Finite Group Databasebeta

← #16834792

Subgroups — #16834792

Order 3712.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#14272182C211yesmaximal, characteristic, complemented
2#14272181C211yesmaximal, characteristic, complemented
3#14272011C212yesmaximal, complemented
4D4⋊#6599C212yesmaximal, complemented
5C4×D4×D29C211yesmaximal, characteristic
6C2×D4×D29C411yescharacteristic
7C22×C4×D29—21no—
8C4×D4×C29C411yescharacteristic
9D4×Dic29C2211yescharacteristic
10C4×C22⋊D29—21no—
11#11745255C2211yescharacteristic
12C4⋊C4×D29C411yescharacteristic
13#11745243—21no—
14C22⋊C4×D29—21no—
15C4×D116C411yescharacteristic
16C42×D29C2211yescharacteristic
17#11745220—21no—
18#11745219—21no—
19#11745219—21no—
20C4⋊#6599C2212yescomplemented
21C4×#6599—21no—
22C4×#6599C2212yescomplemented
23C23×D29—21no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C22×Dic29—21no—
28D4×D29—22no—
29D4×D29C814yescomplemented
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—
40C4⋊C4×C29C2×C411yescharacteristic
41C22⋊C4×C29—21no—
42C42×C29C2×C411yescharacteristic
43C22⋊Dic29—21no—
44#90781—21no—
45#90781—21no—
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48C4×Dic29D411yescharacteristic
49C4×Dic29D411yescharacteristic
50C4×Dic29C2311yescharacteristic
51C23×C29—21no—
52C22×D29—21no—
53C22×D29—24no—
54C22×D29—42no—
55C22×D29—42no—
56C22×D29C22⋊C411yescharacteristic
57D4×C29—21no—
58D4×C29C2×C812yes—
59C2×C4×C29—21no—
60C2×C4×C29—42no—
61C2×C4×C29C22⋊C411yescharacteristic
62C2×C4×C29C22⋊C411yescharacteristic
63C2×C4×C29C22×C411yescharacteristic
64C22⋊D29—24no—
65C2×Dic29—21no—
66C2×Dic29—42no—
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C2×D411yescharacteristic
69C2×Dic29C2×D411yescharacteristic
70D116—21no—
71D116C2×C812yes—
72C4×D29—22no—
73C4×D29—41no—
74C4×D29—42no—
75C4×D29—42no—
76C4×D29—42no—
77C4×D29C2×C812yes—
78C4×D29M1612yes—
79#6599—42no—
80#6599—42no—
81#1478—291nomaximal, Sylow
82C22×C29—22no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29C2×C22⋊C411yescharacteristic
86C2×D29—21no—
87C2×D29—21no—
88C2×D29—22no—
89C2×D29—48no—
90C2×D29—41no—
91C2×D29—41no—
92C2×D29C22⋊C812yes—
93C4×C29—21no—
94C4×C29—21no—
95C4×C29—41no—
96C4×C29C22×C811yescharacteristic
97C4×C29C2×M1611yescharacteristic
98Dic29—21no—
99Dic29—41no—
100Dic29C22⋊C812yes—
101Dic29AGL(1,ℤ/8)12yes—
102C2×C4×D4—291no—
103#431—291no—
104#431—291no—
105D4⋊C8—292no—
106D4⋊C8—292no—
107C2×C29—42no—
108C2×C29C2×C22⋊C811yescharacteristic
109C2×C29#41811yescharacteristic
110C2×C29#42111yescharacteristic
111D29—22no—
112D29—42no—
113C22×D4—291no—
114C23×C4—581no—
115C4×D4—291no—
116C4×D4—291no—
117C4×D4—291no—
118C4×D4—581no—
119C4×D4—581no—
120C4×D4#118111yescharacteristic
121C2×C4⋊C4—291no—
122C2×C22⋊C4—581no—
123C2×C42—291no—
124C4⋊C8—292no—
125C4⋊C8—581no—
126C22⋊C8—581no—
127C22⋊C8—581no—
128C4×C8—292no—
129C4×C8—581no—
130C29#147811yescharacteristic, complemented, Sylow
131C24—581no—
132C2×D4—294no—
133C2×D4—291no—
134C2×D4—582no—
135C2×D4—581no—
136C2×D4C2×#118111yescharacteristic
137C22×C4—21no—
138C22×C4—291no—
139C22×C4—291no—
140C22×C4—291no—
141C22×C4—581no—
142C22×C4—581no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4—1164no—
146C2×C8—582no—
147C2×C8—582no—
148C4⋊C4—291no—
149C4⋊C4—581no—
150C4⋊C4C2×#118111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C42—291no—
156C42—291no—
157C42—291no—
158C42C2×#118111yescharacteristic
159C23—21no—
160C23—291no—
161C23—584no—
162C23—581no—
163C23—1162no—
164C23—1162no—
165D4—21no—
166D4—292no—
167D4—584no—
168D4—581no—
169D4D29⋊C812yes—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—291no—
173C2×C4—291no—
174C2×C4—292no—
175C2×C4—292no—
176C2×C4—291no—
177C2×C4—582no—
178C2×C4—581no—
179C2×C4—1161no—
180C2×C4—1162no—
181C2×C4—1162no—
182C2×C4—1162no—
183C2×C4—1162no—
184C2×C4C22⋊#118111yescharacteristic
185C2×C4C22⋊#118111yescharacteristic
186C2×C4C22×#118111yescharacteristic
187C8—1162no—
188C8—1162no—
189C22—22no—
190C22—41no—
191C22—41no—
192C22—292no—
193C22—581no—
194C22—581no—
195C22—582no—
196C22—1168no—
197C22—1161no—
198C22—1161no—
199C22C2×C22⋊#118111yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—292no—
204C4—292no—
205C4—581no—
206C4—1161no—
207C4C2×D29⋊C811yescharacteristic
208C4D29⋊M1611yescharacteristic
209C2—42no—
210C2—582no—
211C2—1162no—
212C2D29⋊(C22⋊C8)11yescharacteristic
213C2#1427215511yescharacteristic
214C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC4×C29C22×C8
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×D4×D29C4
cosocleC4×Dic29C23
hypercenterC4×D4#1181
hypocenterC29#1478
LCSG ▷ 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. #14272182C2semidirect
2. #14272181C2semidirect
3. #14272011C2semidirect
4. D4⋊#6599C2semidirect
20. C4⋊#6599C22semidirect
22. C4×#6599C22semidirect
29. D4×D29C8semidirect
130. C29#1478semidirect

Maximal subgroups

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

subgroupindex
#142721822
#142721812
#142720112
D4⋊#65992
C4×D4×D292
#147829