Finite Group Databasebeta

← C2×#19128138 #24920587

Subgroups — C2×#19128138 #24920587

Order 10624.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14581815C211yesmaximal, characteristic, complemented
2C2×D8×D83C211yesmaximal, characteristic, complemented
3#19128138C218yesmaximal, direct product factor
4C2×#14581735C211yesmaximal, characteristic, complemented
5C2×D1328C211yesmaximal, characteristic, complemented
6C2×#14581733C211yesmaximal, characteristic, complemented
7C2×#14581731C211yesmaximal, characteristic, complemented
8C2×SD32×C83C211yesmaximal, characteristic, complemented
9C2×#13050591—21no—
10C2×D4×D83—21no—
11#14581815—22no—
12#14581815C2214yescomplemented
13C2×#13050577—21no—
14C2×D664C2211yescharacteristic
15C2×D664C2211yescharacteristic, complemented
16C2×#13050575—21no—
17D8×D83—22no—
18D8×D83C2214yescomplemented
19C2×C8×D83C2211yescharacteristic
20#14581735C2214yescomplemented
21D1328C2214yescomplemented
22#14581733C2214yescomplemented
23#14581731C2214yescomplemented
24C2×C83⋊C16C2211yescharacteristic, complemented
25C2×Q16×C83C2211yescharacteristic, complemented
26C2×D8×C83C2211yescharacteristic
27SD32×C83C2214yescomplemented
28C2×C16×C83C2211yescharacteristic, complemented
29C23×D83—41no—
30#13050591—24no—
31#13050591—42no—
32C2×D332—21no—
33C2×D332—21no—
34C2×D332—41no—
35C2×C22⋊D83—41no—
36D4×D83—24no—
37D4×D83—42no—
38C2×C4×D83—41no—
39C2×C4×D83D411yescharacteristic
40#13050577—24no—
41D664—21no—
42D664—21no—
43D664C2312yes—
44D664C2312yescomplemented
45#13050575—24no—
46C2×C83⋊C8D411yescharacteristic
47C8×D83D412yes—
48C8×D83C2312yes—
49C83⋊C16C2312yescomplemented
50C2×Q8×C83—21no—
51C2×D4×C83—21no—
52Q16×C83—21no—
53Q16×C83C2312yescomplemented
54D8×C83—21no—
55D8×C83C2312yes—
56C2×C8×C83C2311yescharacteristic
57C16×C83C2312yescomplemented
58C23×C83—41no—
59C22×D83—41no—
60C22×D83—41no—
61C22×D83—44no—
62C22×D83—84no—
63C22×D83D811yescharacteristic
64Q8×C83—22no—
65Q8×C83—41no—
66D4×C83—22no—
67D4×C83—41no—
68C2×C4×C83—41no—
69C2×C4×C83C2×D411yescharacteristic
70C22⋊D83—44no—
71C2×Dic83D811yescharacteristic
72D332—22no—
73D332—22no—
74D332—44no—
75D332—41no—
76D332—41no—
77C4×D83—44no—
78C4×D83D812yes—
79C4×D83C2×D412yes—
80C8×C83C2×D411yescharacteristic
81C8×C83C2411yescharacteristic
82C83⋊C8C2×D412yes—
83C22×C83—42no—
84C22×C83—82no—
85C22×C83C2×D811yescharacteristic
86C2×D83—22no—
87C2×D83—42no—
88C2×D83—42no—
89C2×D83—88no—
90C2×D83—82no—
91C2×D83—82no—
92C2×D83C2×D812yes—
93C4×C83—42no—
94C4×C83C2×D811yescharacteristic
95C4×C83C22×D411yescharacteristic
96Dic83C2×D812yes—
97C2×C83—82no—
98C2×C83#50912yescomplemented
99C2×C83C22×D811yescharacteristic
100D83—22no—
101D83—82no—
102D83—82no—
103C2×#509—831nomaximal, Sylow
104C83C2×#50911yescharacteristic, complemented, Sylow
105C2×#135—831no—
106C22×D8—831no—
107#509—838no—
108C2×SD32—831no—
109C2×SD32D8311yescharacteristic, complemented
110C2×D16—831no—
111C2×D16—831no—
112C2×M32—831no—
