Finite Group Databasebeta

← #13077784

Subgroups — #13077784

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#10623059C211yesmaximal, characteristic
2C11×#424C211yesmaximal, characteristic, complemented
3#10622741C211yesmaximal, characteristic, complemented
4#10622740C211yesmaximal, characteristic, complemented
5#10622724C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7#10622613C211yesmaximal, characteristic, complemented
8#10622453C211yesmaximal, characteristic, complemented
9#10622452C211yesmaximal, characteristic, complemented
10#10622451C211yesmaximal, characteristic, complemented
11#10622450C211yesmaximal, characteristic, complemented
12#10622449C211yesmaximal, characteristic, complemented
13#10622448C211yesmaximal, characteristic, complemented
14#10622444C211yesmaximal, characteristic, complemented
15#10622441C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C11×#117C2211yescharacteristic
19C4×C22⋊D11C2211yescharacteristic
20C4×C22⋊D11C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×#4313C2211yescharacteristic
23C2×#4313C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25#66951C411yescharacteristic
26#66949C411yescharacteristic
27#66947C411yescharacteristic
28#66942C411yescharacteristic
29#66938C411yescharacteristic
30#66937C411yescharacteristic
31#66936C411yescharacteristic
32#66932C411yescharacteristic
33C4×D44C2211yescharacteristic
34#66925C2211yescharacteristic
35C42×D11C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C11×C4⋊C8C2211yescharacteristic
38C11×C4⋊C8C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C22⋊(C11⋊C8)C2211yescharacteristic
42C22⋊(C11⋊C8)C2211yescharacteristic
43(C2×D11)⋊C8C2211yescharacteristic
44(C2×D11)⋊C8C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66879C2211yescharacteristic
48#66879C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11C2×C411yescharacteristic
61C2×C22⋊D11C2×C411yescharacteristic
62C2×D44C2×C411yescharacteristic
63C2×C4×D11C2×C411yescharacteristic
64C2×C4×D11C2×C411yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×C4×D11C2311yescharacteristic
67C2×Dic22C2×C411yescharacteristic
68C11×M16—41no—
69C2×C8×C11—41no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4C2×C411yescharacteristic
75C11×C4⋊C4C2×C411yescharacteristic
76C11×C22⋊C4C2×C411yescharacteristic
77C11×C22⋊C4C2×C411yescharacteristic
78C42×C11C2311yescharacteristic
79C42×C11C2311yescharacteristic
80C22⋊Dic11C2×C411yescharacteristic
81C22⋊Dic11C2×C411yescharacteristic
82(C2×D11)⋊C4C2×C411yescharacteristic
83(C2×D11)⋊C4C2×C411yescharacteristic
84(C2×D11)⋊C4C2×C411yescharacteristic
85(C2×D11)⋊C4C2×C411yescharacteristic
86(C2×D11)⋊C4C2×C411yescharacteristic
87(C2×D11)⋊C4C2×C411yescharacteristic
88C4⋊Dic11C2×C411yescharacteristic
89C4⋊Dic11C2×C411yescharacteristic
90Dic11⋊C4C2×C411yescharacteristic
91Dic11⋊C4C2×C411yescharacteristic
92Dic11⋊C4C2×C411yescharacteristic
93Dic11⋊C4C2×C411yescharacteristic
94Dic11⋊C4C2×C411yescharacteristic
95Dic11⋊C4C2×C411yescharacteristic
96C4×Dic11C2×C411yescharacteristic
97C4×Dic11C2×C411yescharacteristic
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—41no—
105#4313—41no—
106#4313—41no—
107C8×D11—41no—
108#2995—111nomaximal, Sylow
109C23×C11C22×C411yescharacteristic
110C22×D11C22×C411yescharacteristic
111C22×D11C22×C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C22×C411yescharacteristic
115C2×C4×C11C22×C411yescharacteristic
116C2×C4×C11C22×C411yescharacteristic
117C2×C4×C11C22×C411yescharacteristic
118C2×C4×C11C22×C411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—41no—
121C22⋊D11—41no—
122C2×Dic11C22×C411yescharacteristic
123C2×Dic11C22×C411yescharacteristic
124C2×Dic11C22×C411yescharacteristic
125C2×Dic11C22×C411yescharacteristic
126C2×Dic11C22×C411yescharacteristic
127C2×Dic11C22×C411yescharacteristic
128D44—41no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—41no—
134C4×D11—41no—
135Dic22—41no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#529—111no—
