Finite Group Databasebeta

← #16834934

Subgroups — #16834934

Order 3712.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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, complemented
2#14272108C211yesmaximal, characteristic, complemented
3#14272016C212yesmaximal, complemented
4#14272014C212yesmaximal
5#14271695C211yesmaximal, characteristic
6C4×D4×C29C411yescharacteristic, complemented
7#11745300C2211yescharacteristic
8#11745298C411yescharacteristic, complemented
9C4×C22⋊D29—21no—
10#11745288—21no—
11#11745259C2211yescharacteristic
12#11745252C411yescharacteristic, complemented
13#11745245—21no—
14#11745241—21no—
15C42×D29C2211yescharacteristic
16C4×Dic58C411yescharacteristic, complemented
17(C2×#1181)⋊C4—21no—
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745220—21no—
21#11745219C2212yes—
22C4×#6599—21no—
23C22×#1181—22no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×C4×D29C2311yescharacteristic
30C2×Dic58C2×C411yescharacteristic
31C2×#6599—22no—
32C4⋊C4×C29C2×C411yescharacteristic
33C22⋊C4×C29—21no—
34C42×C29C2×C411yescharacteristic
35C22⋊Dic29—21no—
36C22⋊Dic29—21no—
37C22⋊Dic29—21no—
38#90781—21no—
39C4⋊Dic29—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29C2×C411yescharacteristic
42#90779—21no—
43#90779—21no—
44C4×Dic29—21no—
45C4×Dic29C2×C411yescharacteristic
46C4×Dic29D411yescharacteristic
47C4×Dic29D411yescharacteristic
48C23×C29—21no—
49C22×D29C2×D411yescharacteristic
50C2×#1181—42no—
51C2×#1181—42no—
52C2×#1181—42no—
53D4×C29—41no—
54C2×C4×C29—21no—
55C2×C4×C29—42no—
56C2×C4×C29C22⋊C411yescharacteristic
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22×C411yescharacteristic
59C22⋊D29—42no—
60C2×Dic29—21no—
61C2×Dic29—21no—
62C2×Dic29C22⋊C411yescharacteristic
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C2×D411yescharacteristic
65C4×D29—22no—
66C4×D29—41no—
67C4×D29—41no—
68Dic58—41no—
69#6599—42no—
70#1521—291nomaximal, Sylow
71C22×C29—41no—
72C22×C29—41no—
73C22×C29—41no—
74C22×C29C2×C22⋊C411yescharacteristic
75C2×D29—21no—
76C2×D29—21no—
77C2×D29#13512yes—
78#1181—82no—
79C4×C29—21no—
80C4×C29—21no—
81C4×C29—21no—
82C4×C29—41no—
83Dic29—21no—
84Dic29—21no—
85Dic29—21no—
86Dic29—41no—
87Dic29—41no—
88#529—291no—
89#431—291no—
90#383—291no—
91#328—292no—
92#327—292no—
93C2×C29—81no—
94C2×C29#41011yescharacteristic
95C2×C29#41611yescharacteristic
96C2×C29#42111yescharacteristic
97D29—22no—
98#126—581no—
99#125—291no—
100#124—291no—
101#123—581no—
102C22⋊Q8—291no—
103#121—291no—
104C4×Q8—291no—
105C4×D4—581no—
106C4×D4#118111yescharacteristic, complemented
107#117—581no—
108C2×C42—291no—
109C4⋊C8—581no—
110C22⋊C8—292no—
111C4×C8—581no—
112#95—292no—
113#95—581no—
114#95—581no—
115C29#152111yescharacteristic, complemented, Sylow
116C2×Q8—291no—
117C2×D4—581no—
118C2×D4C2×#118111yescharacteristic
119C22×C4—21no—
120C22×C4—291no—
121C22×C4—291no—
122C22×C4—291no—
123C22×C4—582no—
124C2×C8—582no—
125C4⋊C4—291no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4C2×#118111yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—581no—
133C22⋊C4—581no—
134C22⋊C4—581no—
135C22⋊C4—581no—
136C42—291no—
137C42—291no—
138C42—291no—
139C42—581no—
140C42C2×#118111yescharacteristic
141C23—21no—
142C23—291no—
143Q8—1161no—
144D4—41no—
145D4—1162no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—291no—
149C2×C4—291no—
150C2×C4—291no—
151C2×C4—582no—
152C2×C4—581no—
153C2×C4—581no—
154C2×C4—1161no—
155C2×C4—1161no—
156C2×C4—1162no—
157C2×C4—1162no—
158C2×C4—1162no—
159C2×C4C22⋊#118111yescharacteristic
160C2×C4C22⋊#118111yescharacteristic
161C2×C4C22×#118111yescharacteristic
162C8—1162no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—292no—
167C22—581no—
168C22—581no—
169C22C2×C22⋊#118111yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—581no—
175C4—581no—
176C4—581no—
177C4—1161no—
178C4—1161no—
179C4—2322no—
180C2—81no—
181C2—582no—
182C2#1427214211yescharacteristic
183C2#1427215311yescharacteristic
184C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#11745300C22
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1521
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272181C2semidirect
2. #14272108C2semidirect
3. #14272016C2semidirect
6. C4×D4×C29C4semidirect
8. #11745298C4semidirect
12. #11745252C4semidirect
16. C4×Dic58C4semidirect
106. C4×D4#1181semidirect
115. C29#1521semidirect

Maximal subgroups

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

subgroupindex
#142721812
#142721082
#142720162
#142720142
#142716952
#152129