Finite Group Databasebeta

← #13081401

Subgroups — #13081401

Order 1408.

340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623252C211yesmaximal, characteristic, complemented
2#10623074C211yesmaximal, characteristic
3C11×#461C211yesmaximal, characteristic
4#10622777C212yesmaximal
5#10622775C212yesmaximal
6#10622694C211yesmaximal, characteristic, complemented
7C4×#4324C211yesmaximal, characteristic
8#10622463C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622410C212yesmaximal, complemented
11#10622409C212yesmaximal, complemented
12C2×C11×SD16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×D4×C11C2211yescharacteristic
15Q8×Dic11C2212yes—
16#66997C2212yes—
17D4×Dic11C2212yes—
18C2×#4324C2211yescharacteristic
19C2×C4⋊Dic11—21no—
20#66977—21no—
21#66943—21no—
22#66943C2212yes—
23#66942—22no—
24#66940—21no—
25#66931—22no—
26#66922C2211yescharacteristic
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×C4⋊C8C2211yescharacteristic
30C11×#103C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33#66896C2211yescharacteristic
34#66882C2212yes—
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66874C2211yescharacteristic
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2312yes—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C22×Dic11—22no—
45C2×Dic22—21no—
46C2×Dic22D411yescharacteristic
47C2×Dic22C2311yescharacteristic
48C11×SD16—24no—
49C2×C8×C11C2312yes—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4C2311yescharacteristic
53C11×C22⋊C4—21no—
54C42×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56#4324—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—21no—
60C4⋊Dic11D411yescharacteristic
61C4⋊Dic11C2311yescharacteristic
62C4⋊Dic11C2312yes—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—21no—
67Dic11⋊C4D412yes—
68C4×Dic11—22no—
69C4×Dic11—21no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#3372—111nomaximal, Sylow
74C23×C11—21no—
75Q8×C11—22no—
76Q8×C11—22no—
77D4×C11—21no—
78D4×C11#4112yes—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—42no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—22no—
88C2×Dic11—82no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D412yes—
91Dic22—22no—
92Dic22—21no—
93Dic22—21no—
94Dic22—81no—
95C8×C11—22no—
96C11⋊C8—21no—
97C11⋊C8—21no—
98#557—111no—
99#554—111no—
100#491—112no—
101#487—111no—
102#479—112no—
103#477—111no—
104#461—112no—
105#461D1111yescharacteristic
106#446—111no—
107#440—112no—
108C4×SD16—111no—
109C22×C11—22no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11C22×D411yescharacteristic
113C4×C11—21no—
114C4×C11—42no—
115C4×C11—41no—
116C4×C11#13712yes—
117C4×C11C2×#4111yescharacteristic
118C4×C112−1+411yescharacteristic
119Dic11—22no—
120Dic11—22no—
121Dic11—41no—
122Dic11—42no—
123Dic11—41no—
124C2×SD16—111no—
125C2×SD16C2×D1112yes—
126C4⋊Q8—112no—
127C4⋊Q8—111no—
128C4⋊Q8C2×D1111yescharacteristic
129#125—112no—
130#125—222no—
131#125—221no—
132C22⋊Q8—222no—
133C22⋊Q8—221no—
134C4×Q8—111no—
135C4×Q8—112no—
136C4×Q8—111no—
137C4×Q8—221no—
138C4×D4—112no—
139C4×D4C2×D1111yescharacteristic
140C2×C4⋊C4—221no—
141#107—112no—
142#106—111no—
143C4⋊C8—112no—
144C4⋊C8C2×D1111yescharacteristic
145#103—112no—
146#103—112no—
147#103—112no—
148#103—111no—
149#103C2×D1112yes—
150#102—111no—
151#97—112no—
152C4×C8—111no—
153C2×C11—42no—
154C2×C11#54811yescharacteristic
155C2×C11C2×#13711yescharacteristic
156C2×C11#57711yescharacteristic
157C2×Q8—111no—
158C2×Q8—111no—
159C2×Q8—221no—
160C2×Q8C22×D1112yes—
161C2×D4C22×D1111yescharacteristic
162C22×C4—21no—
163C22×C4—222no—
164SD16—24no—
165SD16—222no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8C22×D1112yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—111no—
172C4⋊C4—112no—
173C4⋊C4—111no—
174C4⋊C4—112no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—221no—
181C4⋊C4—221no—
182C4⋊C4C22×D1111yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—222no—
185C42—112no—
186C42—222no—
187C42—221no—
188C42C22×D1111yescharacteristic
189C11#337211yescharacteristic, complemented, Sylow
190C23—21no—
191Q8—22no—
192Q8—22no—
193Q8—222no—
194Q8—221no—
195Q8—221no—
196Q8—881no—
197D4—21no—
198D4#434112yes—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—112no—
203C2×C4—112no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—882no—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—221no—
213C8—221no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—222no—
222C4—222no—
223C4—442no—
224C4—441no—
225C4—441no—
226C4#6696812yes—
227C4C2×#434111yescharacteristic
228C4#6704311yescharacteristic
229C2—42no—
230C2#1062312911yescharacteristic
231C2C2×#6696811yescharacteristic
232C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#461C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#461D11
hypocenterC11#3372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10623252C2semidirect
6. #10622694C2semidirect
8. #10622463C2semidirect
9. #10622444C2semidirect
10. #10622410C2semidirect
11. #10622409C2semidirect
189. C11#3372semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106230742
C11×#4612
#106227772
#106227752
#106226942
C4×#43242
#106224632
#106224442
#106224102
#106224092
#337211