Finite Group Databasebeta

← #13078786

Subgroups — #13078786

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#10623211C211yesmaximal, characteristic
2C4×Q8×D11C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622799C211yesmaximal, characteristic, complemented
5#10622797C211yesmaximal, characteristic, complemented
6#10622783C211yesmaximal, characteristic
7#10622777C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622635C211yesmaximal, characteristic, complemented
10#10622448C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622422C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622390C211yesmaximal, characteristic
15#10622370C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C11×#124C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66991C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C4⋊C4×D11—21no—
29C4⋊C4×D11C2211yescharacteristic
30#66940—21no—
31#66940C2211yescharacteristic
32#66936—21no—
33(C22⋊D11)⋊C4—21no—
34#66932—21no—
35#66930—21no—
36C42×D11—21no—
37C42×D11C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55#66879C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64Q8×D11—22no—
65Q8×D11—22no—
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—
74C11×SD16—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C42×C11C2311yescharacteristic
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85#4326—22no—
86#4324—22no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
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×Dic11—21no—
103C4×Dic11D411yescharacteristic
104C4×Dic11D411yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3117—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11#4112yes—
115D4×C11—21no—
116D4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—42no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—24no—
133C4×D11—22no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—41no—
137C4×D11—42no—
138Dic22—24no—
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#479—111no—
151#464—111no—
152#464D1111yescharacteristic, complemented
153#451—111no—
154#448—111no—
155#441—111no—
156#441—111no—
157#440—111no—
158#440—111no—
159#432—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11#13712yes—
167C4×C11—22no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C11C2×#4111yescharacteristic
174Dic11—21no—
175Dic11—22no—
176Dic11—21no—
177Dic11—21no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181C22×Q8—111no—
182C2×Q16—111no—
183C2×Q16C2×D1111yescharacteristic
184C2×SD16—111no—
185C2×SD16C2×D1111yescharacteristic
186#126—221no—
187#125—111no—
188#124C2×D1111yescharacteristic
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#107—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8C2×D1111yescharacteristic
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic
218#102—111no—
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223#97—111no—
224C2×C11—81no—
225C2×C11#52511yescharacteristic
226C2×C11C2×#13711yescharacteristic
227C2×C11#57511yescharacteristic
228D11—22no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8C22×D1111yescharacteristic
234C2×Q8C22×D1111yescharacteristic
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243Q16—22no—
244Q16—222no—
245SD16—22no—
246SD16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—111no—
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⋊C4—221no—
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
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—21no—
280C23—111no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—112no—
285Q8—224no—
286Q8—221no—
287Q8#434112yes—
288D4—21no—
289D4—21no—
290D4—442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—222no—
298C2×C4—224no—
299C2×C4—221no—
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—41no—
316C22—41no—
317C22—41no—
318C22—112no—
319C22—221no—
320C22—221no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—221no—
328C4—221no—
329C4—221no—
330C4—222no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4C2×#434111yescharacteristic
335C4#41×D1111yescharacteristic
336C2—81no—
337C2—222no—
338C2#1062313711yescharacteristic
339C2#1062329911yescharacteristic
340C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#464D11
hypocenterC11#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D11C2semidirect
3. C11×#464C2semidirect
4. #10622799C2semidirect
5. #10622797C2semidirect
7. #10622777C2semidirect
8. #10622667C2semidirect
9. #10622635C2semidirect
10. #10622448C2semidirect
11. #10622442C2semidirect
12. #10622422C2semidirect
13. #10622402C2semidirect
15. #10622370C2semidirect
152. #464D11semidirect
278. C11#3117semidirect

Maximal subgroups

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

subgroupindex
#106232112
C4×Q8×D112
C11×#4642
#106227992
#106227972
#106227832
#106227772
#106226672
#106226352
#106224482
#106224422
#106224222
#106224022
#106223902
#106223702
#311711