Finite Group Databasebeta

← #13080838

Subgroups — #13080838

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#10623170C211yesmaximal, characteristic, complemented
2#10623161C211yesmaximal, characteristic
3C11×#470C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6#10622744C211yesmaximal, characteristic, complemented
7#10622741C211yesmaximal, characteristic, complemented
8#10622659C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622484C211yesmaximal, characteristic, complemented
11#10622476C211yesmaximal, characteristic, complemented
12#10622425C211yesmaximal, characteristic, complemented
13#10622416C211yesmaximal, characteristic, complemented
14#10622413C211yesmaximal, characteristic, complemented
15#10622401C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic, complemented
19C2×C11×M16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22#67000C2211yescharacteristic
23#66999C2211yescharacteristic, complemented
24Q8×Dic11C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27C4×C22⋊D11C2211yescharacteristic
28#66979C2211yescharacteristic
29C2×#4313C2211yescharacteristic, complemented
30#66948—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66946C2211yescharacteristic
34#66945—21no—
35C4⋊C4×D11C2211yescharacteristic, complemented
36#66943C2211yescharacteristic, complemented
37#66942—21no—
38#66936—21no—
39#66935—21no—
40C22⋊C4×D11—21no—
41#66932—21no—
42C11×#106C2211yescharacteristic, complemented
43C11×#103C2211yescharacteristic, complemented
44C11×#103C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66899C2211yescharacteristic, complemented
47C22⋊(C11⋊C8)C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11D411yescharacteristic
64#4343—22no—
65#4343—41no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—22no—
69C2×D44—21no—
70C2×D44—41no—
71C2×D44C2311yescharacteristic
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11C2311yescharacteristic
77C11×Q16—41no—
78C11×M16—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11D411yescharacteristic
89#4325—22no—
90#4325—41no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3323—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—81no—
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44—21no—
139D44—21no—
140D44—42no—
141D44—42no—
142D44—81no—
143D44#4112yes—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147C4×D11—42no—
148C4×D11—81no—
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#470D1111yescharacteristic, complemented
160#468—111no—
161#464—111no—
162#452—111no—
163#450—111no—
164C4×SD16—111no—
165#436—111no—
166#418—111no—
167#417—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C22×D411yescharacteristic
172C2×D11—22no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—41no—
177C2×D11—41no—
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×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×D4—111no—
196C2×Q16C2×D1111yescharacteristic, complemented
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16—111no—
200C2×M16C2×D1111yescharacteristic
201#126—221no—
202#125—111no—
203#125—221no—
204#124—111no—
205#123—221no—
206#123—221no—
207C22⋊Q8—111no—
208C22⋊Q8C2×D1111yescharacteristic
209C22⋊Q8C2×D1111yescharacteristic
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⋊C4—111no—
219C2×C22⋊C4—221no—
220#107—111no—
221#106—111no—
222#106C2×D1111yescharacteristic, complemented
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#102—111no—
233#102—111no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236C4×C8—111no—
237C2×C11—41no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—41no—
242D11—42no—
243D11—81no—
244C24—221no—
245#41—222no—
246#41—441no—
247C2×Q8C22×D1111yescharacteristic
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—222no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262Q16—41no—
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—21no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4C22×D1111yescharacteristic
282C4⋊C4C22×D1111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—111no—
286C22⋊C4—111no—
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—111no—
298C23—221no—
299C23—221no—
300C23—442no—
301C23—442no—
302C23—881no—
303C23D4×D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—112no—
309D4—221no—
310D4—221no—
311D4—221no—
312D4—442no—
313D4—442no—
314D4—441no—
315D4—881no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—881no—
332C2×C4D4×D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—221no—
342C22—221no—
343C22—221no—
344C22—222no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—884no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—221no—
358C4—221no—
359C4—221no—
360C4—441no—
361C4—441no—
362C4#6703711yescharacteristic
363C4#41×D1111yescharacteristic
364C2—41no—
365C2—441no—
366C2—442no—
367C2—881no—
368C2#1062314111yescharacteristic
369C2#1062330811yescharacteristic
370C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
prime radical#10623161C2
hypercenter#470D11
hypocenterC11#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #10623170C2semidirect
3. C11×#470C2semidirect
4. #10622800C2semidirect
5. #10622798C2semidirect
6. #10622744C2semidirect
7. #10622741C2semidirect
8. #10622659C2semidirect
9. #10622658C2semidirect
10. #10622484C2semidirect
11. #10622476C2semidirect
12. #10622425C2semidirect
13. #10622416C2semidirect
14. #10622413C2semidirect
15. #10622401C2semidirect
18. C2×C11×Q16C22semidirect
23. #66999C22semidirect
24. Q8×Dic11C22semidirect
29. C2×#4313C22semidirect
35. C4⋊C4×D11C22semidirect
36. #66943C22semidirect
42. C11×#106C22semidirect
43. C11×#103C22semidirect
44. C11×#103C22semidirect
45. #66899C22semidirect
46. #66899C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. C8×Dic11C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
159. #470D11semidirect
196. C2×Q16C2×D11semidirect
222. #106C2×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
#106231702
#106231612
C11×#4702
#106228002
#106227982
#106227442
#106227412
#106226592
#106226582
#106224842
#106224762
#106224252
#106224162
#106224132
#106224012
#332311