Finite Group Databasebeta

← #18010360

Subgroups — #18010360

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×#11924601C212yesmaximal
2C4×#10596953C211yesmaximal, characteristic, complemented
3#14558469C211yesmaximal, characteristic, complemented
4#14558403C212yesmaximal, complemented
5C4×#10596966C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C4×#3866C2212yes—
8#11924601C418yescomplemented
9#11924591—21no—
10C4×#64438—21no—
11(C2×#3866)⋊C4—21no—
12(C2×#3866)⋊C4—21no—
13C2×#10596966C2211yescharacteristic
14Q8×Dic37C411yescharacteristic, complemented
15C4×D148—21no—
16C4×D148C411yescharacteristic, complemented
17#11924498—21no—
18#11924498C411yescharacteristic, complemented
19#11924494—21no—
20#11924494C2211yescharacteristic
21C42×D37—21no—
22C42×D37C2211yescharacteristic
23C4×Q8×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26#10596966—22no—
27#10596966C2×C414yes—
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37C2311yescharacteristic
36C2×#64438—22no—
37C4×#3866—22no—
38C4×#3866C2×C414yescomplemented
39#10596953—22no—
40#10596953C2×C414yescomplemented
41C4⋊C4×C37—21no—
42C4⋊C4×C37C2×C411yescharacteristic
43C42×C37—21no—
44C42×C37C2×C411yescharacteristic
45#10596938—21no—
46#10596938—21no—
47#10596938—21no—
48C4⋊Dic37—21no—
49C4⋊Dic37C2×C411yescharacteristic
50C4×Dic37—21no—
51C4×Dic37—21no—
52C4×Dic37C2×C411yescharacteristic
53C4×Dic37D411yescharacteristic
54C4×Dic37D411yescharacteristic
55C22×D37—21no—
56C22×D37C2×D411yescharacteristic
57C2×#3866—24no—
58C2×#3866—42no—
59C2×#3866—42no—
60Q8×C37—21no—
61Q8×C37C4212yes—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22×C411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71D148—24no—
72D148—21no—
73D148C4212yes—
74C4×D37—24no—
75C4×D37—41no—
76C4×D37—41no—
77C4×D37—42no—
78C4×D37—42no—
79C4×D37C22×C412yes—
80C4×D37#4112yes—
81#64438—24no—
82C22×C37C2×C22⋊C411yescharacteristic
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—22no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37C4×D412yes—
89#3866—44no—
90C4×C37—22no—
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—41no—
94C4×C37C2×C4211yescharacteristic
95C4×C37#11711yescharacteristic
96Dic37—21no—
97Dic37—21no—
98Dic37—41no—
99Dic37C4×D412yes—
100#1759—371nomaximal, Sylow
101C2×C37C4×C22⋊C411yescharacteristic
102C2×C37#42111yescharacteristic
103C2×C37#42111yescharacteristic
104D37—22no—
105D37—42no—
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#386611yescharacteristic, complemented
116C4×D4—371no—
117C4×D4—371no—
118C4×D4—741no—
119C4×D4—741no—
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×Q8C2×#386611yescharacteristic
133C2×D4—371no—
134C2×D4—741no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C22×C4—741no—
140C22×C4—742no—
141C22×C4—741no—
142M16—374no—
143M16—742no—
144C2×C8—742no—
145C4⋊C4—21no—
146C4⋊C4—371no—
147C4⋊C4—741no—
148C4⋊C4C2×#386611yescharacteristic
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—21no—
153C42—371no—
154C42—371no—
155C42—371no—
156C42—374no—
157C42—741no—
158C42—741no—
159C42—742no—
160C42C2×#386611yescharacteristic
161C23—371no—
162C23—741no—
163Q8—21no—
164Q8C4×#386612yes—
165D4—372no—
166D4—744no—
167D4—741no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—371no—
171C2×C4—372no—
172C2×C4—372no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—744no—
176C2×C4—744no—
177C2×C4—741no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1482no—
181C2×C4—1482no—
182C2×C4—1482no—
183C2×C4—1482no—
184C2×C4C22⋊#386611yescharacteristic
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22×#386611yescharacteristic
187C8—744no—
188C22—372no—
189C22—741no—
190C22—741no—
191C22—742no—
192C22—1481no—
193C22—1481no—
194C22C2×C22⋊#386611yescharacteristic
195C4—22no—
196C4—21no—
197C4—21no—
198C4—41no—
199C4—372no—
200C4—741no—
201C4—741no—
202C4—1484no—
203C4—1481no—
204C4C2×C4×#386611yescharacteristic
205C4#1192461511yescharacteristic
206C2—742no—
207C2—1482no—
208C2C4×C22⋊#386611yescharacteristic
209C2#1455853011yescharacteristic
210C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596966C22
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1759
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#10596953C2semidirect
3. #14558469C2semidirect
4. #14558403C2semidirect
8. #11924601C4semidirect
14. Q8×Dic37C4semidirect
16. C4×D148C4semidirect
18. #11924498C4semidirect
23. C4×Q8×C37C4semidirect
38. C4×#3866C2×C4semidirect
40. #10596953C2×C4semidirect
111. C37#1759semidirect
115. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246012
C4×#105969532
#145584692
#145584032
C4×#105969662
#175937