Finite Group Databasebeta

← #13081123

Subgroups — #13081123

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
1#10623265C211yesmaximal, characteristic, complemented
2#10623089C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622627C211yesmaximal, characteristic, complemented
6#10622498C211yesmaximal, characteristic, complemented
7#10622495C211yesmaximal, characteristic, complemented
8#10622494C211yesmaximal, characteristic, complemented
9#10622493C211yesmaximal, characteristic, complemented
10#10622460C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622395C211yesmaximal, characteristic, complemented
14#10622392C211yesmaximal, characteristic, complemented
15#10622388C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18#67000—21no—
19#67000—21no—
20#66991C2211yescharacteristic
21#66991C2211yescharacteristic
22C2×#4323C2211yescharacteristic
23#66982—21no—
24C4×C22⋊D11—21no—
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66948—21no—
28#66948C2211yescharacteristic
29#66948C2211yescharacteristic
30#66945—21no—
31#66945C2211yescharacteristic
32#66945C2211yescharacteristic
33#66945C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35#66937—21no—
36#66932—21no—
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39#66923C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66873C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44D411yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×C4×D11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82#4323—22no—
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)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11D411yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4313—22no—
104C8×D11—22no—
105#3347—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109C22×D11C2×D411yescharacteristic
110Q8×C11—81no—
111D4×C11—21no—
112D4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11—81no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—41no—
130D44—81no—
131D44—81no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—42no—
137C4×D11—81no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yes—
142#555—111no—
143#553—111no—
144#501—111no—
145#482—111no—
146#482—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#474D1111yescharacteristic, complemented
151#469—111no—
152#466—111no—
153#442—111no—
154#435—111no—
155#428—111no—
156#427—111no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×D8—111no—
183C2×M16—111no—
184C22×C8—111no—
185C4⋊Q8C2×D1111yescharacteristic
186#126—221no—
187#125—111no—
188#124—221no—
189#124—221no—
190#123—221no—
191#121—111no—
192#121—111no—
193#121—111no—
194#121—111no—
195#121—221no—
196#121—221no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—221no—
200C4×D4C2×D1111yescharacteristic
201#117—111no—
202#117—111no—
203#117—111no—
204#117—221no—
205C2×C4⋊C4—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107C2×D1111yescharacteristic
210#107C2×D1111yescharacteristic
211#106—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215C4⋊C8C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102C2×D1111yescharacteristic
221#102C2×D1111yescharacteristic
222C22⋊C8—111no—
223C22⋊C8—111no—
224#97—111no—
225C2×C11—81no—
226C2×C11#54711yescharacteristic
227C2×C11#57511yescharacteristic
228C2×C11#57611yescharacteristic
229D11—41no—
230D11—41no—
231D11—81no—
232C2×Q8—21no—
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4C22×D1111yescharacteristic
240C22×C4—21no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—221no—
244C22×C4—221no—
245D8—222no—
246M16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—222no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—111no—
265C22⋊C4—111no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#334711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—111no—
281C23—111no—
282C23—221no—
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—221no—
287D4—221no—
288D4—441no—
289D4—442no—
290D4—881no—
291D4—881no—
292D4—881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—81no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—442no—
307C2×C4—881no—
308C2×C4D4×D1111yescharacteristic
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—112no—
314C8—221no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—221no—
319C22—221no—
320C22—221no—
321C22—221no—
322C22—221no—
323C22—221no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—221no—
334C4—221no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4#6704011yescharacteristic
339C4#41×D1111yescharacteristic
340C2—81no—
341C2—441no—
342C2—441no—
343C2—881no—
344C2#1062316211yescharacteristic
345C2#1062328811yescharacteristic
346C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
hypercenter#474D11
hypocenterC11#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623265C2semidirect
2. #10623089C2semidirect
3. C11×#474C2semidirect
4. #10622693C2semidirect
5. #10622627C2semidirect
6. #10622498C2semidirect
7. #10622495C2semidirect
8. #10622494C2semidirect
9. #10622493C2semidirect
10. #10622460C2semidirect
11. #10622449C2semidirect
12. #10622397C2semidirect
13. #10622395C2semidirect
14. #10622392C2semidirect
15. #10622388C2semidirect
150. #474D11semidirect
278. C11#3347semidirect

Maximal subgroups

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

subgroupindex
#106232652
#106230892
C11×#4742
#106226932
#106226272
#106224982
#106224952
#106224942
#106224932
#106224602
#106224492
#106223972
#106223952
#106223922
#106223882
#334711