Finite Group Databasebeta

← #13080836

Subgroups — #13080836

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#10623337C211yesmaximal, characteristic
2#10623170C211yesmaximal, characteristic, complemented
3C11×#450C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6#10622786C211yesmaximal, characteristic, complemented
7#10622779C211yesmaximal, characteristic, complemented
8SD16×Dic11C211yesmaximal, characteristic, complemented
9#10622665C211yesmaximal, characteristic, complemented
10#10622390C211yesmaximal, characteristic, complemented
11#10622384C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic, complemented
13#10622379C211yesmaximal, characteristic, complemented
14#10622342C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21#67006—21no—
22C2×C22⋊Dic11—21no—
23#66999C2211yescharacteristic, complemented
24Q8×Dic11C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26#66992—21no—
27#66991C2211yescharacteristic
28#66989C2211yescharacteristic
29#66988—21no—
30D4×Dic11C2211yescharacteristic
31C4×C22⋊D11C2211yescharacteristic
32#66979C2211yescharacteristic
33#66977C2211yescharacteristic
34C2×#4318C2211yescharacteristic
35C2×#4313C2211yescharacteristic, complemented
36#66945—21no—
37C4⋊C4×D11C2211yescharacteristic, complemented
38#66943C2211yescharacteristic, complemented
39#66942—21no—
40#66936—21no—
41#66932—21no—
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66882C2211yescharacteristic, complemented
52#66881C2211yescharacteristic, complemented
53#66880C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72#4341—22no—
73#4341—41no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×SD16—22no—
78C11×SD16—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11D411yescharacteristic
91#4326—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
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
107#4318—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3323—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11C2×D411yescharacteristic
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125D4×C11#4112yes—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—41no—
133C22⋊D11—42no—
134C22⋊D11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—42no—
140C2×Dic11—81no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
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#450D1111yescharacteristic, complemented
164C4×SD16—111no—
165#436—111no—
166#418—111no—
167#417—111no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—84no—
178C22×C11C22×D411yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×D4C2×D1111yescharacteristic
196C2×Q16—111no—
197C2×SD16C2×D1111yescharacteristic
198C2×SD16C2×D1111yescharacteristic
199C2×M16—111no—
200C2×M16—111no—
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⋊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#106—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233#102C2×D1111yescharacteristic
234C22⋊C8—111no—
235C22⋊C8C2×D1111yescharacteristic
236C4×C8—111no—
237C2×C11—41no—
238C2×C11—42no—
239C2×C11—81no—
240C2×C11#54611yescharacteristic
241C2×C11#57511yescharacteristic
242C2×C11#57711yescharacteristic
243D11—41no—
244C24—21no—
245#41—222no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4C22×D1111yescharacteristic
256C2×D4C22×D1111yescharacteristic
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—22no—
264SD16—41no—
265M16—441no—
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—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4C22×D1111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—111no—
285C22⋊C4—111no—
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—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—111no—
303C23D4×D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—221no—
307Q8—221no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—441no—
313D4—442no—
314D4—881no—
315D4#434112yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—221no—
324C2×C4—221no—
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—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—221no—
349C22—221no—
350C22—221no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—221no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4C2×#434111yescharacteristic
363C4#6703711yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—441no—
368C2#1062312211yescharacteristic
369C2#1062329311yescharacteristic
370C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
prime radical#10623337C2
hypercenter#450D11
hypocenterC11#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #10623170C2semidirect
3. C11×#450C2semidirect
4. #10622828C2semidirect
5. #10622787C2semidirect
6. #10622786C2semidirect
7. #10622779C2semidirect
8. SD16×Dic11C2semidirect
9. #10622665C2semidirect
10. #10622390C2semidirect
11. #10622384C2semidirect
12. #10622381C2semidirect
13. #10622379C2semidirect
14. #10622342C2semidirect
15. #10622336C2semidirect
23. #66999C22semidirect
24. Q8×Dic11C22semidirect
25. C2×#4326C22semidirect
35. C2×#4313C22semidirect
37. C4⋊C4×D11C22semidirect
38. #66943C22semidirect
45. #66899C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66882C22semidirect
52. #66881C22semidirect
53. #66880C22semidirect
54. #66880C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
57. #66874C22semidirect
58. #66872C22semidirect
163. #450D11semidirect
296. C11#3323semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106231702
C11×#4502
#106228282
#106227872
#106227862
#106227792
SD16×Dic112
#106226652
#106223902
#106223842
#106223812
#106223792
#106223422
#106223362
#332311