Finite Group Databasebeta

← #28404672

Subgroups — #28404672

Order 14464.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299334C213yesmaximal, complemented
2#20299324C211yesmaximal, characteristic, complemented
3#20299312C213yesmaximal, complemented
4#20299300C213yesmaximal, complemented
5#20299288C213yesmaximal, complemented
6#20299255C211yesmaximal, characteristic, complemented
7#20299255C211yesmaximal, characteristic, complemented
8#20299215C213yesmaximal, complemented
9#20299202C213yesmaximal, complemented
10#20299129C213yesmaximal, complemented
11#20299128C213yesmaximal, complemented
12#20299081C211yesmaximal, characteristic, complemented
13#20299074C211yesmaximal, characteristic, complemented
14#41×Dic113C211yesmaximal, characteristic, complemented
15#550×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17#16813621C2213yes—
18#16813617C2211yescharacteristic
19#16813615C2216yes—
20#16813615C2213yes—
21#16813614C2213yes—
22#16813613C2213yes—
23#16813612C2213yes—
24#16813609C2216yes—
25#16813609C2213yes—
26#16813609C2213yes—
27#16813608C2213yes—
28#16813606C2213yes—
29#16813603C2216yes—
30#16813603C2213yes—
31#16813603C2216yes—
32#16813601C2213yes—
33#16813601C2213yes—
34#16813599C2213yes—
35#16813594C2216yes—
36#16813594C2213yes—
37#16813593C2213yes—
38#16813593C2213yes—
39Q8×Dic113C2211yescharacteristic
40Q8×Dic113C2211yescharacteristic
41Q8×Dic113C2211yescharacteristic
42C4×Dic226C2213yes—
43C4×Dic226C2213yes—
44#16813587C2213yes—
45D4×Dic113C2213yes—
46D4×Dic113C2216yes—
47D4×Dic113C2213yes—
48D4×Dic113C2213yes—
49D4×Dic113C2213yes—
50C4×C22⋊D113C2213yes—
51C4×C22⋊D113C2213yes—
52#16813581C2213yes—
53#16813581C2213yes—
54#16813580C2213yes—
55#16813579C2213yes—
56#16813578C2216yes—
57C2×C4⋊Dic113C2213yes—
58C2×C4×Dic113C2213yes—
59C2×#41×C113C2211yescharacteristic
60C2×#41×C113C2211yescharacteristic
61#127×C113C2213yes—
62#121×C113C2213yes—
63#121×C113C2213yes—
64C4×Q8×C113C2211yescharacteristic
65C4×D4×C113C2213yes—
66C2×Dic226C2313yes—
67C2×Dic226C2313yes—
68Q8×D113—24no—
69C2×C22⋊D113C2313yes—
70C2×C22⋊D113C2313yes—
71C22×Dic113C2313yes—
72C22×Dic113C2313yes—
73C22×Dic113C2316yes—
74C2×C4×D113C2313yes—
75C4⋊Dic113C2313yes—
76C4⋊Dic113C2313yes—
77C4⋊Dic113C2313yes—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2313yes—
80C4⋊Dic113C2313yes—
81#14268626C2313yes—
82#14268626C2316yes—
83#14268626C2313yes—
84#14268626C2313yes—
85#14268626C2313yes—
86#14268626C2311yescharacteristic
87#14268626C2313yes—
88C22⋊Dic113C2316yes—
89C22⋊Dic113C2313yes—
90C22⋊Dic113C2316yes—
91C22⋊Dic113C2313yes—
92C22⋊Dic113C2313yes—
93C22⋊Dic113C2313yes—
94C22⋊Dic113C2316yes—
95#14268624C2311yescharacteristic
96#14268624C2313yes—
97#14268624C2311yescharacteristic
98#14268624C2311yescharacteristic
99C4×Dic113C2311yescharacteristic
100C4×Dic113C2313yes—
101C4×Dic113C2313yes—
