Finite Group Databasebeta

← #18010773

Subgroups — #18010773

Order 4736.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#10596953C211yesmaximal, characteristic
2C4×C4⋊#3866C211yesmaximal, characteristic
3#14558403C212yesmaximal
4#14558403C212yesmaximal
5#14558089C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C4⋊#3866—21no—
8C2×C4×#3866C2212yes—
9#11924591—21no—
10C4×#64438—21no—
11(C2×#3866)⋊C4—21no—
12#11924535C411yescharacteristic, complemented
13#11924535C411yescharacteristic, complemented
14#11924528C411yescharacteristic, complemented
15#11924514—21no—
16#11924514—21no—
17#11924501—21no—
18#11924501—21no—
19#11924494C2211yescharacteristic
20#11924494C2211yescharacteristic
21C42×D37C2211yescharacteristic
22#125×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×C4×D37D411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×C4×D37C2311yescharacteristic
27C2×Dic74—21no—
28C2×Dic74—21no—
29C2×#64438—22no—
30C4⋊#3866—24no—
31C4×#3866—24no—
32#10596953—22no—
33#10596953Q814yescomplemented
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C4⋊C4×C37C2×C411yescharacteristic
38C42×C37C2×C411yescharacteristic
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C22×D37C2×D411yescharacteristic
53C2×#3866—24no—
54C2×#3866—42no—
55C2×#3866—42no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66C4×D37—22no—
67C4×D37—41no—
68C4×D37C2×Q812yes—
69C4×D37#4112yes—
70Dic74—42no—
71Dic74—42no—
72#64438—24no—
73C22×C37C2×C22⋊C411yescharacteristic
74C2×D37—21no—
75C2×D37—21no—
76C2×D37#12411yescharacteristic
77C2×D37C4⋊Q811yescharacteristic
78#3866—44no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—41no—
82C4×C37—41no—
83C4×C37C4×Q812yes—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87Dic37#10412yes—
88Dic37C22⋊Q812yes—
89#1986—371nomaximal, Sylow
90C2×C37#39111yescharacteristic
91C2×C37C2×#10411yescharacteristic
92C2×C37#42111yescharacteristic
93D37—21no—
94D37—21no—
95#533—371no—
96C4×M16—371no—
97C4×C4⋊C4—371no—
98#339—372no—
99#339—372no—
100C37#198611yescharacteristic, complemented, Sylow
101C2×M16—372no—
102C4⋊Q8—371no—
103C4⋊Q8—371no—
104#125—371no—
105#125#386611yescharacteristic, complemented
106C22⋊Q8—741no—
107C22⋊Q8—741no—
108C4×Q8—741no—
109C4×Q8—741no—
110#117—371no—
111#117—371no—
112C2×C4⋊C4—741no—
113C2×C42—371no—
114C2×C42—372no—
115#97—741no—
116C4×C8—741no—
117#95—741no—
118C2×Q8—741no—
119C2×Q8—741no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—742no—
124M16—374no—
125M16—742no—
126C2×C8—742no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—371no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—744no—
134C4⋊C4—741no—
135C4⋊C4—741no—
136C4⋊C4C2×#386611yescharacteristic
137C4⋊C4C2×#386611yescharacteristic
138C22⋊C4—741no—
139C22⋊C4—741no—
140C42—371no—
141C42—371no—
142C42—371no—
143C42—741no—
144C42—741no—
145C42—744no—
146C42C2×#386611yescharacteristic
147C23—371no—
148Q8—1482no—
149Q8—1482no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—371no—
153C2×C4—371no—
154C2×C4—372no—
155C2×C4—372no—
156C2×C4—371no—
157C2×C4—742no—
158C2×C4—744no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—1481no—
162C2×C4—1482no—
163C2×C4—1482no—
164C2×C4C22⋊#386611yescharacteristic
165C2×C4C22⋊#386611yescharacteristic
166C2×C4C22×#386611yescharacteristic
167C8—744no—
168C22—371no—
169C22—371no—
170C22—741no—
171C22—741no—
172C22C2×C22⋊#386611yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—372no—
178C4—372no—
179C4—741no—
180C4—1484no—
181C4—1481no—
182C4—1481no—
183C4Q8×#386612yes—
184C2—741no—
185C2—741no—
186C2(C2×#3866)⋊Q811yescharacteristic
187C2D37⋊#10411yescharacteristic
188C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#125×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenter#125#3866
hypocenterC37#1986
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #11924535C4semidirect
13. #11924535C4semidirect
14. #11924528C4semidirect
22. #125×C37C4semidirect
33. #10596953Q8semidirect
100. C37#1986semidirect
105. #125#3866semidirect

Maximal subgroups

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

subgroupindex
C4×#105969532
C4×C4⋊#38662
#145584032
#145580892
#198637