Finite Group Databasebeta

← #27186493

Subgroups — #27186493

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#20266199C211yesmaximal, characteristic, complemented
2#20266195C211yesmaximal, characteristic, complemented
3#20266025C214yesmaximal, complemented
4#20265728C211yesmaximal, characteristic
5#15692322—21no—
6C4⋊#11717581C2212yes—
7#15692312—21no—
8#15692312—21no—
9#15692310—21no—
10C4×#11717581C2212yes—
11C2×#13108075—21no—
12#15692252C411yescharacteristic
13#15692244—21no—
14#15692230—21no—
15#15692230C412yes—
16#15692217—21no—
17#15692217C2212yes—
18C42×D101C2211yescharacteristic
19C4⋊Q8×C101C411yescharacteristic
20C2×#11717581—22no—
21C2×#11717581—22no—
22#13108075—44no—
23C2×D404—22no—
24C2×D404—21no—
25C2×D404—21no—
26C2×D404C2×C412yes—
27C2×C4×D101—22no—
28C2×C4×D101C2×C411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31#13108051—22no—
32#13108051—22no—
33C4×Dic101D411yescharacteristic
34C4×Dic101D411yescharacteristic
35C4×Dic101C2311yescharacteristic
36C2×Q8×C101—21no—
37C4⋊C4×C101—21no—
38C4⋊C4×C101C2×C412yes—
39C42×C101C2×C411yescharacteristic
40C22×D101—22no—
41C22×D101C22⋊C411yescharacteristic
42Q8×C101—42no—
43C2×C4×C101—22no—
44C2×C4×C101C22⋊C411yescharacteristic
45C2×C4×C101C22⋊C411yescharacteristic
46C2×C4×C101C22×C411yescharacteristic
47C2×Dic101C22⋊C411yescharacteristic
48C2×Dic101C2×D411yescharacteristic
49C2×Dic101C2×D411yescharacteristic
50D404—24no—
51D404—42no—
52D404—42no—
53D404—44no—
54C4×D101—22no—
55C4×D101—22no—
56C4×D101—41no—
57C4×D101—44no—
58#11717581—42no—
59#11717581—42no—
60C22×C101C2×C22⋊C411yescharacteristic
61C2×D101—21no—
62C2×D101—21no—
63C2×D101—21no—
64C2×D101—42no—
65C2×D101—42no—
66C2×D101—42no—
67C4×C101—21no—
68C4×C101—21no—
69C4×C101—42no—
70C4×C101#13112yes—
71Dic101—21no—
72Dic101—21no—
73Dic101AGL(1,ℤ/8)12yes—
74C2×C101#40811yescharacteristic
75C2×C101#41811yescharacteristic
76C2×C101#42111yescharacteristic
77D101—41no—
78D101—82no—
79#1496—1011nomaximal, Sylow
80C101#149611yescharacteristic, complemented, Sylow
81#532—1011no—
82#432—1011no—
83#431—1011no—
84D4⋊C8—1014no—
85C2×#41—2021no—
86C4⋊Q8#8793811yescharacteristic
87#127—1011no—
88#124—2021no—
89#121—1012no—
90#121—2021no—
91C4×D4—1012no—
92C4×D4—2021no—
93C2×C42—1011no—
94C4⋊C8—1012no—
95C4⋊C8—2021no—
96C22⋊C8—2021no—
97C22⋊C8—2021no—
98#97—2021no—
99C4×C8—1012no—
100#41—4044no—
101C2×Q8—21no—
102C2×D4—1012no—
103C2×D4—2022no—
104C2×D4—2021no—
105C2×D4—2021no—
106C22×C4—1011no—
107C22×C4—1011no—
108C22×C4—1011no—
109C22×C4—2022no—
110C2×C8—2022no—
111C2×C8—2022no—
112C4⋊C4—21no—
113C4⋊C4C2×#8793812yes—
114C22⋊C4—2022no—
115C22⋊C4—2022no—
116C42—1011no—
117C42—1011no—
118C42—1011no—
119C42C2×#8793811yescharacteristic
120C23—1011no—
121C23—2022no—
122Q8—42no—
123D4—4042no—
124D4—4042no—
125D4—4044no—
126D4—2024no—
127C2×C4—22no—
128C2×C4—1011no—
129C2×C4—1011no—
130C2×C4—1011no—
131C2×C4—4041no—
132C2×C4—4044no—
133C2×C4—2022no—
134C2×C4—2022no—
135C2×C4C22⋊#8793811yescharacteristic
136C2×C4C22⋊#8793811yescharacteristic
137C2×C4C22×#8793811yescharacteristic
138C8—4042no—
139C8—4042no—
140C22—4042no—
141C22—4042no—
142C22—4042no—
143C22—2021no—
144C22—2021no—
145C22—2021no—
146C22C2×C22⋊#8793811yescharacteristic
147C4—21no—
148C4—21no—
149C4—42no—
150C4—1012no—
151C4—2021no—
152C4—2021no—
153C4#1569234312yes—
154C2—8082no—
155C2—4041no—
156C2#2026615211yescharacteristic
157C2#2026616911yescharacteristic
158C2#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#1496
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. #20266195C2semidirect
3. #20266025C2semidirect
80. C101#1496semidirect

Maximal subgroups

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

subgroupindex
#202661992
#202661952
#202660252
#202657282
#1496101