Finite Group Databasebeta

← C2×#14558202 #18008074

Subgroups — C2×#14558202 #18008074

Order 4736.

1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 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
1C22×#10596966C211yesmaximal, characteristic, complemented
2#14558202C2116yesmaximal, direct product factor
3C2×#11924532C213yesmaximal, complemented
4C2×#11924510C213yesmaximal, complemented
5C2×#11924507C213yesmaximal, complemented
6C2×Q8×Dic37C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D37C213yesmaximal, complemented
8C22×#41×C37C211yesmaximal, characteristic, complemented
9C2×#10596966—28no—
10C2×#10596966C2218yescomplemented
11C22×D148C2213yes—
12C22×C22⋊D37C2213yes—
13C22×C22⋊D37C2216yes—
14C22×C4×D37C2213yes—
15#11924532C22124yescomplemented
16#11924510C22124yescomplemented
17#11924507C22124yescomplemented
18Q8×Dic37C2218yescomplemented
19C4×C22⋊D37C22124yescomplemented
20C2×C4⋊Dic37C2213yes—
21C2×#10596936C2211yescharacteristic
22C2×C22⋊Dic37C2213yes—
23C2×#10596938C2213yes—
24C2×C4×Dic37C2213yes—
25C2×#41×C37—28no—
26C2×#41×C37C2218yescomplemented
27C22×Q8×C37C2211yescharacteristic
28C22×D4×C37C2213yes—
29C23×C4×C37C2213yes—
30C24×C37C2313yes—
31C23×D37C2313yes—
32#41×C37—232no—
33C2×Q8×C37D418yescomplemented
34C2×Q8×C37C2314yes—
35C2×D4×C37—212no—
36C2×D4×C37C23112yes—
37C22×C4×C37—212no—
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C23112yes—
40C22×C4×C37C2313yes—
41C2×C22⋊D37—212no—
42C2×C22⋊D37—412no—
43C2×C22⋊D37C23112yes—
44C2×C22⋊D37C23124yes—
45C22×Dic37C2313yes—
46C22×Dic37C2311yescharacteristic
47C22×Dic37C2311yescharacteristic
48#10596966—232no—
49C2×D148—212no—
50C2×D148C23112yes—
51C2×C4×D37—212no—
52C2×C4×D37C23112yes—
53C22⋊Dic37C23112yes—
54#10596938C23112yes—
55C4⋊Dic37C23112yes—
56#10596936C2314yes—
57C4×Dic37C23112yes—
58C23×C37—26no—
59C23×C37—26no—
60C23×C37—26no—
61C23×C37C2416yes—
62C23×C37C2411yescharacteristic
63C22×D37—26no—
64C22×D37—26no—
65C22×D37—26no—
66C22×D37C2416yes—
67Q8×C37C2×D4116yescomplemented
68D4×C37—224no—
69C2×C4×C37—22no—
70C2×C4×C37—224no—
71C2×C4×C37C2×D4112yes—
72C2×C4×C37C2412yes—
73C2×C4×C37C2416yes—
74C22⋊D37—224no—
75C22⋊D37—424no—
76C2×Dic37—22no—
77C2×Dic37—26no—
78C2×Dic37#4114yescomplemented
79C2×Dic37C2416yes—
80C2×Dic37C2412yes—
81C2×Dic37C2412yes—
82D148—224no—
83C4×D37—224no—
84C22×C37—26no—
85C22×C37—26no—
86C22×C37—26no—
87C22×C37—412no—
88C22×C37C22×D412yes—
89C22×C37C2×#4112yes—
90C22×C37H(5,𝔽2)12yes—
91C22×C37C2511yescharacteristic
92C2×D37—26no—
93C2×D37—26no—
94C2×D37—26no—
95C2×D37—412no—
96C4×C37—22no—
97C4×C37C22×D4112yes—
98Dic37—22no—
99Dic37—26no—
100Dic37C2×#4114yescomplemented
101C2×#550—371nomaximal, Sylow
102C2×C37—46no—
103C2×C37#55014yescomplemented
104C2×C37C23×D411yescharacteristic
105C2×C37C22×#4111yescharacteristic
106C2×C37C2×H(5,𝔽2)11yescharacteristic
107D37—46no—
108C22×#41—371no—
109C22×#41D3711yescharacteristic, complemented
110#550—3716no—
111C2×#127—373no—
112C2×#121—373no—
113C2×#121—373no—
