Finite Group Databasebeta

← #17996270

Subgroups — #17996270

Order 4736.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558104C211yesmaximal, characteristic
2#14557507C211yesmaximal, characteristic
3#14557327C214yesmaximal, complemented
4C37×#410C211yesmaximal, characteristic
5C22×Dic74C411yescharacteristic, complemented
6#11924534C412yescomplemented
7#11924523C2212yes—
8#11924517—21no—
9#11924517—21no—
10#11924515—21no—
11#11924515—21no—
12#11924495—21no—
13#11924495C411yescharacteristic, complemented
14#11924451—21no—
15#11924451C2212yes—
16C2×#41×C37C2211yescharacteristic
17#117×C37—21no—
18#99×C37—21no—
19#99×C37C2212yes—
20#41×C37—41no—
21#41×C37—41no—
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37D411yescharacteristic
24C2×D4×C37D411yescharacteristic
25C2×D4×C37C2311yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×Dic37—21no—
30C2×Dic74—21no—
31C2×Dic74—41no—
32C2×Dic74—41no—
33C2×Dic74C2×C412yes—
34C4⋊C4×C37—41no—
35C22⋊C4×C37—22no—
36C42×C37—41no—
37C22⋊Dic37—21no—
38C22⋊Dic37—22no—
39C22⋊Dic37—22no—
40C22⋊Dic37—22no—
41C4⋊Dic37—21no—
42C4⋊Dic37—41no—
43#10596936—22no—
44#10596936—22no—
45C4×Dic37—41no—
46C4×Dic37C2×C412yes—
47C23×C37C22⋊C411yescharacteristic
48C23×C37C2×D411yescharacteristic
49C23×C37C2×D411yescharacteristic
50Q8×C37—41no—
51D4×C37—41no—
52D4×C37—41no—
53D4×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—42no—
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22⋊C411yescharacteristic
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22×C411yescharacteristic
65C2×Dic37—22no—
66C2×Dic37—22no—
67C2×Dic37—42no—
68C2×Dic37—42no—
69Dic74—41no—
70Dic74—41no—
71Dic74—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37C2×C22⋊C411yescharacteristic
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—82no—
83C4×C37#9911yescharacteristic
84C4×C37#9911yescharacteristic
85Dic37—42no—
86Dic37—42no—
87Dic37—82no—
88#2129—371nomaximal, Sylow
89C2×C37—21no—
90C2×C37—41no—
91C2×C37—41no—
92C2×C37—41no—
93C2×C37C2×#9911yescharacteristic
94#536—371no—
95#410—371no—
96#410D3711yescharacteristic
97#354—374no—
98C37#212911yescharacteristic, complemented, Sylow
99C2×#41C2×D3711yescharacteristic
100C22×Q8—371no—
101C4⋊Q8—372no—
102#124—372no—
103#123—741no—
104#123—741no—
105C22⋊Q8—741no—
106C22⋊Q8—741no—
107#117—21no—
108#117—371no—
109#117—741no—
110#99—21no—
111#99—372no—
112#99—741no—
113#99C2×D3712yes—
114#41—41no—
115#41—41no—
116C2×Q8—372no—
117C2×Q8—741no—
118C2×Q8—1481no—
119C2×Q8—1481no—
120C2×Q8C4×D3711yescharacteristic
121C2×D4D14811yescharacteristic
122C2×D4C22⋊D3711yescharacteristic
123C2×D4C22×D3711yescharacteristic
124C22×C4—741no—
125C22×C4C4×D3711yescharacteristic
126C22×C4D14811yescharacteristic
127C22×C4C22⋊D3711yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—742no—
130C4⋊C4—742no—
131C4⋊C4—741no—
132C4⋊C4—1481no—
133C22⋊C4—22no—
134C22⋊C4—741no—
135C22⋊C4—742no—
136C22⋊C4—742no—
137C22⋊C4—742no—
138C42—41no—
139C42—372no—
140C42—1481no—
141C23#1059693811yescharacteristic
142C23C2×D14811yescharacteristic
143C23C2×C22⋊D3711yescharacteristic
144Q8—41no—
145Q8—1482no—
146Q8—1481no—
147Q8—1481no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—742no—
159C2×C4—742no—
160C2×C4—1482no—
161C2×C4—1482no—
162C2×C4#1059693811yescharacteristic
163C2×C4#1059693811yescharacteristic
164C2×C4#1059693811yescharacteristic
165C2×C4C2×C4×D3711yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×#1059693811yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—2962no—
178C4—1482no—
179C4—1482no—
180C4#1192445011yescharacteristic
181C4#1192445011yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#410C2
socleC2×C37C2×#99
prime radicalC2×#41×C37C22
cosocleC2×D4×C37C23
hypercenter#410D37
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #14557327C2semidirect
5. C22×Dic74C4semidirect
6. #11924534C4semidirect
13. #11924495C4semidirect
98. C37#2129semidirect

Maximal subgroups

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

subgroupindex
#145581042
#145575072
#145573272
C37×#4102
#212937