Finite Group Databasebeta

← #16835682

Subgroups — #16835682

Order 3712.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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#14272105C211yesmaximal, characteristic
2C4×C22⋊#1181C211yesmaximal, characteristic
3#14272041C214yesmaximal
4C2×#11745259C211yesmaximal, characteristic
5C22×C4×D29C2211yescharacteristic
6C22×Dic58C411yescharacteristic, complemented
7C2×C22⋊#1181C2212yes—
8C2×C22⋊#1181C2212yes—
9C2×C4⋊#1181—21no—
10C2×C4×#1181—21no—
11C2×C4⋊C4×C29C411yescharacteristic, complemented
12C2×#90781C2212yes—
13C2×C4⋊Dic29C412yescomplemented
14#11745259—21no—
15#11745259—21no—
16#11745259—21no—
17#11745259—21no—
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4—21no—
20C23×D29C2311yescharacteristic
21C22×#1181—22no—
22C22×#1181—22no—
23C22×C4×C29C2×C412yes—
24C22×C4×C29C2×C411yescharacteristic
25C22×Dic29C2×C412yes—
26C22×Dic29C2×C411yescharacteristic
27C2×C4×D29—42no—
28C2×C4×D29D411yescharacteristic
29C2×C4×D29D411yescharacteristic
30C2×C4×D29D411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58—42no—
35C22⋊#1181—22no—
36C22⋊#1181—24no—
37C22⋊#1181Q814yescomplemented
38C4⋊#1181—42no—
39C4×#1181—42no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42#90781—22no—
43#90781—22no—
44C4⋊Dic29—22no—
45C4⋊Dic29—22no—
46C23×C29C22×C411yescharacteristic
47C22×D29—41no—
48C22×D29—41no—
49C22×D29C2×D411yescharacteristic
50C22×D29C2×D411yescharacteristic
51C22×D29C2×Q812yes—
52C22×D29#4112yes—
53C2×#1181—24no—
54C2×#1181—42no—
55C2×#1181—42no—
56C2×#1181—42no—
57C2×#1181—42no—
58C2×#1181—42no—
59C2×C4×C29—22no—
60C2×C4×C29—22no—
61C2×C4×C29—42no—
62C2×C4×C29C22⋊C411yescharacteristic
63C2×C4×C29C22⋊C411yescharacteristic
64C2×Dic29—22no—
65C2×Dic29—41no—
66C2×Dic29—42no—
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C22⋊C411yescharacteristic
69C4×D29—22no—
70C4×D29—22no—
71C4×D29—41no—
72C4×D29—41no—
73Dic58—42no—
74Dic58—42no—
75#1996—291nomaximal, Sylow
76C22×C29—21no—
77C22×C29—21no—
78C22×C29C2×C22⋊C411yescharacteristic
79C22×C29C4×Q812yes—
80C2×D29—21no—
81C2×D29—21no—
82C2×D29—21no—
83C2×D29—21no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29C22⋊Q812yes—
87C2×D29#12411yescharacteristic
88C2×D29C4⋊Q811yescharacteristic
89#1181—44no—
90#1181—82no—
91C4×C29—21no—
92C4×C29—42no—
93C4×C29#9912yes—
94Dic29—21no—
95Dic29—21no—
96Dic29—42no—
97C2×C22⋊Q8—291no—
98#380—291no—
99C4×C22⋊C4—291no—
100#342—294no—
101C2×C29—22no—
102C2×C29#39111yescharacteristic
103C2×C29C2×#9911yescharacteristic
104C2×C29#41011yescharacteristic
105D29—22no—
106D29—21no—
107D29—21no—
108C22×Q8—291no—
109C23×C4—291no—
110C22⋊Q8—581no—
111C22⋊Q8—581no—
112C22⋊Q8—581no—
113C22⋊Q8—581no—
114C2×C4⋊C4—292no—
115C2×C4⋊C4—581no—
116C2×C4⋊C4#118111yescharacteristic, complemented
117C2×C22⋊C4—292no—
118C2×C22⋊C4—292no—
119C2×C22⋊C4—292no—
120C2×C42—581no—
121#95—581no—
122#95—581no—
123C29#199611yescharacteristic, complemented, Sylow
124C24—291no—
125C2×Q8—581no—
126C2×Q8—581no—
127C2×Q8—1162no—
128C22×C4—291no—
129C22×C4—291no—
130C22×C4—291no—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—292no—
134C22×C4—582no—
135C22×C4—582no—
136C22×C4—1162no—
137C22×C4C2×#118112yes—
138C22×C4C2×#118111yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—582no—
142C4⋊C4—582no—
143C4⋊C4—1162no—
144C22⋊C4—294no—
145C22⋊C4—582no—
146C22⋊C4—582no—
147C22⋊C4—582no—
148C22⋊C4—584no—
149C42—1162no—
150C23—291no—
151C23—291no—
152C23—292no—
153C23—292no—
154C23—1161no—
155C23—1161no—
156C23C22×#118111yescharacteristic
157Q8—1162no—
158Q8—1162no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—291no—
163C2×C4—291no—
164C2×C4—582no—
165C2×C4—582no—
166C2×C4—584no—
167C2×C4—582no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4—1161no—
171C2×C4—1162no—
172C2×C4—1162no—
173C2×C4—1162no—
174C2×C4—1162no—
175C2×C4—1162no—
176C2×C4—1162no—
177C2×C4C22⋊#118111yescharacteristic
178C2×C4C22⋊#118111yescharacteristic
179C22—21no—
180C22—21no—
181C22—292no—
182C22—291no—
183C22—291no—
184C22—581no—
185C22—581no—
186C22—581no—
187C22—581no—
188C22—1162no—
189C22—1162no—
190C22Q8×#118112yes—
191C22C2×C22⋊#118111yescharacteristic
192C4—21no—
193C4—42no—
194C4—581no—
195C4—581no—
196C4—1164no—
197C4—1162no—
198C4—2322no—
199C4#1174521512yes—
200C2—22no—
201C2—582no—
202C2—581no—
203C2—581no—
204C2(C2×#1181)⋊Q811yescharacteristic
205C2C2×#1174521511yescharacteristic
206C2#1427214311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radical, cosocleC23×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1996
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×Dic58C4semidirect
11. C2×C4⋊C4×C29C4semidirect
13. C2×C4⋊Dic29C4semidirect
37. C22⋊#1181Q8semidirect
116. C2×C4⋊C4#1181semidirect
123. C29#1996semidirect

Maximal subgroups

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

subgroupindex
#142721052
C4×C22⋊#11812
#142720412
C2×#117452592
#199629