Finite Group Databasebeta

← #16834929

Subgroups — #16834929

Order 3712.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D29⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#14272105C211yesmaximal, characteristic, complemented
3#14272015C214yesmaximal, complemented
4C2×#11745257C211yesmaximal, characteristic
5C22×D116—21no—
6C22×D116C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×C4⋊#1181—21no—
10C2×D29⋊C8—21no—
11C2×C4⋊C4×C29C411yescharacteristic, complemented
12C2×#90781—21no—
13#11745257—21no—
14#11745257—21no—
15#11745257C412yescomplemented
16#11745257C2212yes—
17C22⋊#6599—21no—
18(C2×#1181)⋊C4C2212yescomplemented
19#11745219C2212yescomplemented
20C23×D29—21no—
21C23×D29D411yescharacteristic
22C22×#1181—22no—
23C22×C4×C29—21no—
24C22×C4×C29C2×C411yescharacteristic
25C22×Dic29D411yescharacteristic
26C2×D116—22no—
27C2×D116—22no—
28C2×D116—21no—
29C2×D116—42no—
30C2×D116—42no—
31C2×D116—42no—
32C2×D116C2×C412yes—
33C2×C4×D29—42no—
34C2×C4×D29C2×C411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29C2311yescharacteristic
38C22⋊#1181—42no—
39C2×#6599—22no—
40C4⋊#1181—42no—
41D29⋊C8—42no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29C2×C412yes—
44#90781—22no—
45#90781—22no—
46C23×C29C22⋊C411yescharacteristic
47C22×D29—22no—
48C22×D29—41no—
49C22×D29—41no—
50C22×D29—42no—
51C22×D29—42no—
52C22×D29—42no—
53C22×D29C22⋊C411yescharacteristic
54C22×D29D812yes—
55C22×D29SD1612yes—
56C22×D29C2×D411yescharacteristic
57C2×#1181—42no—
58C2×#1181—42no—
59C2×#1181—42no—
60C2×C4×C29—22no—
61C2×C4×C29—22no—
62C2×C4×C29—42no—
63C2×C4×C29C22⋊C411yescharacteristic
64C2×C4×C29C22×C411yescharacteristic
65C2×Dic29—41no—
66C2×Dic29C22⋊C411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68D116—42no—
69D116—44no—
70D116—42no—
71D116—42no—
72D116—42no—
73C4×D29—22no—
74C4×D29—22no—
75C4×D29—41no—
76C4×D29—41no—
77#6599—42no—
78#1519—291nomaximal, Sylow
79C22×C29—21no—
80C22×C29—21no—
81C22×C29#10212yes—
82C22×C29C2×C22⋊C411yescharacteristic
83C2×D29—21no—
84C2×D29—21no—
85C2×D29—21no—
86C2×D29—21no—
87C2×D29—42no—
88C2×D29—42no—
89C2×D29—42no—
90C2×D29—42no—
91C2×D29—42no—
92C2×D29—84no—
93C2×D29#10212yes—
94C2×D29C2×D811yescharacteristic
95C2×D29C2×SD1611yescharacteristic
96#1181—82no—
97C4×C29—21no—
98C4×C29—42no—
99C4×C29#9912yes—
100Dic29—21no—
101Dic29—21no—
102C2×#121—291no—
103C2×C22⋊C8—291no—
104#380—291no—
105#327—294no—
106C2×C29—22no—
107C2×C29C2×#9911yescharacteristic
108C2×C29C2×#10211yescharacteristic
109C2×C29#42111yescharacteristic
110D29—21no—
111D29—22no—
112D29—21no—
113D29—82no—
114C22×D4—291no—
115C22×D4—581no—
116C23×C4—291no—
117C22×C8—581no—
118#121—292no—
119#121—292no—
120#121—581no—
121#121—581no—
122C2×C4⋊C4—581no—
123C2×C4⋊C4#118111yescharacteristic, complemented
124C2×C22⋊C4—581no—
125C2×C22⋊C4—581no—
126C22⋊C8—292no—
127C22⋊C8—581no—
128#95—292no—
129C29#151911yescharacteristic, complemented, Sylow
130C24—291no—
131C24—581no—
132C2×D4—292no—
133C2×D4—582no—
134C2×D4—582no—
135C2×D4—581no—
136C2×D4—1162no—
137C2×D4—1162no—
138C2×D4—1162no—
139C22×C4—21no—
140C22×C4—291no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—582no—
146C22×C4—1162no—
147C22×C4C2×#118111yescharacteristic
148C2×C8—582no—
149C2×C8—1162no—
150C4⋊C4—21no—
151C4⋊C4—1162no—
152C4⋊C4C2×#118112yes—
153C22⋊C4—582no—
154C22⋊C4—582no—
155C22⋊C4—1162no—
156C23—291no—
157C23—291no—
158C23—292no—
159C23—292no—
160C23—582no—
161C23—1161no—
162C23—1161no—
163C23—1162no—
164C23—1162no—
165C23—1162no—
166C23C22⋊#118111yescharacteristic
167D4—1162no—
168D4—1162no—
169D4—1164no—
170D4—1162no—
171D4—1162no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—1161no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4—1162no—
183C2×C4—1162no—
184C2×C4—1162no—
185C2×C4C22⋊#118111yescharacteristic
186C2×C4C22×#118111yescharacteristic
187C8—1162no—
188C22—21no—
189C22—21no—
190C22—291no—
191C22—292no—
192C22—291no—
193C22—581no—
194C22—581no—
195C22—581no—
196C22—581no—
197C22—1162no—
198C22—1162no—
199C22—1162no—
200C22—1162no—
201C22—1162no—
202C22—2324no—
203C22#1174522312yes—
204C22C2×C22⋊#118111yescharacteristic
205C4—21no—
206C4—42no—
207C4—581no—
208C4—581no—
209C4—2322no—
210C4#1174521512yes—
211C2—22no—
212C2—581no—
213C2—582no—
214C2—581no—
215C2—2322no—
216C2C2×#1174521511yescharacteristic
217C2C2×#1174522311yescharacteristic
218C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745257C2
cosocleC2×C4×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1519
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D29⋊(C22⋊C8)C2semidirect
2. #14272105C2semidirect
3. #14272015C2semidirect
6. C22×D116C4semidirect
11. C2×C4⋊C4×C29C4semidirect
15. #11745257C4semidirect
18. (C2×#1181)⋊C4C22semidirect
19. #11745219C22semidirect
123. C2×C4⋊C4#1181semidirect
129. C29#1519semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C22⋊C8)2
#142721052
#142720152
C2×#117452572
#151929