Finite Group Databasebeta

← #27186601

Subgroups — #27186601

Order 12928.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266197C211yesmaximal, characteristic, complemented
2C2×#15692310C211yesmaximal, characteristic, complemented
3#20266033C212yesmaximal, complemented
4#20266032C212yesmaximal, complemented
5#20265723C211yesmaximal, characteristic
6C22×#11717581—21no—
7#15692322—21no—
8C22⋊#11717581—21no—
9#15692310—21no—
10#15692310C2212yes—
11#15692310C2212yes—
12C2×#13108074C411yescharacteristic
13#15692253C411yescharacteristic
14#15692251C411yescharacteristic
15#15692244C2211yescharacteristic
16#15692242C2211yescharacteristic
17#15692227—21no—
18#15692227—21no—
19C4×C22⋊D101—21no—
20C4×C22⋊D101—21no—
21C2×C4×Dic101C2211yescharacteristic
22C2×#41×C101C411yescharacteristic
23C2×#11717581—24no—
24C2×#11717581—22no—
25C2×#11717581—22no—
26#13108074—42no—
27C2×Dic202C2×C411yescharacteristic
28C2×D404C2×C411yescharacteristic
29C2×C22⋊D101—21no—
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C22×Dic101D411yescharacteristic
33C22×Dic101D411yescharacteristic
34C2×C4×D101—21no—
35#13108053—21no—
36#13108053—21no—
37C22⋊Dic101—21no—
38C22⋊Dic101—21no—
39#13108051—21no—
40#13108051—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
45#41×C101—42no—
46C2×Q8×C101C2×C411yescharacteristic
47C2×D4×C101—21no—
48C2×D4×C101C2×C411yescharacteristic
49C22×C4×C101—21no—
50C22×C4×C101C2×C411yescharacteristic
51C23×C101—21no—
52C23×C101C22⋊C411yescharacteristic
53C22×D101—21no—
54Q8×C101—41no—
55D4×C101—41no—
56D4×C101—42no—
57C2×C4×C101—22no—
58C2×C4×C101—21no—
59C2×C4×C101—42no—
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101C22×C411yescharacteristic
62C22⋊D101—42no—
63C22⋊D101—42no—
64C22⋊D101—42no—
65C2×Dic101—22no—
66C2×Dic101—21no—
67C2×Dic101—41no—
68C2×Dic101C22⋊C411yescharacteristic
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C2×D411yescharacteristic
71C2×Dic101C2×D411yescharacteristic
72D404—41no—
73C4×D101—42no—
74Dic202—41no—
75#11717581—24no—
76#11717581—42no—
77C22×C101—21no—
78C22×C101—21no—
79C22×C101—41no—
80C22×C101—41no—
81C22×C101—41no—
82C22×C101#10012yes—
83C22×C101C2×C22⋊C411yescharacteristic
84C2×D101—41no—
85C2×D101—41no—
86C2×D101—41no—
87C4×C101—21no—
88C4×C101—21no—
89C4×C101—41no—
90Dic101—21no—
91Dic101—21no—
92Dic101—21no—
93Dic101—41no—
94Dic101#10412yes—
95C2×C101—22no—
96C2×C101—81no—
97C2×C101C2×#10011yescharacteristic
98C2×C101C2×#10411yescharacteristic
99C2×C101#42111yescharacteristic
100D101—81no—
101#1530—1011nomaximal, Sylow
102C101#153011yescharacteristic, complemented, Sylow
103#532—1011no—
104#432—1011no—
105C2×#97—1011no—
106#329—1012no—
107#329—1012no—
108C2×#41—1011no—
109C2×#41#8793811yescharacteristic
110C22×C8—2021no—
111C4⋊Q8—1011no—
112#127—1011no—
113#124—1011no—
114#124—1011no—
115#121—2021no—
116#121—2021no—
117C4×D4—2021no—
118C4×D4—2021no—
119C2×C42—1011no—
120C4⋊C8—2021no—
121C22⋊C8—2021no—
122#97—1012no—
123#97—1012no—
124#97—2021no—
125#41—42no—
126#41—4042no—
127C2×Q8—1011no—
128C2×Q8C2×#8793811yescharacteristic
129C2×D4—21no—
130C2×D4—1011no—
131C2×D4—2021no—
132C2×D4—2021no—
133C2×D4—2021no—
134C2×D4C2×#8793811yescharacteristic
135C22×C4—21no—
136C22×C4—1011no—
137C22×C4—1011no—
138C22×C4—2021no—
139C22×C4C2×#8793811yescharacteristic
140C2×C8—2022no—
141C2×C8—2022no—
142C2×C8—2024no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C22⋊C4—2021no—
146C22⋊C4—2021no—
147C22⋊C4—2021no—
148C22⋊C4—2021no—
149C42—1011no—
150C42—1011no—
151C42—1011no—
152C42—1011no—
153C23—21no—
154C23—2021no—
155C23C22⋊#8793811yescharacteristic
156Q8—41no—
157Q8—4041no—
158D4—41no—
159D4—42no—
160D4—4041no—
161D4—4042no—
162D4—4042no—
163D4—4042no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—1011no—
168C2×C4—1011no—
169C2×C4—1011no—
170C2×C4—1011no—
171C2×C4—4042no—
172C2×C4—4041no—
173C2×C4—2022no—
174C2×C4—2021no—
175C2×C4C22⋊#8793811yescharacteristic
176C2×C4C22×#8793811yescharacteristic
177C8—4042no—
178C8—2024no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—4041no—
185C22—4041no—
186C22—4041no—
187C22#1569231512yes—
188C22C2×C22⋊#8793811yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—1012no—
193C4—4041no—
194C4—2021no—
195C4—2021no—
196C4—2021no—
197C2—22no—
198C2—81no—
199C2—8081no—
200C2C2×#1569231511yescharacteristic
201C2D101⋊#10411yescharacteristic
202C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×#41×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265723C2
cosocleC4×Dic101C23
hypercenterC2×#41#87938
hypocenterC101#1530
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20266197C2semidirect
2. C2×#15692310C2semidirect
3. #20266033C2semidirect
4. #20266032C2semidirect
102. C101#1530semidirect

Maximal subgroups

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

subgroupindex
#202661972
C2×#156923102
#202660332
#202660322
#202657232
#1530101