Finite Group Databasebeta

← #28404676

Subgroups — #28404676

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#20299330C213yesmaximal, complemented
2#20299324C211yesmaximal, characteristic, complemented
3#20299312C213yesmaximal, complemented
4#20299294C213yesmaximal, complemented
5#20299290C213yesmaximal, complemented
6#20299267C211yesmaximal, characteristic, complemented
7#20299259C211yesmaximal, characteristic, complemented
8#20299221C213yesmaximal, complemented
9#20299201C213yesmaximal, complemented
10#20299130C213yesmaximal, complemented
11#20299127C213yesmaximal, complemented
12#20299081C211yesmaximal, characteristic, complemented
13#20299076C211yesmaximal, characteristic, complemented
14C4×#14268648C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17#16813621C2213yes—
18#16813618C2213yes—
19#16813617C2216yes—
20#16813615C2213yes—
21#16813615C2211yescharacteristic
22#16813614C2213yes—
23#16813613C2213yes—
24#16813613C2213yes—
25#16813611C2213yes—
26#16813609C2213yes—
27#16813608C2216yes—
28#16813606C2216yes—
29#16813604C2213yes—
30#16813604C2213yes—
31#16813604C2216yes—
32#16813602C2213yes—
33#16813598C2213yes—
34#16813596C2213yes—
35#16813596C2213yes—
36#16813594C2216yes—
37#16813593C2213yes—
38#16813593C2213yes—
39Q8×Dic113C2211yescharacteristic
40Q8×Dic113C2213yes—
41Q8×Dic113C2211yescharacteristic
42Q8×Dic113C2211yescharacteristic
43Q8×Dic113C2213yes—
44C4×Dic226C2213yes—
45C4×D452C2213yes—
46D4×Dic113C2213yes—
47D4×Dic113C2213yes—
48#16813584C2213yes—
49C4×C22⋊D113C2213yes—
50C4×C22⋊D113C2213yes—
51#16813582C2216yes—
52#16813581C2213yes—
53#16813581C2213yes—
54#16813581C2213yes—
55#16813580C2213yes—
56#16813578C2216yes—
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—
67C2×Dic226C2313yes—
68C2×D452C2313yes—
69C2×C22⋊D113C2316yes—
70C2×C22⋊D113C2313yes—
71C2×C22⋊D113C2313yes—
72C22×Dic113C2316yes—
73C2×C4×D113C2313yes—
74C2×C4×D113C2313yes—
75C2×C4×D113C2313yes—
76C4⋊Dic113C2313yes—
77C4⋊Dic113C2313yes—
78C4⋊Dic113C2313yes—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2313yes—
81C4⋊Dic113C2313yes—
82C4⋊Dic113C2313yes—
83C4⋊Dic113C2313yes—
84#14268626C2313yes—
85#14268626C2316yes—
86#14268626C2313yes—
87#14268626C2311yescharacteristic
88#14268626C2311yescharacteristic
89C22⋊Dic113C2313yes—
90C22⋊Dic113C2311yescharacteristic
91C22⋊Dic113C2313yes—
92C22⋊Dic113C2313yes—
93C22⋊Dic113C2313yes—
94C22⋊Dic113C2311yescharacteristic
95#14268624C2316yes—
96#14268624C2316yes—
97#14268624C2313yes—
98#14268624C2313yes—
99C4×Dic113C2311yescharacteristic
100C4×Dic113C2313yes—
101C4×Dic113C2313yes—
102C4×Dic113C2316yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105#41×C113—24no—
106C2×Q8×C113—24no—
107C2×Q8×C113C2313yes—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2313yes—
110C2×D4×C113C2313yes—
111C22×C4×C113C2313yes—
112C22×C4×C113C2313yes—
113C4⋊C4×C113C2313yes—
114C4⋊C4×C113C2313yes—
115C22⋊C4×C113C2316yes—
116C22⋊C4×C113C2313yes—
117C22⋊C4×C113C2311yescharacteristic
118C42×C113C2313yes—
119C23×C113C2413yes—
120C23×C113C2411yescharacteristic
121C22×D113C2413yes—
122Q8×C113—26no—
123Q8×C113#4114yes—
124D4×C113—26no—
125D4×C113—43no—
126C2×C4×C113—26no—
127C2×C4×C113—26no—
128C2×C4×C113C2411yescharacteristic
129C2×C4×C113C2413yes—
130C2×C4×C113C2413yes—
131C2×C4×C113C2411yescharacteristic
132C2×C4×C113C2413yes—
133C22⋊D113—46no—
134C22⋊D113—43no—
135C22⋊D113—43no—
136C2×Dic113—46no—
137C2×Dic113C2413yes—
138C2×Dic113C2411yescharacteristic
139C2×Dic113C2411yescharacteristic
140C2×Dic113C2411yescharacteristic
141C2×Dic113C2413yes—
142C2×Dic113C2411yescharacteristic
143C2×Dic113C2413yes—
144D452—26no—
145C4×D113—26no—
146C4×D113—43no—
147C4×D113—43no—
148Dic226—43no—
149C22×C113—21no—
150C22×C113—23no—
151C22×C113—23no—
152C22×C113—21no—
153C22×C113—23no—
154C22×C113—21no—
155C22×C113C2511yescharacteristic
156C2×D113—23no—
157C2×D113—23no—
158C2×D113—23no—
159C4×C113—21no—
160C4×C113—23no—
161C4×C113—23no—
162C4×C113—21no—
163C4×C113C2×#4116yes—
164Dic113—21no—
165Dic113—21no—
166Dic113—23no—
167Dic113—21no—
