Finite Group Databasebeta

← C2×#19128370 #24920941

Subgroups — C2×#19128370 #24920941

Order 10624.

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×#13050591C211yesmaximal, characteristic, complemented
2#19128370C2116yesmaximal, direct product factor
3C2×#14581788C213yesmaximal, complemented
4C2×#14581766C213yesmaximal, complemented
5C2×#14581763C213yesmaximal, complemented
6C2×Q8×Dic83C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D83C213yesmaximal, complemented
8C22×#41×C83C211yesmaximal, characteristic, complemented
9C2×#13050591—28no—
10C2×#13050591C2218yescomplemented
11C22×D332C2213yes—
12C22×C22⋊D83C2213yes—
13C22×C22⋊D83C2216yes—
14C22×C4×D83C2213yes—
15#14581788C22124yescomplemented
16#14581766C22124yescomplemented
17#14581763C22124yescomplemented
18Q8×Dic83C2218yescomplemented
19C4×C22⋊D83C22124yescomplemented
20C2×C4⋊Dic83C2213yes—
21C2×Dic83⋊C4C2211yescharacteristic
22C2×C22⋊Dic83C2213yes—
23C2×(C2×D83)⋊C4C2213yes—
24C2×C4×Dic83C2213yes—
25C2×#41×C83—28no—
26C2×#41×C83C2218yescomplemented
27C22×Q8×C83C2211yescharacteristic
28C22×D4×C83C2213yes—
29C23×C4×C83C2213yes—
30C23×D83C2313yes—
31#13050591—232no—
32C2×D332—212no—
33C2×D332C23112yes—
34C2×C22⋊D83—212no—
35C2×C22⋊D83—412no—
36C2×C22⋊D83C23112yes—
37C2×C22⋊D83C23124yes—
38C22×Dic83C2311yescharacteristic
39C22×Dic83C2313yes—
40C22×Dic83C2311yescharacteristic
41C2×C4×D83—212no—
42C2×C4×D83C23112yes—
43C4⋊Dic83C23112yes—
44Dic83⋊C4C2314yes—
45C22⋊Dic83C23112yes—
46(C2×D83)⋊C4C23112yes—
47C4×Dic83C23112yes—
48C24×C83C2313yes—
49#41×C83—232no—
50C2×Q8×C83D418yescomplemented
51C2×Q8×C83C2314yes—
52C2×D4×C83—212no—
53C2×D4×C83C23112yes—
54C22×C4×C83—212no—
55C22×C4×C83C23112yes—
56C22×C4×C83C2311yescharacteristic
57C22×C4×C83C2313yes—
58C23×C83—26no—
59C23×C83—26no—
60C23×C83—26no—
61C23×C83C2416yes—
62C23×C83C2411yescharacteristic
63C22×D83—26no—
64C22×D83—26no—
65C22×D83—26no—
66C22×D83C2416yes—
67Q8×C83C2×D4116yescomplemented
68D4×C83—224no—
69C2×C4×C83—22no—
70C2×C4×C83—224no—
71C2×C4×C83C2×D4112yes—
72C2×C4×C83C2412yes—
73C2×C4×C83C2416yes—
74C22⋊D83—224no—
75C22⋊D83—424no—
76C2×Dic83—22no—
77C2×Dic83—26no—
78C2×Dic83#4114yescomplemented
79C2×Dic83C2416yes—
80C2×Dic83C2412yes—
81C2×Dic83C2412yes—
82D332—224no—
83C4×D83—224no—
84C22×C83—26no—
85C22×C83—26no—
86C22×C83—26no—
87C22×C83—412no—
88C22×C83C22×D412yes—
89C22×C83C2×#4112yes—
90C22×C83H(5,𝔽2)12yes—
91C22×C83C2511yescharacteristic
92C2×D83—26no—
93C2×D83—26no—
94C2×D83—26no—
95C2×D83—412no—
96C4×C83—22no—
97C4×C83C22×D4112yes—
98Dic83—22no—
99Dic83—26no—
100Dic83C2×#4114yescomplemented
101C2×C83—46no—
102C2×C83#55014yescomplemented
103C2×C83C23×D411yescharacteristic
104C2×C83C22×#4111yescharacteristic
105C2×C83C2×H(5,𝔽2)11yescharacteristic
106D83—46no—
107C2×#550—831nomaximal, Sylow
108C83C2×#55011yescharacteristic, complemented, Sylow
109C22×#41—831no—
110C22×#41D8311yescharacteristic, complemented
111#550—8316no—
112C2×#127—833no—
113C2×#121—833no—
114C2×#121—833no—
115C2×C4×Q8—831no—
