Finite Group Databasebeta

← #17996264

Subgroups — #17996264

Order 4736.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558101C211yesmaximal, characteristic
2#99×D37C212yesmaximal, complemented
3#14557328C211yesmaximal, characteristic, complemented
4#14557325C212yesmaximal, complemented
5C37×#354C211yesmaximal, characteristic, complemented
6C2×#10596966C411yescharacteristic, complemented
7C2×D4×D37C2211yescharacteristic
8#11924533C411yescharacteristic, complemented
9#11924532C2211yescharacteristic
10#11924525C411yescharacteristic, complemented
11#11924509—22no—
12#11924506—22no—
13#11924493C411yescharacteristic, complemented
14C22⋊C4×D37—22no—
15#11924451C2212yes—
16#11924450—22no—
17#124×C37C2211yescharacteristic
18#99×C37C2212yes—
19C23×D37D412yes—
20C2×Q8×C37C2×C411yescharacteristic, complemented
21C2×D4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C2×C22⋊D37D412yes—
24#10596966—42no—
25D4×D37—42no—
26C2×D148—21no—
27C2×D148—22no—
28C2×D148C2×C411yescharacteristic
29C2×D148C2×C411yescharacteristic, complemented
30C2×C4×D37—21no—
31C2×C4×D37—42no—
32C2×C4×D37C2×C411yescharacteristic
33C22⋊C4×C37—22no—
34C22⋊C4×C37—22no—
35C42×C37C2×C411yescharacteristic, complemented
36C22⋊Dic37—22no—
37#10596938—21no—
38#10596938—22no—
39#10596938—42no—
40#10596936—21no—
41C4×Dic37C2×C411yescharacteristic, complemented
42C23×C37C2×D412yes—
43C22×D37—22no—
44C22×D37—22no—
45C22×D37—21no—
46C22×D37—82no—
47C22×D37C22⋊C412yes—
48C22×D37C22⋊C411yescharacteristic
49Q8×C37—41no—
50D4×C37—41no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37—42no—
54C2×C4×C37C22×C411yescharacteristic
55C22⋊D37—42no—
56C22⋊D37—82no—
57C2×Dic37—21no—
58C2×Dic37—42no—
59C2×Dic37C22⋊C411yescharacteristic
60D148—41no—
61D148—41no—
62D148—42no—
63D148—82no—
64C4×D37—22no—
65C4×D37—42no—
66C4×D37—84no—
67C22×C37—22no—
68C22×C37—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—22no—
71C2×D37—41no—
72C2×D37—44no—
73C2×D37—42no—
74C2×D37—42no—
75C2×D37—41no—
76C2×D37—82no—
77C2×D37#9912yes—
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—41no—
81C4×C37—82no—
82Dic37—21no—
83Dic37—41no—
84Dic37—82no—
85#2127—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—42no—
88C2×C37C2×#9911yescharacteristic
89D37—22no—
90D37—42no—
91D37—81no—
92#535—371no—
93C2×#99—372no—
94#354—371no—
95#354D3711yescharacteristic, complemented
96#353—372no—
97C37#212711yescharacteristic, complemented, Sylow
98C2×#41—371no—
99C22×D4—371no—
100#127—371no—
101#127—371no—
102#124—371no—
103#124C2×D3711yescharacteristic
104#121—742no—
105#120—742no—
106#117—371no—
107C2×C22⋊C4—742no—
108#99—372no—
109#99—742no—
110#99C2×D3712yes—
111C24—372no—
112#41—1482no—
113C2×Q8C4×D3711yescharacteristic, complemented
114C2×D4—372no—
115C2×D4—371no—
116C2×D4—371no—
117C2×D4—742no—
118C2×D4—741no—
119C2×D4—742no—
120C2×D4—1482no—
121C2×D4C22×D3711yescharacteristic
122C22×C4—371no—
123C22×C4—741no—
124C22×C4—1482no—
125C4⋊C4—741no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—741no—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C22⋊C4—1482no—
132C42—371no—
133C42C4×D3711yescharacteristic, complemented
134C23—371no—
135C23—372no—
136C23—2962no—
137C23—742no—
138C23—742no—
139C23—741no—
140C23D4×D3712yes—
141Q8—41no—
142D4—41no—
143D4—2962no—
144D4—2962no—
145D4—1481no—
146D4—1481no—
147D4—1482no—
148D4—1482no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—371no—
153C2×C4—2964no—
154C2×C4—742no—
155C2×C4—741no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4C2×C4×D3711yescharacteristic
159C22—22no—
160C22—42no—
161C22—372no—
162C22—2962no—
163C22—742no—
164C22—1482no—
165C22—1481no—
166C22—1482no—
167C22—1484no—
168C22—1481no—
169C22C22⋊C4×D3711yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—2962no—
175C4—741no—
176C4—1481no—
177C2—21no—
178C2—42no—
179C2—2961no—
180C2—742no—
181C2—1482no—
182C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#354C2
socleC2×C37C2×#99
prime radical#14558101C2
cosocleC2×D4×C37C23
hypercenter#354D37
hypocenterC37#2127
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D37C2semidirect
3. #14557328C2semidirect
4. #14557325C2semidirect
5. C37×#354C2semidirect
6. C2×#10596966C4semidirect
8. #11924533C4semidirect
10. #11924525C4semidirect
13. #11924493C4semidirect
20. C2×Q8×C37C2×C4semidirect
29. C2×D148C2×C4semidirect
35. C42×C37C2×C4semidirect
41. C4×Dic37C2×C4semidirect
95. #354D37semidirect
97. C37#2127semidirect
113. C2×Q8C4×D37semidirect
133. C42C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145581012
#99×D372
#145573282
#145573252
C37×#3542
#212737