Finite Group Databasebeta

← #123×D101 #20265677

Subgroups — #123×D101 #20265677

Order 6464.

342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×D101C211yesmaximal, characteristic
2C22×C4×D101C211yesmaximal, characteristic, complemented
3#15692240C212yesmaximal, complemented
4#15692239C211yesmaximal, characteristic, complemented
5#15692238C211yesmaximal, characteristic, complemented
6#15692237C212yesmaximal, complemented
7#15692236C211yesmaximal, characteristic, complemented
8C4⋊C4×D101C212yesmaximal, complemented
9C22⋊C4×D101C212yesmaximal, complemented
10C22⋊C4×D101C211yesmaximal, characteristic, complemented
11#123×C101C211yesmaximal, characteristic, complemented
12C23×D101C2211yescharacteristic
13C23×D101C2211yescharacteristic
14C2×D404C2211yescharacteristic
15C2×C22⋊D101C2211yescharacteristic
16C2×C22⋊D101C2211yescharacteristic
17D4×D101—24no—
18C22×Dic101C2211yescharacteristic, complemented
19C2×C4×D101—24no—
20C2×C4×D101C2212yes—
21C2×C4×D101C2211yescharacteristic
22C2×C4×D101C2212yes—
23C2×C4×D101C2212yescomplemented
24C4⋊Dic101C2212yescomplemented
25#13108053C2212yescomplemented
26#13108053C2212yescomplemented
27C22⋊Dic101C2212yescomplemented
28C22⋊Dic101C2211yescharacteristic, complemented
29#13108051C2212yescomplemented
30#13108051C2212yescomplemented
31#13108051C2212yescomplemented
32C2×D4×C101C2211yescharacteristic
33C22×C4×C101C2211yescharacteristic, complemented
34C4⋊C4×C101C2212yescomplemented
35C22⋊C4×C101C2212yescomplemented
36C22⋊C4×C101C2211yescharacteristic, complemented
37C23×C101C2311yescharacteristic
38C23×C101C2311yescharacteristic
39C22×D101—24no—
40C22×D101—22no—
41C22×D101—24no—
42C22×D101D414yes—
43C22×D101C2311yescharacteristic
44C22×D101C2311yescharacteristic
45C22×D101C2311yescharacteristic
46D4×C101—22no—
47C2×C4×C101—22no—
48C2×C4×C101C2312yes—
49C2×C4×C101C2312yes—
50C2×C4×C101C2311yescharacteristic
51C22⋊D101—22no—
52C22⋊D101—22no—
53C2×Dic101—22no—
54C2×Dic101C2312yes—
55C2×Dic101C2312yes—
56C2×Dic101C2311yescharacteristic
57D404—22no—
58C4×D101—24no—
59C4×D101—24no—
60C4×D101—22no—
61C4×D101—24no—
62C22×C101—22no—
63C22×C101—21no—
64C22×C101—22no—
65C22×C101C2×D412yes—
66C22×C101C2411yescharacteristic
67C2×D101—22no—
68C2×D101—28no—
69C2×D101—21no—
70C2×D101—22no—
71C2×D101—44no—
72C2×D101C2×D412yes—
73C2×D101C2×D412yes—
74C2×D101#4114yes—
75C4×C101—22no—
76C4×C101—21no—
77C4×C101—22no—
78Dic101—22no—
79Dic101—21no—
80Dic101—22no—
81C2×C101—22no—
82C2×C101—41no—
83C2×C101C22×D411yescharacteristic
84C2×C101C2×#4112yes—
85D101—22no—
86D101—41no—
87D101#12314yesdirect product factor
88C101C2×#12311yescharacteristic, complemented, Sylow
89C2×#123—1011nomaximal, Sylow
90C22×D4—1011no—
91C23×C4—1011no—
92#123—1011no—
93#123—1011no—
94#123—1012no—
95#123—1012no—
96#123—1011no—
97#123D10111yescharacteristic, direct product factor
98C2×C4⋊C4—1012no—
99C2×C22⋊C4—1011no—
100C2×C22⋊C4—1012no—
101C24—1011no—
102C24—1011no—
103C2×D4—1011no—
104C2×D4—1011no—
105C2×D4—1011no—
106C2×D4—2024no—
107C2×D4C2×D10111yescharacteristic
108C22×C4—1011no—
109C22×C4—1012no—
110C22×C4—1012no—
111C22×C4—1011no—
112C22×C4—1012no—
113C22×C4—2024no—
114C22×C4C2×D10111yescharacteristic, complemented
115C4⋊C4—1012no—
116C4⋊C4—1012no—
117C4⋊C4—1012no—
118C4⋊C4C2×D10112yescomplemented
119C22⋊C4—1011no—
120C22⋊C4—1012no—
121C22⋊C4—1012no—
122C22⋊C4—1012no—
123C22⋊C4—1012no—
124C22⋊C4C2×D10111yescharacteristic, complemented
125C22⋊C4C2×D10112yescomplemented
126C23—1011no—
127C23—1014no—
128C23—1011no—
129C23—1011no—
130C23—2022no—
131C23—2024no—
132C23—2024no—
133C23C22×D10111yescharacteristic
134C23C22×D10111yescharacteristic
135D4—22no—
136D4—2022no—
137D4—2022no—
138D4—2022no—
139C2×C4—22no—
140C2×C4—1012no—
141C2×C4—1012no—
142C2×C4—1011no—
143C2×C4—2024no—
144C2×C4—2024no—
145C2×C4—2022no—
146C2×C4—2024no—
147C2×C4—2022no—
148C2×C4C22×D10112yes—
149C2×C4C22×D10112yes—
150C2×C4C22×D10111yescharacteristic
151C22—22no—
152C22—21no—
153C22—22no—
154C22—1012no—
155C22—1014no—
156C22—1012no—
157C22—4044no—
158C22—2028no—
159C22—2021no—
160C22—2022no—
161C22—2022no—
162C22D4×D10112yes—
163C22C23×D10111yescharacteristic
164C4—22no—
165C4—21no—
166C4—22no—
167C4—2022no—
168C4—2021no—
169C4—2022no—
170C2—22no—
171C2—41no—
172C2—1014no—
173C2—4041no—
174C2—2022no—
175C2C2×D4×D10111yescharacteristic
176C2#41×D10112yes—
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
Fitting#123×C101C2
hypercenter#123D101
hypocenterC101C2×#123
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×D101C2semidirect
3. #15692240C2semidirect
4. #15692239C2semidirect
5. #15692238C2semidirect
6. #15692237C2semidirect
7. #15692236C2semidirect
8. C4⋊C4×D101C2semidirect
9. C22⋊C4×D101C2semidirect
10. C22⋊C4×D101C2semidirect
11. #123×C101C2semidirect
18. C22×Dic101C22semidirect
23. C2×C4×D101C22semidirect
24. C4⋊Dic101C22semidirect
25. #13108053C22semidirect
26. #13108053C22semidirect
27. C22⋊Dic101C22semidirect
28. C22⋊Dic101C22semidirect
29. #13108051C22semidirect
30. #13108051C22semidirect
31. #13108051C22semidirect
33. C22×C4×C101C22semidirect
34. C4⋊C4×C101C22semidirect
35. C22⋊C4×C101C22semidirect
36. C22⋊C4×C101C22semidirect
87. D101#123direct (N × H)
88. C101C2×#123semidirect
97. #123D101direct (N × H)
114. C22×C4C2×D101semidirect
118. C4⋊C4C2×D101semidirect
124. C22⋊C4C2×D101semidirect
125. C22⋊C4C2×D101semidirect