Finite Group Databasebeta

← #13081207

Subgroups — #13081207

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623063C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic, complemented
3C11×#428C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622741C211yesmaximal, characteristic, complemented
6#10622616C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622503C211yesmaximal, characteristic, complemented
9#10622498C211yesmaximal, characteristic, complemented
10#10622494C211yesmaximal, characteristic, complemented
11#10622485C211yesmaximal, characteristic, complemented
12#10622483C211yesmaximal, characteristic, complemented
13#10622478C211yesmaximal, characteristic, complemented
14#10622476C211yesmaximal, characteristic, complemented
15#10622468C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×M16C2211yescharacteristic
18C11×#117C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66983C2211yescharacteristic
21#66983C2211yescharacteristic
22#66982—21no—
23C4×C22⋊D11C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26#66949—21no—
27#66948C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946C2211yescharacteristic
31#66946C2211yescharacteristic
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66941C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37#66937—21no—
38#66928—21no—
39#66925—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66881C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50C8×Dic11C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64#4339—44no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×Dic22—21no—
75C11×M16—22no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C42×C11—21no—
85C22⋊Dic11D411yescharacteristic
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104D88—22no—
105#4313—22no—
106#3354—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—22no—
121C22⋊D11—42no—
122C22⋊D11—81no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44—21no—
130D44—21no—
131D44—21no—
132D44—42no—
133D44—81no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—42no—
137C4×D11—42no—
138C4×D11—42no—
139Dic22—42no—
140Dic22—81no—
141C8×C11—21no—
142C8×C11#4112yescomplemented
143C11⋊C8—21no—
144C11⋊C8—21no—
145#555—111no—
146#547—111no—
147#498—111no—
148#482—111no—
149#482—111no—
150#481—111no—
151#481—111no—
152#476—111no—
153#474—111no—
154#469—111no—
155#469—111no—
156C4×D8—111no—
157#436—111no—
158#428—111no—
159#428D1111yescharacteristic, complemented
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11C2×#4111yescharacteristic
179C4×C112−1+411yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11AGL(1,ℤ/8)12yes—
185C2×#41—221no—
186C2×D8—111no—
187C2×M16—111no—
188C2×M16C2×D1111yescharacteristic
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191#124—221no—
192#124—221no—
193#123—221no—
194#123—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198#121—111no—
199#121—111no—
200#121—221no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—111no—
204#117—111no—
205#117—221no—
206#117C2×D1111yescharacteristic
207C2×C4⋊C4—111no—
208C2×C4⋊C4C2×D1111yescharacteristic
209#107—111no—
210#107C2×D1111yescharacteristic
211#107C2×D1111yescharacteristic
212#106—111no—
213#106—111no—
214#106—111no—
215#106—111no—
216#106C2×D1111yescharacteristic
217#106C2×D1111yescharacteristic
218C4⋊C8—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C22⋊C8—111no—
226C22⋊C8—111no—
227C4×C8—111no—
228C2×C11—41no—
229C2×C11#54711yescharacteristic
230C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C2×C11#57711yescharacteristic
232D11—41no—
233D11—81no—
234D11—81no—
235#41—444no—
236C2×Q8—221no—
237C2×Q8—221no—
238C2×D4—111no—
239C2×D4—111no—
240C2×D4—111no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251D8—222no—
252M16—22no—
253M16—222no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4C22×D1111yescharacteristic
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C4⋊C4C22×D1111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—111no—
271C22⋊C4—111no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C42—21no—
280C42—111no—
281C42—221no—
282C11#335411yescharacteristic, complemented, Sylow
283C23—111no—
284C23—221no—
285C23—221no—
286C23D4×D1111yescharacteristic
287Q8—442no—
288Q8—881no—
289D4—222no—
290D4—221no—
291D4—221no—
292D4—221no—
293D4—221no—
294D4—442no—
295D4—442no—
296D4—881no—
297D4—881no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—111no—
306C2×C4—111no—
307C2×C4—111no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—221no—
319C8—221no—
320C8#433912yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—221no—
325C22—221no—
326C22—221no—
327C22—441no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22C2×D4×D1111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—112no—
340C4—221no—
341C4—221no—
342C4—441no—
343C4—441no—
344C4C2×#433911yescharacteristic
345C4#6704011yescharacteristic
346C2—41no—
347C2—441no—
348C2—881no—
349C2—881no—
350C2#1062303811yescharacteristic
351C2D11×AGL(1,ℤ/8)11yescharacteristic
352C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
hypercenter#428D11
hypocenterC11#3354
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10623063C2semidirect
2. #10623038C2semidirect
3. C11×#428C2semidirect
4. #10622748C2semidirect
5. #10622741C2semidirect
6. #10622616C2semidirect
7. #10622581C2semidirect
8. #10622503C2semidirect
9. #10622498C2semidirect
10. #10622494C2semidirect
11. #10622485C2semidirect
12. #10622483C2semidirect
13. #10622478C2semidirect
14. #10622476C2semidirect
15. #10622468C2semidirect
142. C8×C11#41semidirect
159. #428D11semidirect
282. C11#3354semidirect
320. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106230632
#106230382
C11×#4282
#106227482
#106227412
#106226162
#106225812
#106225032
#106224982
#106224942
#106224852
#106224832
#106224782
#106224762
#106224682
#335411