Finite Group Databasebeta

← #13078464

Subgroups — #13078464

Order 1408.

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#10623260C211yesmaximal, characteristic, complemented
2#10623105C211yesmaximal, characteristic
3C11×#477C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622635C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622503C211yesmaximal, characteristic, complemented
8#10622494C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622417C211yesmaximal, characteristic
13#10622416C211yesmaximal, characteristic
14#10622412C211yesmaximal, characteristic, complemented
15#10622407C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C11×C4⋊Q8C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19#66999—21no—
20Q8×Dic11C2211yescharacteristic
21#66997—21no—
22C2×#4313C2211yescharacteristic
23C2×C8×D11C2211yescharacteristic
24#66949—21no—
25#66946—21no—
26#66946C2211yescharacteristic
27#66945C2211yescharacteristic
28C4⋊C4×D11—21no—
29C4⋊C4×D11C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943C2211yescharacteristic
32#66942—21no—
33#66941C2211yescharacteristic
34C4×D44—21no—
35C4×D44C2211yescharacteristic
36#66925—21no—
37#66925C2211yescharacteristic
38#66923C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61#4343—22no—
62#4343Q814yescomplemented
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—21no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4D411yescharacteristic
85(C2×D11)⋊C4D411yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105C8×D11—22no—
106#3083—111nomaximal, Sylow
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109Q8×C11—21no—
110Q8×C11—81no—
111Q8×C11C2×Q812yes—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—24no—
126D44—21no—
127D44C2×Q812yes—
128C4×D11—24no—
129C4×D11—81no—
130C4×D11—81no—
131C4×D11—81no—
132C4×D11—81no—
133C4×D11C2×Q812yes—
134C4×D11#4112yes—
135Dic22—81no—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140#544—111no—
141#520—111no—
142#479—111no—
143#479—111no—
144#478—111no—
145#478—111no—
146#477—111no—
147#477D1111yescharacteristic, complemented
148#474—111no—
149#474—111no—
150#428—111no—
151C2×#107—111no—
152#424—111no—
153#417—111no—
154#416—111no—
155C22×C11C22×D411yescharacteristic
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11C22⋊Q812yes—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11C22×Q811yescharacteristic
169C4×C11C2×#4111yescharacteristic
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175Dic11C22⋊Q812yes—
176C2×#41—111no—
177C2×M16—111no—
178C22×C8—111no—
179C4⋊Q8—111no—
180C4⋊Q8—221no—
181C4⋊Q8C2×D1111yescharacteristic
182#125—111no—
183#125—111no—
184#125—221no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C4×Q8—111no—
188C4×Q8C2×D1111yescharacteristic
189C4×D4—111no—
190C4×D4—111no—
191C4×D4—221no—
192C4×D4—221no—
193#117—111no—
194#117—111no—
195#117—221no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199#107—111no—
200#107—111no—
201#107—111no—
202#107—111no—
203#107C2×D1111yescharacteristic
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8—111no—
210C4⋊C8C2×D1111yescharacteristic
211#103—111no—
212#103—111no—
213#103C2×D1111yescharacteristic
214#103C2×D1111yescharacteristic
215#102—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219C2×C11C2×C22⋊Q811yescharacteristic
220C2×C11#57611yescharacteristic
221C2×C11#57811yescharacteristic
222D11—22no—
223D11—42no—
224#41—114no—
225#41—222no—
226C2×Q8—21no—
227C2×Q8—221no—
228C2×Q8C22×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—221no—
231C22×C4—111no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C22⋊C4—111no—
262C22⋊C4—111no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C42—21no—
267C42—111no—
268C42—221no—
269C42—221no—
270C42C22×D1111yescharacteristic
271C11#308311yescharacteristic, complemented, Sylow
272C23—111no—
273C23—221no—
274Q8—21no—
275Q8—81no—
276Q8—881no—
277Q8Q8×D1112yes—
278D4—112no—
279D4—224no—
280D4—221no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—111no—
286C2×C4—112no—
287C2×C4—112no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—224no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4D4×D1111yescharacteristic
299C2×C4D4×D1111yescharacteristic
300C2×C4C23×D1111yescharacteristic
301C8—21no—
302C8—21no—
303C8—221no—
304C8—221no—
305C22—112no—
306C22—221no—
307C22—221no—
308C22—222no—
309C22—441no—
310C22—441no—
311C22C2×D4×D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—112no—
319C4—221no—
320C4—221no—
321C4—441no—
322C4—441no—
323C4—441no—
324C4C2×Q8×D1111yescharacteristic
325C4#41×D1111yescharacteristic
326C2—222no—
327C2—442no—
328C2D11×C22⋊Q811yescharacteristic
329C2#1062329711yescharacteristic
330C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC2×#4343C22
hypercenter#477D11
hypocenterC11#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10623260C2semidirect
3. C11×#477C2semidirect
4. #10622700C2semidirect
5. #10622635C2semidirect
6. #10622504C2semidirect
7. #10622503C2semidirect
8. #10622494C2semidirect
9. D11×#107C2semidirect
10. #10622460C2semidirect
11. #10622452C2semidirect
14. #10622412C2semidirect
15. #10622407C2semidirect
62. #4343Q8semidirect
147. #477D11semidirect
271. C11#3083semidirect

Maximal subgroups

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

subgroupindex
#106232602
#106231052
C11×#4772
#106227002
#106226352
#106225042
#106225032
#106224942
D11×#1072
#106224602
#106224522
#106224172
#106224162
#106224122
#106224072
#308311