Finite Group Databasebeta

← #27186522

Subgroups — #27186522

Order 12928.

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

normal subgroups only

This group has 272 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
1#20266200C211yesmaximal, characteristic, complemented
2#20266113C211yesmaximal, characteristic, complemented
3#20266029C212yesmaximal, complemented
4#20266028C212yesmaximal, complemented
5#20265724C211yesmaximal, characteristic
6C2×C4×#87938—21no—
7#15692322—21no—
8#15692312C2212yes—
9#15692310—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—
25C4×#87938—24no—
26#13108074—44no—
27C2×Dic202—21no—
28C2×D404—21no—
29C2×D404C2×C411yescharacteristic
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C2×C22⋊D101—21no—
33C2×C4×D101—21no—
34C2×C4×D101D411yescharacteristic
35C2×C4×D101D411yescharacteristic
36C2×C4×D101C2311yescharacteristic
37C4⋊Dic101C2×C411yescharacteristic
38#13108053—21no—
39C22⋊Dic101—21no—
40#13108051—21no—
41#13108051—21no—
42C4×Dic101C2×C411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101D411yescharacteristic
45C2×D4×C101C2×C411yescharacteristic
46C22×C4×C101—21no—
47C4⋊C4×C101C2×C411yescharacteristic
48C22⋊C4×C101—21no—
49C42×C101C2×C411yescharacteristic
50C23×C101—21no—
51C22×D101—21no—
52C22×D101C2×D411yescharacteristic
53C2×#87938—24no—
54C2×#87938—42no—
55C2×#87938—42no—
56D4×C101—41no—
57C2×C4×C101—21no—
58C2×C4×C101—42no—
59C2×C4×C101C22⋊C411yescharacteristic
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101C22×C411yescharacteristic
62C22⋊D101—42no—
63C22⋊D101—42no—
64C22⋊D101—42no—
65C2×Dic101—21no—
66C2×Dic101C22⋊C411yescharacteristic
67C2×Dic101C22⋊C411yescharacteristic
68C2×Dic101C2×D411yescharacteristic
69D404—41no—
70D404—42no—
71C4×D101—22no—
72C4×D101—22no—
73C4×D101—41no—
74C4×D101—42no—
75Dic202—42no—
76#11717581—42no—
77C22×C101—41no—
78C22×C101—41no—
79C22×C101—41no—
80C22×C101C2×C22⋊C411yescharacteristic
81C2×D101—21no—
82C2×D101—21no—
83C2×D101—41no—
84C2×D101—41no—
85C2×D101—41no—
86C2×D101AGL(1,ℤ/8)12yes—
87#87938—44no—
88C4×C101—21no—
89C4×C101—21no—
90C4×C101—21no—
91C4×C101—41no—
92Dic101—21no—
93Dic101—21no—
94Dic101—41no—
95Dic101#10412yes—
96C2×C101—81no—
97C2×C101#41011yescharacteristic
98C2×C101#41811yescharacteristic
99C2×C101C2×#10411yescharacteristic
100D101—22no—
101D101—81no—
102#1505—1011nomaximal, Sylow
103C101#150511yescharacteristic, complemented, Sylow
104#532—1011no—
105#432—1011no—
106#376—1011no—
107#327—1012no—
108#327—1012no—
109C2×#41—2021no—
110C4⋊Q8—1011no—
111#127—1011no—
112#124—2021no—
113#121—1011no—
114#121—1011no—
115#121—2021no—
116C4×D4—1011no—
117C4×D4—2021no—
118C4×D4#8793811yescharacteristic, complemented
119C2×C42—1011no—
120C2×C42—2021no—
121C4⋊C8—2021no—
122C22⋊C8—1012no—
123#97—2021no—
124#95—1012no—
125#95—2021no—
126#41—4044no—
127C2×Q8—2021no—
128C2×D4—1011no—
129C2×D4—2021no—
130C2×D4—2021no—
131C2×D4—2021no—
132C2×D4—2021no—
133C2×D4C2×#8793811yescharacteristic
134C22×C4—21no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—1011no—
138C22×C4—2022no—
139C22×C4—2021no—
140C2×C8—2022no—
141C4⋊C4—1011no—
142C4⋊C4—2021no—
143C4⋊C4C2×#8793811yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—2021no—
146C22⋊C4—2021no—
147C22⋊C4—2021no—
148C42—1011no—
149C42—1011no—
150C42—1011no—
151C42—2024no—
152C42C2×#8793811yescharacteristic
153C23—21no—
154C23—1011no—
155C23—2021no—
156Q8—4042no—
157D4—41no—
158D4—4041no—
159D4—4042no—
160D4—4042no—
161D4—4042no—
162D4—4042no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—1011no—
166C2×C4—1011no—
167C2×C4—1011no—
168C2×C4—4042no—
169C2×C4—4041no—
170C2×C4—4042no—
171C2×C4—4042no—
172C2×C4—2022no—
173C2×C4—2022no—
174C2×C4—2024no—
175C2×C4—2021no—
176C2×C4C22⋊#8793811yescharacteristic
177C2×C4C22⋊#8793811yescharacteristic
178C2×C4C22×#8793811yescharacteristic
179C8—4042no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—1012no—
184C22—4041no—
185C22—4041no—
186C22—4041no—
187C22—2021no—
188C22—2021no—
189C22C2×C22⋊#8793811yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—1012no—
195C4—4044no—
196C4—4041no—
197C4—2021no—
198C4—2021no—
199C2—81no—
200C2—8081no—
201C2—2022no—
202C2#2026615611yescharacteristic
203C2#2026616911yescharacteristic
204C2D101⋊#10411yescharacteristic
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#1505
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. #20266200C2semidirect
2. #20266113C2semidirect
3. #20266029C2semidirect
4. #20266028C2semidirect
13. #15692254C4semidirect
14. #15692251C4semidirect
19. C4×D404C4semidirect
22. C4×D4×C101C4semidirect
103. C101#1505semidirect
118. C4×D4#87938semidirect

Maximal subgroups

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

subgroupindex
#202662002
#202661132
#202660292
#202660282
#202657242
#1505101