114C2×C4×Q8—371no—
115C2×C4×D4—373no—
116C37C2×#55011yescharacteristic, complemented, Sylow
117C2×#41—28no—
118C2×#41—378no—
119C2×#41—748no—
120C2×#41C2×D3718yescomplemented
121C22×Q8C2×D3711yescharacteristic
122C22×D4—373no—
123C22×D4—376no—
124C22×D4—373no—
125C22×D4C2×D3713yes—
126C23×C4—373no—
127C23×C4C2×D3713yes—
128#127—3724no—
129#121—3724no—
130#121—3724no—
131C4×Q8—378no—
132C4×D4—3724no—
133C2×C4⋊C4—371no—
134C2×C4⋊C4—373no—
135C2×C22⋊C4—373no—
136C2×C22⋊C4—373no—
137C2×C42—373no—
138C24—373no—
139C24C22×D3713yes—
140#41—232no—
141#41—7432no—
142C2×Q8C22⋊D3718yescomplemented
143C2×Q8C22×D3714yes—
144C2×D4—212no—
145C2×D4—3712no—
146C2×D4—3724no—
147C2×D4—3712no—
148C2×D4—7412no—
149C2×D4—7412no—
150C2×D4—14812no—
151C2×D4C22×D37112yes—
152C22×C4—212no—
153C22×C4—371no—
154C22×C4—373no—
155C22×C4—371no—
156C22×C4—3712no—
157C22×C4—7412no—
158C22×C4C22×D37112yes—
159C22×C4C22×D3711yescharacteristic
160C22×C4C22×D3713yes—
161C4⋊C4—374no—
162C4⋊C4—3712no—
163C22⋊C4—3712no—
164C22⋊C4—3712no—
165C42—3712no—
166C23—26no—
167C23—26no—
168C23—26no—
169C23—376no—
170C23—746no—
171C23—746no—
172C23—746no—
173C23C23×D3716yes—
174C23C23×D3711yescharacteristic
175Q8C2×C22⋊D37116yescomplemented
176D4—224no—
177D4—7424no—
178D4—7424no—
179D4—14824no—
180C2×C4—22no—
181C2×C4—224no—
182C2×C4—374no—
183C2×C4—372no—
184C2×C4—376no—
185C2×C4—372no—
186C2×C4—742no—
187C2×C4—746no—
188C2×C4—7424no—
189C2×C4C2×C22⋊D37112yes—
190C2×C4C23×D3712yes—
191C2×C4C23×D3716yes—
192C22—26no—
193C22—26no—
194C22—26no—
195C22—412no—
196C22—746no—
197C22—746no—
198C22—746no—
199C22—14812no—
200C22C22×C22⋊D3712yes—
201C22#41×D3712yes—
202C22#1192458212yes—
203C22C24×D3711yescharacteristic
204C4—22no—
205C4—374no—
206C4—742no—
207C4—746no—
208C4C22×C22⋊D37112yes—
209C2—46no—
210C2—1486no—
211C2#1455820214yesdirect product factor
212C2C23×C22⋊D3711yescharacteristic
213C2C2×#41×D3711yescharacteristic
214C2C2×#1192458211yescharacteristic
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC22×#41×C37C2
socleC23×C37C24
hypercenterC22×#41D37
hypocenterC37C2×#550
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#10596966C2semidirect
2. #14558202C2direct (N × H)
3. C2×#11924532C2semidirect
4. C2×#11924510C2semidirect
5. C2×#11924507C2semidirect
6. C2×Q8×Dic37C2semidirect
7. C2×C4×C22⋊D37C2semidirect
8. C22×#41×C37C2semidirect
10. C2×#10596966C22semidirect
15. #11924532C22semidirect
16. #11924510C22semidirect
17. #11924507C22semidirect
18. Q8×Dic37C22semidirect
19. C4×C22⋊D37C22semidirect
26. C2×#41×C37C22semidirect
33. C2×Q8×C37D4semidirect
67. Q8×C37C2×D4semidirect
78. C2×Dic37#41semidirect
100. Dic37C2×#41semidirect
103. C2×C37#550semidirect
109. C22×#41D37semidirect
116. C37C2×#550semidirect
120. C2×#41C2×D37semidirect
142. C2×Q8C22⋊D37semidirect
175. Q8C2×C22⋊D37semidirect
211. C2#14558202direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969662
#145582022
C2×#119245322
C2×#119245102
C2×#119245072
C2×Q8×Dic372
C2×C4×C22⋊D372
C22×#41×C372
C2×#55037