Finite Group Databasebeta

← #13080049

Subgroups — #13080049

Order 1408.

334 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
1#10623264C211yesmaximal, characteristic
2#10623114C211yesmaximal, characteristic, complemented
3C11×#475C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622641C211yesmaximal, characteristic, complemented
6#10622484C211yesmaximal, characteristic, complemented
7#10622481C211yesmaximal, characteristic, complemented
8#10622477C211yesmaximal, characteristic
9#10622470C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622426C211yesmaximal, characteristic, complemented
14#10622425C211yesmaximal, characteristic
15#10622406C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#67000—21no—
19#66999—21no—
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24C2×Dic44C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4313C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66951—21no—
29#66951—21no—
30#66950C2211yescharacteristic
31#66950C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66946C2211yescharacteristic
35#66943C2211yescharacteristic
36#66942—21no—
37#66940C2211yescharacteristic
38#66929—21no—
39#66928C2211yescharacteristic
40#66925C2211yescharacteristic
41#66923—21no—
42C4×Dic22C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48#66885C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D44—21no—
62C2×D44C2311yescharacteristic
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C42×C11—21no—
75C42×C11C2311yescharacteristic
76#4326—41no—
77#4325—41no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4D411yescharacteristic
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
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
104Dic44—41no—
105#4314—41no—
106#4313—41no—
107C8×D11—41no—
108#3258—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—81no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—81no—
133Dic22—21no—
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#542—111no—
142#541—111no—
143#479—111no—
144#478—111no—
145#477—111no—
146#475D1111yescharacteristic, complemented
147#470—111no—
148#468—111no—
149#467—111no—
150#465—111no—
151#464—111no—
152#464—111no—
153#462—111no—
154#461—111no—
155#424—111no—
156C22×C11C22×D411yescharacteristic
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11H(5,𝔽2)11yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
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—221no—
186#126—221no—
187#126—221no—
188#125—111no—
189#125—221no—
190#125—221no—
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—111no—
196C22⋊Q8—111no—
197C22⋊Q8—221no—
198#121—111no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8C2×D1111yescharacteristic
202C4×D4—111no—
203#117—111no—
204#107—111no—
205#107—111no—
206#106C2×D1111yescharacteristic
207#106C2×D1111yescharacteristic
208C4⋊C8—111no—
209C4⋊C8—111no—
210C4⋊C8—111no—
211C4⋊C8C2×D1111yescharacteristic
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#103C2×D1111yescharacteristic
218#102—111no—
219#102—111no—
220C2×C11#53711yescharacteristic
221C2×C11#57711yescharacteristic
222C2×C11#57811yescharacteristic
223D11—41no—
224D11—81no—
225C2×Q8—21no—
226C2×Q8—111no—
227C2×Q8—111no—
228C2×Q8C22×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—221no—
231C22×C4—111no—
232C22×C4—221no—
233Q16—441no—
234Q16—441no—
235SD16—441no—
236SD16—441no—
237M16—441no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—441no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—111no—
261C22⋊C4—111no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#325811yescharacteristic, complemented, Sylow
275C23—111no—
276C23—221no—
277Q8—21no—
278Q8—21no—
279Q8—81no—
280Q8—221no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284D4—221no—
285D4—221no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4D4×D1111yescharacteristic
301C2×C4D4×D1111yescharacteristic
302C2×C4C23×D1111yescharacteristic
303C8—21no—
304C8—21no—
305C8—221no—
306C8—221no—
307C22—221no—
308C22—221no—
309C22—221no—
310C22—441no—
311C22—441no—
312C22—441no—
313C22C2×D4×D1111yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—221no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4#6704011yescharacteristic
327C4#6704211yescharacteristic
328C2—441no—
329C2—881no—
330C2#1062316011yescharacteristic
331C2#1062329311yescharacteristic
332C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#475D11
hypocenterC11#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #10623114C2semidirect
3. C11×#475C2semidirect
4. #10622704C2semidirect
5. #10622641C2semidirect
6. #10622484C2semidirect
7. #10622481C2semidirect
9. #10622470C2semidirect
10. #10622458C2semidirect
11. #10622452C2semidirect
12. #10622431C2semidirect
13. #10622426C2semidirect
15. #10622406C2semidirect
146. #475D11semidirect
274. C11#3258semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106231142
C11×#4752
#106227042
#106226412
#106224842
#106224812
#106224772
#106224702
#106224582
#106224522
#106224312
#106224262
#106224252
#106224062
#325811