Finite Group Databasebeta

← #13078792

Subgroups — #13078792

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#10623222C211yesmaximal, characteristic
2C4×Q8×D11C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622641C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622476C211yesmaximal, characteristic
9#10622466C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622448C211yesmaximal, characteristic, complemented
12#10622430C211yesmaximal, characteristic, complemented
13#10622421C211yesmaximal, characteristic, complemented
14#10622419C211yesmaximal, characteristic
15#10622402C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22C2×Dic44C2211yescharacteristic
23C2×#4314C2211yescharacteristic
24#66951—21no—
25#66950C2211yescharacteristic
26#66948C2211yescharacteristic
27#66947—21no—
28#66946—21no—
29#66946C2211yescharacteristic
30#66945—21no—
31C4⋊C4×D11—21no—
32C4⋊C4×D11C2211yescharacteristic
33#66940—21no—
34#66940C2211yescharacteristic
35#66940C2211yescharacteristic
36#66928C2211yescharacteristic
37C42×D11—21no—
38C42×D11C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66885C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51#66879C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60Q8×D11—22no—
61Q8×D11—22no—
62C2×D44—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11D411yescharacteristic
68C2×C4×D11D411yescharacteristic
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×Dic22C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
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
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107#4314—22no—
108#3117—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11#4112yes—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44—21no—
128D44—42no—
129C4×D11—24no—
130C4×D11—22no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—41no—
134C4×D11—42no—
135C4×D11—42no—
136Dic22—24no—
137Dic22—21no—
138Dic22—21no—
139Dic22—21no—
140Dic22#4112yes—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#529—111no—
146C2×C4×Q8—111no—
147#484—111no—
148#481—111no—
149#479—111no—
150#479D1111yescharacteristic, complemented
151#464—111no—
152#464—111no—
153#451—111no—
154#448—111no—
155#441—111no—
156#441—111no—
157#440—111no—
158#440—111no—
159#432—111no—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11#13712yes—
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—22no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181C22×Q8—111no—
182C2×Q16—111no—
183C2×Q16—111no—
184C2×SD16—111no—
185C2×SD16—111no—
186#126—221no—
187#125C2×D1111yescharacteristic
188#124—111no—
189#123—221no—
190C22⋊Q8—111no—
191#121—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—221no—
197C4×Q8—221no—
198C4×Q8C2×D1111yescharacteristic
199C4×D4—111no—
200C4×D4—221no—
201#117—221no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C42—111no—
205C2×C42—221no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211C4⋊C8C2×D1111yescharacteristic
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#97—111no—
224C2×C11#52511yescharacteristic
225C2×C11C2×#13711yescharacteristic
226C2×C11#57511yescharacteristic
227D11—22no—
228D11—81no—
229C2×Q8—111no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×Q8—222no—
233C2×Q8—222no—
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—222no—
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—21no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#311711yescharacteristic, complemented, Sylow
279C23—111no—
280C23—221no—
281Q8—21no—
282Q8—112no—
283Q8—224no—
284Q8—221no—
285Q8—221no—
286Q8—221no—
287Q8#434312yes—
288D4—221no—
289D4—221no—
290D4—442no—
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—112no—
316C22—221no—
317C22—221no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—221no—
329C4—221no—
330C4—221no—
331C4—222no—
332C4—441no—
333C4—441no—
334C4C2×#434311yescharacteristic
335C4#41×D1111yescharacteristic
336C2—222no—
337C2—881no—
338C2#1062315811yescharacteristic
339C2#1062329911yescharacteristic
340C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#479D11
hypocenterC11#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D11C2semidirect
3. C11×#479C2semidirect
4. #10622676C2semidirect
5. #10622641C2semidirect
6. #10622502C2semidirect
7. #10622497C2semidirect
9. #10622466C2semidirect
10. #10622458C2semidirect
11. #10622448C2semidirect
12. #10622430C2semidirect
13. #10622421C2semidirect
15. #10622402C2semidirect
150. #479D11semidirect
278. C11#3117semidirect

Maximal subgroups

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

subgroupindex
#106232222
C4×Q8×D112
C11×#4792
#106226762
#106226412
#106225022
#106224972
#106224762
#106224662
#106224582
#106224482
#106224302
#106224212
#106224192
#106224022
#311711