Finite Group Databasebeta

← #27186595

Subgroups — #27186595

Order 12928.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#20266200C211yesmaximal, characteristic
2C4×#13108084C211yesmaximal, characteristic
3#20266034C212yesmaximal, complemented
4#20266034C212yesmaximal, complemented
5#125×D101C211yesmaximal, characteristic
6C2×#13108084—21no—
7#15692322—21no—
8#15692312—21no—
9#15692310C2212yes—
10#15692310C2212yes—
11C4×#11717581—21no—
12#15692247C411yescharacteristic
13#15692246C2211yescharacteristic
14#15692246C2211yescharacteristic
15#15692245—21no—
16#15692245—21no—
17C4⋊C4×D101—21no—
18C4⋊C4×D101—21no—
19C4⋊C4×D101C411yescharacteristic
20C4⋊C4×D101C411yescharacteristic
21C42×D101C2211yescharacteristic
22#125×C101C411yescharacteristic
23#13108084—24no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26C2×C4×D101—21no—
27C2×C4×D101—21no—
28C2×C4×D101C2×C411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33C4⋊Dic101C2×C411yescharacteristic
34C4⋊Dic101C2×C411yescharacteristic
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41C4×Dic101D411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101C2311yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101C2×C411yescharacteristic
49C22×D101C22⋊C411yescharacteristic
50C2×C4×C101—21no—
51C2×C4×C101—21no—
52C2×C4×C101C22⋊C411yescharacteristic
53C2×C4×C101C22⋊C411yescharacteristic
54C2×C4×C101C22×C411yescharacteristic
55C2×Dic101—21no—
56C2×Dic101—21no—
57C2×Dic101C22⋊C411yescharacteristic
58C2×Dic101C2×D411yescharacteristic
59C2×Dic101C2×D411yescharacteristic
60C4×D101—22no—
61C4×D101—22no—
62C4×D101—41no—
63C4×D101—42no—
64C4×D101—42no—
65#11717581—24no—
66#11717581—42no—
67C22×C101C2×C22⋊C411yescharacteristic
68C2×D101—21no—
69C2×D101—21no—
70C2×D101#10412yes—
71C4×C101—21no—
72C4×C101—21no—
73C4×C101—21no—
74C4×C101—41no—
75C4×C101—41no—
76Dic101—21no—
77Dic101—21no—
78Dic101—41no—
79Dic101—41no—
80Dic101#10112yes—
81C2×C101C2×#10111yescharacteristic
82C2×C101C2×#10411yescharacteristic
83C2×C101#42111yescharacteristic
84D101—22no—
85#1528—1011nomaximal, Sylow
86C101#152811yescharacteristic, complemented, Sylow
87C2×#125—1011no—
88#432—1011no—
89C4×M16—1011no—
90#330—1012no—
91#330—1012no—
92C2×M16—2021no—
93#125—1011no—
94#125—1011no—
95#125—1011no—
96#125—2021no—
97#125—2021no—
98#125#8793811yescharacteristic
99C2×C4⋊C4—1011no—
100C2×C4⋊C4—1011no—
101C2×C4⋊C4—2021no—
102C2×C4⋊C4—2021no—
103C2×C42—1011no—
104C4⋊C8—2021no—
105C22⋊C8—2021no—
106#97—1012no—
107#97—1012no—
108C4×C8—2021no—
109C22×C4—1011no—
110C22×C4—1011no—
111C22×C4—1011no—
112C22×C4—2021no—
113C22×C4—2021no—
114M16—2024no—
115C2×C8—2022no—
116C2×C8—2022no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—1011no—
120C4⋊C4—1011no—
121C4⋊C4—2021no—
122C4⋊C4—2021no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4C2×#8793811yescharacteristic
130C4⋊C4C2×#8793811yescharacteristic
131C42—1011no—
132C42—1011no—
133C42—1011no—
134C42C2×#8793811yescharacteristic
135C23—1011no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—1011no—
139C2×C4—1011no—
140C2×C4—1011no—
141C2×C4—4041no—
142C2×C4—4042no—
143C2×C4—4042no—
144C2×C4—2022no—
145C2×C4—2022no—
146C2×C4—2021no—
147C2×C4—2021no—
148C2×C4C22⋊#8793811yescharacteristic
149C2×C4C22⋊#8793811yescharacteristic
150C2×C4C22×#8793811yescharacteristic
151C8—4042no—
152C8—2024no—
153C22—1012no—
154C22—2021no—
155C22—2021no—
156C22C2×C22⋊#8793811yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—1012no—
163C4—4041no—
164C4—4041no—
165C4—2021no—
166C4—2021no—
167C2—2022no—
168C2D101⋊#10111yescharacteristic
169C2D101⋊#10411yescharacteristic
170C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#125×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC4×Dic101C23
hypercenter#125#87938
hypocenterC101#1528
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #20266034C2semidirect
4. #20266034C2semidirect
86. C101#1528semidirect

Maximal subgroups

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

subgroupindex
#202662002
C4×#131080842
#202660342
#125×D1012
#1528101