Finite Group Databasebeta

← #27186882

Subgroups — #27186882

Order 12928.

360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#15692315C212yesmaximal
2C4×#13108083C212yesmaximal, complemented
3#20266057C212yesmaximal, complemented
4C2×#15692215C211yesmaximal, characteristic
5C2×#13108083C2214yes—
6#15692315C418yescomplemented
7#15692310—22no—
8C4×#11717581—22no—
9C22×C22⋊D101C2211yescharacteristic
10C23×Dic101C411yescharacteristic
11C22×C4×D101C411yescharacteristic
12#15692215—22no—
13#15692215—22no—
14C2×#13108053C2211yescharacteristic
15C2×#13108051C411yescharacteristic
16C2×C4×Dic101C2211yescharacteristic
17C2×C22⋊C4×C101C411yescharacteristic
18#13108083—24no—
19#13108083C2×C418yescomplemented
20C2×#11717581—24no—
21C23×D101C2×C411yescharacteristic
22C2×C22⋊D101—22no—
23C2×C22⋊D101—22no—
24C2×C22⋊D101C2×C414yes—
25C22×Dic101—21no—
26C22×Dic101—21no—
27C22×Dic101—42no—
28C22×Dic101C2×C411yescharacteristic
29C22×Dic101C2×C411yescharacteristic
30C22×Dic101C2311yescharacteristic
31C2×C4×D101—21no—
32C2×C4×D101—21no—
33C2×C4×D101—42no—
34#13108053—22no—
35#13108051—22no—
36C4×Dic101D412yes—
37C4×Dic101D412yes—
38C24×C101C2×C411yescharacteristic
39C22×C4×C101C2×C411yescharacteristic
40C22×C4×C101C2×C411yescharacteristic
41C22⋊C4×C101—22no—
42C23×C101—21no—
43C23×C101—21no—
44C23×C101—41no—
45C23×C101—41no—
46C23×C101C4212yes—
47C23×C101C22×C411yescharacteristic
48C22×D101—21no—
49C22×D101—21no—
50C22×D101—41no—
51C22×D101—41no—
52C22×D101C4212yes—
53C2×C4×C101—21no—
54C2×C4×C101—41no—
55C2×C4×C101—41no—
56C2×C4×C101C22⋊C412yes—
57C22⋊D101—28no—
58C2×Dic101—22no—
59C2×Dic101—21no—
60C2×Dic101—42no—
61C2×Dic101—42no—
62C2×Dic101—41no—
63C2×Dic101C22⋊C411yescharacteristic
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C22×C412yes—
66C2×Dic101C2×D412yes—
67C2×Dic101#4112yes—
68C4×D101—42no—
69C4×D101—42no—
70#11717581—28no—
71C22×C101—21no—
72C22×C101—21no—
73C22×C101—22no—
74C22×C101—42no—
75C22×C101—42no—
76C22×C101—41no—
77C22×C101—41no—
78C22×C101C2×C4211yescharacteristic
79C22×C101C2×C22⋊C411yescharacteristic
80C22×C101#11711yescharacteristic
81C2×D101—22no—
82C2×D101—42no—
83C2×D101—41no—
84C2×D101—41no—
85C2×D101—42no—
86C4×C101—22no—
87C4×C101—41no—
88Dic101—21no—
89Dic101—41no—
90Dic101#10012yescomplemented
91Dic101C4×D414yes—
92C2×C101—21no—
93C2×C101—21no—
94C2×C101—42no—
95C2×C101C4×C22⋊C411yescharacteristic
96C2×C101C2×#10011yescharacteristic
97C2×C101#41311yescharacteristic
98D101—42no—
99C4×#100—1011nomaximal, Sylow
100C101C4×#10011yescharacteristic, complemented, Sylow
101C2×C4×D4—1011no—
102C2×#100—1012no—
103C4×M16—1012no—
104#343—1012no—
105C22×D4—1011no—
106C23×C4—1011no—
107C23×C4—1011no—
108C2×M16—1014no—
109C4×D4—2022no—
110C4×D4—2022no—
111C2×C4⋊C4—1011no—
112C2×C22⋊C4—1011no—
113C2×C22⋊C4#8793811yescharacteristic
114C2×C42—1011no—
115#100—1018no—
116#97—2022no—
117C4×C8—2022no—
118C24—1011no—
119C24C2×#8793811yescharacteristic
120C2×D4—1014no—
121C2×D4—2022no—
122C2×D4—2022no—
123C22×C4—1011no—
124C22×C4—1011no—
125C22×C4—1011no—
126C22×C4—4042no—
127C22×C4—4042no—
128C22×C4—2021no—
129C22×C4—2021no—
130C22×C4—2021no—
131C22×C4—2021no—
132C22×C4C2×#8793811yescharacteristic
133C22×C4C2×#8793811yescharacteristic
134M16—1018no—
135M16—2024no—
136C2×C8—2024no—
137C4⋊C4—2022no—
138C22⋊C4—22no—
139C22⋊C4—2022no—
140C42—1012no—
141C42—1012no—
142C23—21no—
143C23—21no—
144C23—41no—
145C23—41no—
146C23—1012no—
147C23—4041no—
148C23—4041no—
149C23—2021no—
150C23—2021no—
151C23C4×#8793812yes—
152C23C22×#8793811yescharacteristic
153D4—2028no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—1012no—
158C2×C4—1012no—
159C2×C4—1011no—
160C2×C4—1012no—
161C2×C4—1011no—
162C2×C4—4042no—
163C2×C4—4042no—
164C2×C4—4042no—
165C2×C4—4042no—
166C2×C4—4041no—
167C2×C4—2022no—
168C2×C4—2021no—
169C2×C4C22⋊#8793812yes—
170C8—2028no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22—4042no—
179C22—4042no—
180C22—4041no—
181C22—4041no—
182C22—2022no—
183C22C2×C4×#8793811yescharacteristic
184C22C2×C22⋊#8793811yescharacteristic
185C22#1569233411yescharacteristic
186C4—22no—
187C4—41no—
188C4—1014no—
189C4—1012no—
190C4—4041no—
191C4—2021no—
192C2—21no—
193C2—21no—
194C2—42no—
195C2—4042no—
196C2C4×C22⋊#8793811yescharacteristic
197C2D101⋊#10011yescharacteristic
198C2#2026616411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC22×C101C2×C42
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×C22⋊D101C22
cosocleC22×Dic101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101C4×#100
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×#13108083C2semidirect
3. #20266057C2semidirect
6. #15692315C4semidirect
19. #13108083C2×C4semidirect
90. Dic101#100semidirect
100. C101C4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×#156923152
C4×#131080832
#202660572
C2×#156922152
C4×#100101