Finite Group Databasebeta

← C2×#19128252 #24920747

Subgroups — C2×#19128252 #24920747

Order 10624.

1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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×#13050591C212yesmaximal, complemented
2#19128252C2116yesmaximal, direct product factor
3C2×#14581789C211yesmaximal, characteristic, complemented
4C2×#14581781C212yesmaximal, complemented
5C2×#14581767C214yesmaximal, complemented
6C2×#14581754C214yesmaximal, complemented
7C2×C42×D83C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C83C211yesmaximal, characteristic, complemented
9C2×#13050591—216no—
10C2×#13050591C22116yescomplemented
11C22×D332C2214yes—
12C22×D332C2214yes—
13C22×D332C2212yes—
14C22×C4×D83C2212yes—
15C22×C4×D83C2214yes—
16C22×C4×D83C2211yescharacteristic
17#14581789C2218yescomplemented
18#14581781C22116yescomplemented
19#14581767C22132yescomplemented
20#14581754C22132yescomplemented
21C2×(C2×D83)⋊C4C2218yes—
22C2×C4×Dic83C2212yes—
23C2×C4×Dic83C2211yescharacteristic
24C42×D83C2218yescomplemented
25C22×Q8×C83C2212yes—
26C4⋊Q8×C83C2218yescomplemented
27C2×C4⋊C4×C83C2214yes—
28C2×C42×C83C2211yescharacteristic
29C23×D83C2314yes—
30C23×D83C2311yescharacteristic
31#13050591—264no—
32C2×D332—216no—
33C2×D332—28no—
34C2×D332—216no—
35C2×D332C23116yes—
36C2×D332C23116yes—
37C2×D332C2318yes—
38C22×Dic83C2312yes—
39C22×Dic83C2311yescharacteristic
40C2×C4×D83—28no—
41C2×C4×D83—216no—
42C2×C4×D83D418yescomplemented
43C2×C4×D83C2318yes—
44C2×C4×D83C23116yes—
45C2×C4×D83C2314yes—
46(C2×D83)⋊C4C23132yes—
47C4×Dic83C2314yes—
48C4×Dic83C2318yes—
49C2×Q8×C83—28no—
50C2×Q8×C83C2318yes—
51C22×C4×C83C2314yes—
52C22×C4×C83C2311yescharacteristic
53C22×C4×C83C2312yes—
54C4⋊C4×C83C23116yes—
55C42×C83C2314yes—
56C23×C83C2411yescharacteristic
57C22×D83—24no—
58C22×D83—28no—
59C22×D83—216no—
60C22×D83C2×D414yes—
61C22×D83C2418yes—
62C22×D83C2412yes—
63Q8×C83—216no—
64C2×C4×C83—28no—
65C2×C4×C83C2×D414yes—
66C2×C4×C83#4118yescomplemented
67C2×C4×C83C2418yes—
68C2×C4×C83C2412yes—
69C2×C4×C83C2414yes—
70C2×Dic83—24no—
71C2×Dic83C2×D414yes—
72C2×Dic83C2414yes—
73C2×Dic83C2412yes—
74D332—232no—
75D332—216no—
76D332—232no—
77C4×D83—216no—
78C4×D83—232no—
79C4×D83C2×D4116yescomplemented
80C22×C83C22×D412yes—
81C22×C83C2×#4114yes—
82C22×C83C2511yescharacteristic
83C2×D83—28no—
84C2×D83—24no—
85C2×D83—28no—
86C2×D83—216no—
87C2×D83—416no—
88C2×D83C22×D414yes—
89C4×C83—28no—
90C4×C83C22×D414yes—
91C4×C83C2×#4118yescomplemented
92Dic83—24no—
93Dic83C22×D414yes—
94C2×C83#53214yescomplemented
95C2×C83C23×D411yescharacteristic
96C2×C83C22×#4112yes—
97D83—24no—
98D83—48no—
99C2×#532—831nomaximal, Sylow
100C83C2×#53211yescharacteristic, complemented, Sylow
101C22×#41—832no—
102#532—8316no—
103C2×C4⋊Q8D8311yescharacteristic, complemented
104C2×#127—831no—
105C2×#124—832no—
106C2×#121—834no—
