Finite Group Databasebeta

← #16835775

Subgroups — #16835775

Order 3712.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272144C212yesmaximal
2#14272070C212yesmaximal, complemented
3#14272069C212yesmaximal, complemented
4#14271738C211yesmaximal, characteristic
5C2×#90809C2211yescharacteristic
6C2×Q8×D29C411yescharacteristic, complemented
7#11745345—22no—
8C29×C4⋊Q8C411yescharacteristic, complemented
9#11745309C2211yescharacteristic
10#11745306C411yescharacteristic, complemented
11#11745258—22no—
12#11745256—22no—
13#11745237C2211yescharacteristic
14#11745234C411yescharacteristic, complemented
15#11745215—22no—
16#11745215C2214yes—
17C2×Q8×C29C2×C411yescharacteristic
18C2×Q8×C29C2×C411yescharacteristic
19#90809—42no—
20Q8×D29—42no—
21C2×D116D412yes—
22C2×D116C2311yescharacteristic
23C2×C4×D29—21no—
24C2×C4×D29C2×C411yescharacteristic
25C2×C4×D29D412yes—
26C2×Dic58—21no—
27C2×Dic58C2×C411yescharacteristic
28C22⋊#1181—24no—
29C4⋊#1181—42no—
30C4×#1181—42no—
31C4⋊C4×C29—22no—
32C42×C29C2×C411yescharacteristic
33#90781—21no—
34#90781—22no—
35#90781—22no—
36#90779—22no—
37#90779—21no—
38C4×Dic29C2×C411yescharacteristic
39C22×D29C22⋊C411yescharacteristic
40C22×D29C2×D412yes—
41C2×#1181—44no—
42Q8×C29—41no—
43Q8×C29—41no—
44C2×C4×C29—21no—
45C2×C4×C29—21no—
46C2×C4×C29C22⋊C412yes—
47C2×C4×C29C22×C411yescharacteristic
48C2×Dic29—21no—
49C2×Dic29—21no—
50C2×Dic29C22⋊C411yescharacteristic
51D116—42no—
52D116—41no—
53C4×D29—22no—
54C4×D29—22no—
55C4×D29—22no—
56C4×D29—42no—
57Dic58—42no—
58Dic58—41no—
59#2129—291nomaximal, Sylow
60C22×C29C2×C22⋊C411yescharacteristic
61C2×D29—21no—
62C2×D29—22no—
63C2×D29—41no—
64C2×D29—42no—
65#1181—84no—
66C4×C29—21no—
67C4×C29—22no—
68C4×C29—41no—
69C4×C29—41no—
70Dic29—41no—
71Dic29—41no—
72Dic29#9912yes—
73#536—291no—
74#410—292no—
75#354—292no—
76#354—292no—
77C2×C29—21no—
78C2×C29C2×#9911yescharacteristic
79D29—42no—
80D29—41no—
81C2×#41—291no—
82C22×Q8—291no—
83C4⋊Q8—291no—
84C4⋊Q8#118111yescharacteristic, complemented
85#124—291no—
86#124—291no—
87#123—582no—
88C22⋊Q8—582no—
89#117—291no—
90#117—582no—
91#99—294no—
92#99—582no—
93C29#212911yescharacteristic, complemented, Sylow
94#41—1162no—
95C2×Q8—291no—
96C2×Q8—581no—
97C2×Q8—1162no—
98C2×Q8C2×#118111yescharacteristic
99C2×Q8C2×#118111yescharacteristic
100C2×D4—292no—
101C2×D4—291no—
102C22×C4—292no—
103C22×C4—291no—
104C22×C4—581no—
105C4⋊C4—22no—
106C4⋊C4—581no—
107C4⋊C4—582no—
108C4⋊C4—1162no—
109C22⋊C4—581no—
110C22⋊C4—582no—
111C22⋊C4—582no—
112C22⋊C4—584no—
113C42—291no—
114C42—1162no—
115C42C2×#118111yescharacteristic
116C23—292no—
117C23—291no—
118Q8—41no—
119Q8—41no—
120Q8—1161no—
121Q8—1162no—
122D4—1162no—
123D4—1161no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—291no—
127C2×C4—582no—
128C2×C4—582no—
129C2×C4—582no—
130C2×C4—581no—
131C2×C4—581no—
132C2×C4—1162no—
133C2×C4—1164no—
134C2×C4C22⋊#118112yes—
135C2×C4C22×#118111yescharacteristic
136C22—582no—
137C22—581no—
138C22—1162no—
139C22—1161no—
140C22C2×C22⋊#118111yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—292no—
146C4—1161no—
147C4—1161no—
148C4—2324no—
149C2—21no—
150C2—1162no—
151C2—1161no—
152C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C4⋊Q8C4
socleC2×C29C2×#99
prime radicalC2×#90809C22
cosocleC2×D116C23
hypercenterC4⋊Q8#1181
hypocenterC29#2129
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14272070C2semidirect
3. #14272069C2semidirect
6. C2×Q8×D29C4semidirect
8. C29×C4⋊Q8C4semidirect
10. #11745306C4semidirect
14. #11745234C4semidirect
84. C4⋊Q8#1181semidirect
93. C29#2129semidirect

Maximal subgroups

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

subgroupindex
#142721442
#142720702
#142720692
#142717382
#212929