Finite Group Databasebeta

← #27186670

Subgroups — #27186670

Order 12928.

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

normal subgroups only

This group has 254 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#20266182C212yesmaximal, complemented
2#20266037C212yesmaximal, complemented
3#20266035C212yesmaximal, complemented
4#20265726C211yesmaximal, characteristic
5C2×#13108084—22no—
6#15692322—22no—
7#15692322C2214yes—
8C2×#13108075C411yescharacteristic
9C2×#13108073C411yescharacteristic
10#15692253C2211yescharacteristic
11#15692251C2211yescharacteristic
12#15692243C411yescharacteristic
13#15692228—22no—
14#15692215—22no—
15C42×D101C2211yescharacteristic
16#124×C101C411yescharacteristic
17#13108084—44no—
18C2×#11717581—24no—
19#13108075—42no—
20#13108073—42no—
21C2×Dic202C2×C411yescharacteristic
22C2×D404—21no—
23C2×D404C2×C411yescharacteristic
24C2×C22⋊D101—21no—
25C2×C22⋊D101—22no—
26C22×Dic101—21no—
27C2×C4×D101—21no—
28C2×C4×D101C2×C411yescharacteristic
29C2×C4×D101D412yes—
30#13108053—22no—
31#13108051—22no—
32C4×Dic101D412yes—
33C4×Dic101C2311yescharacteristic
34C2×Q8×C101C2×C411yescharacteristic
35C2×D4×C101C2×C411yescharacteristic
36C22⋊C4×C101—22no—
37C42×C101C2×C411yescharacteristic
38C23×C101—21no—
39C22×D101—21no—
40C22×D101C22⋊C411yescharacteristic
41Q8×C101—41no—
42D4×C101—41no—
43C2×C4×C101—21no—
44C2×C4×C101C22⋊C412yes—
45C2×C4×C101C22×C411yescharacteristic
46C22⋊D101—42no—
47C22⋊D101—42no—
48C22⋊D101—42no—
49C2×Dic101—21no—
50C2×Dic101—42no—
51C2×Dic101C22⋊C411yescharacteristic
52C2×Dic101C2×D412yes—
53D404—41no—
54D404—42no—
55C4×D101—22no—
56C4×D101—22no—
57C4×D101—22no—
58C4×D101—42no—
59Dic202—41no—
60#11717581—44no—
61C22×C101—41no—
62C22×C101—42no—
63C22×C101C2×C22⋊C411yescharacteristic
64C2×D101—21no—
65C2×D101—22no—
66C2×D101—41no—
67C2×D101—42no—
68C4×C101—21no—
69C4×C101—22no—
70C4×C101—41no—
71Dic101—41no—
72Dic101#10012yes—
73Dic101AGL(1,ℤ/8)12yes—
74Dic101#13712yes—
75C2×C101—81no—
76C2×C101C2×#10011yescharacteristic
77C2×C101#41712yes—
78D101—41no—
79D101—81no—
80#1560—1011nomaximal, Sylow
81C101#156011yescharacteristic, complemented, Sylow
82#532—1011no—
83#423—1012no—
84#333—1012no—
85#331—1012no—
86C2×#41—1011no—
87C2×#41—1011no—
88C2×M16—2022no—
89C4⋊Q8—1011no—
90#127—1011no—
91#124—1011no—
92#124#8793811yescharacteristic
93#121—2022no—
94C4×D4—2022no—
95C2×C42—1011no—
96C4⋊C8—1014no—
97C4⋊C8—2022no—
98#41—4042no—
99#41—4042no—
100C2×Q8—1011no—
101C2×Q8C2×#8793811yescharacteristic
102C2×D4—1011no—
103C2×D4—2021no—
104C2×D4—2022no—
105C2×D4—2021no—
106C2×D4C2×#8793811yescharacteristic
107C22×C4—1012no—
108C22×C4—1011no—
109C22×C4—2021no—
110C22×C4—2021no—
111M16—4044no—
112C2×C8—2024no—
113C4⋊C4—2022no—
114C22⋊C4—22no—
115C22⋊C4—2022no—
116C42—1012no—
117C42—1011no—
118C42C2×#8793811yescharacteristic
119C23—21no—
120C23—1011no—
121C23—2021no—
122Q8—41no—
123Q8—4041no—
124D4—41no—
125D4—4041no—
126D4—4042no—
127D4—4042no—
128D4—4042no—
129D4—4042no—
130C2×C4—21no—
131C2×C4—1012no—
132C2×C4—1011no—
133C2×C4—4042no—
134C2×C4—4042no—
135C2×C4—2022no—
136C2×C4—2022no—
137C2×C4—2022no—
138C2×C4—2021no—
139C2×C4C22⋊#8793812yes—
140C2×C4C22×#8793811yescharacteristic
141C8—4044no—
142C22—41no—
143C22—42no—
144C22—4041no—
145C22—4042no—
146C22—2021no—
147C22—2022no—
148C22C2×C22⋊#8793811yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—1012no—
153C4—1012no—
154C4—1012no—
155C4—4041no—
156C2—81no—
157C2—8081no—
158C2—4041no—
159C2D101⋊#10011yescharacteristic
160C2#2026616812yes—
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#124×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265726C2
cosocleC4×Dic101C23
hypercenter#124#87938
hypocenterC101#1560
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20266182C2semidirect
2. #20266037C2semidirect
3. #20266035C2semidirect
81. C101#1560semidirect

Maximal subgroups

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

subgroupindex
#202661822
#202660372
#202660352
#202657262
#1560101