Finite Group Databasebeta

← #18004393

Subgroups — #18004393

Order 4736.

440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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#14558090C211yesmaximal, characteristic, complemented
2#14557833C214yesmaximal, complemented
3#14557823C212yesmaximal, complemented
4#14557813C212yesmaximal, complemented
5#14557573C212yesmaximal, complemented
6#14557557C211yesmaximal, characteristic, complemented
7#14557538C212yesmaximal
8C2×C4×D4×C37C211yesmaximal, characteristic
9C2×#10596934C2212yes—
10#11924536C2211yescharacteristic, complemented
11#11924536C2211yescharacteristic, complemented
12#11924528C2212yescomplemented
13#11924515—21no—
14#11924515—21no—
15C4×Dic74—21no—
16C4×Dic74—21no—
17#11924495C2212yes—
18#11924469C2214yescomplemented
19#11924467C2214yescomplemented
20C4⋊#64436C2212yescomplemented
21C4⋊#64436C2212yescomplemented
22#11924457C2214yes—
23#11924457C2214yes—
24C22×D4×C37C2211yescharacteristic
25C23×C4×C37—21no—
26C4×D4×C37—21no—
27C4×D4×C37—21no—
28C4×D4×C37C2212yes—
29C4×D4×C37C2212yes—
30C2×C4⋊C4×C37C2211yescharacteristic
31C2×C22⋊C4×C37—21no—
32C2×C42×C37C2211yescharacteristic
33C24×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—22no—
36C2×D4×C37Q814yescomplemented
37C2×D4×C37C2312yes—
38C22×C4×C37—21no—
39C22×C4×C37—22no—
40C22×C4×C37—22no—
41C22×C4×C37—44no—
42C22×C4×C37D411yescharacteristic
43C22×C4×C37D411yescharacteristic
44C22×C4×C37C2311yescharacteristic
45C2×Dic74—21no—
46C2×Dic74—21no—
47C4⋊C4×C37—21no—
48C4⋊C4×C37C2312yes—
49C22⋊C4×C37—22no—
50C22⋊C4×C37—22no—
51C42×C37D411yescharacteristic
52C42×C37D411yescharacteristic
53C42×C37C2311yescharacteristic
54C42×C37C2311yescharacteristic
55C22⋊Dic37—22no—
56C4⋊Dic37—21no—
57C4⋊Dic37—21no—
58C4⋊Dic37C2312yes—
59C4⋊Dic37C2312yes—
60#10596936—22no—
61#10596936—22no—
62C4×Dic37—22no—
63#10596934—24no—
64C2×#64436C2314yes—
65C23×C37—24no—
66C23×C37—22no—
67C23×C37—42no—
68C23×C37—42no—
69C23×C37C2×D411yescharacteristic
70D4×C37—24no—
71D4×C37—22no—
72D4×C37C2×Q814yes—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—41no—
76C2×C4×C37—44no—
77C2×C4×C37—42no—
78C2×C4×C37—44no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×Q812yes—
85C2×C4×C37#4112yes—
86C2×C4×C37C2411yescharacteristic
87C2×Dic37—22no—
88C2×Dic37—22no—
89Dic74—42no—
90Dic74—42no—
91#64436—24no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—24no—
95C22×C37—48no—
96C22×C37—42no—
97C22×C37—42no—
98C22×C37C22⋊Q812yes—
99C22×C37C22×D411yescharacteristic
100C4×C37—21no—
101C4×C37—21no—
102C4×C37—21no—
103C4×C37—42no—
104C4×C37C22⋊Q812yes—
105C4×C37AGL(1,ℤ/8)12yes—
106C4×C37C22×Q811yescharacteristic
107C4×C37C2×#4111yescharacteristic
108Dic37—42no—
109Dic37—42no—
110#3077—371nomaximal, Sylow
111C2×C37—22no—
112C2×C37—44no—
113C2×C37C2×C22⋊Q811yescharacteristic
114C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C37#57511yescharacteristic
116#533—371no—
117C2×C4×D4D3711yescharacteristic
118#478—374no—