116C2×C4×D4—833no—
117C2×#41—28no—
118C2×#41—838no—
119C2×#41—1668no—
120C2×#41C2×D8318yescomplemented
121C22×Q8C2×D8311yescharacteristic
122C22×D4—836no—
123C22×D4—833no—
124C22×D4—833no—
125C22×D4C2×D8313yes—
126C23×C4—833no—
127C23×C4C2×D8313yes—
128#127—8324no—
129#121—8324no—
130#121—8324no—
131C4×Q8—838no—
132C4×D4—8324no—
133C2×C4⋊C4—831no—
134C2×C4⋊C4—833no—
135C2×C22⋊C4—833no—
136C2×C22⋊C4—833no—
137C2×C42—833no—
138C24—833no—
139C24C22×D8313yes—
140#41—232no—
141#41—16632no—
142C2×Q8C22⋊D8318yescomplemented
143C2×Q8C22×D8314yes—
144C2×D4—212no—
145C2×D4—33212no—
146C2×D4—8324no—
147C2×D4—8312no—
148C2×D4—8312no—
149C2×D4—16612no—
150C2×D4—16612no—
151C2×D4C22×D83112yes—
152C22×C4—212no—
153C22×C4—831no—
154C22×C4—833no—
155C22×C4—831no—
156C22×C4—8312no—
157C22×C4—16612no—
158C22×C4C22×D83112yes—
159C22×C4C22×D8311yescharacteristic
160C22×C4C22×D8313yes—
161C4⋊C4—834no—
162C4⋊C4—8312no—
163C22⋊C4—8312no—
164C22⋊C4—8312no—
165C42—8312no—
166C23—26no—
167C23—26no—
168C23—26no—
169C23—836no—
170C23—1666no—
171C23—1666no—
172C23—1666no—
173C23C23×D8316yes—
174C23C23×D8311yescharacteristic
175Q8C2×C22⋊D83116yescomplemented
176D4—224no—
177D4—33224no—
178D4—16624no—
179D4—16624no—
180C2×C4—22no—
181C2×C4—224no—
182C2×C4—834no—
183C2×C4—832no—
184C2×C4—836no—
185C2×C4—832no—
186C2×C4—1662no—
187C2×C4—1666no—
188C2×C4—16624no—
189C2×C4C2×C22⋊D83112yes—
190C2×C4C23×D8312yes—
191C2×C4C23×D8316yes—
192C22—26no—
193C22—26no—
194C22—26no—
195C22—412no—
196C22—33212no—
197C22—1666no—
198C22—1666no—
199C22—1666no—
200C22C22×C22⋊D8312yes—
201C22#41×D8312yes—
202C22#1458183812yes—
203C22C24×D8311yescharacteristic
204C4—22no—
205C4—834no—
206C4—1662no—
207C4—1666no—
208C4C22×C22⋊D83112yes—
209C2—46no—
210C2—3326no—
211C2#1912837014yesdirect product factor
212C2C23×C22⋊D8311yescharacteristic
213C2C2×#41×D8311yescharacteristic
214C2C2×#1458183811yescharacteristic
subgroupG/H
centerC23C23×D83
commutator, cosocleC22×C83C25
FrattiniC22C24×D83
FittingC22×#41×C83C2
socleC23×C83C24
hypercenterC22×#41D83
hypocenterC83C2×#550
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#13050591C2semidirect
2. #19128370C2direct (N × H)
3. C2×#14581788C2semidirect
4. C2×#14581766C2semidirect
5. C2×#14581763C2semidirect
6. C2×Q8×Dic83C2semidirect
7. C2×C4×C22⋊D83C2semidirect
8. C22×#41×C83C2semidirect
10. C2×#13050591C22semidirect
15. #14581788C22semidirect
16. #14581766C22semidirect
17. #14581763C22semidirect
18. Q8×Dic83C22semidirect
19. C4×C22⋊D83C22semidirect
26. C2×#41×C83C22semidirect
50. C2×Q8×C83D4semidirect
67. Q8×C83C2×D4semidirect
78. C2×Dic83#41semidirect
100. Dic83C2×#41semidirect
102. C2×C83#550semidirect
108. C83C2×#550semidirect
110. C22×#41D83semidirect
120. C2×#41C2×D83semidirect
142. C2×Q8C22⋊D83semidirect
175. Q8C2×C22⋊D83semidirect
211. C2#19128370direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505912
#191283702
C2×#145817882
C2×#145817662
C2×#145817632
C2×Q8×Dic832
C2×C4×C22⋊D832
C22×#41×C832
C2×#55083