Finite Group Databasebeta

← #13081563

Subgroups — #13081563

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#10623110C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#446C211yesmaximal, characteristic, complemented
4#10622464C211yesmaximal, characteristic, complemented
5#10622460C211yesmaximal, characteristic
6#10622460C211yesmaximal, characteristic
7#10622455C211yesmaximal, characteristic
8#10622442C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622323C211yesmaximal, characteristic
11#10622323C211yesmaximal, characteristic
12#10622315C211yesmaximal, characteristic, complemented
13#10622315C211yesmaximal, characteristic, complemented
14C4×#4314C211yesmaximal, characteristic
15#10622296C211yesmaximal, characteristic, complemented
16C4×Q8×C11C2211yescharacteristic
17#66999—21no—
18#66997—21no—
19C2×#4314C2211yescharacteristic
20#66949—21no—
21#66949—21no—
22C4⋊C4×D11—21no—
23#66942—21no—
24#66942—21no—
25#66940—21no—
26C4×D44C2211yescharacteristic
27C4×D44C2211yescharacteristic
28C4×D44C2211yescharacteristic
29#66923C2211yescharacteristic
30#66923C2211yescharacteristic
31#66923C2211yescharacteristic
32#66923C2211yescharacteristic
33#66922C2211yescharacteristic
34#66922C2211yescharacteristic
35C4×Dic22C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×C4⋊C8C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#97C2211yescharacteristic
42C11×#97C2211yescharacteristic
43C4×C8×C11C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×Q8×C11D411yescharacteristic
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4D411yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4D411yescharacteristic
74C42×C11C2311yescharacteristic
75C42×C11C2311yescharacteristic
76C42×C11C2311yescharacteristic
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11C2311yescharacteristic
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
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⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102#4314Q814yescomplemented
103#3388—111nomaximal, Sylow
104C22×D11—21no—
105Q8×C11—41no—
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11C2×D411yescharacteristic
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2411yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120D44—21no—
121D44C2×Q812yes—
122C4×D11—42no—
123C4×D11—81no—
124C4×D11—81no—
125Dic22—21no—
126Dic22—42no—
127Dic22—81no—
128Dic22C2×Q812yes—
129C8×C11—21no—
130C8×C11—21no—
131C8×C11—21no—
132C8×C11C2×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#478—111no—
142#476—111no—
143#475—111no—
144#446D1111yescharacteristic, complemented
145#440—111no—
146#440—111no—
147C4×SD16—111no—
148C22×C11C22×D411yescharacteristic
149C2×D11—22no—
150C2×D11—41no—
151C2×D11—41no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11C22×Q811yescharacteristic
159C4×C112−1+411yescharacteristic
160Dic11—22no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
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—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×D4—111no—
188C2×C4⋊C4—221no—
189#107—111no—
190#107—111no—
191#107—111no—
192#107—111no—
193#106—111no—
194#106—111no—
195#106—111no—
196#106—111no—
197#106—111no—
198C4⋊C8C2×D1111yescharacteristic
199C4⋊C8C2×D1111yescharacteristic
200C4⋊C8C2×D1111yescharacteristic
201#103—111no—
202#103—111no—
203#103—111no—
204#102—111no—
205#102—111no—
206#102—111no—
207#97C2×D1111yescharacteristic
208#97C2×D1111yescharacteristic
209C4×C8C2×D1111yescharacteristic
210C2×C11D4×Q811yescharacteristic
211C2×C11#57511yescharacteristic
212C2×C11#57711yescharacteristic
213D11—42no—
214C2×Q8—111no—
215C2×Q8—221no—
216C2×Q8—221no—
217C2×Q8D4411yescharacteristic
218C2×D4—111no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—221no—
222SD16—114no—
223C2×C8C22×D1111yescharacteristic
224C2×C8C22×D1111yescharacteristic
225C2×C8C22×D1111yescharacteristic
226C2×C8C22×D1111yescharacteristic
227C4⋊C4—111no—
228C4⋊C4—111no—
229C4⋊C4—111no—
230C4⋊C4—111no—
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—221no—
234C4⋊C4—221no—
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⋊C4D4411yescharacteristic
247C4⋊C4D4411yescharacteristic
248C4⋊C4D4411yescharacteristic
249C22⋊C4—221no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C42—221no—
253C42—221no—
254C42—221no—
255C42C22×D1111yescharacteristic
256C42C22×D1111yescharacteristic
257C42C22×D1111yescharacteristic
258C11#338811yescharacteristic, complemented, Sylow
259C23—221no—
260Q8—41no—
261Q8—112no—
262Q8—221no—
263Q8—442no—
264Q8—881no—
265D4—112no—
266D4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—442no—
275C2×C4—881no—
276C2×C4—881no—
277C2×C4C2×D4411yescharacteristic
278C2×C4C2×D4411yescharacteristic
279C2×C4C2×D4411yescharacteristic
280C2×C4C2×D4411yescharacteristic
281C2×C4C2×D4411yescharacteristic
282C2×C4C2×D4411yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—21no—
286C8—21no—
287C8Q8×D1112yes—
288C22—222no—
289C22—441no—
290C22—441no—
291C22C22×D4411yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—222no—
299C4—441no—
300C4—441no—
301C4—441no—
302C4—441no—
303C4—441no—
304C4—441no—
305C4C2×Q8×D1111yescharacteristic
306C4#6704311yescharacteristic
307C2—442no—
308C2Q8×D4411yescharacteristic
309C2#1062327911yescharacteristic
310C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#446C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#446D11
hypocenterC11#3388
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
3. C11×#446C2semidirect
4. #10622464C2semidirect
8. #10622442C2semidirect
9. #10622442C2semidirect
12. #10622315C2semidirect
13. #10622315C2semidirect
15. #10622296C2semidirect
102. #4314Q8semidirect
144. #446D11semidirect
258. C11#3388semidirect

Maximal subgroups

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

subgroupindex
#106231102
#106230982
C11×#4462
#106224642
#106224602
#106224552
#106224422
#106223232
#106223152
C4×#43142
#106222962
#338811