Finite Group Databasebeta

← C4×#11924599 #18010364

Subgroups — C4×#11924599 #18010364

Order 4736.

332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 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×#11924599C212yesmaximal
2C4×D37⋊C8C211yesmaximal, characteristic
3C4×C4⋊#3866C211yesmaximal, characteristic
4#14558406C212yesmaximal
5C4×Q8×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866C2212yes—
8C2×C4×#3866—21no—
9#11924599C418yesdirect product factor
10C4×#64438—21no—
11C4×#64438—21no—
12(C2×#3866)⋊C4—21no—
13C2×Q8×D37C2211yescharacteristic
14Q8×Dic37C411yescharacteristic, complemented
15C4×Dic74—21no—
16C4×Dic74C411yescharacteristic, complemented
17#11924501—21no—
18#11924501C411yescharacteristic, complemented
19C4⋊C4×D37—21no—
20C4⋊C4×D37C2211yescharacteristic
21C42×D37—21no—
22C42×D37C2211yescharacteristic
23C4×Q8×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26Q8×D37—22no—
27Q8×D37C2×C414yes—
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37D411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37C2311yescharacteristic
33C2×Dic74—21no—
34C2×Dic74C2×C411yescharacteristic
35C2×#64438—22no—
36C4⋊#3866—22no—
37C4⋊#3866C2×C414yes—
38C4×#3866—42no—
39D37⋊C8—22no—
40D37⋊C8C2×C414yes—
41C4⋊C4×C37—21no—
42C4⋊C4×C37C2×C411yescharacteristic
43C42×C37—21no—
44C42×C37C2×C411yescharacteristic
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37C2×C411yescharacteristic
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C22×D37C2×D411yescharacteristic
57C2×#3866—24no—
58C2×#3866—42no—
59C2×#3866—42no—
60Q8×C37—21no—
61Q8×C37C4212yescomplemented
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22×C411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C2×D411yescharacteristic
72C4×D37—24no—
73C4×D37—22no—
74C4×D37—42no—
75C4×D37SD1612yes—
76C4×D37Q1612yes—
77C4×D37C22×C412yes—
78C4×D37#4112yes—
79Dic74—21no—
80Dic74—24no—
81Dic74C4212yescomplemented
82#64438—24no—
83C22×C37C2×C22⋊C411yescharacteristic
84C2×D37C4×D412yes—
85C2×D37C2×SD1611yescharacteristic
86C2×D37C2×Q1611yescharacteristic
87C2×D37#13512yes—
88#3866—44no—
89C4×C37—22no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37#10312yescomplemented
93C4×C37C2×C4211yescharacteristic
94C4×C37#11711yescharacteristic
95Dic37—22no—
96Dic37—21no—
97Dic37—41no—
98Dic37#10312yescomplemented
99Dic37C4×D412yes—
100C4×#103—371nomaximal, Sylow
101C2×C37C4×C22⋊C411yescharacteristic
102C2×C37C2×#10311yescharacteristic
103C2×C37#41611yescharacteristic
104D37C4×SD1612yes—
105D37C4×Q1612yes—
106C2×C4×Q8—371no—
107C2×#103—372no—
108C2×C4×C8—371no—
109C4×C4⋊C4—371no—
110#340—372no—
111C37C4×#10311yescharacteristic, complemented, Sylow
112C22×Q8—371no—
113C22×C8—372no—
114C4×Q8—371no—
115C4×Q8—371no—
116C4×Q8—371no—
117C4×Q8—741no—
118C4×Q8—741no—
119C4×Q8#386611yescharacteristic, complemented
120C2×C4⋊C4—372no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C42—371no—
124C2×C42—741no—
125C2×C42—741no—
126#103—378no—
127C4×C8—741no—
128C4×C8—741no—
129#95—741no—
130C2×Q8—374no—
131C2×Q8—371no—
132C2×Q8—741no—
133C2×Q8—742no—
134C2×Q8C2×#386611yescharacteristic
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C22×C4—741no—
140C22×C4—742no—
141C2×C8—374no—
142C2×C8—742no—
143C2×C8—742no—
144C4⋊C4—21no—
145C4⋊C4—374no—
146C4⋊C4—371no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—742no—
151C4⋊C4—741no—
152C4⋊C4C2×#386611yescharacteristic
153C42—21no—
154C42—371no—
155C42—371no—
156C42—371no—
157C42—741no—
158C42—741no—
159C42—741no—
160C42—1482no—
161C42C2×#386611yescharacteristic
162C23—371no—
163Q8—21no—
164Q8—372no—
165Q8—744no—
166Q8—741no—
167Q8C4×#386612yescomplemented
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—372no—
173C2×C4—372no—
174C2×C4—372no—
175C2×C4—372no—
176C2×C4—371no—
177C2×C4—742no—
178C2×C4—744no—
179C2×C4—741no—
180C2×C4—744no—
181C2×C4—741no—
182C2×C4—1482no—
183C2×C4—1482no—
184C2×C4—1482no—
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22⋊#386611yescharacteristic
187C2×C4C22×#386611yescharacteristic
188C8—744no—
189C22—372no—
190C22—371no—
191C22—371no—
192C22—372no—
193C22C2×C22⋊#386611yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—372no—
198C4—372no—
199C4—742no—
200C4—741no—
201C4—1484no—
202C4—1481no—
203C4#1192459912yesdirect product factor
204C4C2×C4×#386611yescharacteristic
205C4#1192461511yescharacteristic
206C2—372no—
207C2—372no—
208C2C4×C22⋊#386611yescharacteristic
209C2C2×#1192459911yescharacteristic
210C2#1455852311yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37C4×#103
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. #11924599C4direct (N × H)
14. Q8×Dic37C4semidirect
16. C4×Dic74C4semidirect
18. #11924501C4semidirect
23. C4×Q8×C37C4semidirect
61. Q8×C37C42semidirect
81. Dic74C42semidirect
92. C4×C37#103semidirect
98. Dic37#103semidirect
111. C37C4×#103semidirect
119. C4×Q8#3866semidirect
167. Q8C4×#3866semidirect
203. C4#11924599direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245992
C4×D37⋊C82
C4×C4⋊#38662
#145584062
C4×Q8×D372
C4×#10337