Finite Group Databasebeta

← C2×#14558190 #18008060

Subgroups — C2×#14558190 #18008060

Order 4736.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 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×Q8×D37C211yesmaximal, characteristic, complemented
2#14558190C2116yesmaximal, direct product factor
3C2×#11924523C213yesmaximal, complemented
4C2×#11924515C213yesmaximal, complemented
5C2×#11924507C213yesmaximal, complemented
6C2×Q8×Dic37C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D37C213yesmaximal, complemented
8C22×#41×C37C211yesmaximal, characteristic, complemented
9C22×Dic74C2213yes—
10C2×Q8×D37—28no—
11C2×Q8×D37C2218yescomplemented
12C22×C22⋊D37C2213yes—
13C22×C4×D37C2213yes—
14#11924523C22124yescomplemented
15#11924515C22124yescomplemented
16#11924507C22124yescomplemented
17Q8×Dic37C2218yescomplemented
18C4×C22⋊D37C22124yescomplemented
19C2×C4⋊Dic37C2213yes—
20C2×#10596936C2213yes—
21C2×C22⋊Dic37C2213yes—
22C2×C22⋊Dic37C2216yes—
23C2×#10596938C2211yescharacteristic
24C2×C4×Dic37C2213yes—
25C2×#41×C37—28no—
26C2×#41×C37C2218yescomplemented
27C22×Q8×C37C2211yescharacteristic
28C22×D4×C37C2213yes—
29C23×C4×C37C2213yes—
30C24×C37C2313yes—
31C23×D37C2311yescharacteristic
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⋊D37C23112yes—
43C22×Dic37C2311yescharacteristic
44C22×Dic37C2313yes—
45C22×Dic37C2313yes—
46Q8×D37—232no—
47C2×C4×D37—212no—
48C2×C4×D37C23112yes—
49C2×Dic74—212no—
50C2×Dic74C23112yes—
51C22⋊Dic37C23112yes—
52C22⋊Dic37C23124yes—
53#10596938C2314yes—
54C4⋊Dic37C23112yes—
55#10596936C23112yes—
56C4×Dic37C23112yes—
57C23×C37—26no—
58C23×C37—26no—
59C23×C37—26no—
60C23×C37C2416yes—
61C23×C37C2411yescharacteristic
62C22×D37—22no—
63C22×D37—22no—
64C22×D37#4114yescomplemented
65C22×D37C2412yes—
66Q8×C37C2×D4116yescomplemented
67D4×C37—224no—
68C2×C4×C37—22no—
69C2×C4×C37—224no—
70C2×C4×C37C2×D4112yes—
71C2×C4×C37C2412yes—
72C2×C4×C37C2416yes—
73C22⋊D37—224no—
74C2×Dic37—26no—
75C2×Dic37—26no—
76C2×Dic37—22no—
77C2×Dic37C2412yes—
78C2×Dic37C2416yes—
79C2×Dic37C2416yes—
80C4×D37—224no—
81Dic74—224no—
82C22×C37—26no—
83C22×C37—26no—
84C22×C37—26no—
85C22×C37—412no—
86C22×C37C22×D412yes—
87C22×C37C2×#4112yes—
88C22×C372−1+412yes—
89C22×C37C2511yescharacteristic
90C2×D37—28no—
91C2×D37—22no—
92C2×D37—22no—
93C2×D37C2×#4114yescomplemented
94C4×C37—22no—
95C4×C37C22×D4112yes—
96Dic37—26no—
97Dic37—26no—
98Dic37—22no—
99C2×#548—371nomaximal, Sylow
100C2×C37—46no—
101C2×C37#54814yescomplemented
102C2×C37C23×D411yescharacteristic
103C2×C37C22×#4111yescharacteristic
104C2×C37C2×2−1+411yescharacteristic
105D37—24no—
106C22×#41D3711yescharacteristic, complemented
107C23×Q8—371no—
108#548—3716no—
109C2×#124—373no—
110C2×C22⋊Q8—373no—
111C2×#121—373no—
112C2×C4×Q8—371no—
113C2×C4×D4—373no—
114C37C2×#54811yescharacteristic, complemented, Sylow
115C2×#41—28no—
