Finite Group Databasebeta

← #13078867

Subgroups — #13078867

Order 1408.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623114C211yesmaximal, characteristic, complemented
2#10623076C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622782C211yesmaximal, characteristic
5#10622775C211yesmaximal, characteristic, complemented
6C4×#4325C211yesmaximal, characteristic, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8#10622504C211yesmaximal, characteristic, complemented
9#10622501C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622427C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic
13#10622379C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622322C211yesmaximal, characteristic, complemented
16C2×D4×D11C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic, complemented
19C4×D4×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic, complemented
22C2×#4325C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C4×C22⋊D11—21no—
26C2×(C2×D11)⋊C4—21no—
27C2×#4314C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30#66946C2211yescharacteristic
31#66945C2211yescharacteristic
32#66943C2211yescharacteristic, complemented
33#66942—21no—
34(C22⋊D11)⋊C4—21no—
35C22⋊C4×D11—21no—
36#66929—21no—
37C4×D44C2211yescharacteristic
38#66925C2211yescharacteristic
39#66923—21no—
40C4×Dic22C2211yescharacteristic, complemented
41C11×#107C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65D4×D11—22no—
66D4×D11—22no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22C2311yescharacteristic
72C11×SD16—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82#4325—22no—
83#4324—22no—
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⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4314—22no—
108#3123—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11—24no—
112C22×D11—81no—
113C22×D11—81no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11#4112yes—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—81no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—24no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—81no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44#4112yes—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—81no—
139C4×D11—81no—
140Dic22—21no—
141Dic22—21no—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#541—111no—
147#518—111no—
148#485—111no—
149#485—111no—
150#478—111no—
151#478—111no—
152#461—111no—
153#461—111no—
154#450—111no—
155#450—111no—
156#440—111no—
157#440D1111yescharacteristic, complemented
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—22no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11C22×D411yescharacteristic
165C2×D11—21no—
166C2×D11—22no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—84no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C11C2×#4111yescharacteristic
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C22×D4—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×SD16C2×D1111yescharacteristic
190C4⋊Q8—111no—
191#126—221no—
192#126—221no—
193#125—111no—
194#125—221no—
195#125—221no—
196C22⋊Q8—111no—
197C22⋊Q8—111no—
198C4×Q8—111no—
199C4×Q8C2×D1111yescharacteristic, complemented
200C4×D4—111no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4C2×D1111yescharacteristic
206#117—111no—
207#117—111no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210#107—111no—
211#107C2×D1111yescharacteristic, complemented
212#106—111no—
213#106—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic, complemented
220#102—111no—
221#102—111no—
222#102—111no—
223#102C2×D1111yescharacteristic
224C22⋊C8—111no—
225C22⋊C8—111no—
226#97C2×D1111yescharacteristic, complemented
227C4×C8—111no—
228C2×C11—42no—
229C2×C11#52511yescharacteristic
230C2×C11#57711yescharacteristic
231C2×C11#57711yescharacteristic
232D11—41no—
233D11—42no—
234C24—221no—
235C2×Q8—111no—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—111no—
238C2×D4—221no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4C22×D1111yescharacteristic
242C22×C4—21no—
243C22×C4—111no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247SD16—22no—
248SD16—222no—
249SD16—222no—
250SD16—222no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8C22×D1111yescharacteristic
254C2×C8C22×D1111yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4C22×D1111yescharacteristic
268C4⋊C4C22×D1111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—111no—
271C22⋊C4—111no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C42—21no—
279C42—111no—
280C42—221no—
281C42—221no—
282C42C22×D1111yescharacteristic
283C11#312311yescharacteristic, complemented, Sylow
284C23—21no—
285C23—111no—
286C23—224no—
287C23—221no—
288C23—881no—
289C23—881no—
290Q8—21no—
291Q8—21no—
292Q8—221no—
293Q8—221no—
294D4—21no—
295D4—112no—
296D4—224no—
297D4—221no—
298D4#433912yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4D4×D1111yescharacteristic
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—221no—
320C8—221no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—221no—
325C22—221no—
326C22—221no—
327C22—222no—
328C22—441no—
329C22—441no—
330C22—884no—
331C22C2×D4×D1111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—221no—
338C4—221no—
339C4—221no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4C2×#433911yescharacteristic
344C4#41×D1111yescharacteristic
345C2—42no—
346C2—441no—
347C2—442no—
348C2#1062307811yescharacteristic
349C2#1062330611yescharacteristic
350C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×D4×D11C22
hypercenter#440D11
hypocenterC11#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623114C2semidirect
3. C11×#440C2semidirect
5. #10622775C2semidirect
6. C4×#4325C2semidirect
7. C4×#4324C2semidirect
8. #10622504C2semidirect
9. #10622501C2semidirect
10. #10622431C2semidirect
11. #10622427C2semidirect
13. #10622379C2semidirect
14. #10622323C2semidirect
15. #10622322C2semidirect
18. C4×Q8×C11C22semidirect
21. #66997C22semidirect
32. #66943C22semidirect
40. C4×Dic22C22semidirect
41. C11×#107C22semidirect
42. C11×#103C22semidirect
44. C11×#97C22semidirect
45. #66899C22semidirect
50. #66882C22semidirect
51. #66880C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. #66874C22semidirect
56. #66872C22semidirect
57. #66872C22semidirect
58. C4×C11⋊C8C22semidirect
157. #440D11semidirect
199. C4×Q8C2×D11semidirect
211. #107C2×D11semidirect
219. #103C2×D11semidirect
226. #97C2×D11semidirect
283. C11#3123semidirect

Maximal subgroups

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

subgroupindex
#106231142
#106230762
C11×#4402
#106227822
#106227752
C4×#43252
C4×#43242
#106225042
#106225012
#106224312
#106224272
#106223892
#106223792
#106223232
#106223222
#312311