Finite Group Databasebeta

← #27186663

Subgroups — #27186663

Order 12928.

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

normal subgroups only

This group has 246 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#20266182C211yesmaximal, characteristic, complemented
3#20266036C212yesmaximal, complemented
4#20266035C212yesmaximal, complemented
5#20265724C211yesmaximal, characteristic
6C2×#13108084—21no—
7#15692322—21no—
8#15692322C2212yes—
9#15692322C2212yes—
10#15692312—21no—
11#15692310—21no—
12C2×#13108074—21no—
13#15692254C2211yescharacteristic
14#15692251C2211yescharacteristic
15#15692241—21no—
16#15692230C411yescharacteristic
17#15692228—21no—
18#15692226C411yescharacteristic
19C4×D404C411yescharacteristic
20C4×C22⋊D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic
23#13108084—42no—
24C2×#11717581—22no—
25C2×#11717581—22no—
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×D101C2×C411yescharacteristic
35C2×C4×D101D411yescharacteristic
36C2×C4×D101D411yescharacteristic
37C4⋊Dic101C2×C411yescharacteristic
38#13108053—21no—
39C22⋊Dic101—21no—
40#13108051—21no—
41#13108051—21no—
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4×Dic101C2311yescharacteristic
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×D101C22⋊C411yescharacteristic
53D4×C101—41no—
54C2×C4×C101—21no—
55C2×C4×C101—42no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C22⋊D101—42no—
60C22⋊D101—41no—
61C22⋊D101—42no—
62C22⋊D101—41no—
63C2×Dic101—21no—
64C2×Dic101C22⋊C411yescharacteristic
65C2×Dic101C2×D411yescharacteristic
66C2×Dic101C2×D411yescharacteristic
67D404—41no—
68D404—42no—
69C4×D101—22no—
70C4×D101—21no—
71C4×D101—21no—
72C4×D101—41no—
73C4×D101—42no—
74Dic202—42no—
75#11717581—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—21no—
84C2×D101—41no—
85C2×D101—41no—
86C2×D101—41no—
87C4×C101—21no—
88C4×C101—21no—
89C4×C101—21no—
90C4×C101—41no—
91Dic101—21no—
92Dic101—41no—
93Dic101AGL(1,ℤ/8)11yescharacteristic
94Dic101AGL(1,ℤ/8)12yes—
95Dic101#13711yescharacteristic
96C2×C101—81no—
97C2×C101#41311yescharacteristic
98C2×C101#41711yescharacteristic
99C2×C101#41811yescharacteristic
100D101—41no—
101D101—81no—
102#1557—1011nomaximal, Sylow
103C101#155711yescharacteristic, complemented, Sylow
104#532—1011no—
105#432—1011no—
106#423—1011no—
107#332—1012no—
108#331—1012no—
109C2×#41—2021no—
110C2×M16—2021no—
111C4⋊Q8—1011no—
112#127—1011no—
113#124—2021no—
114#121—1011no—
115#121—1011no—
116#121—2021no—
117C4×D4—1011no—
118C4×D4—2021no—
119C4×D4#8793811yescharacteristic
120C2×C42—1011no—
121C4⋊C8—1012no—
122C4⋊C8—1012no—
123C4⋊C8—2021no—
124C22⋊C8—2021no—
125#97—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—2021no—
139M16—4042no—
140C2×C8—2022no—
141C2×C8—2022no—
142C4⋊C4—1011no—
143C4⋊C4—2021no—
144C4⋊C4C2×#8793811yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2021no—
147C22⋊C4—2021no—
148C22⋊C4—2021no—
149C42—1011no—
150C42—1011no—
151C42—1011no—
152C42C2×#8793811yescharacteristic
153C23—21no—
154C23—1011no—
155C23—2021no—
156Q8—4042no—
157D4—41no—
158D4—4041no—
159D4—4042no—
160D4—4042no—
161D4—4041no—
162D4—4041no—
163D4—4042no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—1011no—
167C2×C4—1011no—
168C2×C4—1011no—
169C2×C4—4042no—
170C2×C4—4041no—
171C2×C4—2021no—
172C2×C4—2022no—
173C2×C4—2021no—
174C2×C4—2021no—
175C2×C4C22⋊#8793811yescharacteristic
176C2×C4C22⋊#8793811yescharacteristic
177C2×C4C22×#8793811yescharacteristic
178C8—4042no—
179C8—4042no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—4041no—
184C22—4041no—
185C22—4041no—
186C22—2021no—
187C22—2021no—
188C22—2021no—
189C22C2×C22⋊#8793811yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—1011no—
195C4—1011no—
196C4—1012no—
197C4—4041no—
198C4—2021no—
199C2—81no—
200C2—8081no—
201C2—4041no—
202C2#2026616311yescharacteristic
203C2#2026616811yescharacteristic
204C2#2026616911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265724C2
cosocleC4×Dic101C23
hypercenterC4×D4#87938
hypocenterC101#1557
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. #20266182C2semidirect
3. #20266036C2semidirect
4. #20266035C2semidirect
103. C101#1557semidirect

Maximal subgroups

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

subgroupindex
#202662002
#202661822
#202660362
#202660352
#202657242
#1557101