Finite Group Databasebeta

← #18010359

Subgroups — #18010359

Order 4736.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#11924600C212yesmaximal
2C4×#10596953C211yesmaximal, characteristic, complemented
3#14558469C211yesmaximal, characteristic, complemented
4#14558403C212yesmaximal, complemented
5C4×#10596964C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C4×#3866C2212yes—
8#11924600C418yescomplemented
9#11924591—21no—
10C4×#64438—21no—
11(C2×#3866)⋊C4—21no—
12(C2×#3866)⋊C4—21no—
13C2×#10596964C2211yescharacteristic
14C4×Dic74C411yescharacteristic, complemented
15#11924501C411yescharacteristic, complemented
16D4×Dic37C411yescharacteristic, complemented
17C4×C22⋊D37—21no—
18#11924496—21no—
19#11924494C2211yescharacteristic
20#11924492—21no—
21C2×C4×Dic37—21no—
22C42×D37C2211yescharacteristic
23C4×D4×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×D4×C37C2×C411yescharacteristic
26C22×C4×C37—21no—
27C2×C22⋊D37—21no—
28C22×Dic37—21no—
29C22×Dic37—21no—
30#10596964—22no—
31#10596964C2×C414yes—
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37C2311yescharacteristic
35C2×Dic74C2×C411yescharacteristic
36C2×#64438—22no—
37C4×#3866—22no—
38C4×#3866C2×C414yescomplemented
39#10596953—22no—
40#10596953C2×C414yescomplemented
41C4⋊C4×C37C2×C411yescharacteristic
42C22⋊C4×C37—21no—
43C42×C37C2×C411yescharacteristic
44C22⋊Dic37—21no—
45#10596938—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C4×Dic37C2×C411yescharacteristic
53C4×Dic37D411yescharacteristic
54C4×Dic37D411yescharacteristic
55C23×C37—21no—
56C22×D37C2×D411yescharacteristic
57C2×#3866—24no—
58C2×#3866—42no—
59C2×#3866—42no—
60D4×C37—21no—
61D4×C37C4212yes—
62C2×C4×C37—21no—
63C2×C4×C37—42no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22×C411yescharacteristic
67C22⋊D37—24no—
68C2×Dic37—21no—
69C2×Dic37—24no—
70C2×Dic37—21no—
71C2×Dic37—42no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C2×D411yescharacteristic
75C4×D37—41no—
76C4×D37—41no—
77C4×D37C22×C412yes—
78C4×D37#4112yes—
79Dic74—21no—
80Dic74C4212yes—
81#64438—24no—
82C22×C37—22no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37C4×D412yes—
89#3866—44no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—41no—
93C4×C37C2×C4211yescharacteristic
94C4×C37#11711yescharacteristic
95Dic37—22no—
96Dic37—21no—
97Dic37—21no—
98Dic37—41no—
99Dic37C4×D412yes—
100#1759—371nomaximal, Sylow
101C2×C37—42no—
102C2×C37C4×C22⋊C411yescharacteristic
103C2×C37#42111yescharacteristic
104C2×C37#42111yescharacteristic
105D37—22no—
106C4×#41—371no—
107C2×#104—372no—
108C4×M16—371no—
109#376—371no—
110#339—372no—
111C37#175911yescharacteristic, complemented, Sylow
112C2×#41—371no—
113C2×M16—372no—
114C4×Q8—371no—
115C4×Q8—371no—
116C4×D4—371no—
117C4×D4—741no—
118C4×D4—741no—
119C4×D4#386611yescharacteristic, complemented
120#117—371no—
121#117—741no—
122C2×C42—371no—
123C2×C42—372no—
124C2×C42—741no—
125#104—378no—
126#97—741no—
127C4×C8—741no—
128#95—741no—
129#95—741no—
130#41—374no—
131#41—742no—
132C2×Q8—371no—
133C2×D4—741no—
134C2×D4C2×#386611yescharacteristic
135C22×C4—21no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—741no—
140C22×C4—741no—
141C22×C4—742no—
142M16—374no—
143M16—742no—
144C2×C8—742no—
145C4⋊C4—371no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4C2×#386611yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—371no—
153C42—371no—
154C42—371no—
155C42—374no—
156C42—741no—
157C42—741no—
158C42—742no—
159C42—741no—
160C42C2×#386611yescharacteristic
161C23—21no—
162C23—371no—
163Q8—372no—
164Q8—741no—
165D4—21no—
166D4—744no—
167D4C4×#386612yes—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—371no—
171C2×C4—372no—
172C2×C4—372no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—744no—
176C2×C4—741no—
177C2×C4—744no—
178C2×C4—741no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1482no—
182C2×C4—1482no—
183C2×C4—1482no—
184C2×C4C22⋊#386611yescharacteristic
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22×#386611yescharacteristic
187C8—744no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22—372no—
192C22—741no—
193C22—741no—
194C22C2×C22⋊#386611yescharacteristic
195C4—21no—
196C4—21no—
197C4—41no—
198C4—372no—
199C4—742no—
200C4—741no—
201C4—741no—
202C4—1484no—
203C4—1481no—
204C4C2×C4×#386611yescharacteristic
205C4#1192461511yescharacteristic
206C2—42no—
207C2—742no—
208C2C4×C22⋊#386611yescharacteristic
209C2#1455853011yescharacteristic
210C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596964C22
cosocleC2×C4×D37C23
hypercenterC4×D4#3866
hypocenterC37#1759
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#10596953C2semidirect
3. #14558469C2semidirect
4. #14558403C2semidirect
8. #11924600C4semidirect
14. C4×Dic74C4semidirect
15. #11924501C4semidirect
16. D4×Dic37C4semidirect
23. C4×D4×C37C4semidirect
38. C4×#3866C2×C4semidirect
40. #10596953C2×C4semidirect
111. C37#1759semidirect
119. C4×D4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246002
C4×#105969532
#145584692
#145584032
C4×#105969642
#175937