Finite Group Databasebeta

← #27204990

Subgroups — #27204990

Order 13184.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268418C211yesmaximal, characteristic, complemented
2#20268270C211yesmaximal, characteristic
3#20268099C211yesmaximal, characteristic, complemented
4#20268097C211yesmaximal, characteristic, complemented
5#20268093C211yesmaximal, characteristic, complemented
6#20268091C211yesmaximal, characteristic, complemented
7#20268085C211yesmaximal, characteristic, complemented
8#20268083C211yesmaximal, characteristic, complemented
9#20268069C211yesmaximal, characteristic, complemented
10#20267832C211yesmaximal, characteristic, complemented
11#107×D103C211yesmaximal, characteristic, complemented
12#20267816C211yesmaximal, characteristic, complemented
13#20267789C211yesmaximal, characteristic
14#20267784C211yesmaximal, characteristic
15#474×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×#13110088C2211yescharacteristic
18C2×C8×D103C2211yescharacteristic
19#15693020C2211yescharacteristic
20#15693019—21no—
21#15693013C2211yescharacteristic
22#15693012C2211yescharacteristic
23#15693011—21no—
24#15692999—21no—
25#15692997—21no—
26C4×Dic206C2211yescharacteristic
27#15692986C2211yescharacteristic
28D4×Dic103C2211yescharacteristic
29C4×C22⋊D103—21no—
30(C22⋊D103)⋊C4—21no—
31#15692979C2211yescharacteristic
32#15692978C2211yescharacteristic
33#15692977—21no—
34C2×Dic103⋊C4—21no—
35C4⋊C4×D103C2211yescharacteristic
36C4⋊C4×D103C2211yescharacteristic
37#15692955C2211yescharacteristic
38#15692954C2211yescharacteristic
39#15692954C2211yescharacteristic
40#15692954C2211yescharacteristic
41#15692953C2211yescharacteristic
42#15692952C2211yescharacteristic
43C4⋊(C103⋊C8)C2211yescharacteristic
44Dic103⋊C8C2211yescharacteristic
45Dic103⋊C8C2211yescharacteristic
46#15692946C2211yescharacteristic
47#15692946C2211yescharacteristic
48#15692944C2211yescharacteristic
49#15692944C2211yescharacteristic
50#15692942C2211yescharacteristic
51#15692942C2211yescharacteristic
52C4⋊Q8×C103C2211yescharacteristic
53C4×D4×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic
55#107×C103C2211yescharacteristic
56C4⋊C8×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59#13110104—22no—
60#13110104Q814yescomplemented
61C2×Dic206—21no—
62C2×Dic206C2311yescharacteristic
63C2×C22⋊D103—21no—
64C22×Dic103—21no—
65C22×Dic103—21no—
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68C2×C4×D103C2311yescharacteristic
69#13110088—22no—
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C8×D103—22no—
73C4⋊Dic103—21no—
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4D411yescharacteristic
86Dic103⋊C4D411yescharacteristic
87C22⋊Dic103—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4D411yescharacteristic
90(C2×D103)⋊C4D411yescharacteristic
91C4×Dic103—21no—
92C4×Dic103—21no—
93C4×Dic103—21no—
94C4×Dic103C2311yescharacteristic
95C2×Q8×C103—21no—
96C2×D4×C103C2311yescharacteristic
97C22×C4×C103—21no—
98C2×C8×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C4⋊C4×C103—21no—
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C22⋊C4×C103—21no—
105C42×C103C2311yescharacteristic
106C23×C103—21no—
107C22×D103C2×D411yescharacteristic
108Q8×C103—81no—
109D4×C103—21no—
110D4×C103C2×Q812yes—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—81no—
115C2×C4×C103C2×D411yescharacteristic
116C2×C4×C103C2×D411yescharacteristic
117C2×C4×C103C2411yescharacteristic
118C22⋊D103—24no—
119C2×Dic103—21no—
120C2×Dic103—24no—
121C2×Dic103—21no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—81no—
125C2×Dic103C2×D411yescharacteristic
126C2×Dic103C2×D411yescharacteristic
127C2×Dic103C2×D411yescharacteristic
128C4×D103—81no—
129C4×D103—81no—
130C4×D103C2×Q812yes—
131C4×D103#4112yes—
132Dic206—21no—
133Dic206—81no—
134Dic206C2×Q812yes—
135C8×C103—21no—
136C8×C103—21no—
137C103⋊C8—21no—
138C103⋊C8—21no—
139C22×C103—22no—
140C22×C103—41no—
141C22×C103—41no—
142C22×C103C22×D411yescharacteristic
143C2×D103—21no—
144C2×D103—21no—
145C2×D103C22⋊Q812yes—
146C4×C103—21no—
147C4×C103—21no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—41no—
151C4×C103C22×Q811yescharacteristic
152C4×C103C2×#4111yescharacteristic
153Dic103—22no—
154Dic103—21no—
155Dic103—21no—
