Finite Group Databasebeta

← #17996249

Subgroups — #17996249

Order 4736.

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

normal subgroups only

This group has 234 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#14557517C211yesmaximal, characteristic
3#14557322C214yesmaximal, complemented
4C37×#410C211yesmaximal, characteristic
5C22×Dic74C411yescharacteristic, complemented
6C2×#10596934—21no—
7#11924534—21no—
8#11924523—21no—
9#11924517C412yescomplemented
10#11924517C2212yes—
11#11924515—21no—
12#11924515—21no—
13#11924495C411yescharacteristic, complemented
14#11924455—21no—
15#11924453C2212yes—
16C2×#41×C37C2211yescharacteristic
17#117×C37—21no—
18#99×C37—21no—
19#99×C37C2212yes—
20#41×C37—41no—
21#41×C37—41no—
22C2×Q8×C37D411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C2×D4×C37D411yescharacteristic
25C2×D4×C37C2311yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×Dic37C2×C412yes—
30C2×Dic74—21no—
31C2×Dic74—21no—
32C2×Dic74—41no—
33C2×Dic74—41no—
34C4⋊C4×C37—41no—
35C22⋊C4×C37—22no—
36C42×C37—41no—
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39C22⋊Dic37C2×C412yes—
40C4⋊Dic37—21no—
41#10596936—22no—
42#10596936—22no—
43C4×Dic37—21no—
44#10596934—22no—
45#10596934—41no—
46C2×#64436—41no—
47C23×C37C22⋊C411yescharacteristic
48C23×C37C22×C411yescharacteristic
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×C37C2×D411yescharacteristic
65C2×Dic37—22no—
66C2×Dic37—22no—
67C2×Dic37—42no—
68Dic74—42no—
69Dic74—41no—
70Dic74—41no—
71#64436—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—
87#2123—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—41no—
90C2×C37—41no—
91C2×C37—41no—
92C2×C37C2×#9911yescharacteristic
93#536—371no—
94#413—371no—
95#410D3711yescharacteristic
96#352—374no—
97C37#212311yescharacteristic, complemented, Sylow
98C2×#41C2×D3711yescharacteristic
99C22×Q8—371no—
100C2×M16—741no—
101C4⋊Q8—741no—
102#124—741no—
103#123—372no—
104#123—372no—
105C22⋊Q8—741no—
106C22⋊Q8—741no—
107#117—21no—
108#117—371no—
109#101—741no—
110#100—372no—
111#99—21no—
112#99C2×D3712yes—
113#41—41no—
114#41—41no—
115C2×Q8—741no—
116C2×Q8—741no—
117C2×Q8—1481no—
118C2×Q8—1481no—
119C2×Q8D14811yescharacteristic
120C2×D4C4×D3711yescharacteristic
121C2×D4C22⋊D3711yescharacteristic
122C2×D4C22×D3711yescharacteristic
123C22×C4—372no—
124C22×C4C4×D3711yescharacteristic
125C22×C4D14811yescharacteristic
126C22×C4C22⋊D3711yescharacteristic
127M16—742no—
128M16—1481no—
129C2×C8—1481no—
130C4⋊C4—41no—
131C4⋊C4—742no—
132C4⋊C4—741no—
133C4⋊C4—742no—
134C22⋊C4—22no—
135C22⋊C4—372no—
136C22⋊C4—742no—
137C22⋊C4—742no—
138C42—41no—
139C42—741no—
140C23#1059693811yescharacteristic
141C23C2×C4×D3711yescharacteristic
142C23C2×C22⋊D3711yescharacteristic
143Q8—41no—
144Q8—1482no—
145Q8—1481no—
146Q8—1481no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—742no—
158C2×C4—742no—
159C2×C4—1482no—
160C2×C4#1059693811yescharacteristic
161C2×C4#1059693811yescharacteristic
162C2×C4#1059693811yescharacteristic
163C2×C4C2×D14811yescharacteristic
164C8—1482no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×#1059693811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—1482no—
177C4—1482no—
178C4#1192445011yescharacteristic
179C4#1192445011yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#410C2
socleC2×C37C2×#99
prime radicalC2×#41×C37C22
cosocleC2×D4×C37C23
hypercenter#410D37
hypocenterC37#2123
LCSG ▷ C23×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. #14557322C2semidirect
5. C22×Dic74C4semidirect
9. #11924517C4semidirect
13. #11924495C4semidirect
97. C37#2123semidirect

Maximal subgroups

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

subgroupindex
#145581042
#145575172
#145573222
C37×#4102
#212337