102C4×Dic113C2313yes—
103C4×Dic113C2316yes—
104C4×Dic113C2313yes—
105#41×C113—24no—
106#41×C113—24no—
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113C2313yes—
109C2×D4×C113C2313yes—
110C2×D4×C113C2316yes—
111C2×D4×C113C2313yes—
112C22×C4×C113C2313yes—
113C22×C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113C2313yes—
117C22⋊C4×C113C2313yes—
118C42×C113C2313yes—
119C23×C113C2413yes—
120C23×C113C2413yes—
121C22×D113C2411yescharacteristic
122Q8×C113#4114yes—
123D4×C113—26no—
124D4×C113—26no—
125D4×C113—46no—
126D4×C113—43no—
127C2×C4×C113—26no—
128C2×C4×C113—26no—
129C2×C4×C113C2411yescharacteristic
130C2×C4×C113C2413yes—
131C2×C4×C113C2411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C2×C4×C113C2413yes—
134C22⋊D113—43no—
135C22⋊D113—43no—
136C2×Dic113—43no—
137C2×Dic113—43no—
138C2×Dic113—46no—
139C2×Dic113C2411yescharacteristic
140C2×Dic113C2411yescharacteristic
141C2×Dic113C2413yes—
142C2×Dic113C2411yescharacteristic
143C2×Dic113C2413yes—
144C2×Dic113C2413yes—
145C2×Dic113C2413yes—
146C4×D113—26no—
147Dic226—26no—
148Dic226—43no—
149C22×C113—23no—
150C22×C113—23no—
151C22×C113—23no—
152C22×C113—23no—
153C22×C113—23no—
154C22×C113—23no—
155C22×C113C2511yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—23no—
162C4×C113—21no—
163C4×C113C2×#4116yes—
164Dic113—23no—
165Dic113—21no—
166Dic113—23no—
167Dic113—21no—
168Dic113—21no—
169Dic113—23no—
170Dic113—23no—
171C2×C113—43no—
172C2×C113—43no—
173C2×C113C22×#4111yescharacteristic
174C2×C113#58511yescharacteristic
175C2×C113#58511yescharacteristic
176D113—41no—
177#3524—1131nomaximal, Sylow
178C113#352411yescharacteristic, complemented, Sylow
179#559—1133no—
180#557—1131no—
181#555—1133no—
182#553—1133no—
183#552—1133no—
184#550D11311yescharacteristic, complemented
185#548—1131no—
186#548—1131no—
187#542—1133no—
188#540—1133no—
189#529—1133no—
190#529—1133no—
191#520—1131no—
192#519—1131no—
193C4×#41—1131no—
194C2×#41C2×D11311yescharacteristic
195C2×#41C2×D11311yescharacteristic
196C22×Q8—1131no—
197C4⋊Q8—1133no—
198#127C2×D11313yes—
199#126—1131no—
200#126—1133no—
201#126—1136no—
202#125—1133no—
203#125—1133no—
204#125—1133no—
205#124—1133no—
206#124—1133no—
207#124—1136no—
208#124—1133no—
209#123—1136no—
210#123—1133no—
211#123—1136no—
212#123—1133no—
213C22⋊Q8—1133no—
214C22⋊Q8—1133no—
215C22⋊Q8—1133no—
216#121—1133no—
217#121—1133no—
218#121—1133no—
219#121—1136no—
220#121C2×D11313yes—
221#121C2×D11313yes—
222C4×Q8—1131no—
223C4×Q8—1131no—
224C4×Q8—1131no—
225C4×Q8—1133no—
226C4×Q8—1133no—
227C4×Q8—1133no—
228C4×Q8C2×D11311yescharacteristic
229C4×D4—1133no—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1133no—
233C4×D4—1136no—
234C4×D4—1133no—
235C4×D4—1133no—
236C4×D4C2×D11313yes—
237#117—1133no—
238#117—1133no—
239#117—1133no—
240#117—1136no—
241#117—1133no—
242C2×C4⋊C4—1133no—
243C2×C42—1133no—