145#446—111no—
146#446—111no—
147#436—111no—
148#436—111no—
149#435—111no—
150#435—111no—
151#435—111no—
152#435—111no—
153#433—111no—
154#433—111no—
155#432—111no—
156#424—111no—
157#424D1111yescharacteristic, complemented
158#423—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11C23×C411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11H(5,𝔽2)11yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182C2×M16—111no—
183C2×M16—111no—
184C2×M16—111no—
185C2×M16C2×D1111yescharacteristic
186C22×C8—111no—
187C22×C8C2×D1111yescharacteristic
188#126—111no—
189#126—111no—
190#125—111no—
191#124—111no—
192#123—111no—
193#123—111no—
194C22⋊Q8—111no—
195#121—111no—
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200#117—111no—
201#117C2×D1111yescharacteristic
202C2×C42—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8—111no—
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8C2×D1111yescharacteristic
210C4⋊C8C2×D1111yescharacteristic
211C4⋊C8C2×D1111yescharacteristic
212C4⋊C8C2×D1111yescharacteristic
213C22⋊C8—111no—
214C22⋊C8—111no—
215C22⋊C8—111no—
216C22⋊C8—111no—
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97—111no—
220#97—111no—
221#97—111no—
222#97—111no—
223C4×C8—111no—
224C4×C8—111no—
225C2×C11—41no—
226C2×C11#52011yescharacteristic
227C2×C11#56811yescharacteristic
228C2×C11#56811yescharacteristic
229D11—41no—
230D11—41no—
231C2×Q8—111no—
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4C22×D1111yescharacteristic
240M16—41no—
241M16—441no—
242M16—441no—
243M16—441no—
244C2×C8—41no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—441no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C2×C8C22×D1111yescharacteristic
253C2×C8C22×D1111yescharacteristic
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4C4×D1111yescharacteristic
263C4⋊C4C4×D1111yescharacteristic
264C22⋊C4—111no—
265C22⋊C4—111no—
266C22⋊C4—111no—
267C22⋊C4—111no—
268C22⋊C4—111no—
269C22⋊C4—111no—
270C22⋊C4—111no—
271C22⋊C4—111no—
272C22⋊C4C4×D1111yescharacteristic
273C22⋊C4C4×D1111yescharacteristic
274C42—111no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42C22×D1111yescharacteristic
279C42C22×D1111yescharacteristic
280C11#299511yescharacteristic, complemented, Sylow
281C23—111no—
282C23—111no—
283C23C2×C4×D1111yescharacteristic
284Q8—441no—
285D4—441no—
286D4—441no—
287D4—441no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4C2×C4×D1111yescharacteristic
303C2×C4C2×C4×D1111yescharacteristic
304C2×C4C2×C4×D1111yescharacteristic
305C2×C4C2×C4×D1111yescharacteristic
306C2×C4C2×C4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—221no—
313C8—221no—
314C8—221no—
315C8—221no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—221no—
320C22—221no—
321C22—221no—
322C22—221no—
323C22—221no—
324C22—221no—
325C22C22×C4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4#6703711yescharacteristic
338C4#6704011yescharacteristic
339C2—41no—
340C2—441no—
341C2—441no—
342C2#1062303511yescharacteristic
343C2#1062328111yescharacteristic
344C2#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D11
commutator, socleC22×C11C23×C4
FittingC11×#424C2
prime radical#66937C4
cosocleC2×C4×C11C24
hypercenter#424D11
hypocenterC11#2995
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C11×#424C2semidirect
3. #10622741C2semidirect
4. #10622740C2semidirect
5. #10622724C2semidirect
6. #10622724C2semidirect
7. #10622613C2semidirect
8. #10622453C2semidirect
9. #10622452C2semidirect
10. #10622451C2semidirect
11. #10622450C2semidirect
12. #10622449C2semidirect
13. #10622448C2semidirect
14. #10622444C2semidirect
15. #10622441C2semidirect
157. #424D11semidirect
280. C11#2995semidirect

Maximal subgroups

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

subgroupindex
#106230592
C11×#4242
#106227412
#106227402
#106227242
#106226132
#106224532
#106224522
#106224512
#106224502
#106224492
#106224482
#106224442
#106224412
#299511