Finite Group Databasebeta

← #18009918

Subgroups — #18009918

Order 4736.

218 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 62 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#14558549C211yesmaximal, characteristic
2C4×#10596957C211yesmaximal, characteristic
3#14558383C212yesmaximal, complemented
4Q8⋊#64438C212yesmaximal, complemented
5#14558085C211yesmaximal, characteristic
6C2×#10596957—21no—
7C4⋊#64438C2212yes—
8C22⋊#64438—21no—
9#11924591—21no—
10C4×#64438—21no—
11C4×#64438C2212yes—
12#11924535C411yescharacteristic
13#11924534C411yescharacteristic
14#11924526—21no—
15#11924515C411yescharacteristic
16#11924513—21no—
17Q8×Dic37C2211yescharacteristic
18#11924501—21no—
19#11924501C2211yescharacteristic
20#11924492—21no—
21C2×C4×Dic37C2211yescharacteristic
22C22⋊Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×Dic37D411yescharacteristic
26C22×Dic37D411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29#10596957—24no—
30C2×#64438—22no—
31C2×#64438—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C22⋊C4×C37—21no—
35C22⋊Dic37—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37C2×C411yescharacteristic
38#10596936—21no—
39#10596936—21no—
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43C4×Dic37—21no—
44C4×Dic37—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C23×C37C22⋊C411yescharacteristic
50Q8×C37—22no—
51C2×C4×C37—22no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22×C411yescharacteristic
56C2×Dic37—22no—
57C2×Dic37—22no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64Dic74—22no—
65Dic74—42no—
66#64438—24no—
67#64438—42no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37C2×C22⋊C411yescharacteristic
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—41no—
75C4×C37#13112yes—
76Dic37—21no—
77Dic37—21no—
78Dic37—41no—
79Dic37—41no—
80Dic37#10412yes—
81Dic37#13712yes—
82#1485—371nomaximal, Sylow
83C2×C37—41no—
84C2×C37#40811yescharacteristic
85C2×C37#41911yescharacteristic
86C2×C37C2×#10411yescharacteristic
87#533—371no—
88#431—371no—
89C4×M16—371no—
90Q8⋊C8—372no—
91Q8⋊C8—372no—
92C37#148511yescharacteristic, complemented, Sylow
93C2×M16—741no—
94C4⋊Q8—371no—
95C4⋊Q8—371no—
96#125—741no—
97C22⋊Q8—371no—
98C22⋊Q8—741no—
99C22⋊Q8#386611yescharacteristic
100C4×Q8—371no—
101C4×Q8—371no—
102C4×Q8—741no—
103#117—741no—
104C2×C42—371no—
105C4⋊C8—372no—
106C22⋊C8—741no—
107#97—741no—
108C4×C8—372no—
109C4×C8—741no—
110C2×Q8—371no—
111C2×Q8—741no—
112C2×Q8C2×#386611yescharacteristic
113C22×C4—371no—
114C22×C4—371no—
115C22×C4C2×#386611yescharacteristic
116M16—744no—
117C2×C8—742no—
118C2×C8—742no—
119C4⋊C4—21no—
120C4⋊C4—371no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4C2×#386611yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—741no—
130C42—371no—
131C42—371no—
132C42—371no—
133C42—371no—
134C42—741no—
135C42—741no—
136C23C22⋊#386611yescharacteristic
137Q8—22no—
138Q8—742no—
139Q8—1482no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—371no—
144C2×C4—371no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—742no—
148C2×C4—742no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4C22⋊#386611yescharacteristic
152C2×C4C22×#386611yescharacteristic
153C8—744no—
154C8—1482no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22C2×C22⋊#386611yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—372no—
163C4—372no—
164C4—741no—
165C4—741no—
166C4—1481no—
167C4—1481no—
168C4#1192462312yes—
169C2—41no—
170C2#1455850611yescharacteristic
171C2#1455852611yescharacteristic
172C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C22⋊C4
cosocleC4×Dic37C23
hypercenterC22⋊Q8#3866
hypocenterC37#1485
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14558383C2semidirect
4. Q8⋊#64438C2semidirect
92. C37#1485semidirect

Maximal subgroups

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

subgroupindex
#145585492
C4×#105969572
#145583832
Q8⋊#644382
#145580852
#148537