Finite Group Databasebeta

← #13078776

Subgroups — #13078776

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623109C211yesmaximal, characteristic, complemented
2C4×#4343C211yesmaximal, characteristic
3C11×#441C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic
5#10622795C211yesmaximal, characteristic, complemented
6#10622643C211yesmaximal, characteristic, complemented
7#10622639C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622480C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622427C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic
13#10622407C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66997C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26#66950C2211yescharacteristic
27#66949—21no—
28#66946—21no—
29#66946C2211yescharacteristic
30#66945—21no—
31#66945C2211yescharacteristic
32#66942—21no—
33#66941C2211yescharacteristic
34C4×D44—21no—
35C4×D44C2211yescharacteristic
36#66925—21no—
37C42×D11—21no—
38C42×D11C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61#4343—22no—
62#4343—22no—
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11D411yescharacteristic
69C2×C4×D11D411yescharacteristic
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—21no—
72C2×Dic22C2311yescharacteristic
73C11×Q16—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C42×C11—21no—
81C42×C11—21no—
82C42×C11C2311yescharacteristic
83#4326—22no—
84#4325—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11D411yescharacteristic
103C4×Dic11D411yescharacteristic
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4314—22no—
108#3116—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11#4112yes—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—24no—
129D44—21no—
130D44#4112yes—
131C4×D11—24no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—22no—
135C4×D11—41no—
136C4×D11—42no—
137C4×D11—42no—
138Dic22—21no—
139Dic22—21no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#533—111no—
146C4×#41—111no—
147#485—111no—
148#485—111no—
149#477—111no—
150#476—111no—
151#462—111no—
152#461—111no—
153#452—111no—
154#452—111no—
155#441—111no—
156#441D1111yescharacteristic, complemented
157#440—111no—
158#440—111no—
159#432—111no—
160C22×C11C22×D411yescharacteristic
161C2×D11—22no—
162C2×D11—21no—
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—22no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C11C2×#4111yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11#13712yes—
181C2×#41—111no—
182C2×Q16—111no—
183C2×Q16C2×D1111yescharacteristic
184C2×SD16—111no—
185C2×SD16—111no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188#125—221no—
189C22⋊Q8—111no—
190C22⋊Q8—111no—
191C22⋊Q8—221no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—221no—
195C4×Q8C2×D1111yescharacteristic
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—221no—
200C4×D4—221no—
201#117—111no—
202#117—221no—
203#117—221no—
204C2×C42—111no—
205C2×C42—221no—
206#107—111no—
207#107—111no—
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211C4⋊C8—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#103C2×D1111yescharacteristic
218#102—111no—
219#102—111no—
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223#97C2×D1111yescharacteristic
224C2×C11#52511yescharacteristic
225C2×C11C2×#13711yescharacteristic
226C2×C11#57511yescharacteristic
227D11—41no—
228D11—42no—
229#41—222no—
230#41—222no—
231C2×Q8—111no—
232C2×Q8—221no—
233C2×Q8C22×D1111yescharacteristic
234C2×Q8C22×D1111yescharacteristic
235C2×D4—111no—
236C2×D4—221no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243Q16—22no—
244Q16—222no—
245SD16—222no—
246SD16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—21no—
271C42—111no—
272C42—111no—
273C42—111no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#311611yescharacteristic, complemented, Sylow
279C23—111no—
280C23—221no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—221no—
285Q8—221no—
286Q8—442no—
287Q8#433912yes—
288D4—112no—
289D4—224no—
290D4—221no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—224no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—441no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4D4×D1111yescharacteristic
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—221no—
314C8—221no—
315C22—221no—
316C22—221no—
317C22—222no—
318C22—221no—
319C22—441no—
320C22—441no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—112no—
329C4—221no—
330C4—221no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4C2×#433911yescharacteristic
335C4#41×D1111yescharacteristic
336C2—441no—
337C2—442no—
338C2#1062307811yescharacteristic
339C2D11×#13711yescharacteristic
340C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#441C2
socleC22×C11C22×D4
prime radicalC2×#4343C22
hypercenter#441D11
hypocenterC11#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #10623109C2semidirect
3. C11×#441C2semidirect
5. #10622795C2semidirect
6. #10622643C2semidirect
7. #10622639C2semidirect
8. #10622483C2semidirect
9. #10622480C2semidirect
10. #10622431C2semidirect
11. #10622427C2semidirect
13. #10622407C2semidirect
14. #10622323C2semidirect
15. #10622318C2semidirect
156. #441D11semidirect
278. C11#3116semidirect

Maximal subgroups

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

subgroupindex
#106231092
C4×#43432
C11×#4412
#106228002
#106227952
#106226432
#106226392
#106224832
#106224802
#106224312
#106224272
#106224232
#106224072
#106223232
#106223182
#311611