Finite Group Databasebeta

← #13081095

Subgroups — #13081095

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#554C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic
3#10622700C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622662C211yesmaximal, characteristic, complemented
6#10622661C211yesmaximal, characteristic, complemented
7#10622658C211yesmaximal, characteristic, complemented
8#10622657C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10#10622635C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622581C211yesmaximal, characteristic, complemented
13#10622580C211yesmaximal, characteristic, complemented
14#10622577C211yesmaximal, characteristic, complemented
15C2×#66871C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125—21no—
18C11×C22⋊Q8—21no—
19C11×C22⋊Q8—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11—21no—
24C4×D4×C11C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66992—21no—
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66951—21no—
36#66936—21no—
37(C22⋊D11)⋊C4—21no—
38C4×D44C2211yescharacteristic
39#66923C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11D411yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88#4325—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3346—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—81no—
112D4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—81no—
134D44—21no—
135D44—21no—
136C4×D11—81no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8#4112yes—
141#554D1111yescharacteristic, complemented
142#553—111no—
143#501—111no—
144#485—111no—
145#484—111no—
146#481—111no—
147#480—111no—
148#479—111no—
149#474—111no—
150#468—111no—
151#465—111no—
152#440—111no—
153#435—111no—
154#428—111no—
155C2×#107—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#13712yes—
162C22×C11C22×D411yescharacteristic
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×SD16—111no—
180C2×M16—111no—
181C22×C8—111no—
182C4⋊Q8C2×D1111yescharacteristic
183#126—221no—
184#125—21no—
185#125—111no—
186#123—221no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8C2×D1111yescharacteristic
190C22⋊Q8C2×D1111yescharacteristic
191#121—111no—
192#121—111no—
193#121—221no—
194C4×Q8C2×D1111yescharacteristic
195C4×D4—21no—
196C4×D4—111no—
197C4×D4—221no—
198C4×D4C2×D1111yescharacteristic
199#117—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4C2×D1111yescharacteristic
202C2×C4⋊C4C2×D1111yescharacteristic
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#106—111no—
210#106—111no—
211#106—111no—
212C4⋊C8—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219C22⋊C8—111no—
220C22⋊C8—111no—
221#97—111no—
222C2×C11—22no—
223C2×C11—41no—
224C2×C11#54711yescharacteristic
225C2×C11C2×#13711yescharacteristic
226C2×C11#57611yescharacteristic
227D11—81no—
228C2×Q8—21no—
229C2×Q8C22×D1111yescharacteristic
230C2×D4—111no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4C22⋊D1111yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4C22×D1111yescharacteristic
239C22×C4C22×D1111yescharacteristic
240SD16—222no—
241M16—222no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22⋊D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4C22⋊D1111yescharacteristic
270C22⋊C4C22⋊D1111yescharacteristic
271C42—21no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#334611yescharacteristic, complemented, Sylow
275C23—221no—
276C23C2×C22⋊D1111yescharacteristic
277C23C2×C22⋊D1111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—221no—
283D4—221no—
284D4—442no—
285D4—881no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×C22⋊D1111yescharacteristic
302C2×C4C2×C22⋊D1111yescharacteristic
303C2×C4C2×C22⋊D1111yescharacteristic
304C2×C4C2×C22⋊D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—112no—
307C8—221no—
308C8—221no—
309C8—221no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22#6699512yes—
319C22C22×C22⋊D1111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4#41×D1111yescharacteristic
332C4#6704311yescharacteristic
333C2—22no—
334C2—41no—
335C2—881no—
336C2C2×#6699511yescharacteristic
337C2#1062335511yescharacteristic
338C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#554C2
socleC22×C11C22×D4
prime radical#10623096C2
hypercenter#554D11
hypocenterC11#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C11×#554C2semidirect
3. #10622700C2semidirect
4. #10622693C2semidirect
5. #10622662C2semidirect
6. #10622661C2semidirect
7. #10622658C2semidirect
8. #10622657C2semidirect
9. #10622639C2semidirect
10. #10622635C2semidirect
11. #10622624C2semidirect
12. #10622581C2semidirect
13. #10622580C2semidirect
14. #10622577C2semidirect
15. C2×#66871C2semidirect
141. #554D11semidirect
274. C11#3346semidirect

Maximal subgroups

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

subgroupindex
C11×#5542
#106230962
#106227002
#106226932
#106226622
#106226612
#106226582
#106226572
#106226392
#106226352
#106226242
#106225812
#106225802
#106225772
C2×#668712
#334611