107C2×C4×D4—834no—
108C22×C42—831no—
109C2×#41—8316no—
110C2×#41—16616no—
111C22×Q8C2×D8312yes—
112C22×D4—834no—
113C22×D4—834no—
114C22×D4—832no—
115C23×C4—831no—
116C23×C4—834no—
117C23×C4—832no—
118C4⋊Q8C2×D8318yescomplemented
119#127—838no—
120#124—8316no—
121#121—8332no—
122C4×D4—8332no—
123C2×C4⋊C4C2×D8314yes—
124C2×C22⋊C4—838no—
125C2×C42—832no—
126C2×C42—831no—
127C2×C42—838no—
128C2×C42C2×D8311yescharacteristic
129C24—831no—
130C24—834no—
131#41—16664no—
132C2×Q8—28no—
133C2×Q8C22×D8318yes—
134C2×D4—8316no—
135C2×D4—8316no—
136C2×D4—838no—
137C2×D4—16616no—
138C2×D4—1668no—
139C2×D4—16616no—
140C22×C4—831no—
141C22×C4—838no—
142C22×C4—834no—
143C22×C4—832no—
144C22×C4—838no—
145C22×C4—8316no—
146C22×C4—16616no—
147C22×C4—1668no—
148C22×C4C22×D8314yes—
149C22×C4C22×D8311yescharacteristic
150C22×C4C22×D8312yes—
151C4⋊C4C22×D83116yes—
152C22⋊C4—8332no—
153C42—838no—
154C42—834no—
155C42C22×D8314yes—
156C23—834no—
157C23—832no—
158C23—838no—
159C23—1668no—
160C23—16616no—
161C23—1664no—
162C23C23×D8311yescharacteristic
163Q8—216no—
164D4—16632no—
165D4—16616no—
166D4—16632no—
167C2×C4—28no—
168C2×C4—834no—
169C2×C4—832no—
170C2×C4—8316no—
171C2×C4—834no—
172C2×C4—16632no—
173C2×C4—1664no—
174C2×C4—16616no—
175C2×C4D4×D8314yes—
176C2×C4#1305059118yescomplemented
177C2×C4C23×D8318yes—
178C2×C4C23×D8312yes—
179C2×C4C23×D8314yes—
180C22—33216no—
181C22—834no—
182C22—1668no—
183C22—16616no—
184C22—1668no—
185C22—1664no—
186C22C2×D4×D8312yes—
187C22C2×#1305059114yes—
188C22C24×D8311yescharacteristic
189C4—28no—
190C4—834no—
191C4—1664no—
192C4C2×D4×D8314yes—
193C4C2×#1305059118yescomplemented
194C2—3328no—
195C2—1664no—
196C2#1912825214yesdirect product factor
197C2C22×D4×D8311yescharacteristic
198C2C22×#1305059112yes—
subgroupG/H
centerC23C23×D83
commutator, cosocleC22×C83C25
FrattiniC22C24×D83
FittingC2×C4⋊Q8×C83C2
socleC23×C83C24
hypercenterC2×C4⋊Q8D83
hypocenterC83C2×#532
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13050591C2semidirect
2. #19128252C2direct (N × H)
3. C2×#14581789C2semidirect
4. C2×#14581781C2semidirect
5. C2×#14581767C2semidirect
6. C2×#14581754C2semidirect
7. C2×C42×D83C2semidirect
8. C2×C4⋊Q8×C83C2semidirect
10. C2×#13050591C22semidirect
17. #14581789C22semidirect
18. #14581781C22semidirect
19. #14581767C22semidirect
20. #14581754C22semidirect
24. C42×D83C22semidirect
26. C4⋊Q8×C83C22semidirect
42. C2×C4×D83D4semidirect
66. C2×C4×C83#41semidirect
79. C4×D83C2×D4semidirect
91. C4×C83C2×#41semidirect
94. C2×C83#532semidirect
100. C83C2×#532semidirect
103. C2×C4⋊Q8D83semidirect
118. C4⋊Q8C2×D83semidirect
176. C2×C4#13050591semidirect
193. C4C2×#13050591semidirect
196. C2#19128252direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505912
#191282522
C2×#145817892
C2×#145817812
C2×#145817672
C2×#145817542
C2×C42×D832
C2×C4⋊Q8×C832
C2×#53283