Finite Group Databasebeta

← #17996261

Subgroups — #17996261

Order 4736.

258 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 73 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#14557507C212yesmaximal, complemented
2#14557328C212yesmaximal, complemented
3#14557326C212yesmaximal, complemented
4C37×#532C211yesmaximal, characteristic
5#11924495—22no—
6#11924451—22no—
7#11924451C2214yes—
8C2×#41×C37C411yescharacteristic, complemented
9C2×#41×C37C2211yescharacteristic
10C4⋊Q8×C37C411yescharacteristic, complemented
11#127×C37C2211yescharacteristic
12#124×C37C411yescharacteristic, complemented
13#124×C37C2211yescharacteristic
14#121×C37—22no—
15C4×D4×C37—22no—
16C2×C42×C37C411yescharacteristic, complemented
17#41×C37—41no—
18#41×C37—41no—
19#41×C37—41no—
20#41×C37—41no—
21C2×Q8×C37C2×C411yescharacteristic
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37—22no—
25C2×D4×C37C2×C411yescharacteristic
26C2×D4×C37D412yes—
27C2×D4×C37C2311yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37D412yes—
32C4⋊C4×C37—22no—
33C22⋊C4×C37—22no—
34C22⋊C4×C37—22no—
35C42×C37—21no—
36C42×C37C2×C411yescharacteristic
37C42×C37C2×C411yescharacteristic
38C22⋊Dic37—24no—
39C4⋊Dic37—42no—
40C4×Dic37—42no—
41C23×C37—21no—
42C23×C37C22⋊C411yescharacteristic
43C23×C37C2×D412yes—
44Q8×C37—41no—
45Q8×C37—41no—
46D4×C37—42no—
47D4×C37—41no—
48D4×C37—41no—
49D4×C37—44no—
50D4×C37—42no—
51C2×C4×C37—21no—
52C2×C4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—42no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C22⋊C412yes—
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22×C411yescharacteristic
64C2×Dic37—44no—
65C22×C37—22no—
66C22×C37—21no—
67C22×C37—41no—
68C22×C37—42no—
69C22×C37—42no—
70C22×C37—41no—
71C22×C37C2×C22⋊C411yescharacteristic
72C4×C37—22no—
73C4×C37—22no—
74C4×C37—21no—
75C4×C37—41no—
76C4×C37—41no—
77C4×C37#9911yescharacteristic
78C4×C37#9911yescharacteristic
79Dic37—84no—
80#2126—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—42no—
83C2×C37—41no—
84C2×C37—81no—
85C2×C37C2×#9911yescharacteristic
86#532D3711yescharacteristic
87#410—372no—
88#354—372no—
89#353—372no—
90C37#212611yescharacteristic, complemented, Sylow
91C2×#41Dic3711yescharacteristic, complemented
92C2×#41C2×D3711yescharacteristic
93C4⋊Q8Dic3711yescharacteristic, complemented
94#127C2×D3711yescharacteristic
95#124Dic3711yescharacteristic, complemented
96#124C2×D3711yescharacteristic
97#121—22no—
98C4×D4—22no—
99#117—742no—
100C2×C42Dic3711yescharacteristic, complemented
101#99—374no—
102#99—742no—
103#41—41no—
104#41—41no—
105#41—41no—
106#41—41no—
107C2×Q8C2×Dic3711yescharacteristic
108C2×Q8C2×Dic3711yescharacteristic
109C2×D4—21no—
110C2×D4—22no—
111C2×D4C2×Dic3711yescharacteristic
112C2×D4C22⋊D3712yes—
113C2×D4C22×D3711yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4C2×Dic3711yescharacteristic
117C22×C4C22⋊D3712yes—
118C4⋊C4—22no—
119C4⋊C4—1482no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—744no—
123C42—21no—
124C42—1482no—
125C42C2×Dic3711yescharacteristic
126C42C2×Dic3711yescharacteristic
127C23—21no—
128C23C22⋊Dic3711yescharacteristic
129C23C2×C22⋊D3712yes—
130Q8—41no—
131Q8—41no—
132D4—42no—
133D4—41no—
134D4—41no—
135D4—44no—
136D4—42no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—1484no—
148C2×C4C22⋊Dic3712yes—
149C2×C4C22⋊Dic3711yescharacteristic
150C2×C4C22×Dic3711yescharacteristic
151C22—22no—
152C22—21no—
153C22—41no—
154C22—42no—
155C22—42no—
156C22—41no—
157C22C2×C22⋊Dic3711yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—2964no—
164C4#1192445111yescharacteristic
165C4#1192445111yescharacteristic
166C2—21no—
167C2—42no—
168C2—41no—
169C2—81no—
170C2C2×#1192445111yescharacteristic
subgroupG/H
centerC4#11924451
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
Fitting, prime radicalC37×#532C2
socleC2×C37C2×#99
cosocleC2×D4×C37C23
hypercenter#532D37
hypocenterC37#2126
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14557507C2semidirect
2. #14557328C2semidirect
3. #14557326C2semidirect
8. C2×#41×C37C4semidirect
10. C4⋊Q8×C37C4semidirect
12. #124×C37C4semidirect
16. C2×C42×C37C4semidirect
90. C37#2126semidirect
91. C2×#41Dic37semidirect
93. C4⋊Q8Dic37semidirect
95. #124Dic37semidirect
100. C2×C42Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575072
#145573282
#145573262
C37×#5322
#212637