Finite Group Databasebeta

← #13079849

Subgroups — #13079849

Order 1408.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623155C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C11×#484C211yesmaximal, characteristic, complemented
4#10622657C211yesmaximal, characteristic, complemented
5#10622581C211yesmaximal, characteristic
6#10622503C212yesmaximal, complemented
7#10622489C212yesmaximal, complemented
8#10622408C212yesmaximal, complemented
9#10622404C212yesmaximal, complemented
10#10622348C211yesmaximal, characteristic
11#10622332C211yesmaximal, characteristic, complemented
12C22×Dic22—21no—
13C11×C22⋊Q8C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15#67000C2211yescharacteristic
16Q8×Dic11C2211yescharacteristic
17#66983C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×C4×Dic11C2211yescharacteristic
21#66951—21no—
22#66946C2211yescharacteristic
23#66945—21no—
24#66943C2211yescharacteristic
25#66941—21no—
26#66941—21no—
27#66941C2212yes—
28#66941C2212yes—
29#66939—21no—
30(C22⋊D11)⋊C4—21no—
31C11×#107C2212yes—
32C11×#103C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66899C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66885C2212yes—
37#66881C2212yes—
38#66879C2212yes—
39Dic11⋊C8C2212yes—
40#66873C2212yes—
41#66872C2212yes—
42#66871C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C22×Dic11—21no—
48C22×Dic11D411yescharacteristic
49C22×Dic11D411yescharacteristic
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22—22no—
53C2×Dic22—22no—
54C2×Dic22—44no—
55C2×C8×C11C2312yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2311yescharacteristic
59C11×C4⋊C4C2312yes—
60C11×C22⋊C4—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2312yes—
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—21no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73C4×Dic11—21no—
74C4×Dic11D411yescharacteristic
75C4×Dic11D411yescharacteristic
76C4×Dic11C2311yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3239—111nomaximal, Sylow
80C23×C11C2×D411yescharacteristic
81C22×D11—21no—
82Q8×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—42no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—42no—
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99C2×Dic11C2×D411yescharacteristic
100D44—22no—
101C4×D11—42no—
102Dic22—44no—
103Dic22—44no—
104C8×C11—22no—
105C11⋊C8—22no—
106C2×C4⋊Q8—111no—
107#529—111no—
108#501—112no—
109#489—112no—
110#484—111no—
111#484D1111yescharacteristic, complemented
112#481—111no—
113#481—111no—
114#475—112no—
115#474—112no—
116#432—111no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11#13712yes—
120C22×C11C22×D411yescharacteristic
121C2×D11—41no—
122C2×D11—41no—
123C2×D11—41no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—42no—
127C4×C11—41no—
128C4×C112−1+412yes—
129Dic11—21no—
130Dic11—21no—
131Dic11—21no—
132Dic11—42no—
133Dic11—41no—
134Dic11AGL(1,ℤ/8)12yes—
135C22×Q8—221no—
136C4⋊Q8—112no—
137C4⋊Q8—112no—
138C4⋊Q8—221no—
139C4⋊Q8—221no—
140#126—221no—
141#125—111no—
142#124—111no—
143#123—221no—
144C22⋊Q8C2×D1111yescharacteristic
145#121—111no—
146C4×Q8—111no—
147C4×D4—111no—
148C4×D4—221no—
149#117—221no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4C2×D1111yescharacteristic
153C2×C42—111no—
154#107—112no—
155#107C2×D1112yes—
156#106—112no—
157#106—112no—
158C4⋊C8—112no—
159#103—112no—
160#103C2×D1112yes—
161#102—112no—
162#102—112no—
163C22⋊C8—111no—
164C22⋊C8C2×D1111yescharacteristic
165#97—112no—
166C2×C11—22no—
167C2×C11#53611yescharacteristic
168C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C11C2×#13711yescharacteristic
170D11—81no—
171C2×Q8—222no—
172C2×Q8—222no—
173C2×Q8—444no—
174C2×Q8C22×D1111yescharacteristic
175C2×D4—111no—
176C2×D4—221no—
177C22×C4—21no—
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—221no—
181C22×C4—221no—
182C22×C4C22×D1111yescharacteristic
183C2×C8—112no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—112no—
188C4⋊C4—111no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4C22×D1112yes—
196C4⋊C4C22×D1111yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—221no—
199C22⋊C4—221no—
200C22⋊C4—221no—
201C22⋊C4—221no—
202C42—111no—
203C42—111no—
204C42—111no—
205C42—111no—
206C42—221no—
207C11#323911yescharacteristic, complemented, Sylow
208C23—221no—
209C23D4×D1111yescharacteristic
210Q8—22no—
211Q8—444no—
212Q8—444no—
213D4—222no—
214D4—442no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—111no—
221C2×C4—111no—
222C2×C4—111no—
223C2×C4—111no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4D4×D1111yescharacteristic
231C2×C4C23×D1111yescharacteristic
232C8—22no—
233C8—222no—
234C22—21no—
235C22—21no—
236C22—441no—
237C22—441no—
238C22—441no—
239C22#6697112yes—
240C22C2×D4×D1111yescharacteristic
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—112no—
246C4—221no—
247C4—221no—
248C4—221no—
249C4—441no—
250C4—442no—
251C4#6704312yes—
252C2—22no—
253C2—881no—
254C2#1062317911yescharacteristic
255C2C2×#6697111yescharacteristic
256C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#484D11
hypocenterC11#3239
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C11×#484C2semidirect
4. #10622657C2semidirect
6. #10622503C2semidirect
7. #10622489C2semidirect
8. #10622408C2semidirect
9. #10622404C2semidirect
11. #10622332C2semidirect
111. #484D11semidirect
207. C11#3239semidirect

Maximal subgroups

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

subgroupindex
#106231552
C2×#669412
C11×#4842
#106226572
#106225812
#106225032
#106224892
#106224082
#106224042
#106223482
#106223322
#323911