113C2×#41—1661no—
114C22×D4—1661no—
115#135—834no—
116#135—1662no—
117C2×Q16C2×D8311yescharacteristic, complemented
118C2×SD16—1661no—
119C2×D8—834no—
120C2×D8—831no—
121C2×D8—831no—
122C2×D8—1662no—
123C2×D8—1661no—
124C2×D8C2×D8311yescharacteristic
125C22×C8—831no—
126SD32—834no—
127SD32C2×D8314yescomplemented
128D16—834no—
129D16—834no—
130M32—834no—
131C2×C16—831no—
132C2×C16C2×D8311yescharacteristic, complemented
133C24—3321no—
134#41—3322no—
135#41—1664no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—3321no—
139C2×D4—3322no—
140C2×D4—3321no—
141C2×D4—1664no—
142C2×D4—1661no—
143C2×D4—1661no—
144C22×C4—3321no—
145C22×C4—831no—
146Q16—21no—
147Q16C22×D8312yescomplemented
148SD16—1664no—
149D8—21no—
150D8—832no—
151D8—832no—
152D8—1664no—
153D8—1661no—
154D8—1661no—
155D8C22×D8312yes—
156C2×C8—831no—
157C2×C8—832no—
158C2×C8—832no—
159C2×C8C22×D8311yescharacteristic
160C16—832no—
161C16C22×D8312yescomplemented
162C23—41no—
163C23—3324no—
164C23—3321no—
165C23—3321no—
166C23—831no—
167C23—6644no—
168Q8—22no—
169Q8—41no—
170D4—22no—
171D4—41no—
172D4—3324no—
173D4—3324no—
174D4—3321no—
175D4—3321no—
176D4—1662no—
177D4—1662no—
178C2×C4—41no—
179C2×C4—3324no—
180C2×C4—831no—
181C2×C4—832no—
182C2×C4—832no—
183C2×C4D4×D8311yescharacteristic
184C8—832no—
185C8D4×D8311yescharacteristic
186C8C23×D8311yescharacteristic
187C22—42no—
188C22—82no—
189C22—3322no—
190C22—3322no—
191C22—832no—
192C22—6648no—
193C22—6642no—
194C22—6642no—
195C22—1662no—
196C22D8×D8311yescharacteristic
197C4—42no—
198C4—832no—
199C4D8×D8311yescharacteristic
200C4C2×D4×D8311yescharacteristic
201C2—82no—
202C2—6642no—
203C2—6642no—
204C2—1662no—
205C2#1912813812yesdirect product factor
206C2C2×D8×D8311yescharacteristic
subgroupG/H
centerC22D8×D83
commutator, cosocleC8×C83C24
FrattiniC8C23×D83
FittingC2×SD32×C83C2
socleC22×C83C2×D8
hypercenterC2×SD32D83
hypocenterC83C2×#509
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#14581815C2semidirect
2. C2×D8×D83C2semidirect
3. #19128138C2direct (N × H)
4. C2×#14581735C2semidirect
5. C2×D1328C2semidirect
6. C2×#14581733C2semidirect
7. C2×#14581731C2semidirect
8. C2×SD32×C83C2semidirect
12. #14581815C22semidirect
15. C2×D664C22semidirect
18. D8×D83C22semidirect
20. #14581735C22semidirect
21. D1328C22semidirect
22. #14581733C22semidirect
23. #14581731C22semidirect
24. C2×C83⋊C16C22semidirect
25. C2×Q16×C83C22semidirect
27. SD32×C83C22semidirect
28. C2×C16×C83C22semidirect
44. D664C23semidirect
49. C83⋊C16C23semidirect
53. Q16×C83C23semidirect
57. C16×C83C23semidirect
98. C2×C83#509semidirect
104. C83C2×#509semidirect
109. C2×SD32D83semidirect
117. C2×Q16C2×D83semidirect
127. SD32C2×D83semidirect
132. C2×C16C2×D83semidirect
147. Q16C22×D83semidirect
161. C16C22×D83semidirect
205. C2#19128138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145818152
C2×D8×D832
#191281382
C2×#145817352
C2×D13282
C2×#145817332
C2×#145817312
C2×SD32×C832
C2×#50983