Finite Group Databasebeta

← #13081398

Subgroups — #13081398

Order 1408.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623098C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic
4#10622775C211yesmaximal, characteristic
5#10622775C211yesmaximal, characteristic
6#10622635C211yesmaximal, characteristic, complemented
7#10622632C211yesmaximal, characteristic
8#10622490C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622410C211yesmaximal, characteristic, complemented
11#10622405C211yesmaximal, characteristic, complemented
12#10622371C211yesmaximal, characteristic
13#10622370C211yesmaximal, characteristic
14#10622316C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66997C2211yescharacteristic
20#66997C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25#66977—21no—
26C2×Dic11⋊C4—21no—
27#66943C2211yescharacteristic
28#66942—21no—
29#66942—21no—
30#66941C2211yescharacteristic
31#66940C2211yescharacteristic
32#66940C2211yescharacteristic
33#66931—21no—
34#66931—21no—
35#66923—21no—
36#66923C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22—21no—
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
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×Dic22D411yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×Dic22C2311yescharacteristic
68C11×SD16—22no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79#4324—22no—
80#4324—22no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11D411yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3372—111nomaximal, Sylow
106C23×C11—21no—
107Q8×C11—21no—
108Q8×C11—21no—
109D4×C11—21no—
110D4×C11#4112yes—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—81no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—42no—
123C2×Dic11—81no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128Dic22—22no—
129Dic22—21no—
130Dic22—21no—
131Dic22—21no—
132Dic22—21no—
133Dic22—81no—
134C8×C11—21no—
135C8×C11—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138#557—111no—
139#554—111no—
140#491—111no—
141#491—111no—
142#487—111no—
143#479—111no—
144#479—111no—
145#477—111no—
146#461—111no—
147#461—111no—
148#461—111no—
149#446—111no—
150#440—111no—
151#440D1111yescharacteristic
152C4×SD16—111no—
153C22×C11—22no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11C22×D411yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11C2×#4111yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11#13712yes—
172C2×SD16—111no—
173C2×SD16—111no—
174C2×SD16C2×D1111yescharacteristic
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177C4⋊Q8—111no—
178C4⋊Q8—111no—
179#125—111no—
180#125—111no—
181#125—221no—
182#125—221no—
183#125—221no—
184C22⋊Q8—221no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—221no—
191C4×Q8C2×D1111yescharacteristic
192C4×D4—111no—
193C4×D4—111no—
194C4×D4C2×D1111yescharacteristic
195C2×C4⋊C4—221no—
196#107—111no—
197#107C2×D1111yescharacteristic
198#106—111no—
199C4⋊C8—111no—
200C4⋊C8—111no—
201C4⋊C8—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#102C2×D1111yescharacteristic
212#97—111no—
213#97C2×D1111yescharacteristic
214C4×C8—111no—
215C2×C11—42no—
216C2×C11#54811yescharacteristic
217C2×C11C2×#13711yescharacteristic
218C2×C11#57711yescharacteristic
219C2×Q8—111no—
220C2×Q8—111no—
221C2×Q8—111no—
222C2×Q8—221no—
223C2×Q8C22×D1111yescharacteristic
224C2×D4C22×D1111yescharacteristic
225C22×C4—21no—
226C22×C4—221no—
227C22×C4—221no—
228SD16—22no—
229SD16—222no—
230SD16—222no—
231C2×C8—111no—
232C2×C8—111no—
233C2×C8C22×D1111yescharacteristic
234C2×C8C22×D1111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
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⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C42—21no—
260C42—111no—
261C42—111no—
262C42—221no—
263C42—221no—
264C42C22×D1111yescharacteristic
265C11#337211yescharacteristic, complemented, Sylow
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—222no—
270Q8—221no—
271Q8—221no—
272Q8—221no—
273Q8—221no—
274Q8—881no—
275D4—21no—
276D4#433912yes—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—111no—
284C2×C4—111no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—442no—
290C2×C4—881no—
291C2×C4D4×D1111yescharacteristic
292C2×C4D4×D1111yescharacteristic
293C2×C4C23×D1111yescharacteristic
294C8—21no—
295C8—21no—
296C8—221no—
297C8—221no—
298C22—22no—
299C22—41no—
300C22—41no—
301C22C2×D4×D1111yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—112no—
308C4—221no—
309C4—221no—
310C4—221no—
311C4—441no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4C2×#433911yescharacteristic
316C4#6704311yescharacteristic
317C2—42no—
318C2#1062308311yescharacteristic
319C2#1062330611yescharacteristic
320C2D11×#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#3372
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. #10623098C2semidirect
6. #10622635C2semidirect
8. #10622490C2semidirect
9. #10622488C2semidirect
10. #10622410C2semidirect
11. #10622405C2semidirect
14. #10622316C2semidirect
15. #10622314C2semidirect
265. C11#3372semidirect

Maximal subgroups

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

subgroupindex
#106230982
#106230702
C11×#4402
#106227752
#106226352
#106226322
#106224902
#106224882
#106224102
#106224052
#106223712
#106223702
#106223162
#106223142
#337211