Finite Group Databasebeta

← #28404164

Subgroups — #28404164

Order 14464.

1112 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#20299330C213yesmaximal, complemented
2#20299324C211yesmaximal, characteristic, complemented
3#20299319C213yesmaximal, complemented
4#20299300C213yesmaximal, complemented
5#20299294C213yesmaximal, complemented
6#20299267C211yesmaximal, characteristic, complemented
7#20299259C211yesmaximal, characteristic, complemented
8#20299143C213yesmaximal, complemented
9#20299134C213yesmaximal, complemented
10#20299127C213yesmaximal, complemented
11#41×Dic113C211yesmaximal, characteristic, complemented
12C4×#14268648C211yesmaximal, characteristic, complemented
13C4×#14268646C213yesmaximal, complemented
14C2×Q8×Dic113C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2213yes—
18#16813621C2213yes—
19#16813618C2213yes—
20#16813617C2216yes—
21#16813615C2216yes—
22#16813614C2213yes—
23#16813613C2213yes—
24#16813611C2213yes—
25#16813608C2216yes—
26#16813606C2216yes—
27#16813604C2216yes—
28#16813598C2213yes—
29#16813596C2213yes—
30#16813596C2213yes—
31#16813594C2216yes—
32#16813593C2213yes—
33Q8×Dic113C2211yescharacteristic
34Q8×Dic113C2213yes—
35Q8×Dic113C2211yescharacteristic
36Q8×Dic113C2213yes—
37Q8×Dic113C2211yescharacteristic
38C4×Dic226C2213yes—
39#16813587C2213yes—
40C4×D452C2213yes—
41D4×Dic113C2213yes—
42D4×Dic113C2213yes—
43D4×Dic113C2213yes—
44#16813584C2213yes—
45C4×C22⋊D113C2213yes—
46C4×C22⋊D113C2213yes—
47#16813582C2213yes—
48#16813582C2213yes—
49#16813582C2216yes—
50#16813581C2213yes—
51#16813580C2213yes—
52#16813580C2213yes—
53#16813578C2211yescharacteristic
54#16813578C2213yes—
55C2×C4⋊Dic113C2213yes—
56C2×C4×Dic113C2213yes—
57C2×C4×Dic113C2213yes—
58C42×D113C2213yes—
59C2×#41×C113C2211yescharacteristic
60C22×Q8×C113C2211yescharacteristic
61#124×C113C2213yes—
62C22⋊Q8×C113C2213yes—
63#121×C113C2213yes—
64C4×Q8×C113C2211yescharacteristic
65C4×D4×C113C2213yes—
66#14268648—24no—
67#14268646—212no—
68C2×Dic226C2313yes—
69C2×D452C2313yes—
70C2×C22⋊D113C2313yes—
71C2×C22⋊D113C2313yes—
72C2×C22⋊D113C2316yes—
73C22×Dic113C2313yes—
74C22×Dic113C2313yes—
75C22×Dic113C2313yes—
76C22×Dic113C2311yescharacteristic
77C2×C4×D113C2313yes—
78C2×C4×D113C2313yes—
79C2×C4×D113C2313yes—
80C4⋊Dic113C2313yes—
81C4⋊Dic113C2313yes—
82C4⋊Dic113C2316yes—
83C4⋊Dic113C2313yes—
84C4⋊Dic113C2313yes—
85#14268626C2311yescharacteristic
86#14268626C2313yes—
87#14268626C2311yescharacteristic
88#14268626C2313yes—
89#14268626C2316yes—
90C22⋊Dic113C2311yescharacteristic
91C22⋊Dic113C2313yes—
92C22⋊Dic113C2316yes—
93#14268624C2313yes—
94#14268624C2313yes—
95#14268624C2316yes—
96#14268624C2316yes—
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2313yes—
99C4×Dic113C2313yes—
100C4×Dic113C2311yescharacteristic
101C4×Dic113C2313yes—
102C4×Dic113C2313yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106#41×C113—24no—
107C2×Q8×C113—24no—
108C2×Q8×C113C2313yes—
109C2×Q8×C113C2311yescharacteristic
