Finite Group Databasebeta

← #13079952

Subgroups — #13079952

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623222C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622641C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622500C211yesmaximal, characteristic, complemented
8#10622477C211yesmaximal, characteristic
9#10622467C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11D11×C4⋊C8C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622426C211yesmaximal, characteristic, complemented
14#10622420C211yesmaximal, characteristic
15#10622406C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66997C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22C2×Dic44C2211yescharacteristic
23C2×#4314C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66950C2211yescharacteristic
29#66949—21no—
30#66948C2211yescharacteristic
31#66947—21no—
32#66946—21no—
33#66946C2211yescharacteristic
34#66945—21no—
35#66942—21no—
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66928C2211yescharacteristic
39#66925—21no—
40C42×D11C2211yescharacteristic
41C4×Dic22—21no—
42C4×Dic22C2211yescharacteristic
43C11×#107C2211yescharacteristic
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#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44—21no—
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11D411yescharacteristic
64C2×C4×D11D411yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79#4326—41no—
80#4325—41no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—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—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11D411yescharacteristic
100C4×Dic11D411yescharacteristic
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104Dic44—41no—
105#4314—41no—
106C8×D11—41no—
107C8×D11—41no—
108#3248—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44—21no—
128D44—42no—
129C4×D11—22no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—22no—
133C4×D11—42no—
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#533—111no—
144#529—111no—
145#479—111no—
146#479D1111yescharacteristic, complemented
147#475—111no—
148#474—111no—
149#467—111no—
150#467—111no—
151#465—111no—
152#465—111no—
153#464—111no—
154#464—111no—
155#462—111no—
156#461—111no—
157C2×C4⋊C8—111no—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11#13712yes—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11H(5,𝔽2)11yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11#13512yes—
179C2×Q16—111no—
180C2×Q16—111no—
181C2×SD16—111no—
182C2×SD16—111no—
183C22×C8—111no—
184C22×C8—111no—
185C4⋊Q8—111no—
186C4⋊Q8—111no—
187#126—221no—
188#125—221no—
189#125C2×D1111yescharacteristic
190#124—111no—
191#123—221no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—221no—
200C4×Q8C2×D1111yescharacteristic
201C4×D4—111no—
202C4×D4—221no—
203#117—221no—
204#117—221no—
205C2×C42—111no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213C4⋊C8C2×D1111yescharacteristic
214#103—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103C2×D1111yescharacteristic
219#103C2×D1111yescharacteristic
220#102—111no—
221#102—111no—
222C2×C11#53711yescharacteristic
223C2×C11C2×#13511yescharacteristic
224C2×C11C2×#13711yescharacteristic
225D11—22no—
226D11—81no—
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×Q8C22×D1111yescharacteristic
231C2×D4—111no—
232C2×D4—221no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—221no—
237Q16—441no—
238Q16—441no—
239SD16—441no—
240SD16—441no—
241C2×C8—111no—
242C2×C8—111no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
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—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#324811yescharacteristic, complemented, Sylow
277C23—111no—
278C23—221no—
279Q8—21no—
280Q8—21no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285Q8—442no—
286D4—221no—
287D4—221no—
288D4—442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—442no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—112no—
312C22—221no—
313C22—221no—
314C22—441no—
315C22—441no—
316C22—441no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—112no—
325C4—221no—
326C4—221no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4#6704011yescharacteristic
331C4#6704211yescharacteristic
332C2—222no—
333C2—881no—
334C2#1062316011yescharacteristic
335C2D11×#13511yescharacteristic
336C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#479D11
hypocenterC11#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #10623109C2semidirect
3. C11×#479C2semidirect
4. #10622676C2semidirect
5. #10622641C2semidirect
6. #10622503C2semidirect
7. #10622500C2semidirect
9. #10622467C2semidirect
10. #10622458C2semidirect
11. D11×C4⋊C8C2semidirect
12. #10622431C2semidirect
13. #10622426C2semidirect
15. #10622406C2semidirect
146. #479D11semidirect
276. C11#3248semidirect

Maximal subgroups

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

subgroupindex
#106232222
#106231092
C11×#4792
#106226762
#106226412
#106225032
#106225002
#106224772
#106224672
#106224582
D11×C4⋊C82
#106224312
#106224262
#106224202
#106224062
#324811