Finite Group Databasebeta

← #28400555

Subgroups — #28400555

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299178C211yesmaximal, characteristic
2#20299078C211yesmaximal, characteristic, complemented
3#20298938C211yesmaximal, characteristic, complemented
4#20298932C211yesmaximal, characteristic, complemented
5#20298931C211yesmaximal, characteristic, complemented
6#20298924C211yesmaximal, characteristic, complemented
7#20298922C211yesmaximal, characteristic, complemented
8#20298913C211yesmaximal, characteristic, complemented
9#20298912C211yesmaximal, characteristic, complemented
10#20298637C211yesmaximal, characteristic, complemented
11#107×D113C211yesmaximal, characteristic, complemented
12#20298598C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813600—21no—
21#16813598C2211yescharacteristic
22#16813597—21no—
23#16813597C2211yescharacteristic
24#16813596C2211yescharacteristic
25#16813595—21no—
26#16813595—21no—
27C4×Dic226—21no—
28C4×D452—21no—
29#16813582—21no—
30#16813582—21no—
31#16813580C2211yescharacteristic
32#16813580C2211yescharacteristic
33C2×C4⋊Dic113C2211yescharacteristic
34C4⋊C4×D113C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—22no—
61#14268647—22no—
62#14268647—22no—
63C2×Dic226D411yescharacteristic
64C2×D452—21no—
65C2×D452—21no—
66C2×D452D411yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C2×C22⋊D113D411yescharacteristic
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77C2×C4×D113C2311yescharacteristic
78#14268630—22no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C8×D113—22no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C2×Q8×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111C22×D113C2×D411yescharacteristic
112Q8×C113—21no—
113Q8×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—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—22no—
123C22⋊D113—22no—
124C22⋊D113—81no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—81no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131D452—22no—
132D452—21no—
133D452—21no—
134D452—42no—
135D452—81no—
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—42no—
139C4×D113—81no—
140C4×D113—81no—
141C4×D113—81no—
142C4×D113#4112yes—
143C4×D113#4112yes—
144Dic226—22no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113#12312yes—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113#12312yes—
174C2×C113—41no—
175C2×C113C2×#12311yescharacteristic
176C2×C113#57611yescharacteristic
177C2×C113#57811yescharacteristic
178D113—22no—
179D113—41no—
180D113—81no—
181#3098—1131nomaximal, Sylow
182C113#309811yescharacteristic, complemented, Sylow
183#537—1131no—
184#520—1131no—
185#485—1131no—
186#485D11311yescharacteristic, complemented
187#484—1131no—
188#484—1131no—
189#482—1131no—
190#482—1131no—
191#480—1131no—
192#480—1131no—
193#428—1131no—
194C2×#107—1131no—
195#417—1131no—
196#416—1131no—
197#408—1131no—
198C2×#41—1131no—
199C2×#41—1131no—
200C2×M16—1131no—
201C22×C8—1131no—
202C22⋊Q8—1131no—
203C22⋊Q8—2261no—
204C22⋊Q8C2×D11311yescharacteristic
205#121—1131no—
206#121—1131no—
207#121—2261no—
208#121—2261no—
209#121—2261no—
210C4×Q8—2261no—
211C4×D4—2261no—
212C4×D4—2261no—
213C4×D4—2261no—
214#117—1131no—
215#117—1131no—
216#117C2×D11311yescharacteristic
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—1131no—
219C2×C4⋊C4—1131no—
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107—1131no—
223#107—1131no—
224#107—1131no—
225#107—1131no—
226#107C2×D11311yescharacteristic
227#106—1131no—
228#106C2×D11311yescharacteristic
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic
232#103C2×D11311yescharacteristic
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239C22⋊C8—1131no—
240C22⋊C8C2×D11311yescharacteristic
241#41—2262no—
242#41—2262no—
243#41—2262no—
244#41—2262no—
245C2×Q8—1131no—
246C2×Q8C22×D11311yescharacteristic
247C2×D4—1131no—
248C2×D4—1131no—
249C2×D4—1131no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2261no—
253C2×D4—2261no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4C22×D11311yescharacteristic
262M16—2262no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—2262no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—1131no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4C22×D11311yescharacteristic
278C4⋊C4C22×D11311yescharacteristic
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C42—21no—
288C42—2261no—
289C42—2261no—
290C23—1131no—
291C23—1131no—
292C23—2261no—
293C23D4×D11311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—2262no—
297D4—9041no—
298D4—9041no—
299D4—4522no—
300D4—2262no—
301D4—2262no—
302D4—2262no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1131no—
312C2×C4—1132no—
313C2×C4—1132no—
314C2×C4—1131no—
315C2×C4—9041no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—4522no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4D4×D11311yescharacteristic
326C2×C4C23×D11311yescharacteristic
327C8—21no—
328C8—21no—
329C8—2261no—
330C8—2261no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—1132no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22—2261no—
342C22—2261no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1132no—
350C4—4521no—
351C4—4521no—
352C4—4521no—
353C4—2261no—
354C4#41×D11311yescharacteristic
355C4#41×D11311yescharacteristic
356C2—41no—
357C2—9041no—
358C2—4521no—
359C2—2262no—
360C2#123×D11311yescharacteristic
361C2#2029940011yescharacteristic
362C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
prime radical#20299178C2
hypercenter#485D113
hypocenterC113#3098
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #20299078C2semidirect
3. #20298938C2semidirect
4. #20298932C2semidirect
5. #20298931C2semidirect
6. #20298924C2semidirect
7. #20298922C2semidirect
8. #20298913C2semidirect
9. #20298912C2semidirect
10. #20298637C2semidirect
11. #107×D113C2semidirect
12. #20298598C2semidirect
13. #20298593C2semidirect
14. #20298563C2semidirect
15. #485×C113C2semidirect
182. C113#3098semidirect
186. #485D113semidirect

Maximal subgroups

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

subgroupindex
#202991782
#202990782
#202989382
#202989322
#202989312
#202989242
#202989222
#202989132
#202989122
#202986372
#107×D1132
#202985982
#202985932
#202985632
#485×C1132
#3098113