Finite Group Databasebeta

← #13080061

Subgroups — #13080061

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623229C211yesmaximal, characteristic
2#10623114C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622640C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622484C211yesmaximal, characteristic, complemented
9#10622477C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622431C211yesmaximal, characteristic, complemented
14#10622425C211yesmaximal, characteristic, complemented
15#10622420C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66997C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22C2×#4314C2211yescharacteristic
23C2×#4314C2211yescharacteristic
24C2×#4313C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66948—21no—
29#66948—21no—
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic
32#66947—21no—
33#66947—21no—
34#66946C2211yescharacteristic
35#66946C2211yescharacteristic
36#66943C2211yescharacteristic
37#66942—21no—
38#66929—21no—
39#66927C2211yescharacteristic
40#66925C2211yescharacteristic
41#66923—21no—
42C4×Dic22C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44—21no—
61C2×D44—21no—
62C2×D44—21no—
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C42×C11—21no—
79C42×C11C2311yescharacteristic
80#4325—41no—
81#4325—41no—
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—
88(C2×D11)⋊C4D411yescharacteristic
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4314—41no—
105#4314—41no—
106#4313—41no—
107C8×D11—41no—
108#3260—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
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×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44—21no—
128D44—21no—
129D44—21no—
130D44—81no—
131D44—81no—
132D44—81no—
133D44—81no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—81no—
137C4×D11—81no—
138Dic22—21no—
139Dic22—21no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#541—111no—
145#540—111no—
146#479—111no—
147#479D1111yescharacteristic, complemented
148#478—111no—
149#478—111no—
150#468—111no—
151#468—111no—
152#465—111no—
153#465—111no—
154#461—111no—
155#461—111no—
156#460—111no—
157#460—111no—
158#424—111no—
159C22×C11C22×D411yescharacteristic
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11H(5,𝔽2)11yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182C2×SD16—111no—
183C2×SD16—111no—
184C2×SD16—111no—
185C2×SD16—111no—
186C2×M16—111no—
187C22×C8—111no—
188C4⋊Q8—111no—
189#127—111no—
190#126—221no—
191#126—221no—
192#125—111no—
193#125—221no—
194#125—221no—
195#125C2×D1111yescharacteristic
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200#121—111no—
201#121—111no—
202#121—221no—
203#121—221no—
204C4×Q8—111no—
205C4×Q8C2×D1111yescharacteristic
206C4×D4—111no—
207C4×D4—111no—
208#117—111no—
209#107—111no—
210#107C2×D1111yescharacteristic
211#106—111no—
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8C2×D1111yescharacteristic
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#103C2×D1111yescharacteristic
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C2×C11#53711yescharacteristic
226C2×C11#57711yescharacteristic
227C2×C11#57711yescharacteristic
228D11—41no—
229D11—81no—
230D11—81no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—441no—
243SD16—441no—
244SD16—441no—
245SD16—441no—
246M16—441no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—441no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4C22×D1111yescharacteristic
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—111no—
269C22⋊C4—111no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C42—21no—
277C42—111no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#326011yescharacteristic, complemented, Sylow
281C23—111no—
282C23—221no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—221no—
289D4—221no—
290D4—221no—
291D4—221no—
292D4—881no—
293D4—881no—
294D4—881no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—221no—
317C22—221no—
318C22—221no—
319C22—441no—
320C22—441no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—221no—
333C4—221no—
334C4—221no—
335C4—441no—
336C4—441no—
337C4#6704011yescharacteristic
338C4#6704211yescharacteristic
339C2—441no—
340C2—881no—
341C2—881no—
342C2#1062316011yescharacteristic
343C2#1062330111yescharacteristic
344C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radical#10623229C2
hypercenter#479D11
hypocenterC11#3260
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. #10623114C2semidirect
3. C11×#479C2semidirect
4. #10622676C2semidirect
5. #10622640C2semidirect
6. #10622504C2semidirect
7. #10622499C2semidirect
8. #10622484C2semidirect
9. #10622477C2semidirect
10. #10622461C2semidirect
11. #10622452C2semidirect
12. #10622431C2semidirect
13. #10622431C2semidirect
14. #10622425C2semidirect
15. #10622420C2semidirect
147. #479D11semidirect
280. C11#3260semidirect

Maximal subgroups

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

subgroupindex
#106232292
#106231142
C11×#4792
#106226762
#106226402
#106225042
#106224992
#106224842
#106224772
#106224612
#106224522
#106224312
#106224252
#106224202
#326011