Finite Group Databasebeta

← #28404574

Subgroups — #28404574

Order 14464.

1122 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#20299324C211yesmaximal, characteristic, complemented
2#20299298C213yesmaximal, complemented
3#20299296C213yesmaximal, complemented
4#20299270C211yesmaximal, characteristic, complemented
5#20299269C213yesmaximal, complemented
6#20299267C211yesmaximal, characteristic, complemented
7#20299267C211yesmaximal, characteristic, complemented
8#20299249C213yesmaximal, complemented
9#20299203C213yesmaximal, complemented
10#20299199C213yesmaximal, complemented
11#20299145C213yesmaximal, complemented
12#20299126C213yesmaximal, complemented
13#20299080C211yesmaximal, characteristic, complemented
14C4×#14268648C211yesmaximal, characteristic, complemented
15#520×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268648C2211yescharacteristic
18C2×#14268647C2216yes—
19#16813621C2213yes—
20#16813619C2213yes—
21#16813618C2213yes—
22#16813618C2213yes—
23#16813617C2213yes—
24#16813615C2213yes—
25#16813614C2213yes—
26#16813613C2213yes—
27#16813612C2211yescharacteristic
28#16813608C2213yes—
29#16813607C2216yes—
30#16813607C2213yes—
31#16813605C2216yes—
32#16813604C2213yes—
33#16813600C2213yes—
34#16813597C2213yes—
35#16813597C2213yes—
36#16813596C2213yes—
37#16813596C2213yes—
38#16813596C2216yes—
39#16813595C2213yes—
40#16813595C2216yes—
41#16813595C2216yes—
42#16813593C2213yes—
43#16813593C2213yes—
44Q8×Dic113C2211yescharacteristic
45Q8×Dic113C2211yescharacteristic
46C4×Dic226C2213yes—
47C4×D452C2213yes—
48C4×D452C2213yes—
49C4×D452C2213yes—
50#16813584C2213yes—
51#16813584C2213yes—
52C4×C22⋊D113C2213yes—
53C4×C22⋊D113C2213yes—
54C4×C22⋊D113C2216yes—
55#16813580C2213yes—
56#16813579C2213yes—
57C4⋊C4×D113C2213yes—
58C42×D113C2213yes—
59C2×#41×C113C2211yescharacteristic
60C4×Q8×C113C2211yescharacteristic
61C4×Q8×C113C2211yescharacteristic
62C4×D4×C113C2213yes—
63C4×D4×C113C2213yes—
64#117×C113C2213yes—
65C2×C4⋊C4×C113C2213yes—
66#14268648—24no—
67#14268648—24no—
68#14268647—412no—
69C2×Dic226C2313yes—
70C2×D452C2313yes—
71C2×D452C2313yes—
72C2×D452C2313yes—
73C2×D452C2316yes—
74C2×C22⋊D113C2313yes—
75C2×C22⋊D113C2316yes—
76C2×C22⋊D113C2313yes—
77C2×C22⋊D113C2316yes—
78C2×C4×D113C2313yes—
79C2×C4×D113C2313yes—
80C2×C4×D113C2313yes—
81C2×C4×D113C2313yes—
82C2×C4×D113C2316yes—
83C4⋊Dic113C2313yes—
84C4⋊Dic113C2313yes—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2313yes—
87#14268626C2313yes—
88#14268626C2311yescharacteristic
89#14268626C2311yescharacteristic
90#14268626C2311yescharacteristic
91#14268626C2316yes—
92#14268626C2311yescharacteristic
93#14268626C2313yes—
94C22⋊Dic113C2313yes—
95C22⋊Dic113C2313yes—
96#14268624C2313yes—
97#14268624C2313yes—
98#14268624C2316yes—
99#14268624C2313yes—
100#14268624C2313yes—
101#14268624C2313yes—
102#14268624C2313yes—
103C4×Dic113C2311yescharacteristic