156Dic103—41no—
157Dic103—41no—
158Dic103—41no—
159Dic103C22⋊Q812yes—
160C2×C103—42no—
161C2×C103C2×C22⋊Q811yescharacteristic
162C2×C103#57611yescharacteristic
163C2×C103#57811yescharacteristic
164D103—22no—
165#3083—1031nomaximal, Sylow
166C103#308311yescharacteristic, complemented, Sylow
167#544—1031no—
168#520—1031no—
169#479—1031no—
170#479—1031no—
171#478—1031no—
172#478—1031no—
173#477—1031no—
174#477—1031no—
175#474—1031no—
176#474D10311yescharacteristic, complemented
177#428—1031no—
178C2×#107—1031no—
179#424—1031no—
180#417—1031no—
181#416—1031no—
182C2×#41—1031no—
183C2×M16—1031no—
184C22×C8—1031no—
185C4⋊Q8—1031no—
186C4⋊Q8—2061no—
187C4⋊Q8C2×D10311yescharacteristic
188#125—1031no—
189#125—1031no—
190#125—2061no—
191C22⋊Q8—2061no—
192C22⋊Q8—2061no—
193C4×Q8—1031no—
194C4×Q8—1031no—
195C4×D4—1031no—
196C4×D4—2061no—
197C4×D4—2061no—
198C4×D4C2×D10311yescharacteristic
199#117—1031no—
200#117—1031no—
201#117—2061no—
202C2×C4⋊C4—1031no—
203C2×C4⋊C4—1031no—
204C2×C4⋊C4—2061no—
205#107—1031no—
206#107—1031no—
207#107—1031no—
208#107—1031no—
209#107C2×D10311yescharacteristic
210#107C2×D10311yescharacteristic
211#106—1031no—
212#106—1031no—
213C4⋊C8—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216C4⋊C8C2×D10311yescharacteristic
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103—1031no—
221#102—1031no—
222#102—1031no—
223#102C2×D10311yescharacteristic
224#102C2×D10311yescharacteristic
225#41—1034no—
226#41—2062no—
227C2×Q8—21no—
228C2×Q8—1031no—
229C2×Q8—2061no—
230C2×D4—2061no—
231C2×D4C22×D10311yescharacteristic
232C22×C4—21no—
233C22×C4—1031no—
234C22×C4—2061no—
235C22×C4—2061no—
236C22×C4—2061no—
237C22×C4—2061no—
238M16—2062no—
239C2×C8—1031no—
240C2×C8—1031no—
241C2×C8—2062no—
242C2×C8C22×D10311yescharacteristic
243C2×C8C22×D10311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—1031no—
246C4⋊C4—1031no—
247C4⋊C4—1031no—
248C4⋊C4—1031no—
249C4⋊C4—1031no—
250C4⋊C4—2061no—
251C4⋊C4—2061no—
252C4⋊C4—2061no—
253C4⋊C4—2061no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4—2061no—
258C4⋊C4—2061no—
259C4⋊C4C22×D10311yescharacteristic
260C4⋊C4C22×D10311yescharacteristic
261C4⋊C4C22×D10311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—1031no—
264C22⋊C4—1031no—
265C22⋊C4—2061no—
266C22⋊C4—2061no—
267C42—1031no—
268C42—2061no—
269C42—2061no—
270C42—2061no—
271C42C22×D10311yescharacteristic
272C23—21no—
273C23—1031no—
274Q8—81no—
275Q8—8241no—
276Q8—1032no—
277Q8—2061no—
278D4—21no—
279D4—2064no—
280D4Q8×D10312yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—8241no—
286C2×C4—8241no—
287C2×C4—8241no—
288C2×C4—1031no—
289C2×C4—1032no—
290C2×C4—1032no—
291C2×C4—1031no—
292C2×C4—1031no—
293C2×C4—2064no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4—2061no—
298C2×C4D4×D10311yescharacteristic
299C2×C4D4×D10311yescharacteristic
300C2×C4C23×D10311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2061no—
304C8—2061no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—1032no—
309C22—2061no—
310C22—2061no—
311C22C2×D4×D10311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—1032no—
318C4—4121no—
319C4—4121no—
320C4—4121no—
321C4—2061no—
322C4—2061no—
323C4—2062no—
324C4C2×Q8×D10311yescharacteristic
325C4#41×D10311yescharacteristic
326C2—42no—
327C2—2062no—
328C2C22⋊Q8×D10311yescharacteristic
329C2#2026859211yescharacteristic
330C2#2026860711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#474×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110104C22
hypercenter#474D103
hypocenterC103#3083
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20268418C2semidirect
3. #20268099C2semidirect
4. #20268097C2semidirect
5. #20268093C2semidirect
6. #20268091C2semidirect
7. #20268085C2semidirect
8. #20268083C2semidirect
9. #20268069C2semidirect
10. #20267832C2semidirect
11. #107×D103C2semidirect
12. #20267816C2semidirect
15. #474×C103C2semidirect
60. #13110104Q8semidirect
166. C103#3083semidirect
176. #474D103semidirect

Maximal subgroups

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

subgroupindex
#202684182
#202682702
#202680992
#202680972
#202680932
#202680912
#202680852
#202680832
#202680692
#202678322
#107×D1032
#202678162
#202677892
#202677842
#474×C1032
#3083103