Finite Group Databasebeta

← #16835783

Subgroups — #16835783

Order 3712.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#14272149C212yesmaximal, complemented
2#14272073C212yesmaximal, complemented
3#14272071C212yesmaximal, complemented
4#14271709C211yesmaximal, characteristic
5C2×#41×C29C411yescharacteristic
6C2×#90805C2211yescharacteristic
7D29⋊M16—22no—
8#11745309C411yescharacteristic
9#11745306C2211yescharacteristic
10#11745302C411yescharacteristic
11#11745301—22no—
12#11745298C2211yescharacteristic
13C4×C22⋊D29—22no—
14C2×C4×Dic29C411yescharacteristic
15#11745229—22no—
16#11745221C2214yes—
17#41×C29—41no—
18#41×C29—41no—
19C2×Q8×C29C2×C411yescharacteristic
20C2×D4×C29—21no—
21C2×D4×C29C2×C411yescharacteristic
22C22×C4×C29—21no—
23C22×C4×C29C2×C411yescharacteristic
24C2×C22⋊D29—22no—
25C2×C22⋊D29D412yes—
26C22×Dic29—21no—
27#90805—41no—
28#90805—41no—
29C2×D116C2×C411yescharacteristic
30C2×C4×D29D412yes—
31C2×Dic58C2311yescharacteristic
32#90800—24no—
33#90796—42no—
34D29⋊C8—42no—
35C22⋊Dic29—22no—
36#90781—22no—
37#90779—22no—
38C4×Dic29—21no—
39C4×Dic29C2×C411yescharacteristic
40C4×Dic29C2×C411yescharacteristic
41C23×C29—21no—
42C23×C29C22⋊C411yescharacteristic
43C22×D29C22⋊C412yes—
44Q8×C29—41no—
45D4×C29—41no—
46D4×C29—42no—
47C2×C4×C29—21no—
48C2×C4×C29—21no—
49C2×C4×C29—21no—
50C2×C4×C29—41no—
51C2×C4×C29—41no—
52C2×C4×C29C22⋊C411yescharacteristic
53C2×C4×C29C22×C411yescharacteristic
54C22⋊D29—42no—
55C22⋊D29—44no—
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—42no—
59C2×Dic29C2×D412yes—
60D116—41no—
61C4×D29—22no—
62C4×D29—22no—
63Dic58—41no—
64#6599—44no—
65#2132—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—41no—
68C22×C29—42no—
69C22×C29—41no—
70C22×C29C2×C22⋊C411yescharacteristic
71C2×D29—22no—
72C2×D29—42no—
73C4×C29—21no—
74C4×C29—41no—
75C4×C29#9911yescharacteristic
76C4×C29#9911yescharacteristic
77Dic29—22no—
78Dic29—22no—
79Dic29—41no—
80#532—291no—
81#413—292no—
82#356—292no—
83#355—292no—
84C2×C29—21no—
85C2×C29—41no—
86C2×C29—81no—
87C2×C29C2×#9911yescharacteristic
88D29—42no—
89C2×#41—291no—
90C2×#41#118111yescharacteristic
91C2×M16—582no—
92C4⋊Q8—291no—
93#127—291no—
94#124—291no—
95#124—291no—
96#121—582no—
97C4×D4—582no—
98C2×C42—291no—
99#101—294no—
100#100—582no—
101C29#213211yescharacteristic, complemented, Sylow
102#41—41no—
103#41—41no—
104#41—1161no—
105#41—1161no—
106C2×Q8—291no—
107C2×Q8C2×#118111yescharacteristic
108C2×D4—21no—
109C2×D4—292no—
110C2×D4—291no—
111C2×D4—582no—
112C2×D4C2×#118111yescharacteristic
113C22×C4—21no—
114C22×C4—292no—
115C22×C4—581no—
116C22×C4C2×#118111yescharacteristic
117M16—584no—
118M16—1162no—
119C2×C8—1162no—
120C4⋊C4—582no—
121C22⋊C4—582no—
122C22⋊C4—582no—
123C42—291no—
124C42—291no—
125C42—581no—
126C23—21no—
127C23—292no—
128C23C22⋊#118111yescharacteristic
129Q8—41no—
130Q8—1161no—
131D4—41no—
132D4—42no—
133D4—1161no—
134D4—1162no—
135D4—1164no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—292no—
142C2×C4—581no—
143C2×C4—582no—
144C2×C4—582no—
145C2×C4—581no—
146C2×C4—1162no—
147C2×C4C22⋊#118111yescharacteristic
148C2×C4C22×#118111yescharacteristic
149C8—1164no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—582no—
155C22—1162no—
156C22C2×C22⋊#118111yescharacteristic
157C4—21no—
158C4—41no—
159C4—582no—
160C4—582no—
161C4—1161no—
162C4#1174522711yescharacteristic
163C4#1174522711yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—1162no—
168C2C2×#1174522711yescharacteristic
subgroupG/H
centerC4#11745227
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×#41×C29C4
socleC2×C29C2×#99
prime radical#14271709C2
cosocleC2×Dic58C23
hypercenterC2×#41#1181
hypocenterC29#2132
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14272149C2semidirect
2. #14272073C2semidirect
3. #14272071C2semidirect
101. C29#2132semidirect

Maximal subgroups

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

subgroupindex
#142721492
#142720732
#142720712
#142717092
#213229