Finite Group Databasebeta

← #27186524

Subgroups — #27186524

Order 12928.

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

normal subgroups only

This group has 228 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
2#20266113C211yesmaximal, characteristic
3#20266030C214yesmaximal
4#20265732C211yesmaximal, characteristic
5C2×C4×#87938—21no—
6C4⋊#11717581—21no—
7#15692312C2212yes—
8#15692310—21no—
9(C2×#87938)⋊C4—21no—
10(C2×#87938)⋊C4C2212yes—
11#15692255C411yescharacteristic, complemented
12#15692246—21no—
13#15692235C2212yes—
14#15692231—21no—
15Q8×Dic101—21no—
16#15692220C412yescomplemented
17#15692213—21no—
18C42×D101C2211yescharacteristic
19C4⋊Q8×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21C2×#11717581—22no—
22C4×#87938—24no—
23C2×Dic202C2×C412yes—
24C2×C4×D101D411yescharacteristic
25C2×C4×D101D411yescharacteristic
26C2×C4×D101C2311yescharacteristic
27C4⋊Dic101—21no—
28C4⋊Dic101—21no—
29C4⋊Dic101—22no—
30#13108053—22no—
31#13108051—22no—
32C4×Dic101—22no—
33C4×Dic101C2×C411yescharacteristic
34C4×Dic101D411yescharacteristic
35C4×Dic101D411yescharacteristic
36C2×Q8×C101—21no—
37C4⋊C4×C101—21no—
38C4⋊C4×C101C2×C412yes—
39C42×C101C2×C411yescharacteristic
40C22×D101C2×D411yescharacteristic
41C2×#87938—24no—
42C2×#87938—42no—
43C2×#87938—42no—
44Q8×C101—42no—
45C2×C4×C101—22no—
46C2×C4×C101C22⋊C411yescharacteristic
47C2×C4×C101C22⋊C411yescharacteristic
48C2×C4×C101C22×C411yescharacteristic
49C2×Dic101—22no—
50C2×Dic101C22⋊C411yescharacteristic
51C2×Dic101C22⋊C411yescharacteristic
52C2×Dic101C2×D411yescharacteristic
53C4×D101—22no—
54C4×D101—22no—
55C4×D101—41no—
56Dic202—42no—
57#11717581—42no—
58C22×C101C2×C22⋊C411yescharacteristic
59C2×D101—21no—
60C2×D101—21no—
61C2×D101#13712yes—
62#87938—44no—
63C4×C101—21no—
64C4×C101—21no—
65C4×C101—42no—
66C4×C101#10412yes—
67Dic101—21no—
68Dic101—21no—
69Dic101—21no—
70Dic101—42no—
71C2×C101#41011yescharacteristic
72C2×C101#41911yescharacteristic
73C2×C101C2×#10411yescharacteristic
74D101—22no—
75#1506—1011nomaximal, Sylow
76C101#150611yescharacteristic, complemented, Sylow
77#533—1011no—
78#432—1011no—
79#376—1011no—
80#328—1014no—
81C4⋊Q8—1011no—
82C4⋊Q8#8793811yescharacteristic, complemented
83#125—2021no—
84C22⋊Q8—1012no—
85C22⋊Q8—2021no—
86C4×Q8—1012no—
87C4×Q8—2021no—
88#117—2021no—
89C2×C42—1011no—
90C2×C42—2021no—
91C4⋊C8—2021no—
92C22⋊C8—1012no—
93#97—2021no—
94#95—1012no—
95#95—2021no—
96C2×Q8—21no—
97C2×Q8—1012no—
98C22×C4—1011no—
99C22×C4—1011no—
100C22×C4—1011no—
101C22×C4—2022no—
102C2×C8—2022no—
103C4⋊C4—21no—
104C4⋊C4—2022no—
105C4⋊C4—2022no—
106C4⋊C4—2021no—
107C4⋊C4—2021no—
108C4⋊C4C2×#8793812yes—
109C22⋊C4—2022no—
110C42—1011no—
111C42—1011no—
112C42—1011no—
113C42—2022no—
114C42—2024no—
115C42C2×#8793811yescharacteristic
116C23—1011no—
117Q8—42no—
118Q8—4042no—
119C2×C4—22no—
120C2×C4—1011no—
121C2×C4—1011no—
122C2×C4—1011no—
123C2×C4—4041no—
124C2×C4—4042no—
125C2×C4—4042no—
126C2×C4—2022no—
127C2×C4—2024no—
128C2×C4—2022no—
129C2×C4—2022no—
130C2×C4C22⋊#8793811yescharacteristic
131C2×C4C22⋊#8793811yescharacteristic
132C2×C4C22×#8793811yescharacteristic
133C8—4042no—
134C22—1012no—
135C22—2021no—
136C22—2021no—
137C22C2×C22⋊#8793811yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—4044no—
142C4—4042no—
143C4—2021no—
144C4—2021no—
145C4—2021no—
146C4#1569231912yes—
147C2—2022no—
148C2#2026615811yescharacteristic
149C2#2026617011yescharacteristic
150C2C2×#1569231911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenterC4⋊Q8#87938
hypocenterC101#1506
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
11. #15692255C4semidirect
16. #15692220C4semidirect
19. C4⋊Q8×C101C4semidirect
76. C101#1506semidirect
82. C4⋊Q8#87938semidirect

Maximal subgroups

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

subgroupindex
#202661992
#202661132
#202660302
#202657322
#1506101