Finite Group Databasebeta

← #18010056

Subgroups — #18010056

Order 4736.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558556C211yesmaximal, characteristic, complemented
2C4×#10596953C211yesmaximal, characteristic, complemented
3#14558389C212yesmaximal, complemented
4#14558388C212yesmaximal, complemented
5#124×D37C211yesmaximal, characteristic
6C2×#10596953—21no—
7#11924603—21no—
8#11924593—21no—
9#11924591C2212yescomplemented
10#11924591C2212yescomplemented
11C4×#64438—21no—
12C2×Q8×D37C411yescharacteristic
13C2×D4×D37C411yescharacteristic
14#11924525C2211yescharacteristic
15#11924524C411yescharacteristic
16#11924523C2211yescharacteristic
17#11924522—21no—
18#11924522—21no—
19C22⋊C4×D37—21no—
20C22⋊C4×D37—21no—
21C42×D37C2211yescharacteristic
22#124×C37C411yescharacteristic
23C23×D37—21no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27Q8×D37—42no—
28D4×D37—42no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×Dic74—21no—
35C2×Dic74C2×C411yescharacteristic
36C2×#64438—22no—
37C2×#64438—22no—
38#10596953—24no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C42×C37C2×C411yescharacteristic
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47#10596938—21no—
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C22×D37—21no—
53C22×D37—42no—
54C22×D37—42no—
55C22×D37—42no—
56C22×D37C22⋊C411yescharacteristic
57Q8×C37—41no—
58D4×C37—41no—
59C2×C4×C37—21no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22×C411yescharacteristic
63C22⋊D37—42no—
64C2×Dic37—21no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C2×D411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68D148—41no—
69C4×D37—22no—
70C4×D37—22no—
71C4×D37—41no—
72C4×D37—42no—
73Dic74—42no—
74Dic74—41no—
75#64438—24no—
76#64438—42no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37C2×C22⋊C411yescharacteristic
81C2×D37—21no—
82C2×D37—21no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—84no—
87C2×D37#10412yes—
88C4×C37—21no—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—41no—
92Dic37—21no—
93Dic37—21no—
94Dic37—41no—
95Dic37#10012yes—
96#1527—371nomaximal, Sylow
97C2×C37—81no—
98C2×C37C2×#10011yescharacteristic
99C2×C37C2×#10411yescharacteristic
100C2×C37#42111yescharacteristic
101D37—22no—
102D37—81no—
103C2×#124—371no—
104#432—371no—
105C4×M16—371no—
106#329—372no—
107#329—372no—
108C37#152711yescharacteristic, complemented, Sylow
109C22×Q8—371no—
110C22×D4—371no—
111C2×M16—741no—
112#124—371no—
113#124—371no—
114#124—371no—
115#124—741no—
116#124—741no—
117#124#386611yescharacteristic
118C2×C22⋊C4—741no—
119C2×C22⋊C4—741no—
120C2×C42—371no—
121C4⋊C8—741no—
122C22⋊C8—741no—
123#97—372no—
124#97—372no—
125C4×C8—741no—
126C24—741no—
127C2×Q8—371no—
128C2×Q8—741no—
129C2×Q8—1482no—
130C2×Q8C2×#386611yescharacteristic
131C2×D4—371no—
132C2×D4—741no—
133C2×D4—1482no—
134C2×D4C2×#386611yescharacteristic
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139M16—744no—
140C2×C8—742no—
141C2×C8—742no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C42—371no—
151C42—371no—
152C42—371no—
153C42C2×#386611yescharacteristic
154C23—21no—
155C23—371no—
156C23—741no—
157C23—1482no—
158C23—1482no—
159C23—1482no—
160Q8—41no—
161Q8—1481no—
162Q8—1482no—
163D4—41no—
164D4—1481no—
165D4—1482no—
166C2×C4—21no—
167C2×C4—371no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—742no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—1481no—
174C2×C4—1482no—
175C2×C4C22⋊#386611yescharacteristic
176C2×C4C22⋊#386611yescharacteristic
177C2×C4C22×#386611yescharacteristic
178C8—744no—
179C8—1482no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—372no—
184C22—2964no—
185C22—741no—
186C22—741no—
187C22—1481no—
188C22—1481no—
189C22—1481no—
190C22C2×C22⋊#386611yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—372no—
196C4—741no—
197C4—741no—
198C4—1481no—
199C2—81no—
200C2—2961no—
201C2—742no—
202C2D37⋊#10011yescharacteristic
203C2D37⋊#10411yescharacteristic
204C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC4×Dic37C23
hypercenter#124#3866
hypocenterC37#1527
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558556C2semidirect
2. C4×#10596953C2semidirect
3. #14558389C2semidirect
4. #14558388C2semidirect
9. #11924591C22semidirect
10. #11924591C22semidirect
108. C37#1527semidirect

Maximal subgroups

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

subgroupindex
#145585562
C4×#105969532
#145583892
#145583882
#124×D372
#152737