Finite Group Databasebeta

← #13081380

Subgroups — #13081380

Order 1408.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623100C211yesmaximal, characteristic, complemented
2#10623090C211yesmaximal, characteristic
3C4×C11×SD16C211yesmaximal, characteristic, complemented
4#10622779C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic
6#10622641C211yesmaximal, characteristic, complemented
7#10622622C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622430C211yesmaximal, characteristic, complemented
11#10622402C211yesmaximal, characteristic, complemented
12#10622378C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic
14#10622310C211yesmaximal, characteristic, complemented
15#10622292C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66989C2211yescharacteristic
25#66982—21no—
26C4×C22⋊D11—21no—
27#66946C2211yescharacteristic
28#66943—21no—
29#66943C2211yescharacteristic
30#66941—21no—
31#66941C2211yescharacteristic
32#66940C2211yescharacteristic
33#66938—21no—
34#66936—21no—
35#66928C2211yescharacteristic
36#66923—21no—
37#66923C2211yescharacteristic
38C4×Dic22—21no—
39C4×Dic22C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C4×C8×C11C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×Dic22—21no—
67C2×Dic22D411yescharacteristic
68C2×Dic22C2311yescharacteristic
69C11×SD16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80#4326—22no—
81#4325—22no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3371—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108Q8×C11—21no—
109Q8×C11#4112yes—
110D4×C11—21no—
111D4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—81no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—42no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44—21no—
130C4×D11—81no—
131Dic22—21no—
132Dic22—21no—
133Dic22—41no—
134Dic22—42no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#559—111no—
140#557—111no—
141#490—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#476—111no—
147#464—111no—
148#464—111no—
149#460—111no—
150#446—111no—
151#441—111no—
152#440—111no—
153C4×SD16D1111yescharacteristic, complemented
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C2×D11—41no—
159C2×D11—41no—
160C2×D11—41no—
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11C2×#4111yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×Q16—111no—
176C2×SD16—111no—
177C2×SD16C2×D1111yescharacteristic
178C4⋊Q8—111no—
179C4⋊Q8—221no—
180#127—111no—
181#125—111no—
182#125—111no—
183#125—221no—
184#125—221no—
185#124—111no—
186#124—111no—
187#124—221no—
188#123—221no—
189#123—221no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—221no—
195C4×Q8C2×D1111yescharacteristic
196C4×D4—111no—
197C4×D4—221no—
198C4×D4C2×D1111yescharacteristic
199#107—111no—
200#106—111no—
201#106C2×D1111yescharacteristic
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103C2×D1111yescharacteristic
209#102—111no—
210#102—111no—
211#102—111no—
212#102—111no—
213#102—111no—
214#102C2×D1111yescharacteristic
215#97—111no—
216#97—111no—
217C4×C8C2×D1111yescharacteristic
218C2×C11—81no—
219C2×C11#54811yescharacteristic
220C2×C11#57511yescharacteristic
221C2×C11#57711yescharacteristic
222D11—81no—
223C2×Q8—111no—
224C2×Q8—111no—
225C2×Q8—221no—
226C2×Q8C22×D1111yescharacteristic
227C2×D4—111no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—21no—
232C22×C4—221no—
233Q16—222no—
234SD16—22no—
235SD16—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C42—21no—
263C42—111no—
264C42—111no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42C22×D1111yescharacteristic
269C11#337111yescharacteristic, complemented, Sylow
270C23—21no—
271C23—221no—
272Q8—21no—
273Q8—221no—
274Q8—221no—
275Q8—441no—
276Q8—442no—
277Q8#433912yes—
278D4—21no—
279D4—21no—
280D4—221no—
281D4—221no—
282D4—442no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—881no—
296C2×C4D4×D1111yescharacteristic
297C2×C4D4×D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—221no—
302C8—221no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22C2×D4×D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—221no—
316C4—221no—
317C4—221no—
318C4—221no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4C2×#433911yescharacteristic
323C4#6704311yescharacteristic
324C2—81no—
325C2—881no—
326C2#1062308311yescharacteristic
327C2#1062329311yescharacteristic
328C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radical#66993C22
hypercenterC4×SD16D11
hypocenterC11#3371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10623100C2semidirect
3. C4×C11×SD16C2semidirect
4. #10622779C2semidirect
6. #10622641C2semidirect
7. #10622622C2semidirect
8. #10622483C2semidirect
9. #10622470C2semidirect
10. #10622430C2semidirect
11. #10622402C2semidirect
12. #10622378C2semidirect
14. #10622310C2semidirect
15. #10622292C2semidirect
153. C4×SD16D11semidirect
269. C11#3371semidirect

Maximal subgroups

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

subgroupindex
#106231002
#106230902
C4×C11×SD162
#106227792
#106227762
#106226412
#106226222
#106224832
#106224702
#106224302
#106224022
#106223782
#106223772
#106223102
#106222922
#337111