Finite Group Databasebeta

← #16834818

Subgroups — #16834818

Order 3712.

312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 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#14272167C211yesmaximal, 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—
19C4⋊#6599—21no—
20C4⋊#6599—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—42no—
35C2×C4×D29—42no—
36C2×C4×D29C2×C411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29D411yescharacteristic
39C2×#6599—22no—
40C2×#6599—22no—
41#90796—42no—
42C4⋊C4×C29C2×C411yescharacteristic
43C22⋊C4×C29—21no—
44C42×C29C2×C411yescharacteristic
45C22⋊Dic29—21no—
46#90781—21no—
47#90781—21no—
48C4⋊Dic29C2×C411yescharacteristic
49#90779—21no—
50C4×Dic29D411yescharacteristic
51C4×Dic29D411yescharacteristic
52C4×Dic29C2311yescharacteristic
53C23×C29—21no—
54C22×D29—24no—
55C22×D29—21no—
56C22×D29—42no—
57C22×D29—42no—
58C22×D29C22⋊C411yescharacteristic
59D4×C29—21no—
60D4×C29M1612yescomplemented
61C2×C4×C29—21no—
62C2×C4×C29—42no—
63C2×C4×C29C22⋊C411yescharacteristic
64C2×C4×C29C22⋊C411yescharacteristic
65C2×C4×C29C22×C411yescharacteristic
66C22⋊D29—24no—
67C2×Dic29—21no—
68C2×Dic29—41no—
69C2×Dic29—41no—
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C2×D411yescharacteristic
72C2×Dic29C2×D411yescharacteristic
73D116—21no—
74D116M1612yescomplemented
75C4×D29—21no—
76C4×D29—21no—
77C4×D29—41no—
78C4×D29—42no—
79C4×D29—42no—
80C4×D29—41no—
81C4×D29—41no—
82C4×D29D812yes—
83C4×D29SD1612yes—
84#6599—42no—
85#6599—42no—
86#1486—291nomaximal, Sylow
87C22×C29—22no—
88C22×C29—41no—
89C22×C29—41no—
90C22×C29C2×C22⋊C411yescharacteristic
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—22no—
94C2×D29—48no—
95C2×D29—41no—
96C2×D29—41no—
97C2×D29#10212yes—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29#10212yes—
101C4×C29C2×M1611yescharacteristic
102C4×C29C2×M1611yescharacteristic
103Dic29—21no—
104Dic29—21no—
105Dic29—41no—
106Dic29C2×D811yescharacteristic
107Dic29C2×SD1611yescharacteristic
108C2×C4×D4—291no—
109#431—291no—
110#423—291no—
111D4⋊C8—292no—
112D4⋊C8—292no—
113C2×C29—42no—
114C2×C29#40711yescharacteristic
115C2×C29C2×#10211yescharacteristic
116C2×C29#42111yescharacteristic
117D29—22no—
118D29—42no—
119C22×D4—291no—
120C23×C4—581no—
121C2×M16—581no—
122C4×D4—291no—
123C4×D4—291no—
124C4×D4—291no—
125C4×D4—581no—
126C4×D4—581no—
127C4×D4#118111yescharacteristic
128C2×C4⋊C4—291no—
129C2×C22⋊C4—581no—
130C2×C42—291no—
131C4⋊C8—292no—
132C4⋊C8—581no—
133C4⋊C8—581no—
134C22⋊C8—581no—
135C4×C8—292no—
136C29#148611yescharacteristic, complemented, Sylow
137C24—581no—
138C2×D4—291no—
139C2×D4—581no—
140C2×D4—582no—
141C2×D4—582no—
142C2×D4C2×#118111yescharacteristic
143C22×C4—21no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—291no—
147C22×C4—581no—
148C22×C4—581no—
149C22×C4—581no—
150C22×C4—581no—
151C22×C4—1162no—
152C22×C4—1162no—
153M16—1162no—
154C2×C8—582no—
155C2×C8—582no—
156C4⋊C4—291no—
157C4⋊C4—581no—
158C4⋊C4C2×#118111yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C42—291no—
164C42—291no—
165C42—291no—
166C42C2×#118111yescharacteristic
167C23—21no—
168C23—291no—
169C23—584no—
170C23—581no—
171C23—1162no—
172C23—1162no—
173D4—21no—
174D4—292no—
175D4—584no—
176D4—581no—
177D4#9079612yescomplemented
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—291no—
181C2×C4—292no—
182C2×C4—292no—
183C2×C4—291no—
184C2×C4—291no—
185C2×C4—581no—
186C2×C4—581no—
187C2×C4—581no—
188C2×C4—1161no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4—1162no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1162no—
195C2×C4C22⋊#118111yescharacteristic
196C2×C4C22⋊#118111yescharacteristic
197C2×C4C22×#118111yescharacteristic
198C8—1162no—
199C8—1162no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—292no—
204C22—581no—
205C22—581no—
206C22—582no—
207C22—1168no—
208C22—1161no—
209C22—1161no—
210C22C2×C22⋊#118111yescharacteristic
211C4—21no—
212C4—41no—
213C4—291no—
214C4—291no—
215C4—581no—
216C4—581no—
217C4—1161no—
218C4#1174522312yes—
219C4C2×#9079611yescharacteristic
220C4D29⋊M1611yescharacteristic
221C2—42no—
222C2—582no—
223C2—1162no—
224C2#1427213411yescharacteristic
225C2C2×#1174522311yescharacteristic
226C2#1427216011yescharacteristic
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#1486
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. #14272182C2semidirect
2. #14272167C2semidirect
3. #14272011C2semidirect
4. D4⋊#6599C2semidirect
21. C4⋊#6599C22semidirect
22. C4×#6599C22semidirect
60. D4×C29M16semidirect
74. D116M16semidirect
136. C29#1486semidirect
177. D4#90796semidirect

Maximal subgroups

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

subgroupindex
#142721822
#142721672
#142720112
D4⋊#65992
C4×D4×D292
#148629