Finite Group Databasebeta

← #13081490

Subgroups — #13081490

Order 1408.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623101C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic
6#10622504C212yesmaximal
7#10622491C212yesmaximal, complemented
8#10622459C211yesmaximal, characteristic
9#10622443C211yesmaximal, characteristic, complemented
10#10622409C212yesmaximal, complemented
11#10622401C212yesmaximal
12C11×C4⋊Q8C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14#66999—22no—
15Q8×Dic11C2212yes—
16C2×#4325C2211yescharacteristic
17#66950—21no—
18#66946C2212yes—
19C4⋊C4×D11—21no—
20#66943—22no—
21#66943C2212yes—
22#66943C2212yes—
23C4×D44C2211yescharacteristic
24#66922—21no—
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22C2211yescharacteristic
28C11×#107C2212yes—
29C11×C4⋊C8C2211yescharacteristic
30C11×#103C2212yes—
31#66899C2211yescharacteristic
32#66885C2212yes—
33#66882C2212yes—
34Dic11⋊C8C2212yes—
35C8×Dic11C2212yes—
36#66873C2211yescharacteristic
37#66872C2211yescharacteristic
38#66872C2212yes—
39#66872C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43C2×D44C2311yescharacteristic
44C2×C4×D11—22no—
45C2×C4×D11—21no—
46C2×Dic22—21no—
47C2×Dic22D411yescharacteristic
48C2×C8×C11C2312yes—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2312yes—
52C11×C4⋊C4C2311yescharacteristic
53C42×C11—21no—
54C42×C11C2311yescharacteristic
55#4325Q814yescomplemented
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—21no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11D411yescharacteristic
63C4⋊Dic11C2312yes—
64C4⋊Dic11C2311yescharacteristic
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4D412yes—
68C4×Dic11—22no—
69C4×Dic11C2312yes—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72#3381—111nomaximal, Sylow
73C22×D11—21no—
74Q8×C11—21no—
75Q8×C11—81no—
76Q8×C11C2×Q812yes—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2411yescharacteristic
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11C2×D412yes—
86C2×Dic11C2×D412yes—
87D44—21no—
88D44C2×Q812yes—
89C4×D11—42no—
90C4×D11—82no—
91Dic22—22no—
92Dic22—42no—
93C8×C11—22no—
94C11⋊C8—21no—
95C11⋊C8C2×Q812yes—
96#557—111no—
97#554—111no—
98#499—112no—
99#498—111no—
100#479—112no—
101#478—112no—
102#477D1111yescharacteristic, complemented
103#474—111no—
104C8×Q8—111no—
105C4×SD16—111no—
106C4×SD16—112no—
107C22×C11C22×D411yescharacteristic
108C2×D11—22no—
109C2×D11—41no—
110C2×D11—41no—
111C4×C11—22no—
112C4×C11—21no—
113C4×C11—41no—
114C4×C11—42no—
115C4×C11#13512yes—
116C4×C11C22×Q811yescharacteristic
117C4×C112−1+411yescharacteristic
118Dic11—22no—
119Dic11—22no—
120Dic11—42no—
121Dic11—41no—
122C2×SD16—111no—
123C4⋊Q8—111no—
124C4⋊Q8—221no—
125C4⋊Q8C2×D1111yescharacteristic
126#125—112no—
127#125—112no—
128#125—222no—
129C22⋊Q8—221no—
130C22⋊Q8—222no—
131C4×Q8—111no—
132C4×Q8—112no—
133C4×Q8—221no—
134C4×Q8C2×D1111yescharacteristic
135C4×D4—112no—
136C4×D4—111no—
137C2×C4⋊C4—221no—
138#107—112no—
139#107C2×D1112yes—
140#106—112no—
141#106—111no—
142#106—112no—
143C4⋊C8—112no—
144C4⋊C8C2×D1111yescharacteristic
145#103—111no—
146#103C2×D1112yes—
147#102—112no—
148#102—111no—
149C4×C8—112no—
150C4×C8—111no—
151C2×C11D4×Q811yescharacteristic
152C2×C11C2×#13511yescharacteristic
153C2×C11#57711yescharacteristic
154D11—42no—
155C2×Q8—21no—
156C2×Q8—111no—
157C2×Q8—221no—
158C2×Q8C22×D1111yescharacteristic
159C2×D4—111no—
160C22×C4—222no—
161C22×C4—221no—
162SD16—114no—
163C2×C8—111no—
164C2×C8—111no—
165C2×C8C22×D1112yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—111no—
169C4⋊C4—112no—
170C4⋊C4—112no—
171C4⋊C4—111no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—221no—
178C4⋊C4C22×D1111yescharacteristic
179C4⋊C4C22×D1112yes—
180C22⋊C4—222no—
181C22⋊C4—221no—
182C42—21no—
183C42—112no—
184C42—222no—
185C42C22×D1111yescharacteristic
186C11#338111yescharacteristic, complemented, Sylow
187C23—221no—
188Q8—21no—
189Q8—81no—
190Q8—222no—
191Q8—442no—
192Q8Q8×D1112yes—
193D4—112no—
194D4—221no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—112no—
199C2×C4—112no—
200C2×C4—222no—
201C2×C4—221no—
202C2×C4—442no—
203C2×C4—882no—
204C2×C4D4×D1111yescharacteristic
205C2×C4D4×D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—22no—
208C8—112no—
209C8—221no—
210C22—222no—
211C22—441no—
212C22—441no—
213C22C2×D4×D1111yescharacteristic
214C4—21no—
215C4—22no—
216C4—42no—
217C4—41no—
218C4—222no—
219C4—222no—
220C4—441no—
221C4—442no—
222C4#6697212yes—
223C4C2×Q8×D1111yescharacteristic
224C4#6704311yescharacteristic
225C2—442no—
226C2#1062316311yescharacteristic
227C2C2×#6697211yescharacteristic
228C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#477D11
hypocenterC11#3381
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. #10623101C2semidirect
3. C11×#477C2semidirect
4. #10622692C2semidirect
7. #10622491C2semidirect
9. #10622443C2semidirect
10. #10622409C2semidirect
55. #4325Q8semidirect
102. #477D11semidirect
186. C11#3381semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106231012
C11×#4772
#106226922
C4×#43252
#106225042
#106224912
#106224592
#106224432
#106224092
#106224012
#338111