Finite Group Databasebeta

← #13081565

Subgroups — #13081565

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#10623216C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic
4#10622677C211yesmaximal, characteristic, complemented
5C4×#4324C211yesmaximal, characteristic
6#10622490C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622469C211yesmaximal, characteristic, complemented
9#10622467C211yesmaximal, characteristic, complemented
10#10622444C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622379C211yesmaximal, characteristic
13#10622374C211yesmaximal, characteristic
14#10622370C211yesmaximal, characteristic
15#10622370C211yesmaximal, characteristic
16C11×#125C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18D4×Dic11C2211yescharacteristic
19D4×Dic11C2211yescharacteristic
20C2×#4324C2211yescharacteristic
21#66977—21no—
22C2×Dic11⋊C4—21no—
23#66943C2211yescharacteristic
24#66943C2211yescharacteristic
25#66942—21no—
26#66942—21no—
27#66941—21no—
28#66941C2211yescharacteristic
29#66941C2211yescharacteristic
30#66940—21no—
31#66940C2211yescharacteristic
32#66940C2211yescharacteristic
33#66931—21no—
34#66931—21no—
35#66923C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66882C2211yescharacteristic
45#66881C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48#66879C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C2×Dic22—21no—
64C2×Dic22—21no—
65C2×Dic22D411yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11C2311yescharacteristic
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78#4324Q814yescomplemented
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11D411yescharacteristic
82C4⋊Dic11C2311yescharacteristic
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—21no—
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4D411yescharacteristic
95Dic11⋊C4D411yescharacteristic
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3388—111nomaximal, Sylow
104C23×C11—21no—
105D4×C11—21no—
106D4×C11C2×Q812yes—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—81no—
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—42no—
119C2×Dic11—81no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124Dic22—21no—
125Dic22—41no—
126Dic22—42no—
127Dic22—81no—
128Dic22C2×Q812yes—
129C8×C11—21no—
130C8×C11—21no—
131C11⋊C8—21no—
132C11⋊C8C2×Q812yes—
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#478D1111yescharacteristic
142#476—111no—
143#475—111no—
144#446—111no—
145#440—111no—
146#440—111no—
147C4×SD16—111no—
148C22×C11—22no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11C22×D411yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11C22×Q811yescharacteristic
158C4×C112−1+411yescharacteristic
159Dic11—22no—
160Dic11—21no—
161Dic11—21no—
162Dic11—21no—
163Dic11—21no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167C2×SD16—111no—
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170C4⋊Q8—221no—
171#125—111no—
172#125—111no—
173#125—111no—
174#125—221no—
175#125—221no—
176#125C2×D1111yescharacteristic
177C22⋊Q8—221no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—111no—
181C4×Q8—111no—
182C4×Q8—111no—
183C4×Q8—111no—
184C4×Q8—221no—
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#106C2×D1111yescharacteristic
198C4⋊C8—111no—
199C4⋊C8—111no—
200C4⋊C8C2×D1111yescharacteristic
201#103—111no—
202#103—111no—
203#103—111no—
204#102—111no—
205#102C2×D1111yescharacteristic
206#102C2×D1111yescharacteristic
207#97—111no—
208#97—111no—
209C4×C8—111no—
210C2×C11—42no—
211C2×C11D4×Q811yescharacteristic
212C2×C11#57511yescharacteristic
213C2×C11#57711yescharacteristic
214C2×Q8—111no—
215C2×Q8—111no—
216C2×Q8—221no—
217C2×Q8—221no—
218C2×D4C22×D1111yescharacteristic
219C22×C4—21no—
220C22×C4—221no—
221C22×C4—221no—
222SD16—114no—
223C2×C8—111no—
224C2×C8—111no—
225C2×C8C22×D1111yescharacteristic
226C2×C8C22×D1111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C42—111no—
253C42—111no—
254C42—221no—
255C42—221no—
256C42—221no—
257C42C22×D1111yescharacteristic
258C11#338811yescharacteristic, complemented, Sylow
259C23—21no—
260Q8—112no—
261Q8—221no—
262Q8—441no—
263Q8—442no—
264Q8—881no—
265D4—21no—
266D4Q8×D1112yes—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—81no—
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—442no—
280C2×C4—881no—
281C2×C4D4×D1111yescharacteristic
282C2×C4D4×D1111yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—21no—
286C8—112no—
287C8—221no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22C2×D4×D1111yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—221no—
298C4—221no—
299C4—221no—
300C4—221no—
301C4—222no—
302C4—441no—
303C4—441no—
304C4—441no—
305C4C2×Q8×D1111yescharacteristic
306C4#6704311yescharacteristic
307C2—42no—
308C2#1062316311yescharacteristic
309C2#1062329911yescharacteristic
310C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#478D11
hypocenterC11#3388
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623216C2semidirect
4. #10622677C2semidirect
6. #10622490C2semidirect
7. #10622489C2semidirect
8. #10622469C2semidirect
9. #10622467C2semidirect
10. #10622444C2semidirect
11. #10622442C2semidirect
78. #4324Q8semidirect
258. C11#3388semidirect

Maximal subgroups

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

subgroupindex
#106232162
#106230702
C11×#4782
#106226772
C4×#43242
#106224902
#106224892
#106224692
#106224672
#106224442
#106224422
#106223792
#106223742
#106223702
#338811