Finite Group Databasebeta

← #27209254

Subgroups — #27209254

Order 13184.

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#20268523C213yesmaximal, complemented
2#20268520C211yesmaximal, characteristic, complemented
3#20268506C213yesmaximal, complemented
4#20268488C213yesmaximal, complemented
5#20268475C213yesmaximal, complemented
6#20268460C211yesmaximal, characteristic, complemented
7#20268452C211yesmaximal, characteristic, complemented
8#20268410C213yesmaximal, complemented
9#20268394C213yesmaximal, complemented
10#20268327C213yesmaximal, complemented
11#20268321C213yesmaximal, complemented
12#20268273C211yesmaximal, characteristic, complemented
13#20268269C211yesmaximal, characteristic, complemented
14#41×Dic103C211yesmaximal, characteristic, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17#15693021C2213yes—
18#15693017C2213yes—
19#15693016C2213yes—
20#15693014C2211yescharacteristic
21#15693014C2216yes—
22#15693012C2213yes—
23#15693012C2213yes—
24#15693011C2213yes—
25#15693010C2213yes—
26#15693007C2213yes—
27#15693007C2216yes—
28#15693005C2213yes—
29#15693005C2216yes—
30#15693003C2216yes—
31#15693002C2213yes—
32#15692998C2213yes—
33#15692997C2213yes—
34#15692995C2213yes—
35#15692995C2213yes—
36#15692993C2213yes—
37#15692992C2216yes—
38#15692992C2213yes—
39Q8×Dic103C2213yes—
40Q8×Dic103C2211yescharacteristic
41Q8×Dic103C2211yescharacteristic
42Q8×Dic103C2213yes—
43Q8×Dic103C2211yescharacteristic
44C4×Dic206C2213yes—
45C4×D412C2213yes—
46D4×Dic103C2213yes—
47D4×Dic103C2213yes—
48#15692983C2213yes—
49C4×C22⋊D103C2213yes—
50C4×C22⋊D103C2213yes—
51(C22⋊D103)⋊C4C2216yes—
52#15692980C2213yes—
53#15692980C2213yes—
54#15692980C2213yes—
55#15692979C2216yes—
56#15692978C2213yes—
57C4⋊C4×D103C2213yes—
58C2×C4×Dic103C2213yes—
59C2×#41×C103C2211yescharacteristic
60C22×Q8×C103C2211yescharacteristic
61#124×C103C2213yes—
62C22⋊Q8×C103C2213yes—
63#121×C103C2213yes—
64C4×Q8×C103C2211yescharacteristic
65C4×D4×C103C2213yes—
66#13110106—24no—
67C2×Dic206C2313yes—
68C2×D412C2313yes—
69C2×C22⋊D103C2316yes—
70C2×C22⋊D103C2313yes—
71C2×C22⋊D103C2313yes—
72C22×Dic103C2313yes—
73C22×Dic103C2313yes—
74C2×C4×D103C2313yes—
75C2×C4×D103C2316yes—
76C4⋊Dic103C2313yes—
77C4⋊Dic103C2316yes—
78C4⋊Dic103C2313yes—
79C4⋊Dic103C2313yes—
80C4⋊Dic103C2313yes—
81C4⋊Dic103C2313yes—
82C4⋊Dic103C2311yescharacteristic
83Dic103⋊C4C2313yes—
84Dic103⋊C4C2311yescharacteristic
85Dic103⋊C4C2313yes—
86Dic103⋊C4C2311yescharacteristic
87Dic103⋊C4C2313yes—
88Dic103⋊C4C2313yes—
89C22⋊Dic103C2313yes—
90C22⋊Dic103C2311yescharacteristic
91C22⋊Dic103C2316yes—
92C22⋊Dic103C2311yescharacteristic
93C22⋊Dic103C2313yes—
94(C2×D103)⋊C4C2313yes—
95(C2×D103)⋊C4C2313yes—
96(C2×D103)⋊C4C2313yes—
97(C2×D103)⋊C4C2316yes—
98(C2×D103)⋊C4C2313yes—
99C4×Dic103C2311yescharacteristic
100C4×Dic103C2313yes—
101C4×Dic103C2313yes—
102C4×Dic103C2313yes—
103C4×Dic103C2316yes—