116C2×#41C2×D3718yescomplemented
117C22×Q8—378no—
118C22×Q8—373no—
119C22×Q8—748no—
120C22×Q8C2×D3711yescharacteristic
121C22×D4—373no—
122C22×D4C2×D3713yes—
123C23×C4—373no—
124C23×C4C2×D3713yes—
125#124—3724no—
126C22⋊Q8—3724no—
127#121—3724no—
128C4×Q8—378no—
129C4×D4—3724no—
130C2×C4⋊C4—373no—
131C2×C4⋊C4—373no—
132C2×C22⋊C4—373no—
133C2×C22⋊C4—376no—
134C2×C22⋊C4—371no—
135C2×C42—373no—
136C24—371no—
137C24C22×D3713yes—
138#41—232no—
139C2×Q8—3712no—
140C2×Q8—7432no—
141C2×Q8—7412no—
142C2×Q8C22⋊D3718yescomplemented
143C2×Q8C22×D3714yes—
144C2×D4—212no—
145C2×D4—3712no—
146C2×D4—7412no—
147C2×D4C22×D37112yes—
148C22×C4—212no—
149C22×C4—371no—
150C22×C4—373no—
151C22×C4—373no—
152C22×C4—3712no—
153C22×C4—7412no—
154C22×C4C22×D37112yes—
155C22×C4C22×D3711yescharacteristic
156C22×C4C22×D3713yes—
157C4⋊C4—3712no—
158C4⋊C4—3712no—
159C22⋊C4—3712no—
160C22⋊C4—3724no—
161C22⋊C4—374no—
162C42—3712no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—374no—
167C23—372no—
168C23—742no—
169C23—742no—
170C23C23×D3716yes—
171C23C23×D3711yescharacteristic
172Q8—7424no—
173Q8C2×C22⋊D37116yescomplemented
174D4—224no—
175D4—7424no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—372no—
179C2×C4—376no—
180C2×C4—376no—
181C2×C4—746no—
182C2×C4—746no—
183C2×C4—742no—
184C2×C4—7424no—
185C2×C4C2×C22⋊D37112yes—
186C2×C4C23×D3712yes—
187C2×C4C23×D3716yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—374no—
193C22—742no—
194C22—742no—
195C22—748no—
196C22C22×C22⋊D3712yes—
197C22#41×D3712yes—
198C22#1192458312yes—
199C22C24×D3711yescharacteristic
200C4—22no—
201C4—746no—
202C4—746no—
203C4—742no—
204C4C22×C22⋊D37112yes—
205C2—46no—
206C2—744no—
207C2#1455819014yesdirect product factor
208C2C23×C22⋊D3711yescharacteristic
209C2C2×#41×D3711yescharacteristic
210C2C2×#1192458311yescharacteristic
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC22×#41×C37C2
socleC23×C37C24
hypercenterC22×#41D37
hypocenterC37C2×#548
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D37C2semidirect
2. #14558190C2direct (N × H)
3. C2×#11924523C2semidirect
4. C2×#11924515C2semidirect
5. C2×#11924507C2semidirect
6. C2×Q8×Dic37C2semidirect
7. C2×C4×C22⋊D37C2semidirect
8. C22×#41×C37C2semidirect
11. C2×Q8×D37C22semidirect
14. #11924523C22semidirect
15. #11924515C22semidirect
16. #11924507C22semidirect
17. Q8×Dic37C22semidirect
18. C4×C22⋊D37C22semidirect
26. C2×#41×C37C22semidirect
33. C2×Q8×C37D4semidirect
64. C22×D37#41semidirect
66. Q8×C37C2×D4semidirect
93. C2×D37C2×#41semidirect
101. C2×C37#548semidirect
106. C22×#41D37semidirect
114. C37C2×#548semidirect
116. C2×#41C2×D37semidirect
142. C2×Q8C22⋊D37semidirect
173. Q8C2×C22⋊D37semidirect
207. C2#14558190direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D372
#145581902
C2×#119245232
C2×#119245152
C2×#119245072
C2×Q8×Dic372
C2×C4×C22⋊D372
C22×#41×C372
C2×#54837