Finite Group Databasebeta

← #13081493

Subgroups — #13081493

Order 1408.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623110C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C8×Q8×C11C211yesmaximal, characteristic, complemented
4#10622463C211yesmaximal, characteristic, complemented
5#10622460C212yesmaximal
6#10622459C211yesmaximal, characteristic
7#10622442C212yesmaximal, complemented
8C4×#4314C211yesmaximal, characteristic
9C4×#4314C212yesmaximal
10#10622296C212yesmaximal, complemented
11#10622293C211yesmaximal, characteristic, complemented
12C4×Q8×C11C2211yescharacteristic
13#66999—21no—
14#66997—21no—
15C2×#4314C2211yescharacteristic
16#66949—22no—
17C4⋊C4×D11—21no—
18#66942—22no—
19#66940—21no—
20C4×D44C2211yescharacteristic
21C4×D44C2212yes—
22#66923C2212yes—
23#66923C2212yes—
24#66922C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22C2212yes—
27C4×Dic22C2211yescharacteristic
28C11×C4⋊C8C2212yes—
29C11×C4⋊C8C2211yescharacteristic
30C4×C8×C11C2211yescharacteristic
31C4×C8×C11C2212yes—
32#66885C2212yes—
33#66885C2211yescharacteristic
34#66882C2212yes—
35#66882C2212yes—
36#66881C2212yes—
37#66881C2212yes—
38#66881C2211yescharacteristic
39#66880C2211yescharacteristic
40#66880C2212yes—
41C2×Q8×C11D411yescharacteristic
42C2×D44C2311yescharacteristic
43C2×C4×D11—21no—
44C2×C4×D11—22no—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C2×C8×C11C2312yes—
50C2×C8×C11C2311yescharacteristic
51C11×C4⋊C4D411yescharacteristic
52C11×C4⋊C4D412yes—
53C42×C11C2311yescharacteristic
54C42×C11C2312yes—
55(C2×D11)⋊C4—21no—
56(C2×D11)⋊C4—22no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11C2312yes—
60C4⋊Dic11C2311yescharacteristic
61C4⋊Dic11C2312yes—
62C4⋊Dic11C2311yescharacteristic
63Dic11⋊C4—21no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C4×Dic11—21no—
71#4314Q814yescomplemented
72#3381—111nomaximal, Sylow
73C22×D11—21no—
74Q8×C11—22no—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2411yescharacteristic
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85D44—21no—
86D44C2×Q812yes—
87C4×D11—42no—
88C4×D11—82no—
89Dic22—21no—
90Dic22—42no—
91Dic22—81no—
92Dic22C2×Q812yes—
93C8×C11—21no—
94C8×C11—22no—
95C8×C11C2×Q812yes—
96#557—111no—
97#554—111no—
98#499—112no—
99#498—111no—
100#479—112no—
101#478—112no—
102#477—111no—
103#474—111no—
104C8×Q8D1111yescharacteristic, complemented
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—22no—
114C4×C11#13512yes—
115C4×C11C22×Q811yescharacteristic
116C4×C112−1+411yescharacteristic
117Dic11—22no—
118Dic11—42no—
119Dic11—41no—
120Dic11—42no—
121Dic11—41no—
122C2×SD16—111no—
123C4⋊Q8—111no—
124C4⋊Q8—111no—
125C4⋊Q8—221no—
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—111no—
136C4×D4—112no—
137C2×C4⋊C4—221no—
138#107—112no—
139#107—112no—
140#106—112no—
141#106—111no—
142#106—112no—
143C4⋊C8C2×D1111yescharacteristic
144C4⋊C8C2×D1112yes—
145#103—112no—
146#103—111no—
147#102—112no—
148#102—111no—
149C4×C8C2×D1111yescharacteristic
150C4×C8C2×D1112yes—
151C2×C11D4×Q811yescharacteristic
152C2×C11C2×#13511yescharacteristic
153C2×C11#57711yescharacteristic
154D11—42no—
155C2×Q8—111no—
156C2×Q8—221no—
157C2×Q8—221no—
158C2×Q8D4411yescharacteristic
159C2×D4—111no—
160C22×C4—221no—
161C22×C4—222no—
162SD16—114no—
163C2×C8C22×D1111yescharacteristic
164C2×C8C22×D1112yes—
165C2×C8C22×D1111yescharacteristic
166C4⋊C4—112no—
167C4⋊C4—111no—
168C4⋊C4—112no—
169C4⋊C4—111no—
170C4⋊C4—222no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—221no—
178C4⋊C4D4411yescharacteristic
179C4⋊C4D4412yes—
180C22⋊C4—221no—
181C22⋊C4—222no—
182C42—222no—
183C42—221no—
184C42C22×D1112yes—
185C42C22×D1111yescharacteristic
186C11#338111yescharacteristic, complemented, Sylow
187C23—221no—
188Q8—22no—
189Q8—112no—
190Q8—221no—
191Q8—442no—
192Q8—881no—
193D4—112no—
194D4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—222no—
198C2×C4—221no—
199C2×C4—222no—
200C2×C4—442no—
201C2×C4—882no—
202C2×C4C2×D4412yes—
203C2×C4C2×D4412yes—
204C2×C4C2×D4411yescharacteristic
205C2×C4C2×D4411yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—21no—
208C8—22no—
209C8Q8×D1112yes—
210C22—222no—
211C22—441no—
212C22—441no—
213C22C22×D4411yescharacteristic
214C4—22no—
215C4—22no—
216C4—21no—
217C4—222no—
218C4—441no—
219C4—442no—
220C4—442no—
221C4—441no—
222C4#6695712yes—
223C4C2×Q8×D1111yescharacteristic
224C4#6704311yescharacteristic
225C2—442no—
226C2Q8×D4411yescharacteristic
227C2C2×#6695711yescharacteristic
228C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC8×Q8×C11C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenterC8×Q8D11
hypocenterC11#3381
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
3. C8×Q8×C11C2semidirect
4. #10622463C2semidirect
7. #10622442C2semidirect
10. #10622296C2semidirect
11. #10622293C2semidirect
71. #4314Q8semidirect
104. C8×Q8D11semidirect
186. C11#3381semidirect

Maximal subgroups

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

subgroupindex
#106231102
#106230982
C8×Q8×C112
#106224632
#106224602
#106224592
#106224422
C4×#43142
#106222962
#106222932
#338111