104C4×Dic103C2313yes—
105#41×C103—24no—
106C2×Q8×C103—24no—
107C2×Q8×C103C2313yes—
108C2×Q8×C103C2311yescharacteristic
109C2×D4×C103C2313yes—
110C2×D4×C103C2313yes—
111C22×C4×C103C2313yes—
112C22×C4×C103C2313yes—
113C4⋊C4×C103C2313yes—
114C4⋊C4×C103C2313yes—
115C22⋊C4×C103C2311yescharacteristic
116C22⋊C4×C103C2313yes—
117C22⋊C4×C103C2316yes—
118C42×C103C2313yes—
119C23×C103C2413yes—
120C23×C103C2411yescharacteristic
121C22×D103C2413yes—
122Q8×C103—26no—
123Q8×C103#4114yes—
124D4×C103—26no—
125D4×C103—43no—
126C2×C4×C103—26no—
127C2×C4×C103—26no—
128C2×C4×C103C2411yescharacteristic
129C2×C4×C103C2413yes—
130C2×C4×C103C2413yes—
131C2×C4×C103C2411yescharacteristic
132C2×C4×C103C2413yes—
133C22⋊D103—43no—
134C22⋊D103—46no—
135C22⋊D103—43no—
136C2×Dic103—43no—
137C2×Dic103—43no—
138C2×Dic103C2411yescharacteristic
139C2×Dic103C2411yescharacteristic
140C2×Dic103C2413yes—
141C2×Dic103C2413yes—
142C2×Dic103C2411yescharacteristic
143C2×Dic103C2413yes—
144C2×Dic103C2411yescharacteristic
145D412—26no—
146C4×D103—26no—
147C4×D103—46no—
148Dic206—43no—
149C22×C103—21no—
150C22×C103—23no—
151C22×C103—23no—
152C22×C103—23no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103C2511yescharacteristic
156C2×D103—23no—
157C2×D103—23no—
158C2×D103—23no—
159C4×C103—21no—
160C4×C103—23no—
161C4×C103—21no—
162C4×C103—23no—
163C4×C103C2×#4116yes—
164Dic103—21no—
165Dic103—23no—
166Dic103—23no—
167Dic103—23no—
168Dic103—21no—
169Dic103—21no—
170Dic103—21no—
171C2×C103—41no—
172C2×C103—43no—
173C2×C103C22×#4111yescharacteristic
174C2×C103#58511yescharacteristic
175C2×C103#58511yescharacteristic
176D103—43no—
177#3524—1031nomaximal, Sylow
178C103#352411yescharacteristic, complemented, Sylow
179#559—1033no—
180#557—1031no—
181#555—1033no—
182#553—1033no—
183#552—1033no—
184#550—1031no—
185#548—1031no—
186#548D10311yescharacteristic, complemented
187#542—1033no—
188#540—1033no—
189#529—1033no—
190#529—1033no—
191#520—1031no—
192#519—1031no—
193C4×#41—1031no—
194C2×#41—1031no—
195C2×#41C2×D10311yescharacteristic
196C22×Q8C2×D10311yescharacteristic
197C4⋊Q8—1033no—
198#127—1033no—
199#126—1033no—
200#126—1031no—
201#126—1036no—
202#125—1033no—
203#125—1033no—
204#125—1033no—
205#124—1033no—
206#124—1033no—
207#124—1036no—
208#124C2×D10313yes—
209#123—1033no—
210#123—1036no—
211#123—1033no—
212#123—1036no—
213C22⋊Q8—1033no—
214C22⋊Q8—1033no—
215C22⋊Q8C2×D10313yes—
216#121—1033no—
217#121—1036no—
218#121—1033no—
219#121—1033no—
220#121—1033no—
221#121C2×D10313yes—
222C4×Q8—1031no—
223C4×Q8—1031no—
224C4×Q8—1033no—
225C4×Q8—1031no—
226C4×Q8—1033no—
227C4×Q8—1033no—
228C4×Q8C2×D10311yescharacteristic
229C4×D4—1033no—
230C4×D4—1033no—
231C4×D4—1033no—
232C4×D4—1033no—
233C4×D4—1033no—
234C4×D4—1036no—
235C4×D4—1033no—
236C4×D4C2×D10313yes—
237#117—1033no—
238#117—1033no—
239#117—1033no—
240#117—1036no—
241#117—1033no—
242C2×C4⋊C4—1033no—