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106C4×Dic113C2313yes—
107#41×C113—24no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2313yes—
110C22×C4×C113C2313yes—
111C22×C4×C113C2316yes—
112C4⋊C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113C2313yes—
117C22⋊C4×C113C2313yes—
118C42×C113C2313yes—
119C42×C113C2313yes—
120C23×C113C2413yes—
121C22×D113C2413yes—
122C22×D113C2413yes—
123Q8×C113#4114yescomplemented
124D4×C113—26no—
125C2×C4×C113—26no—
126C2×C4×C113—46no—
127C2×C4×C113C2411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2413yes—
130C2×C4×C113C2413yes—
131C2×C4×C113C2411yescharacteristic
132C2×C4×C113C2413yes—
133C22⋊D113—26no—
134C22⋊D113—46no—
135C22⋊D113—43no—
136C22⋊D113—46no—
137C2×Dic113C2411yescharacteristic
138C2×Dic113C2411yescharacteristic
139C2×Dic113C2413yes—
140C2×Dic113C2413yes—
141C2×Dic113C2411yescharacteristic
142C2×Dic113C2411yescharacteristic
143D452—26no—
144D452—26no—
145D452—43no—
146D452—46no—
147C4×D113—26no—
148C4×D113—26no—
149C4×D113—26no—
150C4×D113—43no—
151C4×D113—46no—
152Dic226—26no—
153C22×C113—23no—
154C22×C113—23no—
155C22×C113—23no—
156C22×C113C2511yescharacteristic
157C2×D113—23no—
158C2×D113—23no—
159C2×D113—23no—
160C2×D113—23no—
161C2×D113—23no—
162C2×D113—23no—
163C4×C113—21no—
164C4×C113—23no—
165C4×C113—23no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113C2×#4116yes—
169Dic113—21no—
170Dic113—21no—
171Dic113—23no—
172Dic113—23no—
173Dic113—21no—
174Dic113H(5,𝔽2)12yes—
175C2×C113—43no—
176C2×C113C22×#4111yescharacteristic
177C2×C113C2×H(5,𝔽2)11yescharacteristic
178C2×C113#58511yescharacteristic
179D113—43no—
180D113—43no—
181#3517—1131nomaximal, Sylow
182C113#351711yescharacteristic, complemented, Sylow
183#557—1131no—
184#553—1133no—
185#553—1133no—
186#550—1131no—
187#550—1131no—
188#550—1131no—
189#550—1133no—
190#547—1133no—
191#540—1133no—
192#540—1133no—
193#532—1133no—
194#529—1133no—
195#520—1131no—
196#520D11311yescharacteristic, complemented
197C4×#41—1131no—
198C2×#41—1131no—
199C2×#41—1131no—
200C2×#41—1136no—
201C2×#41C2×D11311yescharacteristic
202C4⋊Q8—1133no—
203#127—1133no—
204#127—1133no—
205#127—1133no—
206#126—1133no—
207#126—1133no—
208#125—1131no—
209#125—1133no—
210#125—1133no—
211#124—1133no—
212#123—1136no—
213#123—1133no—
214#123—1136no—
215#123—1133no—
216C22⋊Q8—1133no—
217#121—1133no—
218#121—1133no—
219#121—1133no—
220#121—1136no—
221#121—1133no—
222#121—1133no—
223#121—1133no—
224#121—1133no—
225#121—1136no—
226#121—1136no—
227C4×Q8—1131no—
228C4×Q8—1131no—
229C4×Q8—1133no—
230C4×Q8C2×D11311yescharacteristic
231C4×Q8C2×D11311yescharacteristic
232C4×D4—1133no—
233C4×D4—1133no—
234C4×D4—1136no—
235C4×D4—1133no—
236C4×D4—1133no—
237C4×D4—1133no—
238C4×D4—1133no—
239C4×D4—1133no—
240C4×D4C2×D11313yes—
241C4×D4C2×D11313yes—
242#117—1133no—
243#117—1133no—
244#117C2×D11313yes—
245C2×C4⋊C4—1133no—
246C2×C4⋊C4C2×D11313yes—
247C2×C42—1133no—
