Finite Group Databasebeta

← #28402458

Subgroups — #28402458

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299286C211yesmaximal, characteristic, complemented
2#20299260C211yesmaximal, characteristic
3#20298955C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298913C211yesmaximal, characteristic, complemented
6#20298840C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298821C211yesmaximal, characteristic, complemented
9#20298763C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11C4×#14268637C211yesmaximal, characteristic, complemented
12#20298663C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#479×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic
23#16813617—21no—
24#16813613—21no—
25#16813610—21no—
26#16813610C2211yescharacteristic
27#16813607—21no—
28#16813602—21no—
29#16813602C2211yescharacteristic
30#16813602C2211yescharacteristic
31#16813602C2211yescharacteristic
32#16813597—21no—
33#16813597C2211yescharacteristic
34C4×Dic226C2211yescharacteristic
35C4×D452—21no—
36C4×D452C2211yescharacteristic
37#16813580—21no—
38#16813580C2211yescharacteristic
39C4⋊C4×D113C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452D411yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75Dic452—41no—
76#14268637—22no—
77#14268636—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C8×D113—41no—
82C4⋊Dic113—21no—
83C4⋊Dic113—21no—
84C4⋊Dic113—21no—
85C4⋊Dic113D411yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C4×Dic113—21no—
100C2×Q8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C22×D113—21no—
112C22×D113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
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
128D452—22no—
129D452—21no—
130D452—21no—
131D452—42no—
132D452—42no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138C4×D113—42no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113#13512yes—
159C4×C113—22no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113C2×#4111yescharacteristic
166C4×C113H(5,𝔽2)11yescharacteristic
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113#54611yescharacteristic
173C2×C113C2×#13511yescharacteristic
174C2×C113#57811yescharacteristic
175D113—22no—
176D113—41no—
177D113—81no—
178#3300—1131nomaximal, Sylow
179C113#330011yescharacteristic, complemented, Sylow
180#552—1131no—
181#548—1131no—
182#488—1131no—
183#485—1131no—
184#480—1131no—
185#479D11311yescharacteristic, complemented
186#467—1131no—
187#465—1131no—
188#464—1131no—
189#452—1131no—
190#451—1131no—
191C4×Q16—1131no—
192C8×D4—1131no—
193#416—1131no—
194C2×#103—1131no—
195C2×#41—1131no—
196C22×Q8—1131no—
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×SD16—1131no—
200C22×C8—1131no—
201C22×C8—1131no—
202#126—2261no—
203#125—2261no—
204#125C2×D11311yescharacteristic
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—1131no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212#121—1131no—
213#121—2261no—
214C4×Q8—1131no—
215C4×Q8C2×D11311yescharacteristic
216C4×D4—1131no—
217C4×D4—2261no—
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107C2×D11311yescharacteristic
223#106C2×D11311yescharacteristic
224C4⋊C8C2×D11311yescharacteristic
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#103C2×D11311yescharacteristic
232#102—1131no—
233#102—1131no—
234#102—1131no—
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C4×C8—1131no—
238#41—4521no—
239#41—2262no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—2261no—
244C2×Q8—2262no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4—2261no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255Q16—4521no—
256Q16—2262no—
257SD16—4521no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—4521no—
261C2×C8—4521no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—1131no—
278C22⋊C4—1131no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—2261no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—1131no—
291C23—1131no—
292C23—2261no—
293Q8—21no—
294Q8—4522no—
295Q8—2261no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299Q8#1426864812yes—
300D4—4522no—
301D4—4522no—
302D4—2262no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—4522no—
312C2×C4—4522no—
313C2×C4—4522no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4D4×D11311yescharacteristic
322C2×C4D4×D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—21no—
325C8—21no—
326C8—2261no—
327C8—2261no—
328C22—1132no—
329C22—4521no—
330C22—4521no—
331C22—4521no—
332C22—2261no—
333C22—2261no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4—2261no—
348C4—2261no—
349C4C2×#1426864811yescharacteristic
350C4#1681366811yescharacteristic
351C2—9041no—
352C2—4521no—
353C2—2262no—
354C2#2029923911yescharacteristic
355C2#135×D11311yescharacteristic
356C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radical#20299260C2
hypercenter#479D113
hypocenterC113#3300
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
1. #20299286C2semidirect
3. #20298955C2semidirect
4. #20298942C2semidirect
5. #20298913C2semidirect
6. #20298840C2semidirect
7. #20298828C2semidirect
8. #20298821C2semidirect
9. #20298763C2semidirect
10. #20298755C2semidirect
11. C4×#14268637C2semidirect
12. #20298663C2semidirect
13. #20298593C2semidirect
14. #103×D113C2semidirect
15. #479×C113C2semidirect
179. C113#3300semidirect
185. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202992862
#202992602
#202989552
#202989422
#202989132
#202988402
#202988282
#202988212
#202987632
#202987552
C4×#142686372
#202986632
#202985932
#103×D1132
#479×C1132
#3300113