Finite Group Databasebeta

← #16834819

Subgroups — #16834819

Order 3712.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#14272180C211yesmaximal, characteristic, complemented
2#14272166C211yesmaximal, characteristic, complemented
3#14272011C214yesmaximal, complemented
4C2×#11745255C211yesmaximal, characteristic
5C22×D116C411yescharacteristic
6C22×C4×D29—21no—
7C2×#90800—21no—
8C2×C4⋊C4×C29C411yescharacteristic
9C2×#90781—21no—
10C2×C4×Dic29C2211yescharacteristic
11#11745255—21no—
12#11745255—21no—
13#11745255C412yes—
14#11745255C2212yes—
15C22⋊#6599—21no—
16#11745220—21no—
17#11745220—21no—
18C4⋊#6599C2212yescomplemented
19C4×#6599C2212yescomplemented
20C23×D29—21no—
21C22×C4×C29—21no—
22C22×C4×C29C2×C411yescharacteristic
23C22×Dic29D411yescharacteristic
24C22×Dic29D411yescharacteristic
25C2×D116—21no—
26C2×D116—24no—
27C2×D116C2×C412yes—
28C2×C4×D29—22no—
29C2×C4×D29—22no—
30C2×C4×D29—42no—
31C2×C4×D29—42no—
32#90800—42no—
33C2×#6599—22no—
34C2×#6599—22no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29C2×C412yes—
37#90781—22no—
38#90781—22no—
39C4×Dic29C2×C411yescharacteristic
40C4×Dic29D411yescharacteristic
41C4×Dic29D411yescharacteristic
42C4×Dic29C2311yescharacteristic
43C23×C29C22⋊C411yescharacteristic
44C22×D29—24no—
45C22×D29—22no—
46C22×D29—42no—
47C22×D29—42no—
48C2×C4×C29—22no—
49C2×C4×C29—22no—
50C2×C4×C29—42no—
51C2×C4×C29C22⋊C411yescharacteristic
52C2×C4×C29C22×C411yescharacteristic
53C2×Dic29—41no—
54C2×Dic29C22⋊C411yescharacteristic
55C2×Dic29C22⋊C411yescharacteristic
56C2×Dic29D812yes—
57C2×Dic29SD1612yes—
58C2×Dic29C2×D411yescharacteristic
59C2×Dic29C2×D411yescharacteristic
60D116—24no—
61D116—22no—
62D116M1614yescomplemented
63C4×D29—44no—
64C4×D29—42no—
65C4×D29—42no—
66#6599—42no—
67#6599—42no—
68#1486—291nomaximal, Sylow
69C22×C29—21no—
70C22×C29—21no—
71C22×C29#10212yes—
72C22×C29C2×C22⋊C411yescharacteristic
73C2×D29—24no—
74C2×D29—48no—
75C2×D29—42no—
76C2×D29—42no—
77C4×C29—21no—
78C4×C29—42no—
79C4×C29C2×M1612yes—
80Dic29—21no—
81Dic29—21no—
82Dic29#10212yes—
83Dic29C2×D811yescharacteristic
84Dic29C2×SD1611yescharacteristic
85C2×C4×D4—291no—
86#431—291no—
87#423—291no—
88D4⋊C8—294no—
89C2×C29—22no—
90C2×C29#40711yescharacteristic
91C2×C29C2×#10211yescharacteristic
92C2×C29#42111yescharacteristic
93D29—44no—
94C22×D4—291no—
95C23×C4—581no—
96C2×M16—581no—
97C4×D4—292no—
98C4×D4—292no—
99C4×D4—581no—
100C4×D4—581no—
101C2×C4⋊C4#118111yescharacteristic
102C2×C22⋊C4—581no—
103C2×C42—291no—
104C4⋊C8—292no—
105C4⋊C8—581no—
106C4⋊C8—581no—
107C22⋊C8—581no—
108C4×C8—292no—
109C29#148611yescharacteristic, complemented, Sylow
110C24—581no—
111C2×D4—292no—
112C2×D4—584no—
113C2×D4—581no—
114C22×C4—21no—
115C22×C4—291no—
116C22×C4—291no—
117C22×C4—582no—
118C22×C4—582no—
119C22×C4—1162no—
120C22×C4—1162no—
121C22×C4C2×#118111yescharacteristic
122M16—1162no—
123C2×C8—582no—
124C2×C8—582no—
125C4⋊C4—21no—
126C4⋊C4C2×#118112yes—
127C22⋊C4—582no—
128C22⋊C4—582no—
129C42—291no—
130C42—291no—
131C42—291no—
132C42—291no—
133C23—584no—
134C23—582no—
135C23—1162no—
136C23—1162no—
137C23C22⋊#118111yescharacteristic
138D4—294no—
139D4—584no—
140D4—582no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—291no—
145C2×C4—291no—
146C2×C4—292no—
147C2×C4—292no—
148C2×C4—291no—
149C2×C4—291no—
150C2×C4—1162no—
151C2×C4—1164no—
152C2×C4—1162no—
153C2×C4—1161no—
154C2×C4C22⋊#118111yescharacteristic
155C2×C4C22×#118111yescharacteristic
156C8—1162no—
157C8—1162no—
158C22—21no—
159C22—21no—
160C22—584no—
161C22—1168no—
162C22—1162no—
163C22—1162no—
164C22#1174522312yes—
165C22C2×C22⋊#118111yescharacteristic
166C4—21no—
167C4—42no—
168C4—291no—
169C4—292no—
170C4—291no—
171C4—581no—
172C4—581no—
173C4D29⋊M1612yes—
174C2—22no—
175C2—1164no—
176C2#1427213511yescharacteristic
177C2C2×#1174522311yescharacteristic
178C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D116C4
cosocleC4×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1486
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14272180C2semidirect
2. #14272166C2semidirect
3. #14272011C2semidirect
18. C4⋊#6599C22semidirect
19. C4×#6599C22semidirect
62. D116M16semidirect
109. C29#1486semidirect

Maximal subgroups

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

subgroupindex
#142721802
#142721662
#142720112
C2×#117452552
#148629