Finite Group Databasebeta

← #27187090

Subgroups — #27187090

Order 12928.

252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 66 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#20266257C211yesmaximal, characteristic
2#20266192C212yesmaximal, complemented
3#20266152C211yesmaximal, characteristic
4#20266052C212yesmaximal, complemented
5#20265160C211yesmaximal, characteristic
6#15692343—22no—
7#15692343—22no—
8C2×#13108084C2211yescharacteristic
9D101⋊M16—22no—
10D101⋊M16C2212yes—
11C2×D101⋊C8C2211yescharacteristic
12#15692326—22no—
13#15692325—22no—
14#15692312—22no—
15C2×#13108075C2211yescharacteristic
16M16×D101C2212yes—
17#15692174C411yescharacteristic
18#15692171C412yes—
19#101×C101C411yescharacteristic
20#13108084—22no—
21#13108084—22no—
22#13108084—22no—
23#13108084D412yes—
24#13108084D412yes—
25#13108083—22no—
26D101⋊C8—24no—
27D101⋊C8—22no—
28D101⋊C8—22no—
29C2×#11717581—21no—
30C2×#11717581—21no—
31#13108075—22no—
32#13108075—22no—
33C2×D404C2×C411yescharacteristic
34C2×D404Q812yes—
35C2×C4×D101D412yes—
36C2×C4×D101C2311yescharacteristic
37#13108058C2×C412yes—
38#13108057—22no—
39C8×D101—22no—
40C2×Q8×C101C2×C411yescharacteristic
41M16×C101C2×C412yes—
42C22×D101C4⋊C412yes—
43C22×D101C2×Q811yescharacteristic
44Q8×C101—22no—
45C2×C4×C101C4⋊C412yes—
46C2×C4×C101C22×C411yescharacteristic
47C2×Dic101C2×D411yescharacteristic
48D404—24no—
49D404—22no—
50C4×D101—22no—
51C4×D101—22no—
52C4×D101C2×D412yes—
53C4×D101#4112yes—
54#11717581—22no—
55#11717581—22no—
56#11717581—41no—
57#11717581—41no—
58C8×C101—22no—
59#11717579—22no—
60C22×C101C2×C4⋊C411yescharacteristic
61C2×D101—22no—
62C2×D101—41no—
63C2×D101—42no—
64C2×D101C22⋊Q812yes—
65C4×C101—22no—
66C4×C101C4×D412yes—
67Dic101#12011yescharacteristic
68Dic101#12311yescharacteristic
69C2×C101—21no—
70C2×C101#38511yescharacteristic
71D101—22no—
72D101—42no—
73#1858—1011nomaximal, Sylow
74C101#185811yescharacteristic, complemented, Sylow
75#568—1011no—
76#430—1012no—
77#413—1011no—
78#408—1011no—
79#341—1012no—
80C2×#41—1011no—
81#131—2022no—
82#131—2022no—
83C2×M16—1012no—
84C2×M16—1012no—
85C2×M16—1011no—
86C2×M16—2022no—
87C22×C8—1011no—
88#108—2022no—
89#108—2022no—
90#101—1011no—
91#101#8793811yescharacteristic
92#100—1012no—
93C22⋊C8—2022no—
94#41—2022no—
95#41—2022no—
96C2×Q8C2×#8793811yescharacteristic
97C2×D4—1012no—
98C2×D4—1011no—
99C22×C4—1011no—
100C22×C4—1012no—
101M16—1012no—
102M16—1012no—
103M16—1012no—
104M16—2022no—
105M16—2022no—
106M16—2022no—
107M16—2022no—
108M16—2022no—
109M16C2×#8793812yes—
110C2×C8—2022no—
111C2×C8—2021no—
112C2×C8—2021no—
113C2×C8—2022no—
114C2×C8—2022no—
115C2×C8—2024no—
116C23—1011no—
117C23—1012no—
118Q8—22no—
119D4—2024no—
120D4—2022no—
121C2×C4—1011no—
122C2×C4—1012no—
123C2×C4—1012no—
124C2×C4—2022no—
125C2×C4—2022no—
126C2×C4C4⋊#8793812yes—
127C2×C4C22×#8793811yescharacteristic
128C8—22no—
129C8—4041no—
130C8—4041no—
131C8—2022no—
132C8—2022no—
133C8—2022no—
134C22—1012no—
135C22—4042no—
136C22—4041no—
137C22—2022no—
138C22C2×C4⋊#8793811yescharacteristic
139C4—22no—
140C4—1011no—
141C4—1011no—
142C4D4×#8793812yes—
143C2—21no—
144C2—4042no—
145C2—2022no—
146C2#2026612411yescharacteristic
subgroupG/H
centerC2#20266124
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#101×C101C4
socleC2×C101#385
prime radicalC2×#13108075C22
cosocleC2×C4×D101C23
hypercenter#101#87938
hypocenterC101#1858
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
2. #20266192C2semidirect
4. #20266052C2semidirect
74. C101#1858semidirect

Maximal subgroups

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

subgroupindex
#202662572
#202661922
#202661522
#202660522
#202651602
#1858101