Finite Group Databasebeta

← #16834925

Subgroups — #16834925

Order 3712.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272182C211yesmaximal, characteristic
2#14272107C211yesmaximal, characteristic
3#14272017C212yesmaximal
4#14272016C212yesmaximal
5#14271717C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C4×Q8×C29C411yescharacteristic, complemented
8#11745308C2211yescharacteristic
9#11745306C411yescharacteristic, complemented
10#11745259C2211yescharacteristic
11#11745258—21no—
12#11745251—21no—
13#11745250C411yescharacteristic, complemented
14#11745234—21no—
15C42×D29C2211yescharacteristic
16C4×Dic58—21no—
17C4×Dic58C411yescharacteristic, complemented
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21C4⋊#6599—21no—
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—42no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29C2×C411yescharacteristic
34C42×C29—21no—
35C42×C29C2×C411yescharacteristic
36#90781—21no—
37#90781—21no—
38C4⋊Dic29—21no—
39C4⋊Dic29C2×C411yescharacteristic
40#90779—21no—
41#90779—21no—
42#90779—21no—
43#90779—21no—
44#90779—21no—
45C4×Dic29—21no—
46C4×Dic29C2×C411yescharacteristic
47C4×Dic29D411yescharacteristic
48C4×Dic29D411yescharacteristic
49C22×D29C2×D411yescharacteristic
50C2×#1181—42no—
51C2×#1181—42no—
52C2×#1181—42no—
53Q8×C29—41no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29C22⋊C411yescharacteristic
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22×C411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29—21no—
61C2×Dic29C22⋊C411yescharacteristic
62C2×Dic29C22⋊C411yescharacteristic
63C2×Dic29C2×D411yescharacteristic
64C4×D29—41no—
65C4×D29—41no—
66C4×D29SD1612yes—
67C4×D29Q1612yes—
68Dic58—42no—
69Dic58—41no—
70#6599—42no—
71#1518—291nomaximal, Sylow
72C22×C29C2×C22⋊C411yescharacteristic
73C2×D29—21no—
74C2×D29—21no—
75C2×D29C2×SD1611yescharacteristic
76C2×D29C2×Q1611yescharacteristic
77#1181—82no—
78C4×C29—21no—
79C4×C29—21no—
80C4×C29—41no—
81C4×C29—41no—
82C4×C29#10312yes—
83Dic29—21no—
84Dic29—21no—
85Dic29—41no—
86Dic29—41no—
87Dic29#10312yes—
88#533—291no—
89#431—291no—
90#382—291no—
91#328—292no—
92#328—292no—
93C2×C29#41011yescharacteristic
94C2×C29C2×#10311yescharacteristic
95C2×C29#42111yescharacteristic
96D29—21no—
97D29—21no—
98C4⋊Q8—291no—
99C4⋊Q8—291no—
100#125—581no—
101C22⋊Q8—291no—
102C22⋊Q8—291no—
103C22⋊Q8—581no—
104C4×Q8—291no—
105C4×Q8—581no—
106C4×Q8#118111yescharacteristic, complemented
107#117—581no—
108C2×C4⋊C4—581no—
109C2×C42—291no—
110C4⋊C8—581no—
111C22⋊C8—292no—
112C4×C8—581no—
113#95—292no—
114#95—581no—
115C29#151811yescharacteristic, complemented, Sylow
116C2×Q8—291no—
117C2×Q8—581no—
118C2×Q8C2×#118111yescharacteristic
119C22×C4—291no—
120C22×C4—291no—
121C22×C4—291no—
122C22×C4—582no—
123C2×C8—582no—
124C4⋊C4—21no—
125C4⋊C4—291no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4—1162no—
133C4⋊C4C2×#118111yescharacteristic
134C22⋊C4—581no—
135C22⋊C4—581no—
136C42—21no—
137C42—291no—
138C42—291no—
139C42—291no—
140C42—581no—
141C42C2×#118111yescharacteristic
142C23—291no—
143Q8—41no—
144Q8—1161no—
145Q8—1162no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—291no—
149C2×C4—292no—
150C2×C4—292no—
151C2×C4—291no—
152C2×C4—291no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—1161no—
156C2×C4—1161no—
157C2×C4—1162no—
158C2×C4—1162no—
159C2×C4—1162no—
160C2×C4C22⋊#118111yescharacteristic
161C2×C4C22⋊#118111yescharacteristic
162C2×C4C22×#118111yescharacteristic
163C8—1162no—
164C22—291no—
165C22—291no—
166C22—581no—
167C22—581no—
168C22C2×C22⋊#118111yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—292no—
174C4—581no—
175C4—581no—
176C4—1161no—
177C4—1161no—
178C4—2322no—
179C4#1174522512yes—
180C2—581no—
181C2—581no—
182C2#1427214211yescharacteristic
183C2C2×#1174522511yescharacteristic
184C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#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#1518
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
7. C4×Q8×C29C4semidirect
9. #11745306C4semidirect
13. #11745250C4semidirect
17. C4×Dic58C4semidirect
106. C4×Q8#1181semidirect
115. C29#1518semidirect

Maximal subgroups

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

subgroupindex
#142721822
#142721072
#142720172
#142720162
#142717172
#151829