Finite Group Databasebeta

← #17992985

Subgroups — #17992985

Order 4736.

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

normal subgroups only

This group has 312 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×D4×D37C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic, complemented
3#14557584C211yesmaximal, characteristic, complemented
4#14557262C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D37C411yescharacteristic
9C22×C4×D37—21no—
10C4×D148C2211yescharacteristic
11D4×Dic37C411yescharacteristic
12#11924498C411yescharacteristic
13C4×C22⋊D37—21no—
14#11924496—21no—
15C4⋊C4×D37C411yescharacteristic
16C22⋊C4×D37—21no—
17C42×D37C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic, complemented
19#11924465—21no—
20#11924448—21no—
21#11924448—21no—
22C4×#64436C2211yescharacteristic, complemented
23C8×Dic37—21no—
24C4×D4×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic, complemented
26C4×C8×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32D4×D37—22no—
33D4×D37C814yescomplemented
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—42no—
39C2×C4×D37—42no—
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C8×C37—21no—
44C2×C8×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C22⋊C4×C37—21no—
47C42×C37C2311yescharacteristic
48C22⋊Dic37—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37C2×C411yescharacteristic
52#10596936—21no—
53C4×Dic37C2×C411yescharacteristic
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C2×#64436—21no—
57C2×#64436—21no—
58C23×C37—21no—
59C22×D37—21no—
60C22×D37—24no—
61C22×D37—42no—
62C22×D37—42no—
63C22×D37C22⋊C411yescharacteristic
64D4×C37—21no—
65D4×C37C2×C812yes—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C22⋊D37—24no—
73C2×Dic37—21no—
74C2×Dic37—42no—
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C22⋊C411yescharacteristic
78D148—21no—
79D148C2×C812yes—
80C4×D37—21no—
81C4×D37—21no—
82C4×D37—41no—
83C4×D37—42no—
84C4×D37—42no—
85C4×D37—41no—
86C4×D37—41no—
87C4×D37C2×C812yes—
88C4×D37M1612yes—
89C8×C37—41no—
90C8×C37—41no—
91#64436—41no—
92#64436—41no—
93C22×C37—22no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37C2×C22⋊C411yescharacteristic
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—22no—
100C2×D37—48no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37C22⋊C812yes—
104C4×C37—21no—
105C4×C37—41no—
106C4×C37C22×C811yescharacteristic
107C4×C37C2×M1611yescharacteristic
108C4×C37AGL(1,ℤ/8)11yescharacteristic
109C4×C37AGL(1,ℤ/8)11yescharacteristic
110Dic37—21no—
111Dic37—21no—
112Dic37—41no—
113Dic37C22⋊C812yes—
114#1478—371nomaximal, Sylow
115C2×C37—42no—
116C2×C37C2×C22⋊C811yescharacteristic
117C2×C37#41811yescharacteristic
118C2×C37#42111yescharacteristic
119D37—22no—
120D37—42no—
121C2×C4×D4—371no—
122#431—371no—
123#431—371no—
124D4⋊C8—371no—
125D4⋊C8—371no—
126D4⋊C8—371no—
127D4⋊C8D3711yescharacteristic, complemented
128C37#147811yescharacteristic, complemented, Sylow
129C22×D4—371no—
130C23×C4—741no—
131C4×D4—371no—
132C4×D4—371no—
133C4×D4—371no—
134C4×D4—741no—
135C4×D4—741no—
136C4×D4C2×D3711yescharacteristic
137C2×C4⋊C4—371no—
138C2×C22⋊C4—741no—
139C2×C42—371no—
140C4⋊C8—371no—
141C4⋊C8—741no—
142C4⋊C8C2×D3711yescharacteristic, complemented
143C22⋊C8—741no—
144C22⋊C8—741no—
145C4×C8—371no—
146C4×C8—741no—
147C4×C8C2×D3711yescharacteristic, complemented
148C24—741no—
149C2×D4—374no—
150C2×D4—371no—
151C2×D4—742no—
152C2×D4—741no—
153C2×D4C4×D3711yescharacteristic
154C22×C4—21no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—741no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4—741no—
162C22×C4—1482no—
163C22×C4—1482no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—741no—
167C2×C8—741no—
168C4⋊C4—371no—
169C4⋊C4—741no—
170C4⋊C4C4×D3711yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—741no—
173C22⋊C4—741no—
174C22⋊C4—741no—
175C42—371no—
176C42—371no—
177C42—371no—
178C42C22×D3711yescharacteristic
179C23—21no—
180C23—371no—
181C23—744no—
182C23—741no—
183C23—1482no—
184C23—1482no—
185D4—21no—
186D4—372no—
187D4—744no—
188D4—741no—
189D4C8×D3712yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—371no—
194C2×C4—372no—
195C2×C4—372no—
196C2×C4—371no—
197C2×C4—371no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—741no—
201C2×C4—1481no—
202C2×C4—1482no—
203C2×C4—1482no—
204C2×C4—1482no—
205C2×C4—1481no—
206C2×C4—1481no—
207C2×C4C2×C4×D3711yescharacteristic
208C2×C4D4×D3711yescharacteristic
209C2×C4D4×D3711yescharacteristic
210C8—41no—
211C8—41no—
212C8—1481no—
213C8—1481no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—372no—
218C22—741no—
219C22—741no—
220C22—742no—
221C22—1488no—
222C22—1481no—
223C22—1481no—
224C22C22⋊C4×D3711yescharacteristic
225C4—21no—
226C4—41no—
227C4—372no—
228C4—741no—
229C4—741no—
230C4—1481no—
231C4C2×C8×D3711yescharacteristic
232C4M16×D3711yescharacteristic
233C4#1192456011yescharacteristic
234C4#1192456311yescharacteristic
235C2—42no—
236C2—742no—
237C2—1482no—
238C2C22⋊C8×D3711yescharacteristic
239C2#1455753611yescharacteristic
240C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC4×C37C22×C8
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC42×C37C23
hypercenterD4⋊C8D37
hypocenterC37#1478
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557585C2semidirect
3. #14557584C2semidirect
4. #14557262C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×D4⋊C8C2semidirect
18. C4⋊#64436C22semidirect
22. C4×#64436C22semidirect
25. C4⋊C8×C37C22semidirect
26. C4×C8×C37C22semidirect
33. D4×D37C8semidirect
127. D4⋊C8D37semidirect
128. C37#1478semidirect
142. C4⋊C8C2×D37semidirect
147. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D372
#145575852
#145575842
#145572622
D4⋊#644362
#145572602
C37×D4⋊C82
#147837