Finite Group Databasebeta

← #13078728

Subgroups — #13078728

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#10623155C211yesmaximal, characteristic, complemented
2#10623053C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4#10622660C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622502C211yesmaximal, characteristic, complemented
8#10622482C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622432C211yesmaximal, characteristic, complemented
11#10622430C211yesmaximal, characteristic, complemented
12#10622411C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic
15#10622332C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C11×C22⋊Q8C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#67000C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66983C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25C2×D88C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27#66951—21no—
28#66946C2211yescharacteristic
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66945—21no—
32#66943C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66939—21no—
36(C22⋊D11)⋊C4—21no—
37(C22⋊D11)⋊C4—21no—
38(C22⋊D11)⋊C4—21no—
39#66925—21no—
40C42×D11—21no—
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66885C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C22×Dic11D411yescharacteristic
64C22×Dic11D411yescharacteristic
65#4339—22no—
66#4339—22no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×Dic22C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C42×C11—21no—
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—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
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
106D88—22no—
107#4314—22no—
108#3111—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11—21no—
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114C2×C4×C11—21no—
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—
123C22⋊D11—42no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134D44—21no—
135D44#4112yes—
136C4×D11—24no—
137C4×D11—42no—
138C4×D11—42no—
139C4×D11—42no—
140Dic22—21no—
141Dic22#4112yes—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#529—111no—
147C4×#41—111no—
148#485D1111yescharacteristic, complemented
149#482—111no—
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×C11C22×D411yescharacteristic
165C2×D11—22no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C11C2×#4111yescharacteristic
178Dic11—22no—
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—21no—
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⋊Q8C2×D1111yescharacteristic
194#121—111no—
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#103C2×D1111yescharacteristic
218#103C2×D1111yescharacteristic
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223C22⋊C8—111no—
224C22⋊C8C2×D1111yescharacteristic
225#97—111no—
226#97—111no—
227C2×C11—41no—
228C2×C11#52511yescharacteristic
229C2×C11#57511yescharacteristic
230C2×C11#57511yescharacteristic
231D11—42no—
232D11—81no—
233#41—222no—
234#41—222no—
235C2×Q8—111no—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—111no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
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—21no—
257C4⋊C4—111no—
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—221no—
284C23—221no—
285C23D4×D1111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—112no—
289Q8—221no—
290D4—112no—
291D4—224no—
292D4—221no—
293D4—221no—
294D4—221no—
295D4—442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—224no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—222no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—221no—
339C4—222no—
340C4—441no—
341C4#41×D1111yescharacteristic
342C4#41×D1111yescharacteristic
343C2—41no—
344C2—442no—
345C2—881no—
346C2#1062318711yescharacteristic
347C2#1062329911yescharacteristic
348C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#10622347C2
hypercenter#485D11
hypocenterC11#3111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10623155C2semidirect
2. #10623053C2semidirect
3. C11×#485C2semidirect
4. #10622660C2semidirect
5. #10622616C2semidirect
6. #10622504C2semidirect
7. #10622502C2semidirect
8. #10622482C2semidirect
9. #10622470C2semidirect
10. #10622432C2semidirect
11. #10622430C2semidirect
12. #10622411C2semidirect
13. #10622402C2semidirect
15. #10622332C2semidirect
148. #485D11semidirect
282. C11#3111semidirect

Maximal subgroups

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

subgroupindex
#106231552
#106230532
C11×#4852
#106226602
#106226162
#106225042
#106225022
#106224822
#106224702
#106224322
#106224302
#106224112
#106224022
#106223472
#106223322
#311111