Finite Group Databasebeta

← #27186603

Subgroups — #27186603

Order 12928.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266199C211yesmaximal, characteristic, complemented
2#20266136C211yesmaximal, characteristic, complemented
3#20266033C214yesmaximal, complemented
4#20265728C211yesmaximal, characteristic
5C2×D101⋊C8—21no—
6C4⋊#11717581—21no—
7#15692312—21no—
8#15692310—21no—
9#15692310C2212yes—
10#15692310C2212yes—
11C2×#13108075C412yes—
12#15692252C411yescharacteristic
13#15692244C2212yes—
14#15692230—21no—
15#15692230—21no—
16#15692217—21no—
17#15692217—21no—
18C42×D101C2211yescharacteristic
19C4⋊Q8×C101C411yescharacteristic
20D101⋊C8—24no—
21C2×#11717581—22no—
22C2×#11717581—22no—
23#13108075—44no—
24C2×D404—22no—
25C2×D404—21no—
26C2×D404—21no—
27C2×D404C2×C412yes—
28C2×C4×D101—22no—
29C2×C4×D101C2×C411yescharacteristic
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32#13108051—22no—
33#13108051—22no—
34C4×Dic101D411yescharacteristic
35C4×Dic101D411yescharacteristic
36C4×Dic101C2311yescharacteristic
37C2×Q8×C101C2×C412yes—
38C4⋊C4×C101—21no—
39C4⋊C4×C101—21no—
40C42×C101C2×C411yescharacteristic
41C22×D101—22no—
42C22×D101C22⋊C411yescharacteristic
43Q8×C101—42no—
44C2×C4×C101—22no—
45C2×C4×C101C22⋊C411yescharacteristic
46C2×C4×C101C22⋊C411yescharacteristic
47C2×C4×C101C22×C411yescharacteristic
48C2×Dic101C22⋊C411yescharacteristic
49C2×Dic101C2×D411yescharacteristic
50C2×Dic101C2×D411yescharacteristic
51D404—42no—
52D404—42no—
53D404—44no—
54D404—42no—
55C4×D101—22no—
56C4×D101—22no—
57C4×D101—41no—
58C4×D101—44no—
59#11717581—24no—
60#11717581—42no—
61C22×C101C2×C22⋊C411yescharacteristic
62C2×D101—21no—
63C2×D101—21no—
64C2×D101—42no—
65C2×D101—42no—
66C2×D101—42no—
67C2×D101#10012yes—
68C4×C101—21no—
69C4×C101—21no—
70C4×C101—42no—
71C4×C101#10412yes—
72Dic101—21no—
73Dic101—21no—
74Dic101—21no—
75C2×C101C2×#10011yescharacteristic
76C2×C101C2×#10411yescharacteristic
77C2×C101#42111yescharacteristic
78D101—22no—
79D101—82no—
80#1530—1011nomaximal, Sylow
81C101#153011yescharacteristic, complemented, Sylow
82#532—1011no—
83#432—1011no—
84C2×#97—1011no—
85#329—1014no—
86C2×#41—1012no—
87C22×C8—2021no—
88C4⋊Q8#8793811yescharacteristic
89#127—1011no—
90#124—1012no—
91#121—2021no—
92#121—2021no—
93C4×D4—2021no—
94C4×D4—2021no—
95C2×C42—1011no—
96C4⋊C8—2021no—
97C22⋊C8—2021no—
98#97—1012no—
99#97—1012no—
100#97—2021no—
101#41—4044no—
102C2×Q8C2×#8793812yes—
103C2×D4—1012no—
104C2×D4—2022no—
105C2×D4—2021no—
106C2×D4—2021no—
107C22×C4—1011no—
108C22×C4—1011no—
109C22×C4—1011no—
110C22×C4—2022no—
111C2×C8—2022no—
112C2×C8—2022no—
113C2×C8—2024no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C22⋊C4—2022no—
117C22⋊C4—2022no—
118C42—1011no—
119C42—1011no—
120C42—1011no—
121C42C2×#8793811yescharacteristic
122C23—1011no—
123C23—2022no—
124Q8—42no—
125D4—4042no—
126D4—4042no—
127D4—4044no—
128D4—4042no—
129C2×C4—22no—
130C2×C4—1011no—
131C2×C4—1011no—
132C2×C4—1011no—
133C2×C4—4041no—
134C2×C4—4044no—
135C2×C4—2022no—
136C2×C4—2022no—
137C2×C4C22⋊#8793811yescharacteristic
138C2×C4C22⋊#8793811yescharacteristic
139C2×C4C22×#8793811yescharacteristic
140C8—4042no—
141C8—2024no—
142C22—1012no—
143C22—4042no—
144C22—4042no—
145C22—4042no—
146C22—2021no—
147C22—2021no—
148C22C2×C22⋊#8793811yescharacteristic
149C4—21no—
150C4—21no—
151C4—42no—
152C4—2021no—
153C4—2021no—
154C4—2021no—
155C4#1569232012yes—
156C2—8082no—
157C2—2022no—
158C2D101⋊#10011yescharacteristic
159C2C2×#1569232011yescharacteristic
160C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265728C2
cosocleC4×Dic101C23
hypercenterC4⋊Q8#87938
hypocenterC101#1530
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. #20266136C2semidirect
3. #20266033C2semidirect
81. C101#1530semidirect

Maximal subgroups

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

subgroupindex
#202661992
#202661362
#202660332
#202657282
#1530101