Finite Group Databasebeta

← #27186381

Subgroups — #27186381

Order 12928.

312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266148C212yesmaximal
2#20266023C212yesmaximal, complemented
3#20266022C212yesmaximal, complemented
4C2×C4⋊C4×D101C211yesmaximal, characteristic
5C2×#13108084—22no—
6#15692312—22no—
7C22⋊#11717581C2214yes—
8C22×C4×D101C411yescharacteristic
9C22×C4×D101C411yescharacteristic
10C22×C4×D101C2211yescharacteristic
11C2×C4⋊Dic101C2211yescharacteristic
12C2×#13108053C411yescharacteristic
13C2×#13108053C2211yescharacteristic
14C4⋊C4×D101—22no—
15C4⋊C4×D101—22no—
16C2×C4⋊C4×C101C411yescharacteristic
17#13108084—44no—
18C2×#11717581—24no—
19C23×D101C2×C411yescharacteristic
20C22×Dic101C2×C411yescharacteristic
21C22×Dic101C2×C411yescharacteristic
22C22×Dic101C2311yescharacteristic
23C2×C4×D101—21no—
24C2×C4×D101—21no—
25C2×C4×D101—22no—
26C2×C4×D101—22no—
27C2×C4×D101—21no—
28C2×C4×D101—21no—
29C2×C4×D101—42no—
30C2×C4×D101—42no—
31C2×C4×D101D412yes—
32C2×C4×D101D412yes—
33C4⋊Dic101—22no—
34#13108053—22no—
35#13108053—22no—
36C22×C4×C101C2×C411yescharacteristic
37C22×C4×C101C2×C411yescharacteristic
38C22×C4×C101C2×C411yescharacteristic
39C4⋊C4×C101—22no—
40C23×C101C22×C411yescharacteristic
41C22×D101—21no—
42C22×D101—21no—
43C22×D101—22no—
44C22×D101—22no—
45C22×D101C22⋊C411yescharacteristic
46C22×D101C22⋊C411yescharacteristic
47C2×C4×C101—21no—
48C2×C4×C101—21no—
49C2×C4×C101—21no—
50C2×C4×C101—41no—
51C2×C4×C101—41no—
52C2×C4×C101C22⋊C412yes—
53C2×C4×C101M1612yescomplemented
54C2×Dic101—21no—
55C2×Dic101—21no—
56C2×Dic101—21no—
57C2×Dic101—41no—
58C2×Dic101—41no—
59C2×Dic101M1612yescomplemented
60C2×Dic101C2×D412yes—
61C4×D101—24no—
62C4×D101—24no—
63C4×D101—24no—
64C4×D101—42no—
65C4×D101—42no—
66C4×D101—42no—
67#11717581—44no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101C2×C22⋊C411yescharacteristic
71C22×C101C2×M1611yescharacteristic
72C22×C101C2×M1611yescharacteristic
73C2×D101—24no—
74C2×D101—24no—
75C2×D101—21no—
76C2×D101—21no—
77C2×D101—21no—
78C2×D101—21no—
79C2×D101#9912yes—
80C2×D101#10112yes—
81C4×C101—22no—
82C4×C101—22no—
83C4×C101—41no—
84Dic101—22no—
85Dic101—22no—
86Dic101—41no—
87C2×C101—21no—
88C2×C101—21no—
89C2×C101#40711yescharacteristic
90C2×C101C2×#9911yescharacteristic
91C2×C101C2×#10111yescharacteristic
92D101—22no—
93D101—22no—
94#1463—1011nomaximal, Sylow
95C101#146311yescharacteristic, complemented, Sylow
96C22×C4⋊C4—1011no—
97#407—1012no—
98#324—1012no—
99#324—1012no—
100C23×C4—1011no—
101C23×C4—1011no—
102C23×C4—1011no—
103C2×M16—2022no—
104C2×C4⋊C4—1011no—
105C2×C4⋊C4—1011no—
106C2×C4⋊C4—1011no—
107C2×C4⋊C4—2022no—
108C2×C4⋊C4—2022no—
109C2×C4⋊C4#8793811yescharacteristic
110C22⋊C8—1014no—
111C22⋊C8—2022no—
112C24—1011no—
113C22×C4—1011no—
114C22×C4—1011no—
115C22×C4—1012no—
116C22×C4—1012no—
117C22×C4—1011no—
118C22×C4—4042no—
119C22×C4—4042no—
120C22×C4—2022no—
121C22×C4—2021no—
122C22×C4—2021no—
123C22×C4—2021no—
124C22×C4—2021no—
125C22×C4—2022no—
126C22×C4C2×#8793811yescharacteristic
127C22×C4C2×#8793811yescharacteristic
128C22×C4C2×#8793811yescharacteristic
129M16—4044no—
130C2×C8—2024no—
131C4⋊C4—22no—
132C4⋊C4—2022no—
133C4⋊C4—2022no—
134C4⋊C4—2022no—
135C23—1011no—
136C23—1011no—
137C23—2022no—
138C23—2022no—
139C23—2021no—
140C23—2021no—
141C23C22×#8793811yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—1012no—
148C2×C4—1012no—
149C2×C4—4042no—
150C2×C4—4042no—
151C2×C4—4042no—
152C2×C4—4041no—
153C2×C4—4041no—
154C2×C4—2024no—
155C2×C4—2024no—
156C2×C4—2024no—
157C2×C4—2021no—
158C2×C4—2021no—
159C2×C4—2021no—
160C2×C4C22⋊#8793812yes—
161C2×C4#1310808412yescomplemented
162C8—4044no—
163C22—21no—
164C22—21no—
165C22—1012no—
166C22—1012no—
167C22—2024no—
168C22—2024no—
169C22—2021no—
170C22—2021no—
171C22—2021no—
172C22—2021no—
173C22C2×C22⋊#8793811yescharacteristic
174C22D101⋊M1611yescharacteristic
175C22C2×#1310808411yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—4041no—
180C4—2022no—
181C4—2022no—
182C2—21no—
183C2—21no—
184C2—2022no—
185C2—2022no—
186C2#2026614811yescharacteristic
187C2D101⋊#9911yescharacteristic
188C2D101⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101C2×C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1463
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20266023C2semidirect
3. #20266022C2semidirect
53. C2×C4×C101M16semidirect
59. C2×Dic101M16semidirect
95. C101#1463semidirect
161. C2×C4#13108084semidirect

Maximal subgroups

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

subgroupindex
#202661482
#202660232
#202660222
C2×C4⋊C4×D1012
#1463101