Finite Group Databasebeta

← #27186551

Subgroups — #27186551

Order 12928.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#20266122C211yesmaximal, characteristic, complemented
3#20266029C212yesmaximal, complemented
4#20266028C212yesmaximal, complemented
5#20265724C211yesmaximal, characteristic
6C4⋊#11717581—21no—
7#15692312C2212yes—
8#15692310—21no—
9(C2×#87938)⋊C4—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12C2×#13108074—21no—
13#15692254C411yescharacteristic, complemented
14#15692251C411yescharacteristic, complemented
15#15692241—21no—
16#15692230C2211yescharacteristic
17#15692228—21no—
18#15692226C2211yescharacteristic
19C4×D404C411yescharacteristic, complemented
20C4×C22⋊D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25#13108074—44no—
26C2×Dic202—21no—
27C2×D404—21no—
28C2×D404C2×C411yescharacteristic
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C2×C4×D101—21no—
33C2×C4×D101D411yescharacteristic
34C2×C4×D101D411yescharacteristic
35C2×C4×D101C2311yescharacteristic
36C4⋊Dic101C2×C411yescharacteristic
37#13108053—21no—
38C22⋊Dic101—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C2×D4×C101C2×C411yescharacteristic
45C22×C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C22⋊C4×C101—21no—
48C42×C101C2×C411yescharacteristic
49C23×C101—21no—
50C22×D101—21no—
51C22×D101C2×D411yescharacteristic
52C2×#87938—42no—
53C2×#87938—42no—
54C2×#87938—42no—
55D4×C101—41no—
56C2×C4×C101—21no—
57C2×C4×C101—42no—
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22⋊C411yescharacteristic
60C2×C4×C101C22×C411yescharacteristic
61C22⋊D101—42no—
62C22⋊D101—42no—
63C22⋊D101—42no—
64C2×Dic101—21no—
65C2×Dic101C22⋊C411yescharacteristic
66C2×Dic101C22⋊C411yescharacteristic
67C2×Dic101C2×D411yescharacteristic
68D404—41no—
69D404—42no—
70C4×D101—22no—
71C4×D101—41no—
72C4×D101—41no—
73C4×D101—42no—
74Dic202—42no—
75#11717581—42no—
76C22×C101—41no—
77C22×C101—41no—
78C22×C101—41no—
79C22×C101C2×C22⋊C411yescharacteristic
80C2×D101—21no—
81C2×D101—21no—
82C2×D101—41no—
83C2×D101—41no—
84C2×D101—41no—
85C2×D101AGL(1,ℤ/8)12yes—
86#87938—82no—
87C4×C101—21no—
88C4×C101—21no—
89C4×C101—21no—
90C4×C101—41no—
91Dic101—21no—
92Dic101—21no—
93Dic101—21no—
94Dic101—41no—
95C2×C101—81no—
96C2×C101#41011yescharacteristic
97C2×C101#41811yescharacteristic
98C2×C101#42111yescharacteristic
99D101—22no—
100D101—81no—
101#1514—1011nomaximal, Sylow
102C101#151411yescharacteristic, complemented, Sylow
103#532—1011no—
104#432—1011no—
105#383—1011no—
106#327—1012no—
107#327—1012no—
108C2×#41—2021no—
109C4⋊Q8—1011no—
110#127—1011no—
111#124—2021no—
112#121—1011no—
113#121—1011no—
114#121—2021no—
115C4×D4—1011no—
116C4×D4—2021no—
117C4×D4#8793811yescharacteristic, complemented
118C2×C42—1011no—
119C4⋊C8—2021no—
120C22⋊C8—1012no—
121#97—2021no—
122#95—1012no—
123#95—2021no—
124#95—2021no—
125#41—4044no—
126C2×Q8—2021no—
127C2×D4—1011no—
128C2×D4—2021no—
129C2×D4—2021no—
130C2×D4—2021no—
131C2×D4—2021no—
132C2×D4C2×#8793811yescharacteristic
133C22×C4—21no—
134C22×C4—1011no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—2022no—
138C22×C4—2021no—
139C2×C8—2022no—
140C4⋊C4—1011no—
141C4⋊C4—2021no—
142C4⋊C4C2×#8793811yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2021no—
145C22⋊C4—2021no—
146C22⋊C4—2021no—
147C42—1011no—
148C42—1011no—
149C42—1011no—
150C42C2×#8793811yescharacteristic
151C23—21no—
152C23—1011no—
153C23—2021no—
154Q8—4042no—
155D4—41no—
156D4—4041no—
157D4—4042no—
158D4—4042no—
159D4—4042no—
160D4—4042no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—1011no—
164C2×C4—1011no—
165C2×C4—1011no—
166C2×C4—4042no—
167C2×C4—4041no—
168C2×C4—4041no—
169C2×C4—4042no—
170C2×C4—4042no—
171C2×C4—4042no—
172C2×C4—2022no—
173C2×C4—2021no—
174C2×C4C22⋊#8793811yescharacteristic
175C2×C4C22⋊#8793811yescharacteristic
176C2×C4C22×#8793811yescharacteristic
177C8—4042no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1012no—
182C22—4041no—
183C22—4041no—
184C22—4041no—
185C22—2021no—
186C22—2021no—
187C22C2×C22⋊#8793811yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—8082no—
193C4—4041no—
194C4—2021no—
195C4—2021no—
196C4—2021no—
197C2—81no—
198C2—8081no—
199C2—2022no—
200C2#2026615611yescharacteristic
201C2#2026616911yescharacteristic
202C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265724C2
cosocleC2×C4×D101C23
hypercenterC4×D4#87938
hypocenterC101#1514
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20266199C2semidirect
2. #20266122C2semidirect
3. #20266029C2semidirect
4. #20266028C2semidirect
13. #15692254C4semidirect
14. #15692251C4semidirect
19. C4×D404C4semidirect
22. C4×D4×C101C4semidirect
102. C101#1514semidirect
117. C4×D4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661992
#202661222
#202660292
#202660282
#202657242
#1514101