Finite Group Databasebeta

← C2×SD32×D101 #27184239

Subgroups — C2×SD32×D101 #27184239

Order 12928.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q16×D101C211yesmaximal, characteristic, complemented
2C2×D8×D101C211yesmaximal, characteristic
3C2×#15692200C211yesmaximal, characteristic, complemented
4C2×#15692199C211yesmaximal, characteristic, complemented
5C2×#15692198C211yesmaximal, characteristic, complemented
6SD32×D101C218yesmaximal, direct product factor
7C2×C16×D101C211yesmaximal, characteristic, complemented
8C2×SD32×C101C211yesmaximal, characteristic, complemented
9C2×Q8×D101—21no—
10C2×D4×D101—21no—
11C2×Dic404C2211yescharacteristic, complemented
12C2×#13108064—21no—
13Q16×D101—22no—
14Q16×D101C2214yescomplemented
15C2×D808C2211yescharacteristic
16C2×#13108059—21no—
17D8×D101—22no—
18D8×D101C2214yes—
19C2×C8×D101C2211yescharacteristic
20#15692200C2214yescomplemented
21#15692199C2214yescomplemented
22#15692198C2214yescomplemented
23C2×#13108049C2211yescharacteristic, complemented
24C16×D101C2214yescomplemented
25C2×Q16×C101C2211yescharacteristic, complemented
26C2×D8×C101C2211yescharacteristic
27SD32×C101C2214yescomplemented
28C2×C16×C101C2211yescharacteristic, complemented
29C23×D101—41no—
30C2×Dic202—21no—
31C2×Dic202—41no—
32Q8×D101—24no—
33Q8×D101—42no—
34C2×D404—21no—
35C2×C22⋊D101—41no—
36D4×D101—24no—
37D4×D101—42no—
38C2×C4×D101—41no—
39C2×C4×D101D411yescharacteristic
40Dic404—21no—
41Dic404C2312yescomplemented
42#13108064—24no—
43D808—21no—
44D808C2312yes—
45#13108059—24no—
46C2×#11717579D411yescharacteristic
47C8×D101D412yes—
48C8×D101C2312yes—
49#13108049C2312yescomplemented
50C2×Q8×C101—21no—
51C2×D4×C101—21no—
52Q16×C101—21no—
53Q16×C101C2312yescomplemented
54D8×C101—21no—
55D8×C101C2312yes—
56C2×C8×C101C2311yescharacteristic
57C16×C101C2312yescomplemented
58C23×C101—41no—
59C22×D101—41no—
60C22×D101—44no—
61C22×D101—84no—
62C22×D101D811yescharacteristic
63Q8×C101—22no—
64Q8×C101—41no—
65D4×C101—22no—
66D4×C101—41no—
67C2×C4×C101—41no—
68C2×C4×C101C2×D411yescharacteristic
69C22⋊D101—44no—
70C2×Dic101—41no—
71C2×Dic101D811yescharacteristic
72D404—22no—
73D404—41no—
74C4×D101—44no—
75C4×D101D812yes—
76C4×D101C2×D412yes—
77Dic202—22no—
78Dic202—41no—
79Dic202—44no—
80C8×C101C2×D411yescharacteristic
81C8×C101C2411yescharacteristic
82#11717579C2×D412yes—
83C22×C101—42no—
84C22×C101—82no—
85C22×C101C2×D811yescharacteristic
86C2×D101—42no—
87C2×D101—82no—
88C2×D101—88no—
89C2×D101SD3214yesdirect product factor
90C2×D101C2×D812yes—
91C4×C101—42no—
92C4×C101C2×D811yescharacteristic
93C4×C101C22×D411yescharacteristic
94Dic101—42no—
95Dic101C2×D812yes—
96C2×C101—82no—
97C2×C101C2×SD3212yescomplemented
98C2×C101C22×D811yescharacteristic
99D101—82no—
100D101C2×SD3214yesdirect product factor
101C22×SD32—1011nomaximal, Sylow
102C101C22×SD3211yescharacteristic, complemented, Sylow
103C22×Q16—1011no—
104C22×D8—1011no—
105C2×SD32—1011no—
106C2×SD32—1011no—
107C2×SD32—1018no—
108C2×SD32—1011no—
109C2×SD32D10111yescharacteristic, direct product factor
110C22×C16—1011no—
