Finite Group Databasebeta

← #28400536

Subgroups — #28400536

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299171C211yesmaximal, characteristic
2#20299079C211yesmaximal, characteristic
3#20298942C211yesmaximal, characteristic, complemented
4#20298940C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298936C211yesmaximal, characteristic, complemented
7#20298933C211yesmaximal, characteristic, complemented
8#20298932C211yesmaximal, characteristic, complemented
9#20298930C211yesmaximal, characteristic, complemented
10#20298637C211yesmaximal, characteristic, complemented
11#20298633C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#103×D113C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic
15#483×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813621—21no—
21#16813608—21no—
22#16813607—21no—
23#16813604—21no—
24#16813602C2211yescharacteristic
25#16813601C2211yescharacteristic
26#16813598C2211yescharacteristic
27#16813587—21no—
28#16813584—21no—
29C4×C22⋊D113—21no—
30C4×C22⋊D113—21no—
31#16813581C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34#16813580C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#106×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226—21no—
62C2×Dic226D411yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—22no—
66C2×D452D411yescharacteristic
67C2×C22⋊D113D411yescharacteristic
68C2×C22⋊D113D411yescharacteristic
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268630—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—22no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C2×Q8×C113C2311yescharacteristic
98C22×C4×C113—21no—
99C22×C4×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113C2×D411yescharacteristic
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×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—81no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—22no—
123C22⋊D113—22no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—22no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—42no—
134C4×D113—81no—
135C4×D113—81no—
136C4×D113#4112yes—
137C4×D113#4112yes—
138Dic226—22no—
139Dic226—21no—
140Dic226—21no—
141Dic226—42no—
142C8×C113—21no—
143C8×C113—21no—
144#11744751—21no—
145#11744751—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C2×D113#12312yes—
156C4×C113—21no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113C2×#4111yescharacteristic
162C4×C113C2×#4111yescharacteristic
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168Dic113#12312yes—
169C2×C113—41no—
170C2×C113C2×#12311yescharacteristic
171C2×C113#57711yescharacteristic
172C2×C113#57811yescharacteristic
173D113—22no—
174D113—41no—
175#3097—1131nomaximal, Sylow
176C113#309711yescharacteristic, complemented, Sylow
177#536—1131no—
178#520—1131no—
179#485—1131no—
180#485—1131no—
181#485—1131no—
182#485—1131no—
183#484—1131no—
184#484—1131no—
185#483—1131no—
186#483D11311yescharacteristic, complemented
187#428—1131no—
188#427—1131no—
189#419—1131no—
190C2×#103—1131no—
191#408—1131no—
192C2×#41—1131no—
193C22×Q8—1131no—
194C2×M16—1131no—
195C22×C8—1131no—
196C4⋊Q8—2261no—
197#124—2261no—
198#123—2261no—
199#123—2261no—
200C22⋊Q8—1131no—
201C22⋊Q8—1131no—
202C22⋊Q8—1131no—
203C22⋊Q8C2×D11311yescharacteristic
204C4×Q8—2261no—
205C4×D4—2261no—
206C4×D4—2261no—
207C4×D4—2261no—
208#117—1131no—
209#117—1131no—
210#117—1131no—
211#117—1131no—
212C2×C4⋊C4—1131no—
213C2×C4⋊C4—1131no—
214C2×C4⋊C4C2×D11311yescharacteristic
215#107—1131no—
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#106—1131no—
220#106—1131no—
221#106C2×D11311yescharacteristic
222#106C2×D11311yescharacteristic
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103C2×D11311yescharacteristic
230#103C2×D11311yescharacteristic
231C22⋊C8—1131no—
232C22⋊C8—1131no—
233C22⋊C8—1131no—
234C22⋊C8C2×D11311yescharacteristic
235#41—2262no—
236#41—2262no—
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×Q8—2261no—
240C2×Q8—2262no—
241C2×Q8—2262no—
242C2×Q8C22×D11311yescharacteristic
243C2×D4—1131no—
244C2×D4—1131no—
245C2×D4—1131no—
246C22×C4—21no—
247C22×C4—1131no—
248C22×C4—1131no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252C22×C4C22×D11311yescharacteristic
253M16—2262no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8—2262no—
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4C22×D11311yescharacteristic
270C4⋊C4C22×D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C42—2261no—
281C42—2261no—
282C42—2261no—
283C42—2261no—
284C23—1131no—
285C23—1131no—
286C23D4×D11311yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—4522no—
290Q8—2262no—
291Q8—2261no—
292Q8—2261no—
293D4—2262no—
294D4—2262no—
295D4—2262no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—1131no—
304C2×C4—1132no—
305C2×C4—1132no—
306C2×C4—1131no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—4522no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4D4×D11311yescharacteristic
317C2×C4C23×D11311yescharacteristic
318C8—21no—
319C8—21no—
320C8—2261no—
321C8—2261no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—1132no—
326C22—2261no—
327C22—2261no—
328C22—2261no—
329C22—2261no—
330C22—2261no—
331C22C2×D4×D11311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1132no—
338C4—4521no—
339C4—4521no—
340C4—4521no—
341C4—4521no—
342C4—2261no—
343C4#41×D11311yescharacteristic
344C4#41×D11311yescharacteristic
345C2—41no—
346C2—4521no—
347C2—2262no—
348C2#123×D11311yescharacteristic
349C2#2029940411yescharacteristic
350C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#483×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#483D113
hypocenterC113#3097
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #20298942C2semidirect
4. #20298940C2semidirect
5. #20298937C2semidirect
6. #20298936C2semidirect
7. #20298933C2semidirect
8. #20298932C2semidirect
9. #20298930C2semidirect
10. #20298637C2semidirect
11. #20298633C2semidirect
12. #20298605C2semidirect
13. #103×D113C2semidirect
15. #483×C113C2semidirect
176. C113#3097semidirect
186. #483D113semidirect

Maximal subgroups

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

subgroupindex
#202991712
#202990792
#202989422
#202989402
#202989372
#202989362
#202989332
#202989322
#202989302
#202986372
#202986332
#202986052
#103×D1132
#202985632
#483×C1132
#3097113