Finite Group Databasebeta

← #17994986

Subgroups — #17994986

Order 4736.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11924534C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic
3#14557542C211yesmaximal, characteristic
4C2×#11924454C211yesmaximal, characteristic
5#14557294C211yesmaximal, characteristic
6#14557292C211yesmaximal, characteristic
7C37×#419C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924534—22no—
11#11924534C414yescomplemented
12C4×Dic74—22no—
13#11924501—22no—
14#11924495C2211yescharacteristic
15#11924492—22no—
16C2×#10596936—22no—
17C2×C4×Dic37C2211yescharacteristic
18#11924460—22no—
19#11924454—22no—
20C22×Q8×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22#117×C37C2211yescharacteristic
23#103×C37—22no—
24C2×Q8×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37C2×C412yes—
30C22×C4×C37—21no—
31C22×C4×C37C2311yescharacteristic
32C22×Dic37—21no—
33C22×Dic37D412yes—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74C2×C412yes—
39C2×Dic74D412yes—
40M16×C37—21no—
41M16×C37—21no—
42C2×C8×C37—21no—
43C4⋊C4×C37D412yes—
44C22⋊C4×C37—21no—
45C42×C37—21no—
46C22⋊Dic37—21no—
47C4⋊Dic37D412yes—
48#10596936—24no—
49#10596936—28no—
50C4×Dic37—24no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37C2×C412yes—
54#10596934—21no—
55#10596934—21no—
56C2×#64436—21no—
57C23×C37C2×D411yescharacteristic
58Q8×C37—22no—
59Q8×C37—22no—
60Q8×C37—41no—
61Q8×C37—41no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C22×C411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37#4111yescharacteristic
71C2×C4×C37#4111yescharacteristic
72C2×Dic37—24no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37C22⋊C414yes—
78Dic74—22no—
79Dic74—22no—
80Dic74—22no—
81Dic74—22no—
82C8×C37—41no—
83#64436—41no—
84C22×C37—22no—
85C22×C37C2×C22⋊C411yescharacteristic
86C22×C37#12011yescharacteristic
87C22×C37#12311yescharacteristic
88C4×C37—42no—
89C4×C37—42no—
90C4×C37C4×D411yescharacteristic
91C4×C37C4×D411yescharacteristic
92C4×C37#12111yescharacteristic
93C4×C37#12111yescharacteristic
94Dic37—24no—
95Dic37—24no—
96Dic37—42no—
97#1886—371nomaximal, Sylow
98C2×C37—21no—
99C2×C37—21no—
100C2×C37#38611yescharacteristic
101C2×C37#45612yes—
102C2×C4⋊Q8—371no—
103#519—371no—
104#419—371no—
105#419D3711yescharacteristic
106C2×#101—371no—
107#339—371no—
108#339—371no—
109C37#188611yescharacteristic, complemented, Sylow
110C22×Q8—371no—
111C22×Q8C2×D3711yescharacteristic
112C2×M16—371no—
113C2×M16C2×D3711yescharacteristic
114C4⋊Q8—374no—
115C4⋊Q8—742no—
116C4×Q8—742no—
117C4×Q8—742no—
118#117—371no—
119#117—742no—
120#117C2×D3711yescharacteristic
121C2×C4⋊C4—742no—
122C2×C42—371no—
123#103—22no—
124#103—742no—
125#101—742no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—372no—
132C2×Q8—372no—
133C2×Q8—741no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C2×Q8C4×D3712yes—
138C22×C4—21no—
139C22×C4—372no—
140C22×C4—741no—
141C22×C4C22×D3711yescharacteristic
142M16—21no—
143M16—21no—
144M16—741no—
145M16—741no—
146C2×C8—21no—
147C2×C8—741no—
148C4⋊C4—372no—
149C4⋊C4—748no—
150C4⋊C4—744no—
151C4⋊C4C22⋊D3712yes—
152C22⋊C4—21no—
153C22⋊C4—741no—
154C42—21no—
155C42—372no—
156C42—744no—
157C42—741no—
158C42—741no—
159C23D4×D3711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—742no—
165Q8—742no—
166Q8—742no—
167Q8—742no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—374no—
173C2×C4—744no—
174C2×C4—742no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—742no—
178C2×C4C2×C4×D3711yescharacteristic
179C2×C4#1059696211yescharacteristic
180C2×C4D4×D3711yescharacteristic
181C2×C4D4×D3711yescharacteristic
182C2×C4#1059696411yescharacteristic
183C2×C4C2×C22⋊D3711yescharacteristic
184C8—41no—
185C8—1481no—
186C22—22no—
187C22C22⋊C4×D3711yescharacteristic
188C22#1192450411yescharacteristic
189C22#1192451811yescharacteristic
190C4—42no—
191C4—42no—
192C4—744no—
193C4—744no—
194C4—1482no—
195C4#1192449611yescharacteristic
196C4C4×C22⋊D3711yescharacteristic
197C4#1192450711yescharacteristic
198C4#1192450911yescharacteristic
199C2—21no—
200C2—21no—
201C2#1455740911yescharacteristic
202C2#1455771412yes—
subgroupG/H
centerC22#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#419C2
socleC22×C37#120
prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#419D37
hypocenterC37#1886
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #11924534C4semidirect
109. C37#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#119245342
#145580102
#145575422
C2×#119244542
#145572942
#145572922
C37×#4192
#188637