Finite Group Databasebeta

← #17996246

Subgroups — #17996246

Order 4736.

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

normal subgroups only

This group has 266 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#14557517C211yesmaximal, characteristic, complemented
2#14557507C211yesmaximal, characteristic, complemented
3#14557320C214yesmaximal, complemented
4C37×#535C211yesmaximal, characteristic
5C2×#10596934—21no—
6#11924495—21no—
7#11924455—21no—
8#11924453C2212yes—
9#11924451—21no—
10#11924451C2212yes—
11C2×#41×C37C2211yescharacteristic
12C22×D4×C37C411yescharacteristic, complemented
13#127×C37—21no—
14#124×C37—21no—
15#121×C37—21no—
16#121×C37—21no—
17#120×C37C412yescomplemented
18#120×C37C2212yes—
19#117×C37C411yescharacteristic, complemented
20C24×C37C2×C412yes—
21#41×C37—41no—
22#41×C37—41no—
23C2×Q8×C37D411yescharacteristic
24C2×D4×C37—22no—
25C2×D4×C37—22no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—41no—
29C2×D4×C37—41no—
30C2×D4×C37C2×C411yescharacteristic
31C2×D4×C37D411yescharacteristic
32C2×D4×C37C2311yescharacteristic
33C22×C4×C37C2×C411yescharacteristic
34C22×C4×C37D411yescharacteristic
35C22×C4×C37D411yescharacteristic
36C4⋊C4×C37—21no—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C22⋊C4×C37C2×C412yes—
40C42×C37—21no—
41C22⋊Dic37—22no—
42C4⋊Dic37—41no—
43C4×Dic37—41no—
44#10596934—22no—
45#10596934—41no—
46C2×#64436—41no—
47C23×C37—22no—
48C23×C37—42no—
49C23×C37—82no—
50C23×C37C22⋊C411yescharacteristic
51C23×C37C22×C411yescharacteristic
52C23×C37C2×D411yescharacteristic
53Q8×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—42no—
58D4×C37—41no—
59D4×C37—41no—
60D4×C37—82no—
61D4×C37—82no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—22no—
69C2×C4×C37C22⋊C411yescharacteristic
70C2×C4×C37C22⋊C411yescharacteristic
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×Dic37—42no—
74#64436—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—42no—
82C22×C37—42no—
83C22×C37—42no—
84C22×C37—84no—
85C22×C37C2×C22⋊C411yescharacteristic
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—42no—
90C4×C37#9911yescharacteristic
91C4×C37#9911yescharacteristic
92Dic37—82no—
93#2122—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—41no—
96C2×C37—41no—
97C2×C37—41no—
98C2×C37—82no—
99C2×C37C2×#9911yescharacteristic
100#535D3711yescharacteristic
101#413—371no—
102#410—371no—
103AΣL(1,𝔽16)—374no—
104C37#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D3711yescharacteristic
106C22×D4Dic3711yescharacteristic, complemented
107C2×M16—741no—
108#127—21no—
109#124—21no—
110#121—21no—
111#121—21no—
112#120Dic3712yescomplemented
113#120C2×D3712yes—
114#117—741no—
115#117Dic3711yescharacteristic, complemented
116#101—741no—
117#100—372no—
118#99—372no—
119#99—741no—
120C24C2×Dic3712yes—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D3711yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic3711yescharacteristic
131C2×D4C22⋊D3711yescharacteristic
132C2×D4C22×D3711yescharacteristic
133C22×C4C2×Dic3711yescharacteristic
134C22×C4C22⋊D3711yescharacteristic
135C22×C4C22⋊D3711yescharacteristic
136M16—742no—
137M16—1481no—
138C2×C8—1481no—
139C4⋊C4—21no—
140C4⋊C4—1481no—
141C22⋊C4—22no—
142C22⋊C4—22no—
143C22⋊C4—742no—
144C22⋊C4C2×Dic3712yes—
145C42—21no—
146C42—1481no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23C22⋊Dic3711yescharacteristic
151C23C22×Dic3711yescharacteristic
152C23C2×C22⋊D3711yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—42no—
158D4—41no—
159D4—41no—
160D4—82no—
161D4—82no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—1482no—
170C2×C4C22⋊Dic3711yescharacteristic
171C2×C4C22⋊Dic3711yescharacteristic
172C2×C4C22⋊Dic3711yescharacteristic
173C2×C4C2×C22⋊D3711yescharacteristic
174C8—1482no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—84no—
185C22C2×C22⋊Dic3711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—42no—
190C4—2962no—
191C4#1192445111yescharacteristic
192C4#1192445111yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—82no—
198C2C2×#1192445111yescharacteristic
subgroupG/H
centerC2C2×#11924451
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
Fitting, prime radicalC37×#535C2
socleC2×C37C2×#99
cosocleC2×D4×C37C23
hypercenter#535D37
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14557517C2semidirect
2. #14557507C2semidirect
3. #14557320C2semidirect
12. C22×D4×C37C4semidirect
17. #120×C37C4semidirect
19. #117×C37C4semidirect
104. C37#2122semidirect
106. C22×D4Dic37semidirect
112. #120Dic37semidirect
115. #117Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575172
#145575072
#145573202
C37×#5352
#212237