Finite Group Databasebeta

← #17993041

Subgroups — #17993041

Order 4736.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×Q8×D37C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic
3C4×#10596929C211yesmaximal, characteristic
4#14557265C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557263C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D37C411yescharacteristic
9C2×#10596929—21no—
10Q8×Dic37C411yescharacteristic
11C4×Dic74—21no—
12C4×Dic74C2211yescharacteristic
13#11924501—21no—
14#11924501C411yescharacteristic
15C4⋊C4×D37—21no—
16C4⋊C4×D37C411yescharacteristic
17C42×D37—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic
20#11924448—21no—
21#11924446—21no—
22#11924446—21no—
23C4×#64436C2211yescharacteristic
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28Q8×D37—22no—
29Q8×D37—22no—
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37C2×C411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×Dic74—21no—
36C2×Dic74C2×C411yescharacteristic
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37C2×C411yescharacteristic
41C42×C37—21no—
42C42×C37C2311yescharacteristic
43C4⋊Dic37—21no—
44C4⋊Dic37C2×C411yescharacteristic
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48C4×Dic37—21no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—24no—
57C22×D37C22⋊C411yescharacteristic
58Q8×C37—21no—
59Q8×C37M1612yescomplemented
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37C22×C411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C4×D37—24no—
71C4×D37—22no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—21no—
76C4×D37—42no—
77Dic74—24no—
78Dic74—21no—
79Dic74M1612yescomplemented
80C8×C37—22no—
81C8×C37—41no—
82#64436—22no—
83#64436—41no—
84C22×C37C2×C22⋊C411yescharacteristic
85C2×D37—21no—
86C2×D37—21no—
87C2×D37#10412yes—
88C4×C37—22no—
89C4×C37—21no—
90C4×C37—41no—
91C4×C37C2×M1611yescharacteristic
92C4×C37C2×M1611yescharacteristic
93C4×C37#13711yescharacteristic
94C4×C37#13711yescharacteristic
95Dic37—21no—
96Dic37—22no—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100#1491—371nomaximal, Sylow
101C2×C37#40711yescharacteristic
102C2×C37#41911yescharacteristic
103C2×C37C2×#10411yescharacteristic
104D37—22no—
105C2×C4×Q8—371no—
106#432—371no—
107C4×M16—371no—
108Q8⋊C8—371no—
109Q8⋊C8—371no—
110Q8⋊C8—371no—
111Q8⋊C8D3711yescharacteristic, complemented
112C37#149111yescharacteristic, complemented, Sylow
113C22×Q8—371no—
114C2×M16—741no—
115C4×Q8—371no—
116C4×Q8—371no—
117C4×Q8—371no—
118C4×Q8—741no—
119C4×Q8—741no—
120C4×Q8C2×D3711yescharacteristic
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C42—371no—
124C2×C42—741no—
125C4⋊C8—371no—
126C4⋊C8C2×D3711yescharacteristic
127C22⋊C8—741no—
128#97—741no—
129#97—741no—
130C4×C8—371no—
131C4×C8C2×D3711yescharacteristic
132C2×Q8—371no—
133C2×Q8—741no—
134C2×Q8—742no—
135C2×Q8—742no—
136C2×Q8C4×D3711yescharacteristic
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—741no—
141C22×C4—741no—
142M16—744no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—741no—
146C2×C8—741no—
147C4⋊C4—21no—
148C4⋊C4—371no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4C4×D3711yescharacteristic
154C42—21no—
155C42—371no—
156C42—371no—
157C42—371no—
158C42—741no—
159C42—741no—
160C42—741no—
161C42C22×D3711yescharacteristic
162C23—371no—
163Q8—21no—
164Q8—372no—
165Q8—744no—
166Q8—741no—
167Q8#1059692912yescomplemented
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—742no—
174C2×C4—744no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—1482no—
182C2×C4C2×C4×D3711yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C2×C4D4×D3711yescharacteristic
185C8—22no—
186C8—41no—
187C8—742no—
188C8—1481no—
189C22—372no—
190C22—741no—
191C22—741no—
192C22C22⋊C4×D3711yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—741no—
197C4—742no—
198C4—741no—
199C4—741no—
200C4—1481no—
201C4M16×D3711yescharacteristic
202C4C2×#1059692911yescharacteristic
203C4#1192456511yescharacteristic
204C4#1192456811yescharacteristic
205C2—742no—
206C2#1455749511yescharacteristic
207C2#1455754011yescharacteristic
208C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1491
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #14557265C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557263C2semidirect
7. C37×Q8⋊C8C2semidirect
59. Q8×C37M16semidirect
79. Dic74M16semidirect
111. Q8⋊C8D37semidirect
112. C37#1491semidirect
167. Q8#10596929semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D372
#145575892
C4×#105969292
#145572652
Q8⋊#644362
#145572632
C37×Q8⋊C82
#149137