Finite Group Databasebeta

← #13081396

Subgroups — #13081396

Order 1408.

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

normal subgroups only

This group has 340 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#10623261C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic
6#10622502C212yesmaximal
7#10622490C212yesmaximal, complemented
8#10622454C211yesmaximal, characteristic
9#10622444C211yesmaximal, characteristic, complemented
10#10622431C212yesmaximal
11#10622410C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14#66999—22no—
15#66997C2212yes—
16C2×#4325C2211yescharacteristic
17C2×#4314C2212yes—
18#66950—21no—
19#66946C2212yes—
20C4⋊C4×D11—21no—
21#66943C2212yes—
22#66942—22no—
23#66940C2212yes—
24C4×D44C2211yescharacteristic
25#66923—21no—
26#66922C2211yescharacteristic
27C4×Dic22—21no—
28C4×Dic22C2211yescharacteristic
29C11×#107C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#103C2212yes—
32#66899C2211yescharacteristic
33#66880C2212yes—
34#66879C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2212yes—
37#66874C2212yes—
38#66873C2211yescharacteristic
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43C2×D44C2311yescharacteristic
44C2×C4×D11—22no—
45C2×C4×D11—21no—
46C2×Dic22D411yescharacteristic
47C2×Dic22C2312yes—
48C2×C8×C11C2312yes—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2311yescharacteristic
52C11×C4⋊C4C2312yes—
53C42×C11—21no—
54C42×C11C2311yescharacteristic
55#4325—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—21no—
58C4⋊Dic11—22no—
59C4⋊Dic11—21no—
60C4⋊Dic11—21no—
61C4⋊Dic11D411yescharacteristic
62C4⋊Dic11C2311yescharacteristic
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4D412yes—
68C4×Dic11—22no—
69C4×Dic11C2312yes—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72#4314—24no—
73#3372—111nomaximal, Sylow
74C22×D11—21no—
75Q8×C11—21no—
76Q8×C11—21no—
77Q8×C11—81no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2411yescharacteristic
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11C2×D412yes—
87C2×Dic11C2×D412yes—
88D44—21no—
89D44#4112yes—
90C4×D11—42no—
91C4×D11—82no—
92Dic22—22no—
93Dic22—22no—
94Dic22—22no—
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#477D1111yescharacteristic, complemented
104#461—111no—
105#461—112no—
106#446—111no—
107#440—112no—
108C4×SD16—111no—
109C22×C11C22×D411yescharacteristic
110C2×D11—22no—
111C2×D11—41no—
112C2×D11—41no—
113C4×C11—21no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11—42no—
117C4×C11#13712yes—
118C4×C11C2×#4111yescharacteristic
119C4×C112−1+411yescharacteristic
120Dic11—22no—
121Dic11—22no—
122Dic11—42no—
123Dic11—41no—
124C2×SD16—111no—
125C2×SD16—112no—
126C4⋊Q8—112no—
127C4⋊Q8—111no—
128C4⋊Q8C2×D1111yescharacteristic
129#125—112no—
130#125—221no—
131#125—222no—
132C22⋊Q8—221no—
133C22⋊Q8—222no—
134C4×Q8—111no—
135C4×Q8—112no—
136C4×Q8—221no—
137C4×Q8C2×D1111yescharacteristic
138C4×D4—112no—
139C4×D4—111no—
140C2×C4⋊C4—221no—
141#107C2×D1112yes—
142#106—111no—
143C4⋊C8—112no—
144C4⋊C8C2×D1111yescharacteristic
145#103—111no—
146#103—112no—
147#103—112no—
148#103—112no—
149#103C2×D1112yes—
150#102—111no—
151#97—112no—
152C4×C8—111no—
153C2×C11#54811yescharacteristic
154C2×C11C2×#13711yescharacteristic
155C2×C11#57711yescharacteristic
156D11—42no—
157C2×Q8—21no—
158C2×Q8—111no—
159C2×Q8—112no—
160C2×Q8C22×D1111yescharacteristic
161C2×D4—111no—
162C22×C4—222no—
163C22×C4—221no—
164SD16—224no—
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—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—221no—
180C4⋊C4—221no—
181C4⋊C4C22×D1111yescharacteristic
182C4⋊C4C22×D1112yes—
183C22⋊C4—222no—
184C22⋊C4—221no—
185C42—21no—
186C42—112no—
187C42—222no—
188C42C22×D1111yescharacteristic
189C11#337211yescharacteristic, complemented, Sylow
190C23—221no—
191Q8—21no—
192Q8—21no—
193Q8—81no—
194Q8—222no—
195Q8—222no—
196Q8—222no—
197D4—112no—
198D4—221no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—112no—
203C2×C4—112no—
204C2×C4—222no—
205C2×C4—221no—
206C2×C4—442no—
207C2×C4—882no—
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—221no—
213C8—221no—
214C22—222no—
215C22—441no—
216C22—441no—
217C22C2×D4×D1111yescharacteristic
218C4—21no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—222no—
223C4—222no—
224C4—441no—
225C4—442no—
226C4#6697112yes—
227C4#6704011yescharacteristic
228C4#41×D1111yescharacteristic
229C2—442no—
230C2#1062316411yescharacteristic
231C2C2×#6697111yescharacteristic
232C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#477D11
hypocenterC11#3372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
3. C11×#477C2semidirect
4. #10622706C2semidirect
7. #10622490C2semidirect
9. #10622444C2semidirect
11. #10622410C2semidirect
103. #477D11semidirect
189. C11#3372semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106230982
C11×#4772
#106227062
C4×#43252
#106225022
#106224902
#106224542
#106224442
#106224312
#106224102
#337211