Finite Group Databasebeta

← #13080833

Subgroups — #13080833

Order 1408.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623360C211yesmaximal, characteristic
2#10623044C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622429C211yesmaximal, characteristic, complemented
9#10622427C211yesmaximal, characteristic, complemented
10#10622413C211yesmaximal, characteristic, complemented
11#10622411C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic, complemented
13#10622383C211yesmaximal, characteristic, complemented
14#10622379C211yesmaximal, characteristic, complemented
15#10622371C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic, complemented
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20#67000C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic, complemented
23#66992—21no—
24#66990—21no—
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66983C2211yescharacteristic
28#66982—21no—
29#66982—21no—
30C4×C22⋊D11C2211yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32#66979—21no—
33#66977C2211yescharacteristic, complemented
34C2×#4314C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66951—21no—
37#66950C2211yescharacteristic
38#66945C2211yescharacteristic
39#66943C2211yescharacteristic, complemented
40#66942—21no—
41#66940C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C23×D11—21no—
60C11×#41—22no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11D411yescharacteristic
71C22×Dic11—21no—
72D4×D11—22no—
73D4×D11—41no—
74C2×D44C2311yescharacteristic
75C2×C4×D11C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×M16—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11D411yescharacteristic
86#4326—41no—
87#4324—22no—
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)⋊C4—21no—
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—41no—
110#4313—41no—
111#3323—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—81no—
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—42no—
123D4×C11#4112yes—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—41no—
134C22⋊D11—42no—
135C22⋊D11—81no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—81no—
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145C4×D11—21no—
146C4×D11—21no—
147Dic22—21no—
148Dic22—21no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#552—111no—
154#546—111no—
155#488—111no—
156#485—111no—
157#481—111no—
158#478—111no—
159#470—111no—
160#468—111no—
161#464—111no—
162#452—111no—
163#450—111no—
164C4×SD16—111no—
165#436—111no—
166#418—111no—
167#417D1111yescharacteristic, complemented
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—84no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11C2×#4111yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41C2×D1111yescharacteristic
195C22×D4—111no—
196C2×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16—111no—
200C2×M16C2×D1111yescharacteristic, complemented
201#126—221no—
202#125—111no—
203#125—221no—
204#124—111no—
205#123—221no—
206#123—221no—
207C22⋊Q8—111no—
208C22⋊Q8—111no—
209C22⋊Q8—111no—
210#121—111no—
211#121—221no—
212#120—221no—
213C4×Q8—111no—
214C4×D4—111no—
215C4×D4—111no—
216#117—111no—
217#117—221no—
218C2×C4⋊C4C2×D1111yescharacteristic, complemented
219C2×C22⋊C4—221no—
220#107—111no—
221#106—111no—
222#106—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#103C2×D1111yescharacteristic, complemented
227#103C2×D1111yescharacteristic, complemented
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233#102C2×D1111yescharacteristic
234C22⋊C8—111no—
235C22⋊C8—111no—
236C4×C8—111no—
237C2×C11—42no—
238C2×C11—41no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—41no—
243D11—81no—
244C24—221no—
245#41—22no—
246#41—41no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—222no—
254C2×D4—221no—
255C2×D4—441no—
256C2×D4C22×D1111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—111no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—222no—
264SD16—441no—
265M16—41no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4C22×D1111yescharacteristic
282C4⋊C4C22×D1111yescharacteristic
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—111no—
294C42—221no—
295C42—221no—
296C11#332311yescharacteristic, complemented, Sylow
297C23—21no—
298C23—111no—
299C23—221no—
300C23—442no—
301C23—442no—
302C23—881no—
303C23D4×D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—221no—
307Q8—221no—
308D4—21no—
309D4—42no—
310D4—221no—
311D4—221no—
312D4—441no—
313D4—442no—
314D4—881no—
315D4#433912yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—881no—
332C2×C4D4×D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—884no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—221no—
357C4—221no—
358C4—221no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4C2×#433911yescharacteristic
363C4#6703711yescharacteristic
364C2—41no—
365C2—42no—
366C2—441no—
367C2—881no—
368C2#1062302111yescharacteristic
369C2#1062330411yescharacteristic
370C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radical#10623360C2
hypercenter#417D11
hypocenterC11#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #10623044C2semidirect
3. C11×#417C2semidirect
4. #10622852C2semidirect
5. #10622747C2semidirect
6. #10622741C2semidirect
7. #10622581C2semidirect
8. #10622429C2semidirect
9. #10622427C2semidirect
10. #10622413C2semidirect
11. #10622411C2semidirect
12. #10622389C2semidirect
13. #10622383C2semidirect
14. #10622379C2semidirect
15. #10622371C2semidirect
18. C2×C11×M16C22semidirect
19. C2×C11×C4⋊C4C22semidirect
22. C2×#4326C22semidirect
33. #66977C22semidirect
39. #66943C22semidirect
41. #66940C22semidirect
42. C11×#103C22semidirect
43. C11×#103C22semidirect
46. #66899C22semidirect
48. C22⋊(C11⋊C8)C22semidirect
51. #66882C22semidirect
52. #66880C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
57. #66872C22semidirect
58. #66872C22semidirect
167. #417D11semidirect
200. C2×M16C2×D11semidirect
218. C2×C4⋊C4C2×D11semidirect
226. #103C2×D11semidirect
227. #103C2×D11semidirect
296. C11#3323semidirect

Maximal subgroups

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

subgroupindex
#106233602
#106230442
C11×#4172
#106228522
#106227472
#106227412
#106225812
#106224292
#106224272
#106224132
#106224112
#106223892
#106223832
#106223792
#106223712
#332311