Finite Group Databasebeta

← #13079805

Subgroups — #13079805

Order 1408.

368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623127C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic, complemented
4#10622646C211yesmaximal, characteristic, complemented
5#10622581C211yesmaximal, characteristic, complemented
6#10622484C212yesmaximal, complemented
7#10622469C212yesmaximal, complemented
8#10622379C212yesmaximal, complemented
9#10622377C212yesmaximal, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622332C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C11×#121C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15#66993C2211yescharacteristic
16#66992—21no—
17D4×Dic11C2211yescharacteristic
18#66983C2211yescharacteristic
19C2×C4⋊Dic11—21no—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—21no—
22C2×C4×Dic11C2211yescharacteristic
23#66946C2211yescharacteristic
24#66943—21no—
25#66943—21no—
26#66943C2212yes—
27#66943C2212yes—
28#66941C2211yescharacteristic
29#66938—21no—
30(C22⋊D11)⋊C4—21no—
31C11×#106C2212yes—
32C11×#102C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66896C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66885C2212yes—
37#66882C2212yes—
38#66879C2212yes—
39Dic11⋊C8C2212yes—
40#66873C2212yes—
41#66872C2212yes—
42#66871C2212yes—
43C2×D4×C11—21no—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—21no—
48C2×C22⋊D11—21no—
49C2×C22⋊D11—21no—
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11D411yescharacteristic
53C22×Dic11D411yescharacteristic
54#4341—44no—
55C2×D44C2311yescharacteristic
56C2×C4×D11—21no—
57C2×Dic22—21no—
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2311yescharacteristic
61C11×C4⋊C4C2312yes—
62C11×C22⋊C4—21no—
63C22⋊Dic11—21no—
64(C2×D11)⋊C4—21no—
65(C2×D11)⋊C4—21no—
66C4⋊Dic11—22no—
67C4⋊Dic11—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11C2312yes—
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74C4×Dic11D411yescharacteristic
75C4×Dic11D411yescharacteristic
76C4×Dic11C2311yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3234—111nomaximal, Sylow
80C23×C11—21no—
81C23×C11C2×D411yescharacteristic
82C22×D11—21no—
83D4×C11—22no—
84D4×C11—42no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2411yescharacteristic
91C22⋊D11—42no—
92C22⋊D11—42no—
93C22⋊D11—42no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—21no—
97C2×Dic11—41no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104D44—22no—
105C4×D11—42no—
106Dic22—42no—
107C8×C11—22no—
108C11⋊C8—22no—
109#532—111no—
110C2×#125—111no—
111#501—112no—
112#490—112no—
113#481—111no—
114#481D1111yescharacteristic, complemented
115#480—111no—
116#480—111no—
117#478—112no—
118#478—112no—
119#432—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11AGL(1,ℤ/8)12yes—
126C22×C11C22×D411yescharacteristic
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—41no—
130C4×C11—21no—
131C4×C11—41no—
132C4×C11—42no—
133C4×C112−1+412yes—
134Dic11—21no—
135Dic11—21no—
136Dic11—21no—
137Dic11—21no—
138Dic11—41no—
139Dic11—42no—
140C2×#41—221no—
141C4⋊Q8—111no—
142#127—111no—
143#125—112no—
144#125—112no—
145#125—221no—
146#125—221no—
147#124—221no—
148#121—111no—
149#121—221no—
150#121C2×D1111yescharacteristic
151C4×D4—111no—
152C4×D4—111no—
153C4×D4—221no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C42—111no—
159#107—112no—
160#107—112no—
161#106—112no—
162#106C2×D1112yes—
163C4⋊C8—112no—
164#102—112no—
165#102—112no—
166#102—112no—
167#102C2×D1112yes—
168C22⋊C8—111no—
169C22⋊C8C2×D1111yescharacteristic
170#97—112no—
171C2×C11—22no—
172C2×C11—81no—
173C2×C11#53611yescharacteristic
174C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C11#57511yescharacteristic
176D11—81no—
177#41—444no—
178C2×Q8—221no—
179C2×D4—21no—
180C2×D4—111no—
181C2×D4—221no—
182C2×D4—221no—
183C2×D4—221no—
184C2×D4C22×D1111yescharacteristic
185C22×C4—21no—
186C22×C4—111no—
187C22×C4—111no—
188C22×C4—221no—
189C22×C4—221no—
190C22×C4—221no—
191C22×C4C22×D1111yescharacteristic
192C2×C8—112no—
193C2×C8C22×D1112yes—
194C4⋊C4—21no—
195C4⋊C4—112no—
196C4⋊C4—111no—
197C4⋊C4—222no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—221no—
202C4⋊C4—221no—
203C4⋊C4C22×D1112yes—
204C4⋊C4C22×D1111yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—221no—
207C22⋊C4—221no—
208C22⋊C4—221no—
209C42—111no—
210C42—111no—
211C42—111no—
212C42—111no—
213C11#323411yescharacteristic, complemented, Sylow
214C23—21no—
215C23—221no—
216C23D4×D1111yescharacteristic
217Q8—442no—
218D4—22no—
219D4—42no—
220D4—222no—
221D4—442no—
222D4—442no—
223D4—442no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—111no—
229C2×C4—111no—
230C2×C4—111no—
231C2×C4—111no—
232C2×C4—222no—
233C2×C4—221no—
234C2×C4—222no—
235C2×C4—442no—
236C2×C4—441no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4D4×D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—22no—
242C8—222no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—441no—
249C22—441no—
250C22—441no—
251C22#6696712yes—
252C22C2×D4×D1111yescharacteristic
253C4—21no—
254C4—41no—
255C4—42no—
256C4—221no—
257C4—221no—
258C4—221no—
259C4—221no—
260C4—441no—
261C4—442no—
262C4#6704312yes—
263C2—22no—
264C2—81no—
265C2—881no—
266C2#1062317911yescharacteristic
267C2C2×#6696711yescharacteristic
268C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
prime radical#10623127C2
hypercenter#481D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
3. C11×#481C2semidirect
4. #10622646C2semidirect
5. #10622581C2semidirect
6. #10622484C2semidirect
7. #10622469C2semidirect
8. #10622379C2semidirect
9. #10622377C2semidirect
10. #10622349C2semidirect
11. #10622332C2semidirect
114. #481D11semidirect
213. C11#3234semidirect

Maximal subgroups

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

subgroupindex
#106231272
C2×#669432
C11×#4812
#106226462
#106225812
#106224842
#106224692
#106223792
#106223772
#106223492
#106223322
#323411