248#41—24no—
249#41—45212no—
250#41—2264no—
251#41—2264no—
252C2×Q8—1133no—
253C2×Q8C22×D11311yescharacteristic
254C2×D4—1136no—
255C2×D4—1133no—
256C2×D4—1136no—
257C2×D4—1133no—
258C2×D4—1133no—
259C2×D4—1136no—
260C2×D4—1133no—
261C2×D4—1133no—
262C2×D4C22×D11313yes—
263C22×C4—1133no—
264C22×C4—1136no—
265C22×C4—1133no—
266C22×C4—1133no—
267C22×C4—1133no—
268C22×C4C22×D11313yes—
269C22×C4C22×D11316yes—
270C4⋊C4—1133no—
271C4⋊C4—1133no—
272C4⋊C4—1131no—
273C4⋊C4—1133no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—1136no—
278C4⋊C4—1131no—
279C4⋊C4—1133no—
280C4⋊C4—1133no—
281C4⋊C4C22×D11313yes—
282C4⋊C4C22×D11313yes—
283C4⋊C4C22×D11313yes—
284C4⋊C4C22×D11311yescharacteristic
285C22⋊C4—1133no—
286C22⋊C4—1133no—
287C22⋊C4—1133no—
288C22⋊C4—1136no—
289C22⋊C4—1133no—
290C22⋊C4—1133no—
291C22⋊C4—1133no—
292C22⋊C4—1133no—
293C22⋊C4—1133no—
294C22⋊C4C22×D11313yes—
295C22⋊C4C22×D11313yes—
296C42—1131no—
297C42—1133no—
298C42—1133no—
299C42—1133no—
300C42C22×D11313yes—
301C42C22×D11313yes—
302C23—1133no—
303C23—1133no—
304C23C23×D11313yes—
305Q8—2266no—
306Q8#1426864714yescomplemented
307D4—26no—
308D4—4526no—
309D4—4523no—
310D4—4526no—
311D4—4526no—
312D4—4523no—
313D4—2266no—
314D4—2266no—
315D4—2266no—
316C2×C4—26no—
317C2×C4—46no—
318C2×C4—1131no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1133no—
322C2×C4—1133no—
323C2×C4—1131no—
324C2×C4—4526no—
325C2×C4—4523no—
326C2×C4—2266no—
327C2×C4—2266no—
328C2×C4—2266no—
329C2×C4C23×D11311yescharacteristic
330C2×C4C23×D11313yes—
331C2×C4C23×D11311yescharacteristic
332C2×C4C23×D11313yes—
333C2×C4C23×D11311yescharacteristic
334C2×C4C23×D11313yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—2263no—
339C22—2263no—
340C22—2263no—
341C22—2263no—
342C22—2263no—
343C22—2263no—
344C22C24×D11311yescharacteristic
345C4—21no—
346C4—23no—
347C4—23no—
348C4—21no—
349C4—21no—
350C4—1132no—
351C4—2261no—
352C4—2261no—
353C4—2263no—
354C4—2263no—
355C4—2261no—
356C4C2×#1426864716yes—
357C2—43no—
358C2—4523no—
359C2—4523no—
360C2C22×#1426864711yescharacteristic
361C2H(5,𝔽2)×D11311yescharacteristic
362C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#520×C113C2
hypercenter#520D113
hypocenterC113#3517
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
2. #20299298C2semidirect
3. #20299296C2semidirect
4. #20299270C2semidirect
5. #20299269C2semidirect
6. #20299267C2semidirect
7. #20299267C2semidirect
8. #20299249C2semidirect
9. #20299203C2semidirect
10. #20299199C2semidirect
11. #20299145C2semidirect
12. #20299126C2semidirect
13. #20299080C2semidirect
14. C4×#14268648C2semidirect
15. #520×C113C2semidirect
123. Q8×C113#41semidirect
182. C113#3517semidirect
196. #520D113semidirect
306. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202992982
#202992962
#202992702
#202992692
#202992672
#202992492
#202992032
#202991992
#202991452
#202991262
#202990802
C4×#142686482
#520×C1132
#3517113