Finite Group Databasebeta

← #13081572

Subgroups — #13081572

Order 1408.

348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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#10623070C212yesmaximal, complemented
2C4×C11×D8C211yesmaximal, characteristic
3#10622765C212yesmaximal
4#10622622C212yesmaximal, complemented
5#10622489C212yesmaximal, complemented
6#10622379C212yesmaximal, complemented
7#10622372C212yesmaximal, complemented
8#10622296C211yesmaximal, characteristic, complemented
9#10622292C211yesmaximal, characteristic, complemented
10C2×C11×D8C2211yescharacteristic
11C4×D4×C11C2212yes—
12D4×Dic11C2212yes—
13D4×Dic11C2212yes—
14#66977—22no—
15C2×Dic11⋊C4—22no—
16#66943C2212yes—
17#66941C2212yes—
18#66931—22no—
19#66931—22no—
20#66923C2212yes—
21C4×Dic22C2211yescharacteristic
22C11×#107C2211yescharacteristic
23C11×#102C2212yes—
24C4×C8×C11C2211yescharacteristic
25#66896C2212yes—
26#66896C2212yes—
27#66882C2211yescharacteristic
28#66882C2211yescharacteristic
29#66881C2212yes—
30#66879C2212yes—
31Dic11⋊C8C2212yes—
32#66872C2212yes—
33#66871C2212yes—
34C4⋊(C11⋊C8)C2211yescharacteristic
35C2×D4×C11C2312yes—
36C22×C4×C11—22no—
37C22×Dic11—22no—
38C22×Dic11—22no—
39C2×Dic22—22no—
40C2×Dic22D411yescharacteristic
41C11×D8Q814yescomplemented
42C2×C8×C11C2311yescharacteristic
43C2×C8×C11C2311yescharacteristic
44C11×C4⋊C4C2312yes—
45C11×C22⋊C4—22no—
46C42×C11C2311yescharacteristic
47C22⋊Dic11—22no—
48C22⋊Dic11—22no—
49C4⋊Dic11—22no—
50C4⋊Dic11D411yescharacteristic
51C4⋊Dic11C2312yes—
52C4⋊Dic11C2312yes—
53Dic11⋊C4—22no—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4D412yes—
58C4×Dic11C2312yes—
59C2×C11⋊C8C2312yes—
60#3389—111nomaximal, Sylow
61C23×C11—22no—
62D4×C11—22no—
63D4×C11C2×Q814yes—
64C2×C4×C11—22no—
65C2×C4×C11—82no—
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2411yescharacteristic
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—44no—
72C2×Dic11—82no—
73C2×Dic11C2×D412yes—
74C2×Dic11C2×D412yes—
75Dic22—41no—
76Dic22—82no—
77C8×C11—21no—
78C8×C11C2×Q812yes—
79C11⋊C8—22no—
80#554—112no—
81#501—112no—
82#499—111no—
83#478—112no—
84#478—112no—
85#474—112no—
86#446—111no—
87#442—112no—
88C4×D8D1111yescharacteristic
89C22×C11—24no—
90C22×C11—42no—
91C22×C11—42no—
92C22×C11C22×D411yescharacteristic
93C4×C11—21no—
94C4×C11—21no—
95C4×C11—42no—
96C4×C11C22×Q811yescharacteristic
97C4×C112−1+411yescharacteristic
98Dic11—22no—
99Dic11—22no—
100Dic11—42no—
101Dic11—42no—
102C2×D8C2×D1111yescharacteristic
103C4⋊Q8—112no—
104#125—112no—
105#125—112no—
106C22⋊Q8—222no—
107C22⋊Q8—222no—
108C22⋊Q8—222no—
109C4×Q8—111no—
110C4×D4—112no—
111C4×D4—112no—
112C4×D4C2×D1112yes—
113C2×C4⋊C4—222no—
114#107—111no—
115#107—111no—
116#107—112no—
117#107C2×D1111yescharacteristic
118#106—112no—
119#106—112no—
120C4⋊C8—112no—
121C4⋊C8—111no—
122#102—112no—
123#102—112no—
124#102C2×D1112yes—
125#97—112no—
126C4×C8C2×D1111yescharacteristic
127C2×C11—44no—
128C2×C11D4×Q811yescharacteristic
129C2×C11#57511yescharacteristic
130C2×C11#57611yescharacteristic
131C2×Q8—111no—
132C2×Q8—222no—
133C2×D4C22×D1112yes—
134C22×C4—22no—
135C22×C4—222no—
136C22×C4—222no—
137D8Dic2214yescomplemented
138C2×C8—112no—
139C2×C8C22×D1111yescharacteristic
140C2×C8C22×D1111yescharacteristic
141C4⋊C4—112no—
142C4⋊C4—111no—
143C4⋊C4—112no—
144C4⋊C4—112no—
145C4⋊C4—222no—
146C4⋊C4—222no—
147C4⋊C4—222no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C4⋊C4C22×D1112yes—
151C22⋊C4—22no—
152C22⋊C4—222no—
153C22⋊C4—222no—
154C42—112no—
155C42C22×D1111yescharacteristic
156C11#338911yescharacteristic, complemented, Sylow
157C23—22no—
158Q8—441no—
159Q8—882no—
160D4—22no—
161D4C2×Dic2214yes—
162C2×C4—22no—
163C2×C4—82no—
164C2×C4—112no—
165C2×C4—112no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—444no—
169C2×C4—882no—
170C2×C4D4×D1111yescharacteristic
171C2×C4D4×D1111yescharacteristic
172C2×C4C23×D1111yescharacteristic
173C8—21no—
174C8—222no—
175C8C2×Dic2212yes—
176C22—24no—
177C22—42no—
178C22—42no—
179C22C2×D4×D1111yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—222no—
184C4—222no—
185C4—442no—
186C4—442no—
187C4C22×Dic2211yescharacteristic
188C4#6704311yescharacteristic
189C2—44no—
190C2D4×Dic2211yescharacteristic
191C2#1062328811yescharacteristic
192C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
prime radicalC2×C11×D8C22
hypercenterC4×D8D11
hypocenterC11#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623070C2semidirect
4. #10622622C2semidirect
5. #10622489C2semidirect
6. #10622379C2semidirect
7. #10622372C2semidirect
8. #10622296C2semidirect
9. #10622292C2semidirect
41. C11×D8Q8semidirect
137. D8Dic22semidirect
156. C11#3389semidirect

Maximal subgroups

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

subgroupindex
#106230702
C4×C11×D82
#106227652
#106226222
#106224892
#106223792
#106223722
#106222962
#106222922
#338911