Finite Group Databasebeta

← #13081110

Subgroups — #13081110

Order 1408.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#553C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic, complemented
3#10622679C211yesmaximal, characteristic, complemented
4#10622678C211yesmaximal, characteristic, complemented
5#10622652C211yesmaximal, characteristic, complemented
6#10622651C211yesmaximal, characteristic, complemented
7#10622648C211yesmaximal, characteristic, complemented
8#10622648C211yesmaximal, characteristic, complemented
9#10622627C211yesmaximal, characteristic, complemented
10#10622624C211yesmaximal, characteristic, complemented
11#10622620C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622611C211yesmaximal, characteristic, complemented
14#10622580C211yesmaximal, characteristic, complemented
15#10622577C211yesmaximal, characteristic, complemented
16C11×#126—21no—
17C11×#125C2211yescharacteristic
18C11×#123—21no—
19C11×#121—21no—
20C11×#121C2211yescharacteristic
21C11×#121C2211yescharacteristic
22C4×D4×C11—21no—
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66991—21no—
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979C2211yescharacteristic
32#66979C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66945—21no—
36#66938—21no—
37#66938—21no—
38C4×D44C2211yescharacteristic
39#66922C2211yescharacteristic
40#66896C2211yescharacteristic
41#66896C2211yescharacteristic
42#66896C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11D411yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×Dic22—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3347—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109C22×D11—21no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—41no—
113D4×C11—42no—
114D4×C11—81no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C22⋊D11—81no—
130C22⋊D11—81no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134D44—21no—
135D44—21no—
136C4×D11—42no—
137Dic22—81no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yes—
142#555—111no—
143#553D1111yescharacteristic, complemented
144#501—111no—
145#482—111no—
146#482—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#474—111no—
151#469—111no—
152#466—111no—
153#442—111no—
154#435—111no—
155#428—111no—
156#427—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C112−1+411yescharacteristic
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×D8—111no—
183C2×M16—111no—
184C22×C8—111no—
185C4⋊Q8—111no—
186#126—21no—
187#125C2×D1111yescharacteristic
188#124—221no—
189#124—221no—
190#123—21no—
191#121—21no—
192#121—111no—
193#121—111no—
194#121—221no—
195#121C2×D1111yescharacteristic
196#121C2×D1111yescharacteristic
197C4×D4—21no—
198C4×D4—111no—
199C4×D4C2×D1111yescharacteristic
200C4×D4C2×D1111yescharacteristic
201#117—111no—
202#117—111no—
203#117—221no—
204#117C2×D1111yescharacteristic
205C2×C4⋊C4C2×D1111yescharacteristic
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215C4⋊C8—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222C22⋊C8—111no—
223C22⋊C8—111no—
224#97—111no—
225C2×C11—41no—
226C2×C11—41no—
227C2×C11—81no—
228C2×C11#54711yescharacteristic
229C2×C11#57511yescharacteristic
230C2×C11#57611yescharacteristic
231D11—81no—
232C2×Q8—221no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—111no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4C22⋊D1111yescharacteristic
239C2×D4C22×D1111yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—221no—
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245D8—222no—
246M16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8—111no—
251C2×C8—222no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4C22⋊D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4C22⋊D1111yescharacteristic
273C22⋊C4C22⋊D1111yescharacteristic
274C42—21no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#334711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—221no—
281C23C2×C22⋊D1111yescharacteristic
282C23C2×C22⋊D1111yescharacteristic
283Q8—881no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—221no—
290D4—221no—
291D4—881no—
292D4—881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—442no—
306C2×C4C2×C22⋊D1111yescharacteristic
307C2×C4C2×C22⋊D1111yescharacteristic
308C2×C4C2×C22⋊D1111yescharacteristic
309C2×C4C2×C22⋊D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—112no—
312C8—221no—
313C8—221no—
314C8—221no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C22×C22⋊D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4#41×D1111yescharacteristic
339C4#6704311yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—881no—
344C2#1062335311yescharacteristic
345C2#1062335511yescharacteristic
346C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#553C2
socleC22×C11C22×D4
hypercenter#553D11
hypocenterC11#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C11×#553C2semidirect
2. #10623094C2semidirect
3. #10622679C2semidirect
4. #10622678C2semidirect
5. #10622652C2semidirect
6. #10622651C2semidirect
7. #10622648C2semidirect
8. #10622648C2semidirect
9. #10622627C2semidirect
10. #10622624C2semidirect
11. #10622620C2semidirect
12. #10622616C2semidirect
13. #10622611C2semidirect
14. #10622580C2semidirect
15. #10622577C2semidirect
143. #553D11semidirect
278. C11#3347semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
#106230942
#106226792
#106226782
#106226522
#106226512
#106226482
#106226272
#106226242
#106226202
#106226162
#106226112
#106225802
#106225772
#334711