Finite Group Databasebeta

← #16834923

Subgroups — #16834923

Order 3712.

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

normal subgroups only

This group has 264 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#14272181C211yesmaximal, characteristic, complemented
2#14272107C211yesmaximal, characteristic, complemented
3#14272015C214yesmaximal, complemented
4#14271714C211yesmaximal, characteristic
5C2×#90809—21no—
6C2×C4⋊#1181—21no—
7C29×C4⋊Q8C411yescharacteristic, complemented
8#11745309—21no—
9#11745257—21no—
10#11745257C2212yes—
11#11745255—21no—
12#11745255C412yescomplemented
13#11745236C411yescharacteristic, complemented
14C42×D29C2211yescharacteristic
15(C2×#1181)⋊C4—21no—
16(C2×#1181)⋊C4C2212yes—
17#11745220—21no—
18#11745219C2212yes—
19C4×#6599—21no—
20C22×#1181—22no—
21C2×Q8×C29—21no—
22#90809—42no—
23#90809—42no—
24C2×D116—22no—
25C2×D116—21no—
26C2×D116—21no—
27C2×D116C2×C412yes—
28C2×C4×D29—22no—
29C2×C4×D29D411yescharacteristic
30C2×C4×D29D411yescharacteristic
31C2×C4×D29C2311yescharacteristic
32C2×#6599—22no—
33C4⋊#1181—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29C2×C412yes—
36C42×C29C2×C411yescharacteristic
37#90781—22no—
38#90781—22no—
39C4×Dic29C2×C411yescharacteristic
40C4×Dic29D411yescharacteristic
41C4×Dic29D411yescharacteristic
42C22×D29—22no—
43C22×D29C2×D411yescharacteristic
44C2×#1181—42no—
45C2×#1181—42no—
46C2×#1181—42no—
47Q8×C29—42no—
48C2×C4×C29—22no—
49C2×C4×C29C22⋊C411yescharacteristic
50C2×C4×C29C22⋊C411yescharacteristic
51C2×C4×C29C22×C411yescharacteristic
52C2×Dic29C22⋊C411yescharacteristic
53C2×Dic29C22⋊C411yescharacteristic
54C2×Dic29C2×D411yescharacteristic
55D116—42no—
56D116—42no—
57D116—42no—
58D116—42no—
59D116—42no—
60C4×D29—41no—
61C4×D29—41no—
62C4×D29—44no—
63C4×D29D812yes—
64C4×D29SD1612yes—
65#6599—42no—
66#1517—291nomaximal, Sylow
67C22×C29C2×C22⋊C411yescharacteristic
68C2×D29—21no—
69C2×D29—21no—
70C2×D29—42no—
71C2×D29—42no—
72C2×D29—42no—
73C2×D29C2×D811yescharacteristic
74C2×D29C2×SD1611yescharacteristic
75#1181—82no—
76C4×C29—21no—
77C4×C29—21no—
78C4×C29—42no—
79C4×C29#10212yes—
80Dic29—21no—
81Dic29—21no—
82Dic29#10212yes—
83#532—291no—
84#431—291no—
85#382—291no—
86#327—294no—
87C2×C29#41011yescharacteristic
88C2×C29C2×#10211yescharacteristic
89C2×C29#42111yescharacteristic
90D29—21no—
91D29—21no—
92D29—82no—
93C2×#41—581no—
94C4⋊Q8#118111yescharacteristic, complemented
95#127—291no—
96#124—581no—
97#121—292no—
98#121—581no—
99C4×D4—292no—
100C4×D4—581no—
101C2×C4⋊C4—581no—
102C2×C42—291no—
103C4⋊C8—581no—
104C22⋊C8—292no—
105C4×C8—581no—
106#95—292no—
107#95—581no—
108C29#151711yescharacteristic, complemented, Sylow
109#41—1162no—
110#41—1162no—
111C2×Q8—21no—
112C2×D4—292no—
113C2×D4—582no—
114C2×D4—581no—
115C2×D4—581no—
116C22×C4—291no—
117C22×C4—291no—
118C22×C4—291no—
119C22×C4—582no—
120C22×C4—582no—
121C2×C8—582no—
122C4⋊C4—21no—
123C4⋊C4—1162no—
124C4⋊C4C2×#118112yes—
125C22⋊C4—582no—
126C22⋊C4—582no—
127C42—291no—
128C42—291no—
129C42—291no—
130C42C2×#118111yescharacteristic
131C23—291no—
132C23—582no—
133Q8—42no—
134D4—1162no—
135D4—1162no—
136D4—1162no—
137D4—1162no—
138D4—1162no—
139C2×C4—22no—
140C2×C4—291no—
141C2×C4—292no—
142C2×C4—292no—
143C2×C4—291no—
144C2×C4—291no—
145C2×C4—1161no—
146C2×C4—1161no—
147C2×C4—1164no—
148C2×C4—1162no—
149C2×C4—1162no—
150C2×C4—1162no—
151C2×C4C22⋊#118111yescharacteristic
152C2×C4C22⋊#118111yescharacteristic
153C2×C4C22×#118111yescharacteristic
154C8—1162no—
155C22—291no—
156C22—291no—
157C22—581no—
158C22—581no—
159C22—1162no—
160C22—1162no—
161C22—1162no—
162C22C2×C22⋊#118111yescharacteristic
163C4—21no—
164C4—21no—
165C4—42no—
166C4—292no—
167C4—581no—
168C4—581no—
169C4—2322no—
170C4#1174522312yes—
171C2—581no—
172C2—581no—
173C2—2322no—
174C2#1427214411yescharacteristic
175C2C2×#1174522311yescharacteristic
176C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C4⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radical#14271714C2
cosocleC2×C4×D29C23
hypercenterC4⋊Q8#1181
hypocenterC29#1517
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
1. #14272181C2semidirect
2. #14272107C2semidirect
3. #14272015C2semidirect
7. C29×C4⋊Q8C4semidirect
12. #11745255C4semidirect
13. #11745236C4semidirect
94. C4⋊Q8#1181semidirect
108. C29#1517semidirect

Maximal subgroups

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

subgroupindex
#142721812
#142721072
#142720152
#142717142
#151729