Finite Group Databasebeta

← #17995015

Subgroups — #17995015

Order 4736.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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#14558300C211yesmaximal, characteristic, complemented
2#14557517C211yesmaximal, characteristic, complemented
3#14557497C212yesmaximal, complemented
4#14557303C212yesmaximal, complemented
5C37×#525C211yesmaximal, characteristic
6#11924543—24no—
7C2×#10596934—22no—
8C2×#10596934C2212yes—
9C2×#10596934C2212yes—
10#11924455—21no—
11#11924453—21no—
12C22⋊#64436—24no—
13C2×#41×C37C2211yescharacteristic
14C23×C4×C37C2211yescharacteristic
15#123×C37C412yes—
16C22⋊Q8×C37—21no—
17#121×C37—21no—
18#120×C37C412yes—
19C4×D4×C37—22no—
20#117×C37C2211yescharacteristic
21C24×C37C2×C411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37D411yescharacteristic
25C2×D4×C37—22no—
26C2×D4×C37C2×C412yes—
27C2×D4×C37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37—22no—
31C22×C4×C37—22no—
32C22×C4×C37C2×C411yescharacteristic
33C22×C4×C37D412yes—
34C22×C4×C37C2311yescharacteristic
35C4⋊C4×C37—22no—
36C4⋊C4×C37—21no—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C22⋊C4×C37C2×C412yes—
40C42×C37—21no—
41#10596934—24no—
42#10596934—22no—
43#10596934—22no—
44#10596934—22no—
45#10596934—22no—
46C2×#64436—24no—
47C2×#64436—22no—
48C2×#64436D414yescomplemented
49C23×C37—21no—
50C23×C37—22no—
51C23×C37—42no—
52C23×C37C22⋊C412yes—
53C23×C37C22×C411yescharacteristic
54Q8×C37—22no—
55D4×C37—24no—
56D4×C37—22no—
57D4×C37—44no—
58C2×C4×C37—22no—
59C2×C4×C37—22no—
60C2×C4×C37—22no—
61C2×C4×C37—21no—
62C2×C4×C37—22no—
63C2×C4×C37—41no—
64C2×C4×C37—42no—
65C2×C4×C37—41no—
66C2×C4×C37C22⋊C412yes—
67C2×C4×C37C2×D412yes—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37#4112yes—
71#64436—24no—
72#64436—42no—
73C22×C37—22no—
74C22×C37—24no—
75C22×C37—22no—
76C22×C37—41no—
77C22×C37—42no—
78C22×C37—41no—
79C22×C37—42no—
80C22×C37—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C22×C37C4×D412yes—
83C4×C37—22no—
84C4×C37—42no—
85C4×C37—41no—
86C4×C37#12011yescharacteristic
87C4×C37#12112yes—
88C4×C37#12311yescharacteristic
89#1891—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37—22no—
92C2×C37—42no—
93C2×C37—42no—
94C2×C37#38611yescharacteristic
95#568—371no—
96#525D3711yescharacteristic
97#413—371no—
98#407—372no—
99#344—372no—
100C37#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D3711yescharacteristic
102C23×C4C2×D3711yescharacteristic
103#131—744no—
104C2×M16—372no—
105C2×M16—372no—
106C2×M16—742no—
107#123Dic3712yes—
108C22⋊Q8—21no—
109#121—21no—
110#120Dic3712yes—
111C4×D4—22no—
112#117C2×D3711yescharacteristic
113#101—741no—
114#100—741no—
115C22⋊C8—744no—
116C24C2×Dic3711yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D3711yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic3712yes—
122C2×D4C22⋊D3711yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×Dic3711yescharacteristic
128C22×C4C22⋊D3712yes—
129C22×C4C22×D3711yescharacteristic
130M16—744no—
131M16—742no—
132M16—742no—
133M16—742no—
134M16—742no—
135C2×C8—374no—
136C2×C8—744no—
137C2×C8—742no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic3712yes—
143C42—21no—
144C23—21no—
145C23—22no—
146C23—42no—
147C23C22⋊Dic3712yes—
148C23C22×Dic3711yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4C22⋊Dic3712yes—
162C2×C4D4×D3712yes—
163C2×C4#1059696412yes—
164C2×C4C2×C22⋊D3711yescharacteristic
165C2×C4C2×C22⋊D3711yescharacteristic
166C8—744no—
167C8—1482no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic3711yescharacteristic
177C22D4×Dic3712yes—
178C4—22no—
179C4—42no—
180C4—41no—
181C4#1192450411yescharacteristic
182C4#1192450812yes—
183C4#1192451711yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#1455741311yescharacteristic
subgroupG/H
centerC4#11924504
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#525C2
socleC2×C37#386
cosocleC22×C4×C37C23
hypercenter#525D37
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14558300C2semidirect
2. #14557517C2semidirect
3. #14557497C2semidirect
4. #14557303C2semidirect
48. C2×#64436D4semidirect
100. C37#1891semidirect

Maximal subgroups

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

subgroupindex
#145583002
#145575172
#145574972
#145573032
C37×#5252
#189137