Finite Group Databasebeta

← C2×#14557871 #18004485

Subgroups — C2×#14557871 #18004485

Order 4736.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924495C211yesmaximal, characteristic
2#14557871C218yesmaximal, direct product factor
3C2×#11924469C211yesmaximal, characteristic, complemented
4C2×#11924467C211yesmaximal, characteristic, complemented
5C2×#11924460C211yesmaximal, characteristic, complemented
6C2×#11924460C211yesmaximal, characteristic, complemented
7C2×C22⋊#64436C211yesmaximal, characteristic
8C2×C22⋊Q8×C37C211yesmaximal, characteristic
9C22×#64436C2211yescharacteristic
10C22×#64436C2211yescharacteristic
11#11924495—22no—
12#11924495C2214yes—
13C2×C4⋊Dic37C2211yescharacteristic
14C2×C4⋊Dic37C2211yescharacteristic
15C2×C22⋊Dic37—21no—
16C2×C4×Dic37—21no—
17#11924469C2214yescomplemented
18#11924467C2214yescomplemented
19#11924460C2214yescomplemented
20#11924460C2214yescomplemented
21C22⋊#64436C2214yes—
22C22×Q8×C37C2211yescharacteristic
23C23×C4×C37C2211yescharacteristic
24C22⋊Q8×C37—22no—
25C22⋊Q8×C37C2214yes—
26C2×C4⋊C4×C37—21no—
27C2×C4⋊C4×C37C2211yescharacteristic
28C2×C22⋊C4×C37—21no—
29C24×C37D411yescharacteristic
30C2×Q8×C37—21no—
31C2×Q8×C37—22no—
32C2×Q8×C37—22no—
33C2×Q8×C37C2312yes—
34C22×C4×C37—22no—
35C22×C4×C37—22no—
36C22×C4×C37—21no—
37C22×C4×C37—21no—
38C22×C4×C37D411yescharacteristic
39C22×C4×C37D412yes—
40C22×C4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C22×Dic37—21no—
43C22×Dic37—21no—
44C4⋊C4×C37—24no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—24no—
48C22⋊Dic37—24no—
49C4⋊Dic37—21no—
50C4⋊Dic37—21no—
51C4⋊Dic37C2312yes—
52C4⋊Dic37C2312yes—
53C4×Dic37—24no—
54C2×#64436—22no—
55C2×#64436—22no—
56C2×#64436C2312yes—
57C2×#64436C2312yes—
58C23×C37—22no—
59C23×C37—22no—
60C23×C37—22no—
61C23×C37C2×D412yes—
62C23×C37C2×D411yescharacteristic
63Q8×C37—22no—
64Q8×C37—22no—
65Q8×C37—42no—
66C2×C4×C37—22no—
67C2×C4×C37—24no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—42no—
73C2×C4×C37—42no—
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37#4112yes—
77C2×C4×C37#4112yes—
78C2×C4×C37C2411yescharacteristic
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—42no—
82C2×Dic37—42no—
83#64436—22no—
84#64436—22no—
85C22×C37—22no—
86C22×C37—22no—
87C22×C37—22no—
88C22×C37—44no—
89C22×C37#12312yes—
90C22×C37#13512yes—
91C22×C37#13712yes—
92C22×C37C22×D411yescharacteristic
93C4×C37—22no—
94C4×C37—42no—
95C4×C37—42no—
96C4×C37#12312yes—
97C4×C37C2×#4111yescharacteristic
98C4×C37C2×#4111yescharacteristic
99Dic37—42no—
100Dic37—42no—
101C2×#485—371nomaximal, Sylow
102C2×C37—42no—
103C2×C37#48514yescomplemented
104C2×C37C2×#12311yescharacteristic
105C2×C37C2×#13511yescharacteristic
106C2×C37C2×#13711yescharacteristic
107C2×C22⋊Q8D3711yescharacteristic
108C2×#117—371no—
109#485—378no—
110C2×#107—371no—
111C2×#106—371no—
112C2×#103—371no—
113C2×#103—371no—
114C2×C22⋊C8—371no—
115C37C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8C2×D3711yescharacteristic
117C23×C4C2×D3711yescharacteristic
118C22×C8—371no—
119C22×C8—371no—
120C22⋊Q8—22no—
121C22⋊Q8C2×D3714yes—
122#117—374no—
123#117—742no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—371no—
126C2×C4⋊C4—371no—
127C2×C4⋊C4C2×D3711yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—741no—
130C2×C42—741no—
131#107—374no—
132#106—374no—
133#103—374no—
134#103—374no—
135C22⋊C8—374no—
136C24C22⋊D3711yescharacteristic
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D3712yes—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—741no—
146C22×C4—741no—
147C22×C4C22⋊D3712yes—
148C22×C4C22⋊D3711yescharacteristic
149C22×C4C22×D3712yes—
150C22×C4C22×D3711yescharacteristic
151C2×C8—372no—
152C2×C8—372no—
153C2×C8—742no—
154C2×C8—742no—
155C4⋊C4—24no—
156C4⋊C4—21no—
157C4⋊C4—372no—
158C4⋊C4—372no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4C22×D3712yes—
162C22⋊C4—24no—
163C22⋊C4—744no—
164C42—744no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D3712yes—
169C23C2×C22⋊D3711yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—742no—
182C2×C4—742no—
183C2×C4—1482no—
184C2×C4—1482no—
185C2×C4#1059696412yes—
186C2×C4#1059696412yes—
187C2×C4C2×C22⋊D3712yes—
188C2×C4C2×C22⋊D3711yescharacteristic
189C2×C4C23×D3711yescharacteristic
190C8—742no—
191C8—742no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1192451712yes—
197C22#1192455612yes—
198C22#1192456712yes—
199C22C22×C22⋊D3711yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—1482no—
204C4—1482no—
205C4#1192451712yes—
206C4C2×#1059696411yescharacteristic
207C4C2×#1059696411yescharacteristic
208C2—42no—
209C2#1455787114yesdirect product factor
210C2C2×#1192451711yescharacteristic
211C2C2×#1192455611yescharacteristic
212C2C2×#1192456711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C22⋊Q8×C37C2
socleC23×C37C2×D4
prime radicalC24×C37D4
hypercenterC2×C22⋊Q8D37
hypocenterC37C2×#485
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14557871C2direct (N × H)
3. C2×#11924469C2semidirect
4. C2×#11924467C2semidirect
5. C2×#11924460C2semidirect
6. C2×#11924460C2semidirect
17. #11924469C22semidirect
18. #11924467C22semidirect
19. #11924460C22semidirect
20. #11924460C22semidirect
103. C2×C37#485semidirect
115. C37C2×#485semidirect
209. C2#14557871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119244952
#145578712
C2×#119244692
C2×#119244672
C2×#119244602
C2×C22⋊#644362
C2×C22⋊Q8×C372
C2×#48537