Finite Group Databasebeta

← #16834931

Subgroups — #16834931

Order 3712.

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

normal subgroups only

This group has 288 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
2#14272105C211yesmaximal, characteristic
3#14272016C214yesmaximal, complemented
4C2×#11745259C211yesmaximal, characteristic
5C22×C4×D29C2211yescharacteristic
6C22×Dic58C411yescharacteristic, complemented
7C2×C22⋊#1181—21no—
8C2×C4⋊#1181—21no—
9C2×D29⋊C8—21no—
10C2×C4⋊C4×C29C411yescharacteristic, complemented
11C2×#90781—21no—
12C2×C4⋊Dic29—21no—
13#11745259—21no—
14#11745259—21no—
15#11745259C412yescomplemented
16#11745259C2212yes—
17C22⋊#6599—21no—
18(C2×#1181)⋊C4C2212yes—
19#11745219C2212yes—
20C23×D29D411yescharacteristic
21C22×#1181—22no—
22C22×C4×C29—21no—
23C22×C4×C29C2×C411yescharacteristic
24C22×Dic29—21no—
25C22×Dic29D411yescharacteristic
26C2×C4×D29—42no—
27C2×C4×D29C2×C411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×C4×D29D411yescharacteristic
30C2×C4×D29C2311yescharacteristic
31C2×Dic58—21no—
32C2×Dic58—42no—
33C2×Dic58C2×C412yes—
34C22⋊#1181—42no—
35C2×#6599—22no—
36C4⋊#1181—42no—
37D29⋊C8—42no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29C2×C412yes—
40#90781—22no—
41#90781—22no—
42C4⋊Dic29—22no—
43C4⋊Dic29—22no—
44C23×C29C22⋊C411yescharacteristic
45C22×D29—41no—
46C22×D29—41no—
47C22×D29C22⋊C411yescharacteristic
48C22×D29SD1612yes—
49C22×D29Q1612yes—
50C22×D29C2×D411yescharacteristic
51C2×#1181—42no—
52C2×#1181—42no—
53C2×#1181—42no—
54C2×C4×C29—22no—
55C2×C4×C29—22no—
56C2×C4×C29—42no—
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22×C411yescharacteristic
59C2×Dic29—22no—
60C2×Dic29—41no—
61C2×Dic29—42no—
62C2×Dic29C22⋊C411yescharacteristic
63C2×Dic29C2×D411yescharacteristic
64C4×D29—22no—
65C4×D29—22no—
66C4×D29—41no—
67C4×D29—41no—
68Dic58—42no—
69Dic58—42no—
70#6599—42no—
71#1520—291nomaximal, Sylow
72C22×C29—21no—
73C22×C29—21no—
74C22×C29#10312yes—
75C22×C29C2×C22⋊C411yescharacteristic
76C2×D29—21no—
77C2×D29—21no—
78C2×D29—21no—
79C2×D29—21no—
80C2×D29—42no—
81C2×D29—42no—
82C2×D29#10312yes—
83C2×D29C2×SD1611yescharacteristic
84C2×D29C2×Q1611yescharacteristic
85#1181—82no—
86C4×C29—21no—
87C4×C29—42no—
88C4×C29#9912yes—
89Dic29—21no—
90Dic29—21no—
91Dic29—42no—
92C2×C22⋊Q8—291no—
93C2×C22⋊C8—291no—
94#380—291no—
95#328—294no—
96C2×C29—22no—
97C2×C29C2×#9911yescharacteristic
98C2×C29C2×#10311yescharacteristic
99C2×C29#42111yescharacteristic
100D29—21no—
101D29—22no—
102D29—21no—
103C22×Q8—291no—
104C23×C4—291no—
105C22×C8—581no—
106C22⋊Q8—292no—
107C22⋊Q8—292no—
108C22⋊Q8—581no—
109C22⋊Q8—581no—
110C2×C4⋊C4—581no—
111C2×C4⋊C4—581no—
112C2×C4⋊C4#118111yescharacteristic, complemented
113C2×C22⋊C4—581no—
114C2×C22⋊C4—581no—
115C22⋊C8—292no—
116C22⋊C8—581no—
117#95—292no—
118C29#152011yescharacteristic, complemented, Sylow
119C24—291no—
120C2×Q8—292no—
121C2×Q8—581no—
122C2×Q8—1162no—
123C22×C4—21no—
124C22×C4—291no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—291no—
128C22×C4—291no—
129C22×C4—581no—
130C22×C4—582no—
131C22×C4—1162no—
132C22×C4C2×#118111yescharacteristic
133C2×C8—582no—
134C2×C8—1162no—
135C4⋊C4—21no—
136C4⋊C4—582no—
137C4⋊C4—582no—
138C4⋊C4—1162no—
139C4⋊C4C2×#118112yes—
140C22⋊C4—582no—
141C22⋊C4—582no—
142C22⋊C4—1162no—
143C23—291no—
144C23—291no—
145C23—292no—
146C23—292no—
147C23—1161no—
148C23—1161no—
149C23C22⋊#118111yescharacteristic
150Q8—1162no—
151Q8—1162no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—291no—
156C2×C4—291no—
157C2×C4—582no—
158C2×C4—582no—
159C2×C4—582no—
160C2×C4—1161no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4—1162no—
164C2×C4—1162no—
165C2×C4—1162no—
166C2×C4—1162no—
167C2×C4C22⋊#118111yescharacteristic
168C2×C4C22×#118111yescharacteristic
169C8—1162no—
170C22—21no—
171C22—21no—
172C22—291no—
173C22—292no—
174C22—291no—
175C22—581no—
176C22—581no—
177C22—581no—
178C22—581no—
179C22—1162no—
180C22—1162no—
181C22#1174522512yes—
182C22C2×C22⋊#118111yescharacteristic
183C4—21no—
184C4—42no—
185C4—581no—
186C4—581no—
187C4—1162no—
188C4—2322no—
189C4#1174521512yes—
190C2—22no—
191C2—581no—
192C2—582no—
193C2—581no—
194C2C2×#1174521511yescharacteristic
195C2C2×#1174522511yescharacteristic
196C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC2×C4×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1520
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
3. #14272016C2semidirect
6. C22×Dic58C4semidirect
10. C2×C4⋊C4×C29C4semidirect
15. #11745259C4semidirect
112. C2×C4⋊C4#1181semidirect
118. C29#1520semidirect

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
#142720162
C2×#117452592
#152029