Finite Group Databasebeta

← #28400787

Subgroups — #28400787

Order 14464.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299209C211yesmaximal, characteristic, complemented
2#20299080C211yesmaximal, characteristic
3#20298932C211yesmaximal, characteristic, complemented
4#20298927C211yesmaximal, characteristic, complemented
5#20298905C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298800C211yesmaximal, characteristic, complemented
8#20298759C211yesmaximal, characteristic
9#20298759C211yesmaximal, characteristic
10#20298705C211yesmaximal, characteristic, complemented
11#20298701C211yesmaximal, characteristic, complemented
12Q16×Dic113C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#462×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19#16813617—21no—
20#16813617—21no—
21#16813614C2211yescharacteristic
22#16813612—21no—
23#16813612—21no—
24#16813598C2211yescharacteristic
25#16813598C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29C4×D452—21no—
30C4×D452C2211yescharacteristic
31#16813584—21no—
32#16813584C2211yescharacteristic
33#16813579—21no—
34#16813579C2211yescharacteristic
35C4⋊C4×D113—21no—
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C4⋊Q8×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—22no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C4×D113—21no—
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268634—22no—
69#14268634—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
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#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98Q16×C113—22no—
99Q16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C22×D113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113#4112yes—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—24no—
130D452—21no—
131D452#4112yes—
132C4×D113—24no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—81no—
136C4×D113—81no—
137C4×D113—81no—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113C22×D411yescharacteristic
143C2×D113—21no—
144C2×D113—22no—
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—22no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C113C2×#4111yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113#52511yescharacteristic
164C2×C113#57711yescharacteristic
165C2×C113#57811yescharacteristic
166D113—41no—
167D113—42no—
168#3120—1131nomaximal, Sylow
169C113#312011yescharacteristic, complemented, Sylow
170#541—1131no—
171#520—1131no—
172#484—1131no—
173#483—1131no—
174#479—1131no—
175#478—1131no—
176#462D11311yescharacteristic, complemented
177#461—1131no—
178#452—1131no—
179#452—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C2×#41—1131no—
186C2×Q16C2×D11311yescharacteristic
187C2×Q16C2×D11311yescharacteristic
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8C2×D11311yescharacteristic
191#126—2261no—
192#126—2261no—
193#125—1131no—
194#125—2261no—
195#125—2261no—
196C22⋊Q8—1131no—
197C22⋊Q8—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8C2×D11311yescharacteristic
202C4×D4—1131no—
203C4×D4—1131no—
204C4×D4—2261no—
205C4×D4—2261no—
206#117—1131no—
207#117—2261no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—2261no—
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C4×C8—1131no—
228#41—2262no—
229#41—2262no—
230C2×Q8C22×D11311yescharacteristic
231C2×Q8C22×D11311yescharacteristic
232C2×Q8C22×D11311yescharacteristic
233C2×D4—1131no—
234C2×D4—2261no—
235C22×C4—1131no—
236C22×C4—2261no—
237C22×C4—2261no—
238C22×C4—2261no—
239C22×C4—2261no—
240Q16—22no—
241Q16—22no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—1131no—
266C22⋊C4—1131no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C42—21no—
272C42—1131no—
273C42—2261no—
274C42—2261no—
275C42—2261no—
276C42C22×D11311yescharacteristic
277C23—1131no—
278C23—2261no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8#1426864612yes—
285D4—1132no—
286D4—2264no—
287D4—2261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—9041no—
296C2×C4—9041no—
297C2×C4—9041no—
298C2×C4—2264no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2261no—
310C8—2261no—
311C22—4521no—
312C22—4521no—
313C22—2262no—
314C22—2261no—
315C22—2261no—
316C22—2261no—
317C22C2×D4×D11311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4—2261no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4C2×#1426864611yescharacteristic
332C2—4522no—
333C2—4521no—
334C2#2029910811yescharacteristic
335C2#2029940711yescharacteristic
336C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#462×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268648C22
hypercenter#462D113
hypocenterC113#3120
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298932C2semidirect
4. #20298927C2semidirect
5. #20298905C2semidirect
6. #20298899C2semidirect
7. #20298800C2semidirect
10. #20298705C2semidirect
11. #20298701C2semidirect
12. Q16×Dic113C2semidirect
13. #20298683C2semidirect
14. #20298658C2semidirect
15. #462×C113C2semidirect
169. C113#3120semidirect
176. #462D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202990802
#202989322
#202989272
#202989052
#202988992
#202988002
#202987592
#202987052
#202987012
Q16×Dic1132
#202986832
#202986582
#462×C1132
#3120113