Finite Group Databasebeta

← #18010874

Subgroups — #18010874

Order 4736.

286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D37⋊#99C212yesmaximal, complemented
2#14558439C212yesmaximal, complemented
3#14558438C212yesmaximal, complemented
4#14558101C211yesmaximal, characteristic
5C2×C22⋊#3866—22no—
6#11924595C2214yes—
7#11924594—22no—
8C2×#10596966C411yescharacteristic, complemented
9C2×D4×D37C2211yescharacteristic
10#11924533C2211yescharacteristic
11#11924532C411yescharacteristic, complemented
12#11924525C2211yescharacteristic
13#11924509—22no—
14#11924506—22no—
15#11924493C411yescharacteristic, complemented
16#124×C37C411yescharacteristic, complemented
17C23×D37D412yes—
18C22×#3866—42no—
19C2×Q8×C37C2×C411yescharacteristic, complemented
20C2×D4×C37C2×C411yescharacteristic
21C2×C22⋊D37—22no—
22C2×C22⋊D37D412yes—
23#10596966—42no—
24D4×D37—42no—
25C2×D148—21no—
26C2×D148—22no—
27C2×D148C2×C411yescharacteristic, complemented
28C2×D148C2311yescharacteristic
29C2×C4×D37—21no—
30C2×C4×D37C2×C411yescharacteristic
31C22⋊#3866—24no—
32C22⋊#3866—42no—
33C22⋊C4×C37—22no—
34C42×C37C2×C411yescharacteristic, complemented
35#10596938—21no—
36#10596938—22no—
37#10596936—21no—
38C4×Dic37C2×C411yescharacteristic, complemented
39C23×C37C22⋊C412yes—
40C22×D37—22no—
41C22×D37—22no—
42C22×D37—21no—
43C22×D37—82no—
44C22×D37C22⋊C411yescharacteristic
45C22×D37C2×D412yes—
46C2×#3866—44no—
47C2×#3866—84no—
48Q8×C37—41no—
49D4×C37—41no—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C22×C411yescharacteristic
53C22⋊D37—42no—
54C22⋊D37—82no—
55C2×Dic37—21no—
56C2×Dic37C22⋊C411yescharacteristic
57D148—41no—
58D148—41no—
59D148—42no—
60D148—82no—
61C4×D37—22no—
62C4×D37—42no—
63C22×C37—22no—
64C22×C37—42no—
65C22×C37C2×C22⋊C411yescharacteristic
66C2×D37—22no—
67C2×D37—41no—
68C2×D37—44no—
69C2×D37—42no—
70C2×D37—42no—
71C2×D37—41no—
72C2×D37—82no—
73C2×D37#9912yes—
74#3866—84no—
75C4×C37—21no—
76C4×C37—41no—
77C4×C37—41no—
78Dic37—21no—
79Dic37—41no—
80#2127—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—42no—
83C2×C37C2×#9911yescharacteristic
84D37—22no—
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#386611yescharacteristic, complemented
98#121—742no—
99#120—742no—
100#117—371no—
101C2×C22⋊C4—742no—
102#99—374no—
103#99—742no—
104C24—372no—
105#41—1482no—
106C2×Q8C2×#386611yescharacteristic, complemented
107C2×D4—372no—
108C2×D4—371no—
109C2×D4—371no—
110C2×D4—742no—
111C2×D4—741no—
112C2×D4—742no—
113C2×D4—1482no—
114C2×D4C2×#386611yescharacteristic
115C22×C4—371no—
116C22×C4—741no—
117C22×C4—1482no—
118C4⋊C4—741no—
119C22⋊C4—22no—
120C22⋊C4—741no—
121C22⋊C4—742no—
122C22⋊C4—744no—
123C22⋊C4—1482no—
124C42—371no—
125C42C2×#386611yescharacteristic, complemented
126C23—371no—
127C23—372no—
128C23—2962no—
129C23—742no—
130C23—742no—
131C23—741no—
132C23C22⋊#386612yes—
133Q8—41no—
134D4—41no—
135D4—2962no—
136D4—2962no—
137D4—1481no—
138D4—1481no—
139D4—1482no—
140D4—1482no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—371no—
144C2×C4—2964no—
145C2×C4—742no—
146C2×C4—741no—
147C2×C4—1482no—
148C2×C4—1484no—
149C2×C4C22×#386611yescharacteristic
150C22—22no—
151C22—42no—
152C22—372no—
153C22—2962no—
154C22—742no—
155C22—1482no—
156C22—1481no—
157C22—1482no—
158C22—1484no—
159C22—1481no—
160C22C2×C22⋊#386611yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—2964no—
165C4—741no—
166C4—1481no—
167C2—21no—
168C2—42no—
169C2—2961no—
170C2—742no—
171C2—1482no—
172C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37C2×#99
prime radical#14558101C2
cosocleC2×D148C23
hypercenter#124#3866
hypocenterC37#2127
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D37⋊#99C2semidirect
2. #14558439C2semidirect
3. #14558438C2semidirect
8. C2×#10596966C4semidirect
11. #11924532C4semidirect
15. #11924493C4semidirect
16. #124×C37C4semidirect
19. C2×Q8×C37C2×C4semidirect
27. C2×D148C2×C4semidirect
34. C42×C37C2×C4semidirect
38. C4×Dic37C2×C4semidirect
91. C37#2127semidirect
97. #124#3866semidirect
106. C2×Q8C2×#3866semidirect
125. C42C2×#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#992
#145584392
#145584382
#145581012
#212737