Finite Group Databasebeta

← #13079804

Subgroups — #13079804

Order 1408.

368 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
1D11×#125C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622622C211yesmaximal, characteristic, complemented
6#10622495C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622476C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622448C211yesmaximal, characteristic, complemented
12#10622390C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622377C211yesmaximal, characteristic, complemented
15#10622377C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C11×#125C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66993C2211yescharacteristic
20#66991C2211yescharacteristic
21C4×C22⋊D11—21no—
22#66948C2211yescharacteristic
23C4⋊C4×D11—21no—
24C4⋊C4×D11—21no—
25C4⋊C4×D11C2211yescharacteristic
26C4⋊C4×D11C2211yescharacteristic
27#66943C2211yescharacteristic
28#66943C2211yescharacteristic
29#66942—21no—
30#66942—21no—
31#66941C2211yescharacteristic
32#66938—21no—
33#66937—21no—
34C4×D44C2211yescharacteristic
35C42×D11C2211yescharacteristic
36#66923C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#102C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66879C2211yescharacteristic
51#66879C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64#4339—44no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11D411yescharacteristic
71C2×C4×D11D411yescharacteristic
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C42×C11C2311yescharacteristic
83C22⋊Dic11—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11D411yescharacteristic
99C4×Dic11D411yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3234—111nomaximal, Sylow
104C23×C11—21no—
105C22×D11—21no—
106C22×D11C2×D411yescharacteristic
107D4×C11—21no—
108D4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2411yescharacteristic
116C22⋊D11—42no—
117C22⋊D11—42no—
118C22⋊D11—42no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—21no—
126D44—21no—
127D44—42no—
128C4×D11—22no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—41no—
132C4×D11—42no—
133C4×D11—42no—
134C4×D11—42no—
135Dic22—42no—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140#532—111no—
141C2×#125—111no—
142#501—111no—
143#501—111no—
144#490—111no—
145#490—111no—
146#481—111no—
147#481—111no—
148#480—111no—
149#480—111no—
150#478—111no—
151#478—111no—
152#478—111no—
153#478D1111yescharacteristic, complemented
154#432—111no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11AGL(1,ℤ/8)12yes—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C112−1+411yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—21no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178C2×#41—221no—
179C4⋊Q8—111no—
180#127—111no—
181#125—111no—
182#125—111no—
183#125—111no—
184#125—221no—
185#125—221no—
186#125C2×D1111yescharacteristic
187#124—221no—
188#121—111no—
189#121—111no—
190#121—221no—
191C4×D4—111no—
192C4×D4—221no—
193C4×D4C2×D1111yescharacteristic
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C42—111no—
199#107—111no—
200#107—111no—
201#107—111no—
202#107C2×D1111yescharacteristic
203#106—111no—
204#106—111no—
205#106—111no—
206#106C2×D1111yescharacteristic
207C4⋊C8—111no—
208C4⋊C8C2×D1111yescharacteristic
209#102—111no—
210#102—111no—
211#102—111no—
212#102—111no—
213#102—111no—
214#102—111no—
215#102C2×D1111yescharacteristic
216#102C2×D1111yescharacteristic
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97—111no—
220#97—111no—
221C2×C11—81no—
222C2×C11#53611yescharacteristic
223C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C2×C11#57511yescharacteristic
225D11—22no—
226D11—81no—
227#41—444no—
228C2×Q8—221no—
229C2×D4—111no—
230C2×D4—221no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4—221no—
234C2×D4C22×D1111yescharacteristic
235C22×C4—21no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8C22×D1111yescharacteristic
245C2×C8C22×D1111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
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⋊C4—221no—
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—111no—
268C42—111no—
269C42—111no—
270C42C22×D1111yescharacteristic
271C11#323411yescharacteristic, complemented, Sylow
272C23—21no—
273C23—111no—
274C23—221no—
275Q8—442no—
276D4—21no—
277D4—21no—
278D4—221no—
279D4—221no—
280D4—442no—
281D4—442no—
282D4—442no—
283D4—442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—222no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4D4×D1111yescharacteristic
302C2×C4D4×D1111yescharacteristic
303C2×C4C23×D1111yescharacteristic
304C8—21no—
305C8—21no—
306C8—221no—
307C8—221no—
308C22—41no—
309C22—41no—
310C22—41no—
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—221no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4#6704011yescharacteristic
330C4#6704311yescharacteristic
331C2—81no—
332C2—222no—
333C2—881no—
334C2#1062315911yescharacteristic
335C2#1062329911yescharacteristic
336C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radical#10623079C2
hypercenter#478D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. D11×#125C2semidirect
3. C11×#478C2semidirect
4. #10622679C2semidirect
5. #10622622C2semidirect
6. #10622495C2semidirect
7. #10622489C2semidirect
8. #10622476C2semidirect
9. #10622469C2semidirect
10. #10622460C2semidirect
11. #10622448C2semidirect
12. #10622390C2semidirect
13. #10622387C2semidirect
14. #10622377C2semidirect
15. #10622377C2semidirect
153. #478D11semidirect
271. C11#3234semidirect

Maximal subgroups

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

subgroupindex
D11×#1252
#106230792
C11×#4782
#106226792
#106226222
#106224952
#106224892
#106224762
#106224692
#106224602
#106224482
#106223902
#106223872
#106223772
#323411