119#476—372no—
120#474—372no—
121#428—372no—
122#423—371no—
123#418—372no—
124C37#307711yescharacteristic, complemented, Sylow
125C22×D4C2×D3711yescharacteristic
126C23×C4—21no—
127C2×M16—372no—
128C4⋊Q8—371no—
129C4⋊Q8—371no—
130#125—372no—
131C22⋊Q8—741no—
132C22⋊Q8—741no—
133C4×Q8—741no—
134C4×Q8—741no—
135C4×D4—21no—
136C4×D4—21no—
137C4×D4C2×D3712yes—
138C4×D4C2×D3712yes—
139#117—372no—
140C2×C4⋊C4C2×D3711yescharacteristic
141C2×C22⋊C4—21no—
142C2×C42C2×D3711yescharacteristic
143#107—374no—
144#106—374no—
145C4⋊C8—372no—
146C4⋊C8—372no—
147#102—374no—
148#102—374no—
149C24—21no—
150C2×Q8—741no—
151C2×Q8—741no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4Dic7414yescomplemented
155C2×D4C22×D3712yes—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—44no—
160C22×C4C22⋊D3711yescharacteristic
161C22×C4C22⋊D3711yescharacteristic
162C22×C4C22×D3711yescharacteristic
163M16—744no—
164C2×C8—374no—
165C4⋊C4—21no—
166C4⋊C4—372no—
167C4⋊C4—372no—
168C4⋊C4—742no—
169C4⋊C4—742no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C4⋊C4C22×D3712yes—
173C22⋊C4—22no—
174C22⋊C4—22no—
175C22⋊C4—742no—
176C42—742no—
177C42C22⋊D3711yescharacteristic
178C42C22⋊D3711yescharacteristic
179C42C22×D3711yescharacteristic
180C42C22×D3711yescharacteristic
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23C2×C22⋊D3711yescharacteristic
186Q8—1482no—
187Q8—1482no—
188D4—24no—
189D4—22no—
190D4C2×Dic7414yes—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4C2×Dic7412yes—
200C2×C4#1059696212yes—
201C2×C4C2×C22⋊D3711yescharacteristic
202C2×C4C2×C22⋊D3711yescharacteristic
203C2×C4C2×C22⋊D3711yescharacteristic
204C2×C4C2×C22⋊D3711yescharacteristic
205C2×C4C2×C22⋊D3711yescharacteristic
206C2×C4C23×D3711yescharacteristic
207C8—744no—
208C22—21no—
209C22—21no—
210C22—24no—
211C22—48no—
212C22—42no—
213C22—42no—
214C22#1192451512yes—
215C22C22×C22⋊D3711yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—1482no—
221C4—1482no—
222C4#1192451512yes—
223C4#1192456212yes—
224C4C22×Dic7411yescharacteristic
225C4C2×#1059696211yescharacteristic
226C2—22no—
227C2—44no—
228C2C2×#1192451511yescharacteristic
229C2C2×#1192456211yescharacteristic
230C2#1455833111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C4×D4×C37C2
socleC22×C37C22×D4
prime radicalC22×D4×C37C22
hypercenterC2×C4×D4D37
hypocenterC37#3077
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558090C2semidirect
2. #14557833C2semidirect
3. #14557823C2semidirect
4. #14557813C2semidirect
5. #14557573C2semidirect
6. #14557557C2semidirect
10. #11924536C22semidirect
11. #11924536C22semidirect
12. #11924528C22semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. C4⋊#64436C22semidirect
21. C4⋊#64436C22semidirect
36. C2×D4×C37Q8semidirect
124. C37#3077semidirect
154. C2×D4Dic74semidirect

Maximal subgroups

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

subgroupindex
#145580902
#145578332
#145578232
#145578132
#145575732
#145575572
#145575382
C2×C4×D4×C372
#307737