Finite Group Databasebeta

← #18010858

Subgroups — #18010858

Order 4736.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558519C211yesmaximal, characteristic
2#14558512C211yesmaximal, characteristic
3#14558435C214yesmaximal, complemented
4#14558107C211yesmaximal, characteristic
5D37⋊M16—21no—
6#11924615—21no—
7#11924597—21no—
8#11924596C2212yes—
9#11924595—21no—
10#11924594C2212yes—
11C2×#10596962C2211yescharacteristic
12#11924534—21no—
13#11924525—21no—
14#11924519C412yescomplemented
15#11924519C2212yes—
16#11924512—21no—
17#11924512—21no—
18#11924495C411yescharacteristic, complemented
19C22×Q8×C37C411yescharacteristic, complemented
20C2×Q8×C37—21no—
21C2×Q8×C37—21no—
22C2×Q8×C37—41no—
23C2×Q8×C37—41no—
24C22×C4×C37C2×C412yes—
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37C2×C411yescharacteristic
27C2×C22⋊D37C2311yescharacteristic
28#10596962—41no—
29#10596962—41no—
30C2×D148D411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×Dic74D411yescharacteristic
34C22⋊#3866—22no—
35#10596957—22no—
36C4⋊#3866—41no—
37C4×#3866—41no—
38#10596953—41no—
39D37⋊C8—41no—
40C22⋊Dic37C2×C412yes—
41#10596938—22no—
42#10596938—22no—
43C4⋊Dic37—21no—
44#10596936—22no—
45#10596936—22no—
46C4×Dic37—21no—
47C23×C37C22×C411yescharacteristic
48C22×D37C22⋊C411yescharacteristic
49C22×D37C2×D411yescharacteristic
50C2×#3866—42no—
51Q8×C37—42no—
52Q8×C37—41no—
53Q8×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—22no—
57C2×C4×C37—42no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C22⋊D37—41no—
61C22⋊D37—41no—
62C2×Dic37—22no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65D148—41no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—21no—
69C4×D37—21no—
70Dic74—41no—
71#64438—42no—
72C22×C37—21no—
73C22×C37—41no—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—41no—
78C2×D37—41no—
79#3866—82no—
80C4×C37—21no—
81C4×C37—42no—
82C4×C37#9911yescharacteristic
83C4×C37#9911yescharacteristic
84Dic37—21no—
85Dic37—21no—
86Dic37—42no—
87#2123—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—41no—
90C2×C37C2×#9911yescharacteristic
91D37—41no—
92D37—41no—
93#536—371no—
94#413—371no—
95#410—371no—
96#352—374no—
97C37#212311yescharacteristic, complemented, Sylow
98C2×#41—371no—
99C22×Q8#386611yescharacteristic, complemented
100C2×M16—741no—
101C4⋊Q8—741no—
102#124—741no—
103#123—372no—
104#123—372no—
105C22⋊Q8—741no—
106C22⋊Q8—741no—
107#117—371no—
108#117—741no—
109#101—741no—
110#100—372no—
111#99—372no—
112#99—741no—
113#41—1481no—
114#41—1481no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—371no—
120C2×D4—371no—
121C2×D4—371no—
122C2×D4—371no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4C2×#386612yes—
126C22×C4C2×#386611yescharacteristic
127M16—742no—
128M16—1481no—
129C2×C8—1481no—
130C4⋊C4—742no—
131C4⋊C4—742no—
132C4⋊C4—741no—
133C4⋊C4—1481no—
134C22⋊C4—372no—
135C22⋊C4—742no—
136C22⋊C4—742no—
137C22⋊C4—742no—
138C42—741no—
139C42—1481no—
140C23—371no—
141C23—371no—
142C23C22×#386611yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—1481no—
147D4—1481no—
148D4—1481no—
149D4—1481no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—742no—
161C2×C4—1482no—
162C2×C4C22⋊#386611yescharacteristic
163C2×C4C22⋊#386611yescharacteristic
164C8—1482no—
165C22—21no—
166C22—41no—
167C22—741no—
168C22—741no—
169C22—1481no—
170C22—1481no—
171C22C2×C22⋊#386611yescharacteristic
172C4—21no—
173C4—42no—
174C4—2962no—
175C4—741no—
176C4—741no—
177C4—1482no—
178C4#1192459411yescharacteristic
179C4#1192459411yescharacteristic
180C2—21no—
181C2—41no—
182C2—1481no—
183C2—1481no—
184C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC22×Q8×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596962C22
cosocleC2×C22⋊D37C23
hypercenterC22×Q8#3866
hypocenterC37#2123
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #14558435C2semidirect
14. #11924519C4semidirect
18. #11924495C4semidirect
19. C22×Q8×C37C4semidirect
97. C37#2123semidirect
99. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145585122
#145584352
#145581072
#212337