Finite Group Databasebeta

← #16834885

Subgroups — #16834885

Order 3712.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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
2#14272099C211yesmaximal, 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#11745220—21no—
21#11745219C2212yes—
22#11745218—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⋊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—24no—
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—22no—
65C4×D29—22no—
66C4×D29—41no—
67Dic58—42no—
68Dic58—41no—
69#6599—42no—
70#1506—291nomaximal, Sylow
71C22×C29C2×C22⋊C411yescharacteristic
72C2×D29—21no—
73C2×D29—21no—
74C2×D29#13712yes—
75#1181—44no—
76C4×C29—21no—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—41no—
80C4×C29—41no—
81Dic29—21no—
82Dic29—21no—
83Dic29—41no—
84Dic29—41no—
85Dic29#10412yes—
86#533—291no—
87#432—291no—
88#376—291no—
89#328—292no—
90#328—292no—
91C2×C29#41011yescharacteristic
92C2×C29#41911yescharacteristic
93C2×C29C2×#10411yescharacteristic
94D29—22no—
95C4⋊Q8—291no—
96C4⋊Q8—291no—
97#125—581no—
98C22⋊Q8—291no—
99C22⋊Q8—291no—
100C22⋊Q8—581no—
101C4×Q8—291no—
102C4×Q8—581no—
103C4×Q8#118111yescharacteristic, complemented
104#117—581no—
105C2×C42—291no—
106C2×C42—581no—
107C4⋊C8—581no—
108C22⋊C8—292no—
109#97—581no—
110#95—292no—
111#95—581no—
112C29#150611yescharacteristic, complemented, Sylow
113C2×Q8—291no—
114C2×Q8—581no—
115C2×Q8C2×#118111yescharacteristic
116C22×C4—291no—
117C22×C4—291no—
118C22×C4—291no—
119C22×C4—582no—
120C2×C8—582no—
121C4⋊C4—21no—
122C4⋊C4—291no—
123C4⋊C4—581no—
124C4⋊C4—581no—
125C4⋊C4—581no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4C2×#118111yescharacteristic
130C22⋊C4—581no—
131C22⋊C4—581no—
132C42—21no—
133C42—291no—
134C42—291no—
135C42—291no—
136C42—584no—
137C42—581no—
138C42C2×#118111yescharacteristic
139C23—291no—
140Q8—41no—
141Q8—1161no—
142Q8—1162no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—291no—
146C2×C4—291no—
147C2×C4—291no—
148C2×C4—582no—
149C2×C4—582no—
150C2×C4—584no—
151C2×C4—581no—
152C2×C4—581no—
153C2×C4—1161no—
154C2×C4—1162no—
155C2×C4—1162no—
156C2×C4C22⋊#118111yescharacteristic
157C2×C4C22⋊#118111yescharacteristic
158C2×C4C22×#118111yescharacteristic
159C8—1162no—
160C22—292no—
161C22—581no—
162C22—581no—
163C22C2×C22⋊#118111yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—292no—
170C4—581no—
171C4—581no—
172C4—1164no—
173C4—1161no—
174C4—1161no—
175C2—582no—
176C2#1427214211yescharacteristic
177C2#1427215611yescharacteristic
178C2D29⋊#10411yescharacteristic
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#1506
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
103. C4×Q8#1181semidirect
112. C29#1506semidirect

Maximal subgroups

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

subgroupindex
#142721862
#142720992
#142720172
#142720162
#142717172
#150629