Finite Group Databasebeta

← #13081527

Subgroups — #13081527

Order 1408.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic22C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic
4#10622777C211yesmaximal, characteristic
5SD16×Dic11C211yesmaximal, characteristic
6#10622635C211yesmaximal, characteristic, complemented
7#10622620C211yesmaximal, characteristic
8#10622489C211yesmaximal, characteristic, complemented
9#10622487C211yesmaximal, characteristic, complemented
10#10622412C211yesmaximal, characteristic, complemented
11#10622407C211yesmaximal, characteristic, complemented
12#10622374C211yesmaximal, characteristic
13#10622372C211yesmaximal, characteristic
14#10622315C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23#66977—21no—
24C2×Dic11⋊C4—21no—
25#66943C2211yescharacteristic
26#66941—21no—
27#66941—21no—
28#66941C2211yescharacteristic
29#66941C2211yescharacteristic
30#66941C2211yescharacteristic
31#66931—21no—
32#66931—21no—
33#66923C2211yescharacteristic
34#66922—21no—
35#66922C2211yescharacteristic
36C4×Dic22—21no—
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#103C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#97C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66882C2211yescharacteristic
47#66882C2211yescharacteristic
48#66881C2211yescharacteristic
49#66881C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22D411yescharacteristic
69C11×SD16Q814yescomplemented
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11D411yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4D411yescharacteristic
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3385—111nomaximal, Sylow
104C23×C11—21no—
105Q8×C11—21no—
106Q8×C11C2×Q812yes—
107D4×C11—21no—
108D4×C11C2×Q812yes—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—81no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2411yescharacteristic
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—42no—
121C2×Dic11—81no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126Dic22—22no—
127Dic22—81no—
128Dic22—81no—
129Dic22—81no—
130Dic22—81no—
131C8×C11—21no—
132C8×C11C2×Q812yes—
133C11⋊C8—21no—
134C11⋊C8—21no—
135Q82—111no—
136#554—111no—
137#501—111no—
138#501—111no—
139#500—111no—
140#479—111no—
141#479—111no—
142#477—111no—
143#476—111no—
144#474—111no—
145#474—111no—
146#446—111no—
147#440—111no—
148#440D1111yescharacteristic
149C4×SD16—111no—
150C22×C11—22no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11C22×D411yescharacteristic
154C4×C11—22no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11C22×Q811yescharacteristic
160C4×C112−1+411yescharacteristic
161Dic11—21no—
162Dic11—21no—
163Dic11—21no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11#13712yes—
169C2×SD16C2×D1111yescharacteristic
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—111no—
173C4⋊Q8—111no—
174C4⋊Q8—221no—
175C4⋊Q8—221no—
176C4⋊Q8—221no—
177#125—111no—
178#125—111no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C4×Q8—111no—
183C4×Q8—111no—
184C4×Q8—111no—
185C4×Q8—221no—
186C4×Q8C2×D1111yescharacteristic
187C4×D4—111no—
188C4×D4—111no—
189C4×D4C2×D1111yescharacteristic
190C2×C4⋊C4—221no—
191#107—111no—
192#107—111no—
193#107—111no—
194#107—111no—
195#107—111no—
196#107C2×D1111yescharacteristic
197#106—111no—
198#106—111no—
199#106—111no—
200C4⋊C8—111no—
201C4⋊C8—111no—
202C4⋊C8—111no—
203#103—111no—
204#103—111no—
205#103C2×D1111yescharacteristic
206#102—111no—
207#102—111no—
208#102C2×D1111yescharacteristic
209#97—111no—
210#97C2×D1111yescharacteristic
211C4×C8—111no—
212C2×C11—42no—
213C2×C11D4×Q811yescharacteristic
214C2×C11C2×#13711yescharacteristic
215C2×C11#57611yescharacteristic
216C2×Q8—111no—
217C2×Q8—221no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4C22×D1111yescharacteristic
223C22×C4—21no—
224C22×C4—221no—
225C22×C4—221no—
226SD16Dic2214yescomplemented
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4C22×D1111yescharacteristic
250C4⋊C4C22×D1111yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—21no—
255C42—111no—
256C42—111no—
257C42—221no—
258C42—221no—
259C42C22×D1111yescharacteristic
260C11#338511yescharacteristic, complemented, Sylow
261C23—21no—
262Q8—21no—
263Q8—222no—
264Q8—881no—
265Q8—881no—
266Q8—881no—
267Q8—881no—
268Q8C2×Dic2212yes—
269D4—21no—
270D4C2×Dic2212yes—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—81no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—442no—
284C2×C4—881no—
285C2×C4D4×D1111yescharacteristic
286C2×C4D4×D1111yescharacteristic
287C2×C4C23×D1111yescharacteristic
288C8—21no—
289C8—221no—
290C8—221no—
291C8C2×Dic2212yes—
292C22—22no—
293C22—41no—
294C22—41no—
295C22C2×D4×D1111yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—112no—
302C4—221no—
303C4—221no—
304C4—221no—
305C4—441no—
306C4—441no—
307C4—441no—
308C4—441no—
309C4C22×Dic2211yescharacteristic
310C4#6704311yescharacteristic
311C2—42no—
312C2D4×Dic2211yescharacteristic
313C2#1062330511yescharacteristic
314C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#440D11
hypocenterC11#3385
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. Q8×Dic22C2semidirect
6. #10622635C2semidirect
8. #10622489C2semidirect
9. #10622487C2semidirect
10. #10622412C2semidirect
11. #10622407C2semidirect
14. #10622315C2semidirect
15. #10622314C2semidirect
69. C11×SD16Q8semidirect
226. SD16Dic22semidirect
260. C11#3385semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic222
#106230702
C11×#4402
#106227772
SD16×Dic112
#106226352
#106226202
#106224892
#106224872
#106224122
#106224072
#106223742
#106223722
#106223152
#106223142
#338511