244#41—24no—
245#41—24no—
246C2×Q8—1133no—
247C2×Q8—1133no—
248C2×Q8—2264no—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1133no—
251C2×D4—1133no—
252C2×D4C22×D11313yes—
253C2×D4C22×D11313yes—
254C2×D4C22×D11316yes—
255C2×D4C22×D11313yes—
256C22×C4—1133no—
257C22×C4—1133no—
258C22×C4—1136no—
259C22×C4—1133no—
260C22×C4C22×D11313yes—
261C22×C4C22×D11313yes—
262C4⋊C4—1133no—
263C4⋊C4—1133no—
264C4⋊C4—1133no—
265C4⋊C4—1131no—
266C4⋊C4—1133no—
267C4⋊C4—1133no—
268C4⋊C4—1133no—
269C4⋊C4—1133no—
270C4⋊C4—1136no—
271C4⋊C4—1133no—
272C4⋊C4—1133no—
273C4⋊C4—1131no—
274C4⋊C4—1133no—
275C4⋊C4C22×D11313yes—
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—1133no—
278C22⋊C4—1136no—
279C22⋊C4—1133no—
280C22⋊C4—1136no—
281C22⋊C4—1133no—
282C22⋊C4—1136no—
283C22⋊C4—1133no—
284C22⋊C4—1131no—
285C22⋊C4—1133no—
286C22⋊C4—1131no—
287C22⋊C4—1131no—
288C22⋊C4C22×D11313yes—
289C22⋊C4C22×D11313yes—
290C42—1131no—
291C42—1133no—
292C42—1133no—
293C42—1133no—
294C42—1136no—
295C42—1133no—
296C42C22×D11313yes—
297C23—1131no—
298C23C23×D11313yes—
299C23C23×D11313yes—
300Q8—4523no—
301Q8—2266no—
302Q8#1426864614yes—
303D4—26no—
304D4—26no—
305D4—46no—
306D4—43no—
307D4—4523no—
308D4—4523no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1133no—
314C2×C4—1131no—
315C2×C4—1133no—
316C2×C4—1133no—
317C2×C4—1133no—
318C2×C4—4523no—
319C2×C4—4523no—
320C2×C4—4526no—
321C2×C4—2266no—
322C2×C4C23×D11311yescharacteristic
323C2×C4C23×D11313yes—
324C2×C4C23×D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C2×C4C23×D11313yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—23no—
331C22—23no—
332C22—23no—
333C22—2261no—
334C22—2261no—
335C22—2261no—
336C22C24×D11311yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—21no—
341C4—2263no—
342C4—2261no—
343C4—2263no—
344C4—2261no—
345C4—2261no—
346C4—2263no—
347C4—2263no—
348C4C2×#1426864616yes—
349C2—43no—
350C2—43no—
351C2—4521no—
352C2C22×#1426864611yescharacteristic
353C2#2029943311yescharacteristic
354C2#2029943411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#550×C113C2
hypercenter#550D113
hypocenterC113#3524
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #20299334C2semidirect
2. #20299324C2semidirect
3. #20299312C2semidirect
4. #20299300C2semidirect
5. #20299288C2semidirect
6. #20299255C2semidirect
7. #20299255C2semidirect
8. #20299215C2semidirect
9. #20299202C2semidirect
10. #20299129C2semidirect
11. #20299128C2semidirect
12. #20299081C2semidirect
13. #20299074C2semidirect
14. #41×Dic113C2semidirect
15. #550×C113C2semidirect
178. C113#3524semidirect
184. #550D113semidirect

Maximal subgroups

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

subgroupindex
#202993342
#202993242
#202993122
#202993002
#202992882
#202992552
#202992152
#202992022
#202991292
#202991282
#202990812
#202990742
#41×Dic1132
#550×C1132
#3524113