yescharacteristic
106C22×D113C2×D411yescharacteristic
107Q8×C113—21no—
108Q8×C113C2×Q812yes—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2411yescharacteristic
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C4×D113—24no—
124C4×D113—81no—
125C4×D113C2×Q812yes—
126C4×D113#4112yes—
127Dic226—21no—
128Dic226—24no—
129Dic226—81no—
130Dic226—81no—
131Dic226C2×Q812yes—
132C8×C113—21no—
133C8×C113—21no—
134#11744751—21no—
135#11744751—21no—
136C22×C113C22×D411yescharacteristic
137C2×D113—21no—
138C2×D113—21no—
139C2×D113C22⋊Q812yes—
140C4×C113—22no—
141C4×C113—21no—
142C4×C113—21no—
143C4×C113—41no—
144C4×C113—41no—
145C4×C113—41no—
146C4×C113C22×Q811yescharacteristic
147C4×C113C2×#4111yescharacteristic
148Dic113—22no—
149Dic113—21no—
150Dic113—21no—
151Dic113—41no—
152Dic113—41no—
153Dic113—41no—
154Dic113C22⋊Q812yes—
155C2×C113C2×C22⋊Q811yescharacteristic
156C2×C113#57711yescharacteristic
157C2×C113#57811yescharacteristic
158D113—22no—
159#3082—1131nomaximal, Sylow
160C113#308211yescharacteristic, complemented, Sylow
161#544—1131no—
162#519—1131no—
163#479—1131no—
164#479—1131no—
165#479—1131no—
166#479D11311yescharacteristic, complemented
167#477—1131no—
168#477—1131no—
169#475—1131no—
170#475—1131no—
171#428—1131no—
172#427—1131no—
173#424—1131no—
174#419—1131no—
175C2×#103—1131no—
176C22×Q8—1131no—
177C2×M16—1131no—
178C22×C8—1131no—
179C4⋊Q8—1131no—
180C4⋊Q8—1131no—
181C4⋊Q8—2261no—
182#125—1131no—
183#125—2261no—
184#125C2×D11311yescharacteristic
185C22⋊Q8—2261no—
186C22⋊Q8—2261no—
187C4×Q8—1131no—
188C4×Q8—1131no—
189C4×Q8—1131no—
190C4×Q8—2261no—
191C4×Q8—2261no—
192C4×Q8C2×D11311yescharacteristic
193#117—1131no—
194#117—1131no—
195#117—1131no—
196#117—2261no—
197#117—2261no—
198C2×C4⋊C4—1131no—
199#107—1131no—
200#107—1131no—
201#107—1131no—
202#107C2×D11311yescharacteristic
203#106—1131no—
204#106—1131no—
205#106—1131no—
206#106C2×D11311yescharacteristic
207C4⋊C8—1131no—
208C4⋊C8—1131no—
209C4⋊C8—1131no—
210C4⋊C8C2×D11311yescharacteristic
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103C2×D11311yescharacteristic
218#103C2×D11311yescharacteristic
219C2×Q8—1134no—
220C2×Q8—1131no—
221C2×Q8—2261no—
222C2×Q8—2261no—
223C2×Q8—2262no—
224C2×Q8—2261no—
225C2×Q8C22×D11311yescharacteristic
226C22×C4—1131no—
227C22×C4—2261no—
228C22×C4—2261no—
229M16—2262no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—2262no—
233C2×C8C22×D11311yescharacteristic
234C2×C8C22×D11311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—1131no—
239C4⋊C4—1131no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4C22×D11311yescharacteristic
252C4⋊C4C22×D11311yescharacteristic
253C4⋊C4C22×D11311yescharacteristic
254C22⋊C4—1131no—
255C22⋊C4—1131no—
256C22⋊C4—2261no—
257C22⋊C4—2261no—
258C42—21no—
259C42—1131no—
260C42—2261no—
261C42—2261no—
262C42—2261no—
263C42—2261no—
264C42—2261no—
265C42C22×D11311yescharacteristic
266C23—1131no—
267Q8—21no—
268Q8—1132no—
269Q8—9041no—
270Q8—9041no—
271Q8—2264no—
272Q8—2261no—
273Q8Q8×D11312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—1131no—
279C2×C4—1132no—
280C2×C4—1132no—
281C2×C4—1131no—
282C2×C4—1131no—
283C2×C4—9041no—
284C2×C4—2264no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2261no—
289C2×C4D4×D11311yescharacteristic
290C2×C4D4×D11311yescharacteristic
291C2×C4C23×D11311yescharacteristic
292C8—21no—
293C8—21no—
294C8—2261no—
295C8—2261no—
296C22—1132no—
297C22—2261no—
298C22—2261no—
299C22C2×D4×D11311yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—1132no—
307C4—4521no—
308C4—4521no—
309C4—4521no—
310C4—2262no—
311C4—2261no—
312C4—2261no—
313C4C2×Q8×D11311yescharacteristic
314C4#41×D11311yescharacteristic
315C2—2262no—
316C2C22⋊Q8×D11311yescharacteristic
317C2#2029940511yescharacteristic
318C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#479D113
hypocenterC113#3082
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #20298908C2semidirect
4. #20298903C2semidirect
5. #20298902C2semidirect
6. #20298893C2semidirect
7. #20298892C2semidirect
8. #20298884C2semidirect
9. #20298881C2semidirect
15. #479×C113C2semidirect
64. Q8×D113Q8semidirect
160. C113#3082semidirect
166. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202992282
#202990742
#202989082
#202989032
#202989022
#202988932
#202988922
#202988842
#202988812
#202986392
#202986332
#202986232
#202986052
#103×D1132
#479×C1132
#3082113