Finite Group Databasebeta

← #13078720

Subgroups — #13078720

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623131C211yesmaximal, characteristic, complemented
2#10623053C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622650C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622490C211yesmaximal, characteristic, complemented
8#10622484C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622400C211yesmaximal, characteristic, complemented
11#10622398C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622332C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C11×#121C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#66989C2211yescharacteristic
20#66988—21no—
21D4×Dic11—21no—
22D4×Dic11C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66977C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27C2×Dic44C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66943C2211yescharacteristic
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35(C22⋊D11)⋊C4—21no—
36(C22⋊D11)⋊C4—21no—
37#66932—21no—
38#66930—21no—
39#66925—21no—
40C42×D11—21no—
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66885C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C22×Dic11D411yescharacteristic
65C22×Dic11D411yescharacteristic
66#4339—22no—
67#4339—22no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×Dic22C2311yescharacteristic
73C2×Dic22C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86#4324—22no—
87#4323—22no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107#4314—22no—
108#3111—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—24no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—42no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—21no—
134D44#4112yes—
135C4×D11—24no—
136C4×D11—42no—
137C4×D11—42no—
138Dic22—21no—
139Dic22—21no—
140Dic22—21no—
141Dic22#4112yes—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#529—111no—
147C4×#41—111no—
148#485—111no—
149#482D1111yescharacteristic, complemented
150#479—111no—
151#478—111no—
152#464—111no—
153#463—111no—
154#452—111no—
155#449—111no—
156#442—111no—
157#441—111no—
158#440—111no—
159#440—111no—
160#432—111no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—22no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11C2×#4111yescharacteristic
177Dic11—22no—
178Dic11—21no—
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184C2×#41—111no—
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×D8—111no—
189#126—221no—
190#125—111no—
191#124—111no—
192#123—221no—
193C22⋊Q8—111no—
194#121C2×D1111yescharacteristic
195C4×Q8—111no—
196C4×Q8—111no—
197C4×Q8—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C4×D4—221no—
203C4×D4—221no—
204#117—221no—
205#117—221no—
206#117C2×D1111yescharacteristic
207C2×C42—111no—
208C2×C42—221no—
209#107—111no—
210#107C2×D1111yescharacteristic
211#106—111no—
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102C2×D1111yescharacteristic
222#102C2×D1111yescharacteristic
223C22⋊C8—111no—
224C22⋊C8C2×D1111yescharacteristic
225#97—111no—
226#97—111no—
227C2×C11—41no—
228C2×C11—81no—
229C2×C11#52511yescharacteristic
230C2×C11#57511yescharacteristic
231C2×C11#57511yescharacteristic
232D11—42no—
233#41—222no—
234#41—222no—
235C2×Q8—111no—
236C2×Q8—111no—
237C2×D4—21no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4C22×D1111yescharacteristic
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4C22×D1111yescharacteristic
248Q16—222no—
249SD16—222no—
250SD16—222no—
251D8—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C4⋊C4C22×D1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—21no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42—111no—
279C42—221no—
280C42—221no—
281C42—221no—
282C11#311111yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285C23D4×D1111yescharacteristic
286Q8—112no—
287Q8—221no—
288Q8—221no—
289Q8—221no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—112no—
294D4—224no—
295D4—221no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—224no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—442no—
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—222no—
327C22—441no—
328C22—441no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4#41×D1111yescharacteristic
342C4#41×D1111yescharacteristic
343C2—41no—
344C2—81no—
345C2—442no—
346C2#1062318711yescharacteristic
347C2#1062329911yescharacteristic
348C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radical#10622650C2
hypercenter#482D11
hypocenterC11#3111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #10623131C2semidirect
2. #10623053C2semidirect
3. C11×#482C2semidirect
5. #10622609C2semidirect
6. #10622502C2semidirect
7. #10622490C2semidirect
8. #10622484C2semidirect
9. #10622466C2semidirect
10. #10622400C2semidirect
11. #10622398C2semidirect
12. #10622380C2semidirect
13. #10622370C2semidirect
14. #10622346C2semidirect
15. #10622332C2semidirect
149. #482D11semidirect
282. C11#3111semidirect

Maximal subgroups

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

subgroupindex
#106231312
#106230532
C11×#4822
#106226502
#106226092
#106225022
#106224902
#106224842
#106224662
#106224002
#106223982
#106223802
#106223702
#106223462
#106223322
#311111