Finite Group Databasebeta

← #16834976

Subgroups — #16834976

Order 3712.

200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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#14272186C211yesmaximal, characteristic, complemented
2#14272185C211yesmaximal, characteristic, complemented
3#14272020C212yesmaximal, complemented
4#14272018C212yesmaximal, complemented
5#14271695C211yesmaximal, characteristic
6C4×D4×C29C411yescharacteristic
7#11745300C411yescharacteristic
8#11745298C2211yescharacteristic
9C4×C22⋊D29—21no—
10#11745288—21no—
11#11745259C411yescharacteristic
12#11745252C2211yescharacteristic
13#11745245—21no—
14#11745241—21no—
15C42×D29C2211yescharacteristic
16C4×Dic58C411yescharacteristic
17#11745220—21no—
18#11745219—21no—
19#11745219—21no—
20#11745218C2212yes—
21#11745218C2212yes—
22C4⋊#6599—21no—
23C2×D4×C29C2×C411yescharacteristic
24C22×C4×C29—21no—
25C2×C22⋊D29—21no—
26C2×C4×D29C2×C411yescharacteristic
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×Dic58C2×C411yescharacteristic
30C2×#6599—22no—
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×Dic29D411yescharacteristic
46C4×Dic29D411yescharacteristic
47C4×Dic29C2311yescharacteristic
48C23×C29—21no—
49C22×D29C22⋊C411yescharacteristic
50D4×C29—41no—
51C2×C4×C29—21no—
52C2×C4×C29—42no—
53C2×C4×C29C22⋊C411yescharacteristic
54C2×C4×C29C22⋊C411yescharacteristic
55C2×C4×C29C22×C411yescharacteristic
56C22⋊D29—42no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29C22⋊C411yescharacteristic
60C2×Dic29C2×D411yescharacteristic
61C2×Dic29C2×D411yescharacteristic
62C4×D29—41no—
63C4×D29—41no—
64C4×D29—41no—
65Dic58—41no—
66#6599—42no—
67#6599—42no—
68#1535—291nomaximal, Sylow
69C22×C29—41no—
70C22×C29—41no—
71C22×C29—41no—
72C22×C29C2×C22⋊C411yescharacteristic
73C2×D29—21no—
74C2×D29—21no—
75C2×D29—21no—
76C4×C29—21no—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—41no—
80Dic29—21no—
81Dic29—21no—
82Dic29—21no—
83Dic29—41no—
84Dic29—41no—
85#529—291no—
86#432—291no—
87#432—291no—
88#330—292no—
89#329—292no—
90C2×C29—81no—
91C2×C29#41311yescharacteristic
92C2×C29#42111yescharacteristic
93C2×C29#42111yescharacteristic
94D29—41no—
95#126—581no—
96#125—291no—
97#124—291no—
98#123—581no—
99C22⋊Q8—291no—
100#121—291no—
101C4×Q8—291no—
102C4×D4—581no—
103C4×D4#118111yescharacteristic
104#117—581no—
105C2×C42—291no—
106C4⋊C8—581no—
107C4⋊C8—581no—
108C22⋊C8—581no—
109C22⋊C8—581no—
110#97—292no—
111#97—292no—
112C29#153511yescharacteristic, complemented, Sylow
113C2×Q8—291no—
114C2×D4—581no—
115C2×D4C2×#118111yescharacteristic
116C22×C4—21no—
117C22×C4—291no—
118C22×C4—291no—
119C22×C4—291no—
120C2×C8—582no—
121C2×C8—582no—
122C4⋊C4—291no—
123C4⋊C4—581no—
124C4⋊C4—581no—
125C4⋊C4—581no—
126C4⋊C4—581no—
127C4⋊C4C2×#118111yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—581no—
130C22⋊C4—581no—
131C22⋊C4—581no—
132C22⋊C4—581no—
133C42—291no—
134C42—291no—
135C42—291no—
136C42—581no—
137C42C2×#118111yescharacteristic
138C23—21no—
139C23—291no—
140Q8—1161no—
141D4—41no—
142D4—1162no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—291no—
146C2×C4—291no—
147C2×C4—291no—
148C2×C4—581no—
149C2×C4—581no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4C22⋊#118111yescharacteristic
154C2×C4C22⋊#118111yescharacteristic
155C2×C4C22×#118111yescharacteristic
156C8—1162no—
157C8—1162no—
158C22—41no—
159C22—41no—
160C22—41no—
161C22—581no—
162C22—581no—
163C22—581no—
164C22C2×C22⋊#118111yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—41no—
169C4—581no—
170C4—581no—
171C4—581no—
172C4—1161no—
173C4—1161no—
174C2—81no—
175C2—1161no—
176C2#1427214911yescharacteristic
177C2#1427216011yescharacteristic
178C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#11745300C4
cosocleC4×Dic29C23
hypercenterC4×D4#1181
hypocenterC29#1535
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. #14272186C2semidirect
2. #14272185C2semidirect
3. #14272020C2semidirect
4. #14272018C2semidirect
112. C29#1535semidirect

Maximal subgroups

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

subgroupindex
#142721862
#142721852
#142720202
#142720182
#142716952
#153529