Finite Group Databasebeta

← #28400790

Subgroups — #28400790

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#20299210C211yesmaximal, characteristic, complemented
2#20299078C211yesmaximal, characteristic
3#20298934C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298906C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298809C211yesmaximal, characteristic, complemented
8#20298804C211yesmaximal, characteristic, complemented
9#20298762C211yesmaximal, characteristic
10#20298762C211yesmaximal, characteristic
11#20298706C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13C4×Dic452C211yesmaximal, characteristic, complemented
14C4×#14268636C211yesmaximal, characteristic, complemented
15#433×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21#16813622C2211yescharacteristic
22#16813615—21no—
23#16813615—21no—
24#16813614C2211yescharacteristic
25#16813612—21no—
26#16813612—21no—
27#16813601C2211yescharacteristic
28#16813601C2211yescharacteristic
29C4×Dic226C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×Dic226C2211yescharacteristic
32C4×Dic226C2211yescharacteristic
33C4×D452C2211yescharacteristic
34C4×D452C2211yescharacteristic
35#16813582—21no—
36#16813582—21no—
37#16813580—21no—
38C2×C4⋊Dic113C2211yescharacteristic
39C4⋊C4×D113—21no—
40#16813556C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52#117×C113C2211yescharacteristic
53C4⋊C8×C113C2211yescharacteristic
54C4⋊C8×C113C2211yescharacteristic
55C22⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57#97×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70Dic452—22no—
71Dic452—22no—
72#14268636—22no—
73#14268636—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C22×C4×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113D411yescharacteristic
103C4⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C22⋊C4×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113C2×D411yescharacteristic
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—24no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—81no—
127D452—21no—
128D452#4112yes—
129C4×D113—24no—
130C4×D113—81no—
131C4×D113—81no—
132Dic226—21no—
133Dic226—21no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226#4112yes—
138C8×C113—21no—
139C8×C113—21no—
140C8×C113—21no—
141C8×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113C22×D411yescharacteristic
146C2×D113—22no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—21no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113C2×#4111yescharacteristic
155C4×C113C2×#4111yescharacteristic
156Dic113—22no—
157Dic113—41no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—41no—
164C2×C113#52511yescharacteristic
165C2×C113#57711yescharacteristic
166C2×C113#57811yescharacteristic
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#462—1131no—
177#461—1131no—
178#452—1131no—
179#452—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433D11311yescharacteristic, complemented
185C2×#41—1131no—
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8—1131no—
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×Q8—1131no—
202C4×D4—1131no—
203C4×D4—1131no—
204C4×D4—2261no—
205C4×D4—2261no—
206#117—2261no—
207#117C2×D11311yescharacteristic
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—2261no—
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8C2×D11311yescharacteristic
215C4⋊C8C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#102—1131no—
223#102—1131no—
224C22⋊C8C2×D11311yescharacteristic
225C22⋊C8C2×D11311yescharacteristic
226#97C2×D11311yescharacteristic
227C4×C8C2×D11311yescharacteristic
228#41—2262no—
229#41—2262no—
230C2×Q8—1131no—
231C2×Q8—1131no—
232C2×Q8—1131no—
233C2×D4—1131no—
234C2×D4—2261no—
235C22×C4—2261no—
236C22×C4—2261no—
237C22×C4—2261no—
238C22×C4—2261no—
239C22×C4C22×D11311yescharacteristic
240Q16—2262no—
241Q16—2262no—
242SD16—2262no—
243SD16—2262no—
244C2×C8C22×D11311yescharacteristic
245C2×C8C22×D11311yescharacteristic
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4D45211yescharacteristic
264C4⋊C4D45211yescharacteristic
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4D45211yescharacteristic
270C22⋊C4D45211yescharacteristic
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C42C22×D11311yescharacteristic
276C42C22×D11311yescharacteristic
277C23—2261no—
278C23C2×D45211yescharacteristic
279Q8—1132no—
280Q8—2261no—
281Q8—2261no—
282Q8—2261no—
283Q8—2261no—
284Q8—2261no—
285D4—1132no—
286D4—2264no—
287D4—2261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—9041no—
291C2×C4—9041no—
292C2×C4—9041no—
293C2×C4—2264no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4C2×D45211yescharacteristic
302C2×C4C2×D45211yescharacteristic
303C2×C4C2×D45211yescharacteristic
304C2×C4C2×D45211yescharacteristic
305C2×C4C2×D45211yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4521no—
315C22—4521no—
316C22—2262no—
317C22C22×D45211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4—4521no—
328C4—4521no—
329C4—2262no—
330C4#41×D11311yescharacteristic
331C4#41×D11311yescharacteristic
332C2—41no—
333C2—4522no—
334C2#2029911011yescharacteristic
335C2#2029941011yescharacteristic
336C2#2029941511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#433×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#433D113
hypocenterC113#3120
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20299210C2semidirect
3. #20298934C2semidirect
4. #20298929C2semidirect
5. #20298906C2semidirect
6. #20298899C2semidirect
7. #20298809C2semidirect
8. #20298804C2semidirect
11. #20298706C2semidirect
12. #20298700C2semidirect
13. C4×Dic452C2semidirect
14. C4×#14268636C2semidirect
15. #433×C113C2semidirect
169. C113#3120semidirect
184. #433D113semidirect

Maximal subgroups

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

subgroupindex
#202992102
#202990782
#202989342
#202989292
#202989062
#202988992
#202988092
#202988042
#202987622
#202987062
#202987002
C4×Dic4522
C4×#142686362
#433×C1132
#3120113