Finite Group Databasebeta

← #27186636

Subgroups — #27186636

Order 12928.

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

normal subgroups only

This group has 246 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#20266195C212yesmaximal, complemented
2#20266037C212yesmaximal, complemented
3#20266035C212yesmaximal, complemented
4#20265726C211yesmaximal, characteristic
5#15692322C2214yes—
6#15692312—22no—
7C4×#11717581—22no—
8C2×#13108075C411yescharacteristic
9C2×#13108073C411yescharacteristic
10#15692253C2211yescharacteristic
11#15692251C2211yescharacteristic
12#15692243C411yescharacteristic
13#15692228—22no—
14#15692215—22no—
15C42×D101C2211yescharacteristic
16#124×C101C411yescharacteristic
17C2×#11717581—24no—
18#13108075—42no—
19#13108073—42no—
20C2×Dic202C2×C411yescharacteristic
21C2×D404—21no—
22C2×D404C2×C411yescharacteristic
23C2×C22⋊D101—21no—
24C2×C22⋊D101—22no—
25C22×Dic101—21no—
26C2×C4×D101—21no—
27C2×C4×D101C2×C411yescharacteristic
28C2×C4×D101D412yes—
29#13108053—22no—
30#13108051—22no—
31C4×Dic101D412yes—
32C4×Dic101C2311yescharacteristic
33C2×Q8×C101C2×C411yescharacteristic
34C2×D4×C101C2×C411yescharacteristic
35C22⋊C4×C101—22no—
36C42×C101C2×C411yescharacteristic
37C23×C101—21no—
38C22×D101—21no—
39C22×D101C22⋊C411yescharacteristic
40Q8×C101—41no—
41D4×C101—41no—
42C2×C4×C101—21no—
43C2×C4×C101C22⋊C412yes—
44C2×C4×C101C22×C411yescharacteristic
45C22⋊D101—42no—
46C22⋊D101—44no—
47C2×Dic101—21no—
48C2×Dic101—42no—
49C2×Dic101C22⋊C411yescharacteristic
50C2×Dic101C2×D412yes—
51D404—41no—
52D404—42no—
53C4×D101—22no—
54C4×D101—24no—
55C4×D101—42no—
56Dic202—41no—
57#11717581—44no—
58C22×C101—41no—
59C22×C101—42no—
60C22×C101C2×C22⋊C411yescharacteristic
61C2×D101—21no—
62C2×D101—22no—
63C2×D101—41no—
64C2×D101—42no—
65C4×C101—21no—
66C4×C101—22no—
67C4×C101—41no—
68Dic101—41no—
69Dic101#10012yes—
70Dic101#13514yes—
71C2×C101—81no—
72C2×C101C2×#10011yescharacteristic
73C2×C101#41612yes—
74D101—41no—
75D101—81no—
76#1543—1011nomaximal, Sylow
77C101#154311yescharacteristic, complemented, Sylow
78#532—1011no—
79#431—1012no—
80#333—1012no—
81#331—1012no—
82C2×#41—1011no—
83C2×#41—1011no—
84C4⋊Q8—1011no—
85#127—1011no—
86#124—1011no—
87#124#8793811yescharacteristic
88#121—2022no—
89C4×D4—2022no—
90C2×C42—1011no—
91C4⋊C8—1014no—
92C22⋊C8—2022no—
93C4×C8—2022no—
94#41—4042no—
95#41—4042no—
96C2×Q8—1011no—
97C2×Q8C2×#8793811yescharacteristic
98C2×D4—1011no—
99C2×D4—2021no—
100C2×D4—2022no—
101C2×D4—2021no—
102C2×D4C2×#8793811yescharacteristic
103C22×C4—1012no—
104C22×C4—1011no—
105C22×C4—2021no—
106C22×C4—2021no—
107C2×C8—2024no—
108C4⋊C4—2022no—
109C22⋊C4—22no—
110C22⋊C4—2022no—
111C42—1012no—
112C42—1011no—
113C42C2×#8793811yescharacteristic
114C23—21no—
115C23—1011no—
116C23—2021no—
117Q8—41no—
118Q8—4041no—
119D4—41no—
120D4—4041no—
121D4—4042no—
122D4—4044no—
123D4—4042no—
124C2×C4—21no—
125C2×C4—1012no—
126C2×C4—1011no—
127C2×C4—4042no—
128C2×C4—4042no—
129C2×C4—2022no—
130C2×C4—2024no—
131C2×C4—2021no—
132C2×C4C22⋊#8793812yes—
133C2×C4C22×#8793811yescharacteristic
134C8—4044no—
135C22—41no—
136C22—42no—
137C22—4041no—
138C22—4042no—
139C22—2021no—
140C22—2022no—
141C22C2×C22⋊#8793811yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—1012no—
146C4—1014no—
147C4—4041no—
148C2—81no—
149C2—8081no—
150C2—4041no—
151C2D101⋊#10011yescharacteristic
152C2#2026616712yes—
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#1543
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. #20266195C2semidirect
2. #20266037C2semidirect
3. #20266035C2semidirect
77. C101#1543semidirect

Maximal subgroups

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

subgroupindex
#202661952
#202660372
#202660352
#202657262
#1543101