Finite Group Databasebeta

← #16835792

Subgroups — #16835792

Order 3712.

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

normal subgroups only

This group has 262 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#14272150C212yesmaximal, complemented
2#14272072C212yesmaximal, complemented
3#14272071C212yesmaximal, complemented
4#14271726C211yesmaximal, characteristic
5C2×#90807C2211yescharacteristic
6C2×D4×D29C411yescharacteristic
7C2×#90800—22no—
8C29×#127C411yescharacteristic
9#11745302C411yescharacteristic
10#11745301—22no—
11#11745299—22no—
12#11745298C2211yescharacteristic
13#11745237C2211yescharacteristic
14#11745234C411yescharacteristic
15#11745229—22no—
16#11745221C2214yescomplemented
17C23×D29—21no—
18C2×D4×C29—22no—
19C2×D4×C29C2×C411yescharacteristic
20C2×D4×C29C2×C411yescharacteristic
21C2×C22⋊D29—22no—
22C2×C22⋊D29—21no—
23C2×C22⋊D29D412yes—
24C22×Dic29D412yes—
25#90807—42no—
26D4×D29—42no—
27C2×D116C2×C411yescharacteristic
28C2×C4×D29C2×C411yescharacteristic
29C2×Dic58C2311yescharacteristic
30#90800—24no—
31#90800—42no—
32C2×#6599—42no—
33C42×C29C2×C411yescharacteristic
34C22⋊Dic29—22no—
35#90781—21no—
36#90781—22no—
37#90779—21no—
38C4×Dic29C2×C411yescharacteristic
39C23×C29—21no—
40C23×C29C22⋊C412yes—
41C22×D29—21no—
42C22×D29—42no—
43C22×D29—82no—
44C22×D29C22⋊C411yescharacteristic
45D4×C29—41no—
46D4×C29—41no—
47D4×C29—82no—
48C2×C4×C29—21no—
49C2×C4×C29C22×C411yescharacteristic
50C22⋊D29—42no—
51C22⋊D29—42no—
52C22⋊D29—82no—
53C2×Dic29—22no—
54C2×Dic29—22no—
55C2×Dic29—21no—
56C2×Dic29C22⋊C411yescharacteristic
57C2×Dic29C2×D412yes—
58D116—41no—
59C4×D29—22no—
60Dic58—41no—
61#6599—44no—
62#2134—291nomaximal, Sylow
63C22×C29—22no—
64C22×C29—42no—
65C22×C29—42no—
66C22×C29—41no—
67C22×C29C2×C22⋊C411yescharacteristic
68C2×D29—21no—
69C2×D29—41no—
70C2×D29—42no—
71C2×D29—41no—
72C2×D29—84no—
73C4×C29—21no—
74C4×C29—41no—
75Dic29—22no—
76Dic29—41no—
77Dic29#9912yes—
78#535—291no—
79#413—292no—
80#355—292no—
81#355—292no—
82C2×C29—21no—
83C2×C29—42no—
84C2×C29—81no—
85C2×C29C2×#9911yescharacteristic
86D29—41no—
87D29—81no—
88C2×#41—291no—
89C22×D4—291no—
90C2×M16—582no—
91#127—291no—
92#127#118111yescharacteristic
93#124—291no—
94#124—291no—
95#121—582no—
96#120—582no—
97#117—291no—
98#101—294no—
99#100—582no—
100C29#213411yescharacteristic, complemented, Sylow
101C24—581no—
102#41—1162no—
103C2×Q8—291no—
104C2×D4—22no—
105C2×D4—292no—
106C2×D4—291no—
107C2×D4—581no—
108C2×D4—582no—
109C2×D4—1162no—
110C2×D4C2×#118111yescharacteristic
111C2×D4C2×#118111yescharacteristic
112C22×C4—292no—
113C22×C4—291no—
114M16—584no—
115M16—1162no—
116C2×C8—1162no—
117C4⋊C4—581no—
118C22⋊C4—582no—
119C22⋊C4—581no—
120C22⋊C4—582no—
121C42—291no—
122C42C2×#118111yescharacteristic
123C23—21no—
124C23—291no—
125C23—581no—
126C23—1162no—
127C23—2322no—
128C23C22⋊#118112yes—
129Q8—1161no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—1161no—
134D4—1162no—
135D4—1162no—
136D4—2322no—
137C2×C4—21no—
138C2×C4—291no—
139C2×C4—292no—
140C2×C4—582no—
141C2×C4—582no—
142C2×C4—582no—
143C2×C4—581no—
144C2×C4C22×#118111yescharacteristic
145C8—1164no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—581no—
151C22—1161no—
152C22—1162no—
153C22—1161no—
154C22—2324no—
155C22C2×C22⋊#118111yescharacteristic
156C4—21no—
157C4—41no—
158C4—292no—
159C4—582no—
160C4—1161no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—1161no—
165C2—2321no—
166C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC2×C29C2×#99
prime radical#14271726C2
cosocleC2×Dic58C23
hypercenter#127#1181
hypocenterC29#2134
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14272150C2semidirect
2. #14272072C2semidirect
3. #14272071C2semidirect
16. #11745221C22semidirect
100. C29#2134semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142720722
#142720712
#142717262
#213429