168Dic113—23no—
169Dic113—23no—
170Dic113—21no—
171C2×C113—41no—
172C2×C113—43no—
173C2×C113C22×#4111yescharacteristic
174C2×C113#58511yescharacteristic
175C2×C113#58511yescharacteristic
176D113—43no—
177#3524—1131nomaximal, Sylow
178C113#352411yescharacteristic, complemented, Sylow
179#559—1133no—
180#557—1131no—
181#555—1133no—
182#553—1133no—
183#552—1133no—
184#550—1131no—
185#548—1131no—
186#548D11311yescharacteristic, complemented
187#542—1133no—
188#540—1133no—
189#529—1133no—
190#529—1133no—
191#520—1131no—
192#519—1131no—
193C4×#41—1131no—
194C2×#41—1131no—
195C2×#41C2×D11311yescharacteristic
196C22×Q8C2×D11311yescharacteristic
197C4⋊Q8—1133no—
198#127—1133no—
199#126—1136no—
200#126—1131no—
201#126—1133no—
202#125—1133no—
203#125—1133no—
204#125—1133no—
205#124—1133no—
206#124—1133no—
207#124—1136no—
208#124C2×D11313yes—
209#123—1136no—
210#123—1133no—
211#123—1133no—
212#123—1136no—
213C22⋊Q8—1133no—
214C22⋊Q8—1133no—
215C22⋊Q8C2×D11313yes—
216#121—1133no—
217#121—1133no—
218#121—1136no—
219#121—1133no—
220#121—1133no—
221#121C2×D11313yes—
222C4×Q8—1131no—
223C4×Q8—1133no—
224C4×Q8—1131no—
225C4×Q8—1133no—
226C4×Q8—1131no—
227C4×Q8—1133no—
228C4×Q8C2×D11311yescharacteristic
229C4×D4—1133no—
230C4×D4—1133no—
231C4×D4—1133no—
232C4×D4—1133no—
233C4×D4—1133no—
234C4×D4—1136no—
235C4×D4—1133no—
236C4×D4C2×D11313yes—
237#117—1133no—
238#117—1133no—
239#117—1133no—
240#117—1133no—
241#117—1136no—
242C2×C4⋊C4—1133no—
243C2×C42—1133no—
244#41—24no—
245#41—2264no—
246C2×Q8—24no—
247C2×Q8—1133no—
248C2×Q8C22×D11313yes—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1133no—
251C2×D4—1136no—
252C2×D4—1133no—
253C2×D4—1133no—
254C2×D4C22×D11313yes—
255C2×D4C22×D11313yes—
256C22×C4—1136no—
257C22×C4—1133no—
258C22×C4—1133no—
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—1131no—
272C4⋊C4—1133no—
273C4⋊C4—1131no—
274C4⋊C4—1133no—
275C4⋊C4C22×D11313yes—
276C4⋊C4C22×D11313yes—
277C22⋊C4—1131no—
278C22⋊C4—1133no—
279C22⋊C4—1133no—
280C22⋊C4—1133no—
281C22⋊C4—1133no—
282C22⋊C4—1131no—
283C22⋊C4—1136no—
284C22⋊C4—1133no—
285C22⋊C4—1136no—
286C22⋊C4—1133no—
287C22⋊C4C22×D11316yes—
288C22⋊C4C22×D11313yes—
289C22⋊C4C22×D11311yescharacteristic
290C42—1131no—
291C42—1133no—
292C42—1133no—
293C42—1136no—
294C42—1133no—
295C42—1133no—
296C42C22×D11313yes—
297C23—1133no—
298C23C23×D11311yescharacteristic
299C23C23×D11313yes—
300Q8—26no—
301Q8—4523no—
302Q8#1426864614yes—
303D4—26no—
304D4—43no—
305D4—4526no—
306D4—4523no—
307D4—4523no—
308D4—2266no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1133no—
314C2×C4—1131no—
315C2×C4—1133no—
316C2×C4—1131no—
317C2×C4—1133no—
318C2×C4—4523no—
319C2×C4—4523no—
320C2×C4—4526no—
321C2×C4—2266no—
322C2×C4C23×D11313yes—
323C2×C4C23×D11311yescharacteristic
324C2×C4C23×D11313yes—
325C2×C4C23×D11311yescharacteristic
326C2×C4C23×D11313yes—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22—2263no—
334C22—2263no—
335C22—2263no—
336C22C24×D11311yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—2261no—
342C4—2261no—
343C4—2263no—
344C4—2261no—
345C4—2263no—
346C4—2263no—
347C4—2261no—
348C4C2×#1426864616yes—
349C2—41no—
350C2—43no—
351C2—4523no—
352C2C22×#1426864611yescharacteristic
353C2#2029943411yescharacteristic
354C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#548×C113C2
hypercenter#548D113
hypocenterC113#3524
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. #20299312C2semidirect
4. #20299294C2semidirect
5. #20299290C2semidirect
6. #20299267C2semidirect
7. #20299259C2semidirect
8. #20299221C2semidirect
9. #20299201C2semidirect
10. #20299130C2semidirect
11. #20299127C2semidirect
12. #20299081C2semidirect
13. #20299076C2semidirect
14. C4×#14268648C2semidirect
15. #548×C113C2semidirect
178. C113#3524semidirect
186. #548D113semidirect

Maximal subgroups

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

subgroupindex
#202993302
#202993242
#202993122
#202992942
#202992902
#202992672
#202992592
#202992212
#202992012
#202991302
#202991272
#202990812
#202990762
C4×#142686482
#548×C1132
#3524113