Finite Group Databasebeta

← #18010873

Subgroups — #18010873

Order 4736.

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×#11924595C212yesmaximal, complemented
2#14558440C212yesmaximal, complemented
3#14558438C212yesmaximal, complemented
4#14558102C211yesmaximal, characteristic
5C2×C22⋊#3866—22no—
6#11924595—22no—
7#11924595C2214yes—
8C2×#10596962C411yescharacteristic, complemented
9C22×D148C2211yescharacteristic
10#11924533C411yescharacteristic, complemented
11#11924533C2211yescharacteristic
12#11924524C411yescharacteristic, complemented
13#11924524C2211yescharacteristic
14#11924511—22no—
15#11924506—22no—
16#117×C37C411yescharacteristic, complemented
17C23×D37D412yes—
18C22×#3866—42no—
19C22×C4×C37C2×C411yescharacteristic
20C2×C22⋊D37—21no—
21#10596962—42no—
22C2×D148—22no—
23C2×D148—22no—
24C2×D148—42no—
25C2×D148C2×C411yescharacteristic
26C2×D148C2×C411yescharacteristic, complemented
27C2×D148D412yes—
28C2×D148C2311yescharacteristic
29C2×C4×D37—21no—
30C2×Dic74C2×C411yescharacteristic, complemented
31C22⋊#3866—24no—
32C22⋊#3866—42no—
33C4⋊C4×C37—21no—
34C22⋊C4×C37—21no—
35C42×C37C2×C411yescharacteristic, complemented
36C42×C37C2×C411yescharacteristic, complemented
37#10596938—22no—
38#10596938—22no—
39C23×C37C22⋊C411yescharacteristic
40C22×D37—22no—
41C22×D37—22no—
42C22×D37—21no—
43C22×D37—82no—
44C22×D37C22⋊C412yes—
45C22×D37C2×D412yes—
46C2×#3866—44no—
47C2×#3866—84no—
48C2×C4×C37—22no—
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37C22⋊C411yescharacteristic
52C2×C4×C37C22×C411yescharacteristic
53C22⋊D37—42no—
54C2×Dic37—21no—
55D148—41no—
56D148—42no—
57D148—41no—
58D148—41no—
59D148—82no—
60D148—82no—
61C4×D37—42no—
62Dic74—41no—
63C22×C37—41no—
64C22×C37#9912yes—
65C22×C37C2×C22⋊C411yescharacteristic
66C2×D37—22no—
67C2×D37—22no—
68C2×D37—44no—
69C2×D37—42no—
70C2×D37—42no—
71C2×D37—42no—
72C2×D37—41no—
73C2×D37—82no—
74#3866—84no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79Dic37—41no—
80#2127—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—22no—
83C2×C37C2×#9911yescharacteristic
84D37—42no—
85D37—42no—
86D37—81no—
87#535—371no—
88C2×#99—372no—
89#354—372no—
90#353—372no—
91C37#212711yescharacteristic, complemented, Sylow
92C2×#41—371no—
93C22×D4—371no—
94#127—371no—
95#127—371no—
96#124—371no—
97#124—371no—
98#121—742no—
99#120—742no—
100#117#386611yescharacteristic, complemented
101C2×C22⋊C4—742no—
102#99—374no—
103#99—742no—
104C24—372no—
105#41—1482no—
106C2×Q8—371no—
107C2×D4—372no—
108C2×D4—371no—
109C2×D4—371no—
110C2×D4—371no—
111C2×D4—742no—
112C2×D4—742no—
113C2×D4—741no—
114C2×D4—1482no—
115C22×C4—741no—
116C22×C4—1482no—
117C22×C4C2×#386611yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—21no—
120C22⋊C4—742no—
121C22⋊C4—742no—
122C22⋊C4—744no—
123C22⋊C4—1482no—
124C42C2×#386611yescharacteristic, complemented
125C42C2×#386611yescharacteristic, complemented
126C23—372no—
127C23—372no—
128C23—2962no—
129C23—742no—
130C23—742no—
131C23—741no—
132C23C22⋊#386611yescharacteristic
133Q8—1481no—
134D4—2962no—
135D4—2962no—
136D4—1482no—
137D4—1481no—
138D4—1481no—
139D4—1481no—
140D4—1482no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—2964no—
145C2×C4—741no—
146C2×C4—1482no—
147C2×C4—1484no—
148C2×C4C22⋊#386611yescharacteristic
149C2×C4C22×#386611yescharacteristic
150C22—41no—
151C22—2962no—
152C22—742no—
153C22—742no—
154C22—1482no—
155C22—1482no—
156C22—1482no—
157C22—1484no—
158C22—1481no—
159C22#1192459512yes—
160C22C2×C22⋊#386611yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—2964no—
166C4—1481no—
167C2—21no—
168C2—22no—
169C2—2961no—
170C2—1482no—
171C2—1482no—
172C2C2×#1192459511yescharacteristic
subgroupG/H
centerC2C2×#11924595
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC2×C37C2×#99
prime radical#14558102C2
cosocleC2×D148C23
hypercenter#117#3866
hypocenterC37#2127
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#11924595C2semidirect
2. #14558440C2semidirect
3. #14558438C2semidirect
8. C2×#10596962C4semidirect
10. #11924533C4semidirect
12. #11924524C4semidirect
16. #117×C37C4semidirect
26. C2×D148C2×C4semidirect
30. C2×Dic74C2×C4semidirect
35. C42×C37C2×C4semidirect
36. C42×C37C2×C4semidirect
91. C37#2127semidirect
100. #117#3866semidirect
124. C42C2×#3866semidirect
125. C42C2×#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245952
#145584402
#145584382
#145581022
#212737