Finite Group Databasebeta

← C2×#20266080 #27187382

Subgroups — C2×#20266080 #27187382

Order 12928.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#15692315C211yesmaximal, characteristic
2C2×#15692313C211yesmaximal, characteristic
3#20266080C214yesmaximal, direct product factor
4C2×#15692239C211yesmaximal, characteristic
5C2×#13108083—21no—
6C2×C22⋊#87938—21no—
7#15692315—21no—
8#15692315C2212yes—
9#15692313—21no—
10#15692313C2212yes—
11C22×C22⋊D101C2211yescharacteristic
12C23×Dic101C411yescharacteristic, complemented
13#15692239—21no—
14#15692239—21no—
15#15692239C412yescomplemented
16#15692239C2212yes—
17C2×C4⋊Dic101—21no—
18C2×#13108051—21no—
19C2×C22⋊C4×C101C411yescharacteristic, complemented
20C22×#87938—41no—
21#13108083—22no—
22#13108083—41no—
23C2×#11717581—41no—
24C22⋊#87938—22no—
25C22⋊#87938—41no—
26C23×D101D411yescharacteristic
27C2×C22⋊D101—41no—
28C2×C22⋊D101—41no—
29C2×C22⋊D101C2×C411yescharacteristic
30C2×C22⋊D101D411yescharacteristic
31C2×C22⋊D101D411yescharacteristic
32C2×C22⋊D101C2311yescharacteristic
33C22×Dic101—21no—
34C22×Dic101—21no—
35C22×Dic101—41no—
36C22×Dic101—41no—
37C22×Dic101C2×C412yescomplemented
38C22×Dic101D411yescharacteristic
39C4⋊Dic101—22no—
40C4⋊Dic101—22no—
41#13108051—22no—
42#13108051—22no—
43C24×C101C2×C411yescharacteristic
44C22×C4×C101—21no—
45C22⋊C4×C101—21no—
46C22⋊C4×C101C2×C412yescomplemented
47C23×C101—21no—
48C23×C101—21no—
49C23×C101—42no—
50C23×C101C22⋊C411yescharacteristic
51C23×C101C22⋊C411yescharacteristic
52C23×C101C22×C411yescharacteristic
53C22×D101—21no—
54C22×D101—21no—
55C22×D101—42no—
56C22×D101C22⋊C411yescharacteristic
57C22×D101C2×D411yescharacteristic
58C2×#87938—42no—
59C2×#87938—82no—
60C2×C4×C101—22no—
61C2×C4×C101—42no—
62C22⋊D101—41no—
63C22⋊D101—41no—
64C22⋊D101—41no—
65C22⋊D101—41no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—22no—
69C2×Dic101—42no—
70C2×Dic101—41no—
71C2×Dic101—41no—
72C2×Dic101—42no—
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C2×D411yescharacteristic
75#11717581—42no—
76C22×C101—22no—
77C22×C101—21no—
78C22×C101—21no—
79C22×C101—41no—
80C22×C101—41no—
81C22×C101—42no—
82C22×C101—42no—
83C22×C101#9911yescharacteristic
84C22×C101#9911yescharacteristic
85C22×C101C2×C22⋊C411yescharacteristic
86C2×D101—21no—
87C2×D101—21no—
88C2×D101—42no—
89C2×D101—41no—
90C2×D101—41no—
91C2×D101—81no—
92#87938—82no—
93C4×C101—42no—
94Dic101—21no—
95Dic101—21no—
96Dic101—42no—
97C2×C101—21no—
98C2×C101—21no—
99C2×C101—41no—
100C2×C101—41no—
101C2×C101#35212yescomplemented
102C2×C101C2×#9911yescharacteristic
103D101—41no—
104D101—41no—
105C2×#352—1011nomaximal, Sylow
106C101C2×#35211yescharacteristic, complemented, Sylow
107C2×#123—1011no—
108C2×#100—1011no—
109C2×#99—1011no—
110#352—1014no—
111C22×D4—1011no—
112C23×C4—1011no—
113C2×M16—2021no—
114#123—1012no—
115#123—1012no—
116#123—2021no—
117#123—2021no—
118C2×C4⋊C4—2021no—
119C2×C22⋊C4—2021no—
120C2×C22⋊C4—2021no—
121C2×C22⋊C4#8793811yescharacteristic, complemented
122#100—1012no—
123#100—2021no—
124#99—1012no—
125#99—2021no—
126C24—1011no—
127C24C2×#8793811yescharacteristic
128C2×D4—1011no—
129C2×D4—1011no—
130C2×D4—1011no—
131C2×D4—1011no—
132C2×D4—4041no—
133C2×D4—4041no—
134C22×C4—21no—
135C22×C4—1011no—
136C22×C4—1012no—
137C22×C4—4041no—
138C22×C4—4041no—
139C22×C4—4041no—
140C22×C4—2021no—
141C22×C4—2021no—
142M16—4041no—
143M16—2022no—
144C2×C8—4041no—
145C4⋊C4—2022no—
146C4⋊C4—2022no—
147C22⋊C4—21no—
148C22⋊C4—4041no—
149C22⋊C4—2022no—
150C22⋊C4—2022no—
151C22⋊C4—2022no—
152C22⋊C4C2×#8793812yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—1011no—
157C23—1011no—
158C23—4042no—
159C23—2021no—
160C23—2021no—
161C23C22⋊#8793811yescharacteristic
162C23C22⋊#8793811yescharacteristic
163C23C22×#8793811yescharacteristic
164D4—4041no—
165D4—4041no—
166D4—4041no—
167D4—4041no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—8082no—
171C2×C4—1011no—
172C2×C4—1011no—
173C2×C4—4042no—
174C2×C4—4042no—
175C2×C4—4041no—
176C2×C4—4041no—
177C2×C4—4042no—
178C2×C4—2022no—
179C2×C4—2021no—
180C2×C4—2021no—
181C8—4042no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—8081no—
190C22—4041no—
191C22—4041no—
192C22—4042no—
193C22—2021no—
194C22—2021no—
195C22#1569231411yescharacteristic
196C22#1569231411yescharacteristic
197C22C2×C22⋊#8793811yescharacteristic
198C4—42no—
199C4—8082no—
200C4—4042no—
201C4—2021no—
202C4—2021no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—4041no—
208C2—4041no—
209C2#2026608012yesdirect product factor
210C2C2×#1569231411yescharacteristic
subgroupG/H
centerC22#15692314
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC22×C101#99
prime radicalC22×C22⋊D101C22
cosocleC2×C22⋊D101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101C2×#352
LCSG ▷ C23×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #20266080C2direct (N × H)
12. C23×Dic101C4semidirect
15. #15692239C4semidirect
19. C2×C22⋊C4×C101C4semidirect
37. C22×Dic101C2×C4semidirect
46. C22⋊C4×C101C2×C4semidirect
101. C2×C101#352semidirect
106. C101C2×#352semidirect
121. C2×C22⋊C4#87938semidirect
152. C22⋊C4C2×#87938semidirect
209. C2#20266080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156923152
C2×#156923132
#202660802
C2×#156922392
C2×#352101