243C2×C42—1033no—
244#41—24no—
245#41—2064no—
246C2×Q8—24no—
247C2×Q8—1033no—
248C2×Q8C22×D10313yes—
249C2×Q8C22×D10311yescharacteristic
250C2×D4—1033no—
251C2×D4—1036no—
252C2×D4—1033no—
253C2×D4—1033no—
254C2×D4C22×D10313yes—
255C2×D4C22×D10313yes—
256C22×C4—1033no—
257C22×C4—1033no—
258C22×C4—1036no—
259C22×C4—1033no—
260C22×C4C22×D10313yes—
261C22×C4C22×D10313yes—
262C4⋊C4—1033no—
263C4⋊C4—1031no—
264C4⋊C4—1031no—
265C4⋊C4—1033no—
266C4⋊C4—1033no—
267C4⋊C4—1033no—
268C4⋊C4—1033no—
269C4⋊C4—1033no—
270C4⋊C4—1033no—
271C4⋊C4—1033no—
272C4⋊C4—1033no—
273C4⋊C4—1036no—
274C4⋊C4—1031no—
275C4⋊C4C22×D10313yes—
276C4⋊C4C22×D10313yes—
277C22⋊C4—1031no—
278C22⋊C4—1033no—
279C22⋊C4—1036no—
280C22⋊C4—1031no—
281C22⋊C4—1033no—
282C22⋊C4—1033no—
283C22⋊C4—1033no—
284C22⋊C4—1033no—
285C22⋊C4—1036no—
286C22⋊C4—1033no—
287C22⋊C4C22×D10316yes—
288C22⋊C4C22×D10311yescharacteristic
289C22⋊C4C22×D10313yes—
290C42—1031no—
291C42—1033no—
292C42—1033no—
293C42—1033no—
294C42—1036no—
295C42—1033no—
296C42C22×D10313yes—
297C23—1033no—
298C23C23×D10311yescharacteristic
299C23C23×D10313yes—
300Q8—26no—
301Q8—4123no—
302Q8#1311010414yes—
303D4—26no—
304D4—43no—
305D4—4123no—
306D4—4123no—
307D4—4126no—
308D4—2066no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—1031no—
312C2×C4—1033no—
313C2×C4—1031no—
314C2×C4—1033no—
315C2×C4—1031no—
316C2×C4—1033no—
317C2×C4—1031no—
318C2×C4—4126no—
319C2×C4—4123no—
320C2×C4—4123no—
321C2×C4—2066no—
322C2×C4C23×D10311yescharacteristic
323C2×C4C23×D10313yes—
324C2×C4C23×D10311yescharacteristic
325C2×C4C23×D10313yes—
326C2×C4C23×D10313yes—
327C22—21no—
328C22—23no—
329C22—23no—
330C22—21no—
331C22—23no—
332C22—21no—
333C22—2063no—
334C22—2063no—
335C22—2063no—
336C22C24×D10311yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—2061no—
342C4—2063no—
343C4—2061no—
344C4—2061no—
345C4—2061no—
346C4—2063no—
347C4—2063no—
348C4C2×#1311010416yes—
349C2—41no—
350C2—43no—
351C2—4123no—
352C2C22×#1311010411yescharacteristic
353C2#2026862711yescharacteristic
354C2#2026862811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#548×C103C2
hypercenter#548D103
hypocenterC103#3524
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #20268523C2semidirect
2. #20268520C2semidirect
3. #20268506C2semidirect
4. #20268488C2semidirect
5. #20268475C2semidirect
6. #20268460C2semidirect
7. #20268452C2semidirect
8. #20268410C2semidirect
9. #20268394C2semidirect
10. #20268327C2semidirect
11. #20268321C2semidirect
12. #20268273C2semidirect
13. #20268269C2semidirect
14. #41×Dic103C2semidirect
15. #548×C103C2semidirect
178. C103#3524semidirect
186. #548D103semidirect

Maximal subgroups

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

subgroupindex
#202685232
#202685202
#202685062
#202684882
#202684752
#202684602
#202684522
#202684102
#202683942
#202683272
#202683212
#202682732
#202682692
#41×Dic1032
#548×C1032
#3524103