110C2×D4×C113C2313yes—
111C2×D4×C113C2313yes—
112C22×C4×C113C2313yes—
113C22×C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C4⋊C4×C113C2313yes—
116C22⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113C2313yes—
118C22⋊C4×C113C2316yes—
119C42×C113C2313yes—
120C23×C113C2413yes—
121C23×C113C2411yescharacteristic
122C22×D113C2413yes—
123Q8×C113—26no—
124Q8×C113#4114yescomplemented
125D4×C113—26no—
126D4×C113—26no—
127C2×C4×C113—26no—
128C2×C4×C113—26no—
129C2×C4×C113C2411yescharacteristic
130C2×C4×C113C2413yes—
131C2×C4×C113C2413yes—
132C2×C4×C113C2411yescharacteristic
133C2×C4×C113C2413yes—
134C22⋊D113—26no—
135C22⋊D113—26no—
136C22⋊D113—46no—
137C2×Dic113—26no—
138C2×Dic113—43no—
139C2×Dic113—43no—
140C2×Dic113#4114yescomplemented
141C2×Dic113C2411yescharacteristic
142C2×Dic113C2413yes—
143C2×Dic113C2411yescharacteristic
144C2×Dic113C2413yes—
145C2×Dic113C2413yes—
146C2×Dic113C2411yescharacteristic
147C2×Dic113C2411yescharacteristic
148D452—26no—
149C4×D113—26no—
150C4×D113—26no—
151C4×D113—43no—
152Dic226—26no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—23no—
156C22×C113—23no—
157C22×C113—23no—
158C22×C113C2×#4112yes—
159C22×C113C2511yescharacteristic
160C2×D113—23no—
161C2×D113—23no—
162C2×D113—23no—
163C4×C113—23no—
164C4×C113—21no—
165C4×C113—23no—
166C4×C113—21no—
167C4×C113C2×#4116yes—
168Dic113—23no—
169Dic113—21no—
170Dic113—23no—
171Dic113—21no—
172Dic113—23no—
173Dic113C2×#4112yes—
174Dic113C2×#4112yes—
175C2×C113—22no—
176C2×C113—43no—
177C2×C113C22×#4111yescharacteristic
178C2×C113C22×#4111yescharacteristic
179C2×C113#58511yescharacteristic
180D113—43no—
181#3480—1131nomaximal, Sylow
182C113#348011yescharacteristic, complemented, Sylow
183#559—1133no—
184#557—1131no—
185#556—1133no—
186#553—1133no—
187#553—1133no—
188#550—1131no—
189#548—1131no—
190#548D11311yescharacteristic, complemented
191#532—1133no—
192#529—1133no—
193#529—1133no—
194C4×#41—1131no—
195C4×#41—1131no—
196C4×#41—1133no—
197C2×C4×Q8—1131no—
198C2×#41—1131no—
199C2×#41—1133no—
200C2×#41C2×D11311yescharacteristic
201C22×Q8C2×D11311yescharacteristic
202C4⋊Q8—1133no—
203#127—1133no—
204#126—1136no—
205#126—1136no—
206#125—1133no—
207#125—1133no—
208#124—1133no—
209#124—1136no—
210#124C2×D11313yes—
211#123—1136no—
212#123—1136no—
213C22⋊Q8—1133no—
214C22⋊Q8C2×D11313yes—
215#121—1133no—
216#121—1136no—
217#121—1133no—
218#121—1133no—
219#121C2×D11313yes—
220C4×Q8—1131no—
221C4×Q8—1133no—
222C4×Q8—1131no—
223C4×Q8—1133no—
224C4×Q8—1131no—
225C4×Q8—1133no—
226C4×Q8—1133no—
227C4×Q8C2×D11311yescharacteristic
228C4×D4—1133no—
229C4×D4—1133no—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1133no—
233C4×D4—1133no—
234C4×D4—1133no—
235C4×D4—1133no—
236C4×D4—1136no—
237C4×D4—1133no—
238C4×D4C2×D11313yes—
239#117—1133no—
240#117—1133no—
241#117—1133no—
242#117—1131no—
243#117—1133no—
244C2×C4⋊C4—1133no—
245C2×C42—1133no—
246C2×C42—1133no—
247C2×C42—1133no—
248#41—24no—
249#41—22612no—
250#41—2264no—
