Finite Group Databasebeta

← #13081461

Subgroups — #13081461

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623216C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic
4#10622682C211yesmaximal, characteristic, complemented
5#10622631C211yesmaximal, characteristic
6#10622488C211yesmaximal, characteristic, complemented
7#10622486C211yesmaximal, characteristic, complemented
8#10622470C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic
13#10622380C211yesmaximal, characteristic
14#10622380C211yesmaximal, characteristic
15#10622378C211yesmaximal, characteristic
16C11×#125C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18#66989C2211yescharacteristic
19#66989C2211yescharacteristic
20C2×#4324C2211yescharacteristic
21#66979—21no—
22#66977—21no—
23C2×Dic44C2211yescharacteristic
24C2×Dic44C2211yescharacteristic
25#66943C2211yescharacteristic
26#66942—21no—
27#66942—21no—
28#66941—21no—
29#66941C2211yescharacteristic
30#66940—21no—
31#66940C2211yescharacteristic
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66932—21no—
36#66932—21no—
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45#66896C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48#66879C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×Dic22—21no—
62C2×Dic22D411yescharacteristic
63C2×Dic22C2311yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C42×C11C2311yescharacteristic
75C22⋊Dic11—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79#4324—22no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11D411yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—21no—
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4D411yescharacteristic
93Dic11⋊C4D411yescharacteristic
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103Dic44—22no—
104Dic44—22no—
105#3377—111nomaximal, Sylow
106C23×C11—21no—
107D4×C11—21no—
108D4×C11—21no—
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×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124Dic22—21no—
125Dic22—21no—
126Dic22—21no—
127Dic22—21no—
128Dic22—21no—
129Dic22—41no—
130Dic22—42no—
131Dic22#4112yes—
132C8×C11—21no—
133C8×C11—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#557—111no—
137#556—111no—
138#491—111no—
139#489—111no—
140#488—111no—
141#479—111no—
142#478D1111yescharacteristic
143#477—111no—
144#464—111no—
145#464—111no—
146#462—111no—
147#446—111no—
148#441—111no—
149#440—111no—
150C4×Q16—111no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11C22×D411yescharacteristic
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11C2×#4111yescharacteristic
161C4×C112−1+411yescharacteristic
162Dic11—22no—
163Dic11—21no—
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16—111no—
172C2×SD16—111no—
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175C4⋊Q8—221no—
176#126—221no—
177#126—221no—
178#125—111no—
179#125—221no—
180#125—221no—
181#125C2×D1111yescharacteristic
182#124—111no—
183#124—111no—
184C22⋊Q8—221no—
185C4×Q8—111no—
186C4×Q8—111no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—111no—
191C4×Q8—221no—
192C4×D4C2×D1111yescharacteristic
193#117—221no—
194#107—111no—
195#107C2×D1111yescharacteristic
196#106C2×D1111yescharacteristic
197C4⋊C8—111no—
198C4⋊C8—111no—
199C4⋊C8C2×D1111yescharacteristic
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#103—111no—
206#103—111no—
207#102—111no—
208#102C2×D1111yescharacteristic
209#102C2×D1111yescharacteristic
210#97—111no—
211#97—111no—
212C4×C8—111no—
213C2×C11—81no—
214C2×C11#54811yescharacteristic
215C2×C11#57511yescharacteristic
216C2×C11#57811yescharacteristic
217C2×Q8—111no—
218C2×Q8—111no—
219C2×Q8—111no—
220C2×Q8—111no—
221C2×Q8—221no—
222C2×D4C22×D1111yescharacteristic
223C22×C4—21no—
224Q16—222no—
225Q16—222no—
226SD16—222no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
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
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C42—111no—
256C42—111no—
257C42—221no—
258C42—221no—
259C42—221no—
260C42—221no—
261C42—221no—
262C42C22×D1111yescharacteristic
263C11#337711yescharacteristic, complemented, Sylow
264C23—21no—
265Q8—112no—
266Q8—221no—
267Q8—221no—
268Q8—221no—
269Q8—221no—
270Q8—221no—
271Q8—441no—
272Q8—442no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4D4×D1111yescharacteristic
288C2×C4D4×D1111yescharacteristic
289C2×C4C23×D1111yescharacteristic
290C8—21no—
291C8—21no—
292C8—221no—
293C8—221no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D1111yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—221no—
304C4—221no—
305C4—221no—
306C4—221no—
307C4—222no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4#6704011yescharacteristic
312C4#41×D1111yescharacteristic
313C2—81no—
314C2#1062316411yescharacteristic
315C2#1062330211yescharacteristic
316C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#478D11
hypocenterC11#3377
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. #10622682C2semidirect
6. #10622488C2semidirect
7. #10622486C2semidirect
8. #10622470C2semidirect
9. #10622466C2semidirect
10. #10622462C2semidirect
11. #10622441C2semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
#106232162
#106230732
C11×#4782
#106226822
#106226312
#106224882
#106224862
#106224702
#106224662
#106224622
#106224412
#106223812
#106223802
#106223782
#337711