Finite Group Databasebeta

← #16834832

Subgroups — #16834832

Order 3712.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272185C211yesmaximal, characteristic, complemented
2C4×#90796C211yesmaximal, characteristic, complemented
3#14272011C212yesmaximal, complemented
4D4⋊#6599C212yesmaximal, complemented
5C4×D4×D29C211yesmaximal, characteristic
6C2×D4×D29C411yescharacteristic
7C22×C4×D29—21no—
8C2×#90796—21no—
9C4×D4×C29C411yescharacteristic
10D4×Dic29C2211yescharacteristic
11C4×C22⋊D29—21no—
12#11745255C2211yescharacteristic
13C4⋊C4×D29C411yescharacteristic
14#11745243—21no—
15C22⋊C4×D29—21no—
16C4×D116C411yescharacteristic
17C42×D29C2211yescharacteristic
18#11745219—21no—
19#11745218—21no—
20#11745218—21no—
21C4⋊#6599C2212yescomplemented
22C4×#6599C2212yescomplemented
23C23×D29—21no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C22×Dic29—21no—
28D4×D29—22no—
29D4×D29—22no—
30C2×D116C2×C411yescharacteristic
31C2×C4×D29—21no—
32C2×C4×D29—21no—
33C2×C4×D29—21no—
34C2×C4×D29—44no—
35C2×C4×D29C2×C411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×#6599—22no—
39C2×#6599—22no—
40#90796—24no—
41C4⋊C4×C29C2×C411yescharacteristic
42C22⋊C4×C29—21no—
43C42×C29C2×C411yescharacteristic
44C22⋊Dic29—21no—
45#90781—21no—
46#90781—21no—
47C4⋊Dic29C2×C411yescharacteristic
48#90779—21no—
49C4×Dic29D411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29C2311yescharacteristic
52C23×C29—21no—
53C22×D29—24no—
54C22×D29—21no—
55C22×D29—42no—
56C22×D29—42no—
57C22×D29C22⋊C411yescharacteristic
58D4×C29—21no—
59D4×C29M1612yescomplemented
60C2×C4×C29—21no—
61C2×C4×C29—42no—
62C2×C4×C29C22⋊C411yescharacteristic
63C2×C4×C29C22⋊C411yescharacteristic
64C2×C4×C29C22×C411yescharacteristic
65C22⋊D29—24no—
66C2×Dic29—21no—
67C2×Dic29—42no—
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C2×D411yescharacteristic
70C2×Dic29C2×D411yescharacteristic
71D116—21no—
72D116M1612yescomplemented
73C4×D29—22no—
74C4×D29—21no—
75C4×D29—21no—
76C4×D29—22no—
77C4×D29—42no—
78C4×D29—42no—
79C4×D29—42no—
80#6599—24no—
81#6599—42no—
82#1490—291nomaximal, Sylow
83C22×C29—22no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29C2×C22⋊C411yescharacteristic
87C2×D29—21no—
88C2×D29—21no—
89C2×D29—22no—
90C2×D29—48no—
91C2×D29—41no—
92C2×D29—41no—
93C2×D29#10412yes—
94C4×C29—21no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29C2×M1611yescharacteristic
98C4×C29C2×M1611yescharacteristic
99Dic29—21no—
100Dic29—21no—
101Dic29—41no—
102Dic29AGL(1,ℤ/8)12yes—
103C2×C4×D4—291no—
104#432—291no—
105C4×M16—291no—
106D4⋊C8—292no—
107D4⋊C8—292no—
108C2×C29—42no—
109C2×C29#40711yescharacteristic
110C2×C29#41811yescharacteristic
111C2×C29C2×#10411yescharacteristic
112D29—22no—
113D29—42no—
114C22×D4—291no—
115C23×C4—581no—
116C2×M16—581no—
117C4×D4—291no—
118C4×D4—291no—
119C4×D4—291no—
120C4×D4—581no—
121C4×D4—581no—
122C4×D4#118111yescharacteristic
123C2×C4⋊C4—291no—
124C2×C22⋊C4—581no—
125C2×C42—291no—
126C4⋊C8—292no—
127C22⋊C8—581no—
128#97—581no—
129#97—581no—
130C4×C8—292no—
131C29#149011yescharacteristic, complemented, Sylow
132C24—581no—
133C2×D4—291no—
134C2×D4—581no—
135C2×D4—582no—
136C2×D4—582no—
137C2×D4C2×#118111yescharacteristic
138C22×C4—21no—
139C22×C4—291no—
140C22×C4—291no—
141C22×C4—291no—
142C22×C4—581no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4—581no—
146C22×C4—1164no—
147M16—584no—
148C2×C8—582no—
149C2×C8—582no—
150C4⋊C4—291no—
151C4⋊C4—581no—
152C4⋊C4C2×#118111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C42—291no—
158C42—291no—
159C42—291no—
160C42C2×#118111yescharacteristic
161C23—21no—
162C23—291no—
163C23—584no—
164C23—581no—
165C23—1162no—
166C23—1162no—
167D4—21no—
168D4—292no—
169D4—584no—
170D4—581no—
171D4#9079612yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—291no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—1162no—
183C2×C4—1162no—
184C2×C4—1162no—
185C2×C4—1162no—
186C2×C4C22⋊#118111yescharacteristic
187C2×C4C22⋊#118111yescharacteristic
188C2×C4C22×#118111yescharacteristic
189C8—584no—
190C8—1162no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—292no—
195C22—581no—
196C22—581no—
197C22—582no—
198C22—1168no—
199C22—1161no—
200C22—1161no—
201C22C2×C22⋊#118111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—292no—
206C4—581no—
207C4—581no—
208C4—1161no—
209C4C2×#9079611yescharacteristic
210C4D29⋊M1611yescharacteristic
211C2—42no—
212C2—582no—
213C2—1162no—
214C2#1427213411yescharacteristic
215C2#1427215511yescharacteristic
216C2D29⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×D4×D29C4
cosocleC4×Dic29C23
hypercenterC4×D4#1181
hypocenterC29#1490
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272185C2semidirect
2. C4×#90796C2semidirect
3. #14272011C2semidirect
4. D4⋊#6599C2semidirect
21. C4⋊#6599C22semidirect
22. C4×#6599C22semidirect
59. D4×C29M16semidirect
72. D116M16semidirect
131. C29#1490semidirect
171. D4#90796semidirect

Maximal subgroups

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

subgroupindex
#142721852
C4×#907962
#142720112
D4⋊#65992
C4×D4×D292
#149029