111C22×Q8—2021no—
112C22×D4—2021no—
113C2×Q16—1014no—
114C2×Q16—1011no—
115C2×Q16—2022no—
116C2×Q16—2021no—
117C2×Q16C2×D10111yescharacteristic, complemented
118C2×D8—1014no—
119C2×D8—1011no—
120C2×D8—2022no—
121C2×D8—2021no—
122C2×D8C2×D10111yescharacteristic
123C22×C8—1011no—
124SD32—1014no—
125SD32—1014no—
126SD32—1014no—
127SD32C2×D10114yesdirect product factor
128C2×C16—1011no—
129C2×C16—1014no—
130C2×C16C2×D10111yescharacteristic, complemented
131C24—4041no—
132C2×Q8—21no—
133C2×Q8—4041no—
134C2×Q8—4042no—
135C2×Q8—2024no—
136C2×Q8—2021no—
137C2×D4—21no—
138C2×D4—4042no—
139C2×D4—4041no—
140C2×D4—2024no—
141C2×D4—2021no—
142C22×C4—1011no—
143C22×C4—4041no—
144Q16—21no—
145Q16—1012no—
146Q16—2024no—
147Q16—2021no—
148Q16C22×D10112yescomplemented
149D8—21no—
150D8—1012no—
151D8—2024no—
152D8—2021no—
153D8C22×D10112yes—
154C2×C8—1011no—
155C2×C8—1012no—
156C2×C8—1012no—
157C2×C8C22×D10111yescharacteristic
158C16—1012no—
159C16C22×D10112yescomplemented
160C23—41no—
161C23—8084no—
162C23—1011no—
163C23—4044no—
164C23—4041no—
165Q8—22no—
166Q8—41no—
167Q8—4044no—
168Q8—4041no—
169Q8—2022no—
170D4—22no—
171D4—41no—
172D4—4044no—
173D4—4041no—
174D4—2022no—
175C2×C4—41no—
176C2×C4—1011no—
177C2×C4—1012no—
178C2×C4—1012no—
179C2×C4—4044no—
180C2×C4—4041no—
181C2×C4D4×D10111yescharacteristic
182C8—1012no—
183C8D4×D10111yescharacteristic
184C8C23×D10111yescharacteristic
185C22—42no—
186C22—82no—
187C22—8088no—
188C22—8082no—
189C22—1014no—
190C22—1012no—
191C22—4042no—
192C22D8×D10111yescharacteristic
193C4—42no—
194C4—1012no—
195C4—4042no—
196C4D8×D10111yescharacteristic
197C4C2×D4×D10111yescharacteristic
198C2—82no—
199C2—8082no—
200C2—1014no—
201C2SD32×D10112yesdirect product factor
202C2C2×D8×D10111yescharacteristic
subgroupG/H
centerC22D8×D101
commutator, cosocleC8×C101C24
FrattiniC8C23×D101
FittingC2×SD32×C101C2
socleC22×C101C2×D8
prime radicalC2×D8×D101C2
hypercenterC2×SD32D101
hypocenterC101C22×SD32
LCSG ▷ C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D101C2semidirect
3. C2×#15692200C2semidirect
4. C2×#15692199C2semidirect
5. C2×#15692198C2semidirect
6. SD32×D101C2direct (N × H)
7. C2×C16×D101C2semidirect
8. C2×SD32×C101C2semidirect
11. C2×Dic404C22semidirect
14. Q16×D101C22semidirect
20. #15692200C22semidirect
21. #15692199C22semidirect
22. #15692198C22semidirect
23. C2×#13108049C22semidirect
24. C16×D101C22semidirect
25. C2×Q16×C101C22semidirect
27. SD32×C101C22semidirect
28. C2×C16×C101C22semidirect
41. Dic404C23semidirect
49. #13108049C23semidirect
53. Q16×C101C23semidirect
57. C16×C101C23semidirect
89. C2×D101SD32direct (N × H)
97. C2×C101C2×SD32semidirect
100. D101C2×SD32direct (N × H)
102. C101C22×SD32semidirect
109. C2×SD32D101direct (N × H)
117. C2×Q16C2×D101semidirect
127. SD32C2×D101direct (N × H)
130. C2×C16C2×D101semidirect
148. Q16C22×D101semidirect
159. C16C22×D101semidirect
201. C2SD32×D101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q16×D1012
C2×D8×D1012
C2×#156922002
C2×#156921992
C2×#156921982
SD32×D1012
C2×C16×D1012
C2×SD32×C1012
C22×SD32101