Finite Group Databasebeta

← #27186433

Subgroups — #27186433

Order 12928.

312 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 84 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
1#20266193C211yesmaximal, characteristic, complemented
2#20266193C211yesmaximal, characteristic, complemented
3#20266025C214yesmaximal, complemented
4C2×#15692217C211yesmaximal, characteristic
5C4⋊#11717581—21no—
6C4⋊#11717581C2212yescomplemented
7C22⋊#11717581—21no—
8C22⋊#11717581—21no—
9C4×#11717581—21no—
10C4×#11717581C2212yescomplemented
11C22×D404C411yescharacteristic
12C22×C4×D101—21no—
13#15692217—21no—
14#15692217—21no—
15#15692217C412yes—
16#15692217C2212yes—
17C2×#13108051—21no—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20C2×#11717581—22no—
21C2×#11717581—22no—
22C23×D101—21no—
23C2×D404—21no—
24C2×D404—22no—
25C2×D404C814yescomplemented
26C2×D404C2×C412yes—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C2×C4×D101—22no—
30C2×C4×D101—22no—
31C2×C4×D101—44no—
32#13108051—22no—
33#13108051—22no—
34C4×Dic101C2×C411yescharacteristic
35C4×Dic101D411yescharacteristic
36C4×Dic101D411yescharacteristic
37C4×Dic101C2311yescharacteristic
38C22×C4×C101—21no—
39C22×C4×C101C2×C411yescharacteristic
40C4⋊C4×C101—21no—
41C4⋊C4×C101C2×C412yes—
42C23×C101C22⋊C411yescharacteristic
43C22×D101—24no—
44C22×D101—22no—
45C22×D101—42no—
46C22×D101—42no—
47C2×C4×C101—22no—
48C2×C4×C101—42no—
49C2×C4×C101C22⋊C411yescharacteristic
50C2×C4×C101C2×C812yes—
51C2×C4×C101M1612yes—
52C2×C4×C101C22×C411yescharacteristic
53C2×Dic101—22no—
54C2×Dic101—41no—
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C2×D411yescharacteristic
58C2×Dic101C2×D411yescharacteristic
59D404—24no—
60D404—22no—
61D404C2×C814yes—
62C4×D101—44no—
63C4×D101—44no—
64#11717581—42no—
65#11717581—42no—
66C22×C101—21no—
67C22×C101—21no—
68C22×C101C22⋊C812yes—
69C22×C101C2×C22⋊C411yescharacteristic
70C2×D101—24no—
71C2×D101—48no—
72C2×D101—42no—
73C2×D101—42no—
74C4×C101—42no—
75C4×C101C22⋊C812yes—
76C4×C101C22×C811yescharacteristic
77C4×C101C2×M1611yescharacteristic
78Dic101—21no—
79Dic101—21no—
80Dic101—21no—
81Dic101AGL(1,ℤ/8)12yes—
82C2×C101—22no—
83C2×C101C2×C22⋊C811yescharacteristic
84C2×C101#41811yescharacteristic
85C2×C101#42111yescharacteristic
86D101—44no—
87#1478—1011nomaximal, Sylow
88C101#147811yescharacteristic, complemented, Sylow
89C2×C4×D4—1011no—
90#431—1011no—
91#431—1011no—
92D4⋊C8—1014no—
93C22×D4—1011no—
94C23×C4—2021no—
95C4×D4—1012no—
96C4×D4—1012no—
97C4×D4—2021no—
98C4×D4—2021no—
99C2×C4⋊C4#8793811yescharacteristic
100C2×C22⋊C4—2021no—
101C2×C42—1011no—
102C4⋊C8—1012no—
103C4⋊C8—2021no—
104C22⋊C8—2021no—
105C22⋊C8—2021no—
106C4×C8—1012no—
107C4×C8—2021no—
108C24—2021no—
109C2×D4—1014no—
110C2×D4—1012no—
111C2×D4—2021no—
112C2×D4—2022no—
113C22×C4—21no—
114C22×C4—1011no—
115C22×C4—1011no—
116C22×C4—4044no—
117C22×C4—2022no—
118C22×C4—2022no—
119C22×C4C2×#8793811yescharacteristic
120C2×C8—2022no—
121C2×C8—2022no—
122C4⋊C4—21no—
123C4⋊C4C2×#8793812yes—
124C22⋊C4—2022no—
125C22⋊C4—2022no—
126C42—1011no—
127C42—1011no—
128C42—1011no—
129C42—1011no—
130C23—4042no—
131C23—4042no—
132C23—2024no—
133C23—2022no—
134C23C22⋊#8793811yescharacteristic
135D4—1014no—
136D4—2024no—
137D4—2022no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—1011no—
141C2×C4—1011no—
142C2×C4—1011no—
143C2×C4—1011no—
144C2×C4—4044no—
145C2×C4—4044no—
146C2×C4—4041no—
147C2×C4—2022no—
148C2×C4C22⋊#8793811yescharacteristic
149C2×C4D101⋊C812yes—
150C2×C4#1310808412yes—
151C2×C4C22×#8793811yescharacteristic
152C8—4042no—
153C8—4042no—
154C22—21no—
155C22—21no—
156C22—4048no—
157C22—4042no—
158C22—4042no—
159C22—2024no—
160C22#1569231212yes—
161C22C2×C22⋊#8793811yescharacteristic
162C4—42no—
163C4—1012no—
164C4—2021no—
165C4—2021no—
166C4—2021no—
167C4#1569231212yes—
168C4C2×D101⋊C811yescharacteristic
169C4C2×#1310808411yescharacteristic
170C2—22no—
171C2—4044no—
172C2C2×#1569231211yescharacteristic
173C2#2026616911yescharacteristic
174C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC4×C101C22×C8
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D404C4
cosocleC4×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1478
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266193C2semidirect
2. #20266193C2semidirect
3. #20266025C2semidirect
6. C4⋊#11717581C22semidirect
10. C4×#11717581C22semidirect
25. C2×D404C8semidirect
88. C101#1478semidirect

Maximal subgroups

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

subgroupindex
#202661932
#202660252
C2×#156922172
#1478101