Finite Group Databasebeta

← #13079286

Subgroups — #13079286

Order 1408.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#541C211yesmaximal, characteristic, complemented
2#10623065C211yesmaximal, characteristic
3#10622699C211yesmaximal, characteristic, complemented
4#10622694C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622678C211yesmaximal, characteristic, complemented
7#10622665C211yesmaximal, characteristic, complemented
8#10622664C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic
10#10622661C211yesmaximal, characteristic
11#10622643C211yesmaximal, characteristic, complemented
12C4×#4326C211yesmaximal, characteristic, complemented
13#10622639C211yesmaximal, characteristic, complemented
14C4×#4325C211yesmaximal, characteristic, complemented
15#10622610C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#125—21no—
20C11×#125—21no—
21C11×#125C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23C11×C22⋊Q8C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×Q8×C11C2211yescharacteristic
26C11×#117C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31#66983C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66951—21no—
36#66949—21no—
37#66938—21no—
38#66936—21no—
39#66928C2211yescharacteristic
40C4×D44C2211yescharacteristic
41#66922C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66867C2211yescharacteristic
56#66867C2211yescharacteristic
57C4×C11⋊C8C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4D411yescharacteristic
82C11×C22⋊C4D411yescharacteristic
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88#4326—22no—
89#4326—22no—
90#4325—22no—
91#4325—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102#4318—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3178—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11—21no—
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×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×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—81no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131D44—21no—
132D44—21no—
133C4×D11—81no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139C11⋊C8#4112yes—
140C11⋊C8#4112yes—
141#542—111no—
142#541D1111yescharacteristic, complemented
143#501—111no—
144#497—111no—
145#488—111no—
146#487—111no—
147#470—111no—
148#468—111no—
149#467—111no—
150#465—111no—
151#441—111no—
152#440—111no—
153C4×Q16—111no—
154C4×SD16—111no—
155#405—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11C22×D411yescharacteristic
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C11C2×#4111yescharacteristic
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×Q16—111no—
178C2×Q16—111no—
179C2×SD16—111no—
180C2×SD16—111no—
181C2×M16—111no—
182C22×C8—111no—
183C4⋊Q8—111no—
184C4⋊Q8C2×D1111yescharacteristic
185#126—21no—
186#126—21no—
187#126—221no—
188#125—21no—
189#125—21no—
190#125C2×D1111yescharacteristic
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196C22⋊Q8C2×D1111yescharacteristic
197C22⋊Q8C2×D1111yescharacteristic
198#121—111no—
199C4×Q8—111no—
200C4×Q8C2×D1111yescharacteristic
201C4×Q8C2×D1111yescharacteristic
202C4×D4—111no—
203#117C2×D1111yescharacteristic
204#107—111no—
205#107—111no—
206#106—111no—
207#106—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102—111no—
216#97—111no—
217#97—111no—
218C4×C8—111no—
219C4×C8—111no—
220C2×C11—41no—
221C2×C11#53211yescharacteristic
222C2×C11#57711yescharacteristic
223C2×C11#57811yescharacteristic
224D11—81no—
225C2×Q8—111no—
226C2×Q8—221no—
227C2×Q8C22×D1111yescharacteristic
228C2×Q8C22×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—221no—
231C22×C4—221no—
232C22×C4C22×D1111yescharacteristic
233Q16—222no—
234Q16—222no—
235SD16—222no—
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—222no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4C22⋊D1111yescharacteristic
257C4⋊C4C22⋊D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4C22⋊D1111yescharacteristic
268C22⋊C4C22⋊D1111yescharacteristic
269C42—21no—
270C42—21no—
271C42—221no—
272C42C22×D1111yescharacteristic
273C42C22×D1111yescharacteristic
274C11#317811yescharacteristic, complemented, Sylow
275C23—221no—
276C23C2×C22⋊D1111yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—221no—
282Q8—221no—
283Q8—881no—
284D4—221no—
285D4—221no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—881no—
297C2×C4C2×C22⋊D1111yescharacteristic
298C2×C4C2×C22⋊D1111yescharacteristic
299C2×C4C2×C22⋊D1111yescharacteristic
300C2×C4C2×C22⋊D1111yescharacteristic
301C2×C4C2×C22⋊D1111yescharacteristic
302C2×C4C23×D1111yescharacteristic
303C8—112no—
304C8—112no—
305C8—221no—
306C8—221no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—441no—
311C22—441no—
312C22—441no—
313C22C22×C22⋊D1111yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4#41×D1111yescharacteristic
327C4#41×D1111yescharacteristic
328C2—41no—
329C2—881no—
330C2#1062336311yescharacteristic
331C2#1062336811yescharacteristic
332C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#541C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#541D11
hypocenterC11#3178
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C11×#541C2semidirect
3. #10622699C2semidirect
4. #10622694C2semidirect
5. #10622681C2semidirect
6. #10622678C2semidirect
7. #10622665C2semidirect
8. #10622664C2semidirect
11. #10622643C2semidirect
12. C4×#4326C2semidirect
13. #10622639C2semidirect
14. C4×#4325C2semidirect
15. #10622610C2semidirect
142. #541D11semidirect
274. C11#3178semidirect

Maximal subgroups

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

subgroupindex
C11×#5412
#106230652
#106226992
#106226942
#106226812
#106226782
#106226652
#106226642
#106226622
#106226612
#106226432
C4×#43262
#106226392
C4×#43252
#106226102
#317811