251C2×Q8—24no—
252C2×Q8—1133no—
253C2×Q8C22×D11313yes—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—1136no—
256C2×D4—1133no—
257C2×D4—1133no—
258C2×D4—1133no—
259C2×D4C22×D11313yes—
260C2×D4C22×D11313yes—
261C22×C4—1131no—
262C22×C4—1133no—
263C22×C4—1133no—
264C22×C4—1133no—
265C22×C4—1133no—
266C22×C4—1133no—
267C22×C4—1133no—
268C22×C4C22×D11313yes—
269C22×C4C22×D11313yes—
270C4⋊C4—1133no—
271C4⋊C4—1133no—
272C4⋊C4—1136no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1133no—
276C4⋊C4—1133no—
277C4⋊C4—1133no—
278C4⋊C4—1133no—
279C4⋊C4—1136no—
280C4⋊C4C22×D11313yes—
281C4⋊C4C22×D11313yes—
282C22⋊C4—1131no—
283C22⋊C4—1133no—
284C22⋊C4—1136no—
285C22⋊C4—1133no—
286C22⋊C4—1136no—
287C22⋊C4—1133no—
288C22⋊C4—1136no—
289C22⋊C4C22×D11311yescharacteristic
290C22⋊C4C22×D11313yes—
291C22⋊C4C22×D11316yes—
292C42—1131no—
293C42—1131no—
294C42—1133no—
295C42—1133no—
296C42—1133no—
297C42—1133no—
298C42—1133no—
299C42—1133no—
300C42—1133no—
301C42C22×D11313yes—
302C23—1133no—
303C23C23×D11313yes—
304C23C23×D11311yescharacteristic
305Q8—26no—
306Q8—2266no—
307Q8#1426864614yescomplemented
308D4—26no—
309D4—26no—
310D4—4526no—
311D4—2266no—
312D4—2266no—
313D4—2266no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—1134no—
317C2×C4—1131no—
318C2×C4—1131no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1133no—
322C2×C4—1133no—
323C2×C4—1133no—
324C2×C4—4523no—
325C2×C4—4523no—
326C2×C4—4523no—
327C2×C4—2266no—
328C2×C4—2266no—
329C2×C4—2266no—
330C2×C4C23×D11311yescharacteristic
331C2×C4C23×D11313yes—
332C2×C4C23×D11311yescharacteristic
333C2×C4C23×D11313yes—
334C2×C4C23×D11313yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—2263no—
341C22—2263no—
342C22—2263no—
343C22#41×D11312yes—
344C22C24×D11311yescharacteristic
345C4—23no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—1132no—
350C4—1132no—
351C4—2263no—
352C4—2261no—
353C4—2263no—
354C4—2261no—
355C4—2263no—
356C4C2×#1426864616yes—
357C2—22no—
358C2—43no—
359C2—4523no—
360C2C2×#41×D11311yescharacteristic
361C2C22×#1426864611yescharacteristic
362C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#548×C113C2
hypercenter#548D113
hypocenterC113#3480
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #20299330C2semidirect
2. #20299324C2semidirect
3. #20299319C2semidirect
4. #20299300C2semidirect
5. #20299294C2semidirect
6. #20299267C2semidirect
7. #20299259C2semidirect
8. #20299143C2semidirect
9. #20299134C2semidirect
10. #20299127C2semidirect
11. #41×Dic113C2semidirect
12. C4×#14268648C2semidirect
13. C4×#14268646C2semidirect
14. C2×Q8×Dic113C2semidirect
15. #548×C113C2semidirect
124. Q8×C113#41semidirect
140. C2×Dic113#41semidirect
182. C113#3480semidirect
190. #548D113semidirect
307. Q8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202993302
#202993242
#202993192
#202993002
#202992942
#202992672
#202992592
#202991432
#202991342
#202991272
#41×Dic1132
C4×#142686482
C4×#142686462
C2×Q8×Dic1132
#548×C1132
#3480113