Finite Group Databasebeta

← #16834874

Subgroups — #16834874

Order 3712.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272181C211yesmaximal, characteristic
2C4×C4⋊#1181C211yesmaximal, characteristic
3#14272017C212yesmaximal
4#14272016C212yesmaximal
5#14271717C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C2×C4×#1181—21no—
8C4×Q8×C29C411yescharacteristic, complemented
9#11745308C2211yescharacteristic
10#11745306C411yescharacteristic, complemented
11#11745259C2211yescharacteristic
12#11745258—21no—
13#11745251—21no—
14#11745250C411yescharacteristic, complemented
15#11745234—21no—
16C42×D29C2211yescharacteristic
17C4×Dic58—21no—
18C4×Dic58C411yescharacteristic, complemented
19(C2×#1181)⋊C4C2212yes—
20#11745220—21no—
21#11745219C2212yes—
22C4×#6599—21no—
23C22×#1181—22no—
24C2×Q8×C29C2×C411yescharacteristic
25C2×C4×D29D411yescharacteristic
26C2×C4×D29D411yescharacteristic
27C2×C4×D29C2311yescharacteristic
28C2×Dic58—21no—
29C2×Dic58C2×C411yescharacteristic
30C2×#6599—22no—
31C4⋊#1181—24no—
32C4×#1181—42no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29C2×C411yescharacteristic
35C42×C29—21no—
36C42×C29C2×C411yescharacteristic
37#90781—21no—
38#90781—21no—
39C4⋊Dic29—21no—
40C4⋊Dic29C2×C411yescharacteristic
41#90779—21no—
42#90779—21no—
43#90779—21no—
44#90779—21no—
45#90779—21no—
46C4×Dic29—21no—
47C4×Dic29C2×C411yescharacteristic
48C4×Dic29D411yescharacteristic
49C4×Dic29D411yescharacteristic
50C22×D29C2×D411yescharacteristic
51C2×#1181—24no—
52C2×#1181—42no—
53C2×#1181—42no—
54Q8×C29—41no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22×C411yescharacteristic
60C2×Dic29—21no—
61C2×Dic29—21no—
62C2×Dic29C22⋊C411yescharacteristic
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C2×D411yescharacteristic
65C4×D29—22no—
66C4×D29—41no—
67C4×D29SD1612yes—
68C4×D29Q1612yes—
69Dic58—42no—
70Dic58—41no—
71#6599—42no—
72#1503—291nomaximal, Sylow
73C22×C29C2×C22⋊C411yescharacteristic
74C2×D29—21no—
75C2×D29—21no—
76C2×D29C2×SD1611yescharacteristic
77C2×D29C2×Q1611yescharacteristic
78#1181—44no—
79C4×C29—21no—
80C4×C29—21no—
81C4×C29—41no—
82C4×C29—41no—
83C4×C29#10312yes—
84Dic29—21no—
85Dic29—41no—
86Dic29—41no—
87Dic29#10312yes—
88Dic29#10412yes—
89#533—291no—
90#431—291no—
91C4×C4⋊C4—291no—
92#328—292no—
93#328—292no—
94C2×C29#41011yescharacteristic
95C2×C29C2×#10311yescharacteristic
96C2×C29C2×#10411yescharacteristic
97D29—21no—
98D29—21no—
99C4⋊Q8—291no—
100C4⋊Q8—291no—
101#125—581no—
102C22⋊Q8—291no—
103C22⋊Q8—291no—
104C22⋊Q8—581no—
105C4×Q8—291no—
106C4×Q8—581no—
107C4×Q8#118111yescharacteristic, complemented
108#117—581no—
109C2×C4⋊C4—581no—
110C2×C42—291no—
111C2×C42—581no—
112C4⋊C8—581no—
113C22⋊C8—292no—
114C4×C8—581no—
115#95—292no—
116C29#150311yescharacteristic, complemented, Sylow
117C2×Q8—291no—
118C2×Q8—581no—
119C2×Q8C2×#118111yescharacteristic
120C22×C4—291no—
121C22×C4—291no—
122C22×C4—291no—
123C22×C4—582no—
124C2×C8—582no—
125C4⋊C4—21no—
126C4⋊C4—291no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4—584no—
133C4⋊C4—581no—
134C4⋊C4C2×#118111yescharacteristic
135C22⋊C4—581no—
136C22⋊C4—581no—
137C42—21no—
138C42—291no—
139C42—291no—
140C42—291no—
141C42—581no—
142C42—1162no—
143C42C2×#118111yescharacteristic
144C23—291no—
145Q8—41no—
146Q8—1161no—
147Q8—1162no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—291no—
151C2×C4—291no—
152C2×C4—292no—
153C2×C4—292no—
154C2×C4—291no—
155C2×C4—582no—
156C2×C4—584no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—1161no—
160C2×C4—1162no—
161C2×C4—1162no—
162C2×C4C22⋊#118111yescharacteristic
163C2×C4C22⋊#118111yescharacteristic
164C2×C4C22×#118111yescharacteristic
165C8—1162no—
166C22—291no—
167C22—291no—
168C22—581no—
169C22—581no—
170C22C2×C22⋊#118111yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—292no—
176C4—292no—
177C4—581no—
178C4—1164no—
179C4—1161no—
180C4—1161no—
181C4#1174522512yes—
182C2—581no—
183C2—581no—
184C2#1427214211yescharacteristic
185C2C2×#1174522511yescharacteristic
186C2D29⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×Q8×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D29C2×D4
cosocleC2×C4×D29C23
hypercenterC4×Q8#1181
hypocenterC29#1503
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
8. C4×Q8×C29C4semidirect
10. #11745306C4semidirect
14. #11745250C4semidirect
18. C4×Dic58C4semidirect
107. C4×Q8#1181semidirect
116. C29#1503semidirect

Maximal subgroups

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

subgroupindex
#142721812
C4×C4⋊#11812
#142720172
#142720162
#142717172
#150329