Finite Group Databasebeta

← #17992982

Subgroups — #17992982

Order 4736.

264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10596966C211yesmaximal, characteristic
2#14557584C211yesmaximal, characteristic, complemented
3C4⋊C8×D37C211yesmaximal, characteristic, complemented
4Q8⋊#64436C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596966C411yescharacteristic
9C2×C8×D37—21no—
10Q8×Dic37C411yescharacteristic
11C4×D148—21no—
12C4×D148C2211yescharacteristic
13#11924498—21no—
14#11924498C411yescharacteristic
15#11924494—21no—
16#11924494C411yescharacteristic
17C42×D37—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic
20#11924465—21no—
21#11924465—21no—
22#11924448—21no—
23C4×#64436C2211yescharacteristic
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28#10596966—22no—
29#10596966C814yescomplemented
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C8×C37—21no—
39C2×C8×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37C2×C411yescharacteristic
42C42×C37—21no—
43C42×C37C2311yescharacteristic
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37C2×C411yescharacteristic
49C4×Dic37—21no—
50C4×Dic37—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56C8×D37—42no—
57C22×D37—21no—
58C22×D37C22⋊C411yescharacteristic
59Q8×C37—21no—
60Q8×C37C2×C812yescomplemented
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37C22×C411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×Dic37—21no—
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70D148—24no—
71D148—21no—
72D148C2×C812yescomplemented
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—24no—
76C4×D37—41no—
77C4×D37—42no—
78C4×D37—41no—
79C4×D37—41no—
80C4×D37C2×C812yes—
81C4×D37M1612yes—
82C8×C37—41no—
83C8×C37—41no—
84#64436—41no—
85#64436—41no—
86C22×C37C2×C22⋊C411yescharacteristic
87C2×D37—21no—
88C2×D37—21no—
89C2×D37—22no—
90C2×D37—41no—
91C2×D37—41no—
92C2×D37C22⋊C812yes—
93C4×C37—22no—
94C4×C37—21no—
95C4×C37—41no—
96C4×C37C22×C811yescharacteristic
97C4×C37C2×M1611yescharacteristic
98C4×C37AGL(1,ℤ/8)11yescharacteristic
99C4×C37#13711yescharacteristic
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103Dic37C22⋊C812yes—
104#1477—371nomaximal, Sylow
105C2×C37C2×C22⋊C811yescharacteristic
106C2×C37#41711yescharacteristic
107C2×C37#42111yescharacteristic
108D37—22no—
109D37—42no—
110C4×#41—371no—
111#431—371no—
112C2×C4⋊C8—371no—
113Q8⋊C8—371no—
114Q8⋊C8D3711yescharacteristic, complemented
115D4⋊C8—371no—
116D4⋊C8—371no—
117C37#147711yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C22×C8—741no—
120C4×Q8—371no—
121C4×Q8C2×D3711yescharacteristic
122C4×D4—371no—
123C4×D4—371no—
124C4×D4—741no—
125C4×D4—741no—
126#117—371no—
127#117—741no—
128C2×C42—371no—
129C2×C42—741no—
130C4⋊C8—371no—
131C4⋊C8—741no—
132C4⋊C8—741no—
133C4⋊C8C2×D3711yescharacteristic
134C22⋊C8—741no—
135C4×C8—371no—
136C4×C8C2×D3711yescharacteristic
137#41—374no—
138#41—742no—
139C2×Q8C4×D3711yescharacteristic
140C2×D4—371no—
141C2×D4—741no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—741no—
146C22×C4—741no—
147C22×C4—741no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—741no—
151C2×C8—741no—
152C2×C8—1482no—
153C4⋊C4—21no—
154C4⋊C4—371no—
155C4⋊C4—741no—
156C4⋊C4C4×D3711yescharacteristic
157C22⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C42—21no—
161C42—371no—
162C42—371no—
163C42—371no—
164C42—741no—
165C42—741no—
166C42C22×D3711yescharacteristic
167C23—371no—
168C23—741no—
169Q8—21no—
170Q8C8×D3712yescomplemented
171D4—372no—
172D4—744no—
173D4—741no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—371no—
177C2×C4—372no—
178C2×C4—372no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—744no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—1481no—
186C2×C4—1482no—
187C2×C4—1481no—
188C2×C4—1481no—
189C2×C4C2×C4×D3711yescharacteristic
190C2×C4D4×D3711yescharacteristic
191C2×C4D4×D3711yescharacteristic
192C8—41no—
193C8—41no—
194C8—1481no—
195C8—1481no—
196C22—372no—
197C22—741no—
198C22—741no—
199C22—742no—
200C22—1481no—
201C22—1481no—
202C22C22⋊C4×D3711yescharacteristic
203C4—22no—
204C4—21no—
205C4—41no—
206C4—372no—
207C4—741no—
208C4—741no—
209C4—1481no—
210C4C2×C8×D3711yescharacteristic
211C4M16×D3711yescharacteristic
212C4#1192456311yescharacteristic
213C4#1192456811yescharacteristic
214C2—742no—
215C2—1482no—
216C2C22⋊C8×D3711yescharacteristic
217C2#1455753311yescharacteristic
218C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC4×C37C22×C8
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596966C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1477
LCSG ▷ 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
2. #14557584C2semidirect
3. C4⋊C8×D37C2semidirect
4. Q8⋊#64436C2semidirect
5. #14557262C2semidirect
6. #14557260C2semidirect
7. C37×Q8⋊C8C2semidirect
29. #10596966C8semidirect
60. Q8×C37C2×C8semidirect
72. D148C2×C8semidirect
114. Q8⋊C8D37semidirect
117. C37#1477semidirect
170. Q8C8×D37semidirect

Maximal subgroups

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

subgroupindex
C4×#105969662
#145575842
C4⋊C8×D372
Q8⋊#644362
#145572622
#145572602
C37×Q8⋊C82
#147737