Finite Group Databasebeta

← #13081566

Subgroups — #13081566

Order 1408.

334 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623100C211yesmaximal, characteristic, complemented
2#10623074C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic
4#10622777C211yesmaximal, characteristic
5SD16×Dic11C211yesmaximal, characteristic
6#10622633C211yesmaximal, characteristic, complemented
7#10622622C211yesmaximal, characteristic
8#10622491C211yesmaximal, characteristic, complemented
9#10622489C211yesmaximal, characteristic, complemented
10#10622412C211yesmaximal, characteristic, complemented
11#10622409C211yesmaximal, characteristic, complemented
12#10622379C211yesmaximal, characteristic
13#10622374C211yesmaximal, 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
23C2×C4⋊Dic11—21no—
24#66977—21no—
25#66943—21no—
26#66943C2211yescharacteristic
27#66943C2211yescharacteristic
28#66943C2211yescharacteristic
29#66941—21no—
30#66941C2211yescharacteristic
31#66931—21no—
32#66931—21no—
33#66923—21no—
34#66923C2211yescharacteristic
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#66872C2211yescharacteristic
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×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22D411yescharacteristic
67C11×SD16Q814yescomplemented
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C42×C11—21no—
75C42×C11C2311yescharacteristic
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊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#3388—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—42no—
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—81no—
121C2×Dic11—81no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126Dic22—41no—
127Dic22—42no—
128Dic22—81no—
129C8×C11—21no—
130C8×C11C2×Q812yes—
131C11⋊C8—21no—
132C11⋊C8—21no—
133#557—111no—
134#554—111no—
135#501—111no—
136#501—111no—
137#499—111no—
138#479—111no—
139#479—111no—
140#478—111no—
141#478—111no—
142#476—111no—
143#475—111no—
144#446—111no—
145#440—111no—
146#440D1111yescharacteristic
147C4×SD16—111no—
148C22×C11—22no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11C22×D411yescharacteristic
152C4×C11—22no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11C22×Q811yescharacteristic
158C4×C112−1+411yescharacteristic
159Dic11—21no—
160Dic11—21no—
161Dic11—21no—
162Dic11—21no—
163Dic11—41no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167C2×SD16C2×D1111yescharacteristic
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170C4⋊Q8—221no—
171#125—111no—
172#125—111no—
173#125—111no—
174#125—111no—
175#125—221no—
176#125—221no—
177C22⋊Q8—221no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—111no—
181C4×Q8—111no—
182C4×Q8—111no—
183C4×Q8—221no—
184C4×Q8C2×D1111yescharacteristic
185C4×D4—111no—
186C4×D4—111no—
187C4×D4C2×D1111yescharacteristic
188C2×C4⋊C4—221no—
189#107—111no—
190#107—111no—
191#107—111no—
192#107C2×D1111yescharacteristic
193#106—111no—
194#106—111no—
195#106—111no—
196#106—111no—
197#106—111no—
198C4⋊C8—111no—
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103C2×D1111yescharacteristic
204#102—111no—
205#102—111no—
206#102C2×D1111yescharacteristic
207#97—111no—
208#97C2×D1111yescharacteristic
209C4×C8—111no—
210C2×C11—42no—
211C2×C11D4×Q811yescharacteristic
212C2×C11#57511yescharacteristic
213C2×C11#57711yescharacteristic
214C2×Q8—111no—
215C2×Q8—221no—
216C2×Q8—221no—
217C2×Q8C22×D1111yescharacteristic
218C2×D4C22×D1111yescharacteristic
219C22×C4—21no—
220C22×C4—221no—
221C22×C4—221no—
222SD16Dic2214yescomplemented
223C2×C8—111no—
224C2×C8—111no—
225C2×C8C22×D1111yescharacteristic
226C2×C8C22×D1111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—111no—
229C4⋊C4—111no—
230C4⋊C4—111no—
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C42—21no—
253C42—111no—
254C42—111no—
255C42—221no—
256C42—221no—
257C42C22×D1111yescharacteristic
258C11#338811yescharacteristic, complemented, Sylow
259C23—21no—
260Q8—21no—
261Q8—441no—
262Q8—442no—
263Q8—881no—
264Q8C2×Dic2212yes—
265D4—21no—
266D4C2×Dic2212yes—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—111no—
272C2×C4—111no—
273C2×C4—111no—
274C2×C4—111no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4D4×D1111yescharacteristic
282C2×C4D4×D1111yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—221no—
286C8—221no—
287C8C2×Dic2212yes—
288C22—22no—
289C22—41no—
290C22—41no—
291C22C2×D4×D1111yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—41no—
296C4—41no—
297C4—221no—
298C4—221no—
299C4—221no—
300C4—221no—
301C4—441no—
302C4—441no—
303C4—441no—
304C4—441no—
305C4C22×Dic2211yescharacteristic
306C4#6704311yescharacteristic
307C2—42no—
308C2D4×Dic2211yescharacteristic
309C2#1062330411yescharacteristic
310C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#440D11
hypocenterC11#3388
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. #10623100C2semidirect
6. #10622633C2semidirect
8. #10622491C2semidirect
9. #10622489C2semidirect
10. #10622412C2semidirect
11. #10622409C2semidirect
14. #10622315C2semidirect
15. #10622314C2semidirect
67. C11×SD16Q8semidirect
222. SD16Dic22semidirect
258. C11#3388semidirect

Maximal subgroups

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

subgroupindex
#106231002
#106230742
C11×#4402
#106227772
SD16×Dic112
#106226332
#106226222
#106224912
#106224892
#106224122
#106224092
#106223792
#106223742
#106223152
#106223142
#338811