Finite Group Databasebeta

← #13081370

Subgroups — #13081370

Order 1408.

358 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#10623116C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622778C211yesmaximal, characteristic, complemented
5#10622778C211yesmaximal, characteristic, complemented
6#10622635C211yesmaximal, characteristic, complemented
7#10622628C211yesmaximal, characteristic
8#10622504C211yesmaximal, characteristic, complemented
9#10622503C211yesmaximal, characteristic, complemented
10#10622413C211yesmaximal, characteristic, complemented
11#10622408C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic, complemented
14#10622326C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#67000C2211yescharacteristic
20#67000C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66977—21no—
26C2×Dic11⋊C4—21no—
27#66947—21no—
28#66947—21no—
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66943C2211yescharacteristic
32#66941C2211yescharacteristic
33#66931—21no—
34#66931—21no—
35#66928—21no—
36#66927C2211yescharacteristic
37C4×D44—21no—
38#66923C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×Dic22—21no—
71C2×Dic22D411yescharacteristic
72C11×SD16—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83#4323—22no—
84#4323—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⋊Dic11D411yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3370—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108C22×D11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111D4×C11—21no—
112D4×C11#4112yes—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—42no—
123C2×Dic11—81no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44—21no—
130D44—21no—
131D44—21no—
132D44—42no—
133D44—81no—
134C4×D11—81no—
135C4×D11—81no—
136Dic22—41no—
137Dic22—81no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#559—111no—
143#554—111no—
144#490—111no—
145#489—111no—
146#488—111no—
147#479—111no—
148#478—111no—
149#474—111no—
150#463—111no—
151#463—111no—
152#459—111no—
153#446—111no—
154#442—111no—
155#440D1111yescharacteristic, complemented
156C4×D8—111no—
157C22×C11—22no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C112−1+411yescharacteristic
174Dic11—21no—
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—41no—
179Dic11—41no—
180C2×SD16C2×D1111yescharacteristic
181C2×D8—111no—
182C2×D8—111no—
183C4⋊Q8—111no—
184#127—111no—
185#125—111no—
186#125—111no—
187#124—111no—
188#124—111no—
189#124—221no—
190#123—221no—
191#123—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C22⋊Q8—221no—
195C4×Q8—111no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C4×D4C2×D1111yescharacteristic
203C2×C4⋊C4—221no—
204#107—111no—
205#107C2×D1111yescharacteristic
206#106—111no—
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8—111no—
210#103—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#102—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102C2×D1111yescharacteristic
220#97—111no—
221#97C2×D1111yescharacteristic
222C4×C8—111no—
223C2×C11—42no—
224C2×C11#54811yescharacteristic
225C2×C11#57511yescharacteristic
226C2×C11#57611yescharacteristic
227D11—81no—
228D11—81no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×Q8C22×D1111yescharacteristic
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—22no—
243D8—222no—
244D8—222no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—21no—
272C42—111no—
273C42—111no—
274C42C22×D1111yescharacteristic
275C11#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—221no—
278C23—221no—
279Q8—21no—
280Q8—21no—
281Q8—441no—
282Q8—881no—
283D4—21no—
284D4—221no—
285D4—221no—
286D4—221no—
287D4—221no—
288D4—442no—
289D4—881no—
290D4#433912yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—442no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4D4×D1111yescharacteristic
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—221no—
311C8—221no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—221no—
328C4—221no—
329C4—221no—
330C4—221no—
331C4—441no—
332C4—441no—
333C4C2×#433911yescharacteristic
334C4#6704311yescharacteristic
335C2—42no—
336C2—881no—
337C2—881no—
338C2#1062308311yescharacteristic
339C2#1062330511yescharacteristic
340C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10622628C2
hypercenter#440D11
hypocenterC11#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623116C2semidirect
2. #10623070C2semidirect
3. C11×#440C2semidirect
4. #10622778C2semidirect
5. #10622778C2semidirect
6. #10622635C2semidirect
8. #10622504C2semidirect
9. #10622503C2semidirect
10. #10622413C2semidirect
11. #10622408C2semidirect
12. #10622398C2semidirect
13. #10622369C2semidirect
14. #10622326C2semidirect
15. #10622314C2semidirect
155. #440D11semidirect
275. C11#3370semidirect

Maximal subgroups

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

subgroupindex
#106231162
#106230702
C11×#4402
#106227782
#106226352
#106226282
#106225042
#106225032
#106224132
#106224082
#106223982
#106223692
#106223262
#106223142
#337011