Finite Group Databasebeta

← #13080830

Subgroups — #13080830

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#10623161C211yesmaximal, characteristic
2#10623060C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4#10622665C211yesmaximal, characteristic, complemented
5#10622614C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622476C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622416C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic, complemented
13#10622411C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#67000C2211yescharacteristic
21C2×#4326C2211yescharacteristic, complemented
22C4×C22⋊D11C2211yescharacteristic
23#66977C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27C2×#4313C2211yescharacteristic, complemented
28#66950C2211yescharacteristic, complemented
29#66948—21no—
30#66948C2211yescharacteristic
31#66947—21no—
32#66946C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic, complemented
34#66943C2211yescharacteristic, complemented
35#66940C2211yescharacteristic, complemented
36#66936—21no—
37#66935—21no—
38C22⋊C4×D11—21no—
39#66932—21no—
40#66925—21no—
41#66923—21no—
42C11×#107C2211yescharacteristic, complemented
43C11×#106C2211yescharacteristic, complemented
44C11×#103C2211yescharacteristic, complemented
45C11×#103C2211yescharacteristic, complemented
46C11×C22⋊C8C2211yescharacteristic
47#66899C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51Dic11⋊C8C2211yescharacteristic, complemented
52C8×Dic11C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63#4343—22no—
64#4343—41no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—22no—
68C2×D44—21no—
69C2×D44—41no—
70C2×D44C2311yescharacteristic
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11D411yescharacteristic
88#4326—41no—
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
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#4314—41no—
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—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C22⋊D11—41no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135D44—21no—
136D44—21no—
137D44—21no—
138D44—42no—
139D44—42no—
140D44—81no—
141D44#4112yes—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145C4×D11—42no—
146C4×D11—81no—
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#485D1111yescharacteristic, complemented
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#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×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
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—221no—
217#117C2×D1111yescharacteristic
218C2×C4⋊C4—111no—
219C2×C22⋊C4—221no—
220#107C2×D1111yescharacteristic, complemented
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⋊C8C2×D1111yescharacteristic
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×Q8—111no—
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—441no—
263SD16—222no—
264SD16—441no—
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—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22×D1111yescharacteristic
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—21no—
294C42—111no—
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—221no—
307Q8—221no—
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#41×D1111yescharacteristic
363C4#6704211yescharacteristic
364C2—41no—
365C2—441no—
366C2—442no—
367C2—881no—
368C2#1062318511yescharacteristic
369C2#1062330111yescharacteristic
370C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#10623161C2
hypercenter#485D11
hypocenterC11#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #10623060C2semidirect
3. C11×#485C2semidirect
4. #10622665C2semidirect
5. #10622614C2semidirect
6. #10622504C2semidirect
7. #10622499C2semidirect
8. #10622476C2semidirect
9. #10622465C2semidirect
10. #10622423C2semidirect
11. #10622416C2semidirect
12. #10622413C2semidirect
13. #10622411C2semidirect
14. #10622344C2semidirect
15. #10622342C2semidirect
21. C2×#4326C22semidirect
27. C2×#4313C22semidirect
28. #66950C22semidirect
33. C4⋊C4×D11C22semidirect
34. #66943C22semidirect
35. #66940C22semidirect
42. C11×#107C22semidirect
43. C11×#106C22semidirect
44. C11×#103C22semidirect
45. C11×#103C22semidirect
47. #66899C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. Dic11⋊C8C22semidirect
52. C8×Dic11C22semidirect
53. #66874C22semidirect
58. #66872C22semidirect
156. #485D11semidirect
220. #107C2×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
#106231612
#106230602
C11×#4852
#106226652
#106226142
#106225042
#106224992
#106224762
#106224652
#106224232
#106224162
#106224132
#106224112
#106223442
#106223422
#332311