Finite Group Databasebeta

← #27170129

Subgroups — #27170129

Order 12928.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#20265505C211yesmaximal, characteristic, complemented
2#20265488C211yesmaximal, characteristic
3#20265107C211yesmaximal, characteristic, complemented
4#20264914C211yesmaximal, characteristic, complemented
5#20264911C211yesmaximal, characteristic
6#20264903C211yesmaximal, characteristic, complemented
7#539×C101C211yesmaximal, characteristic
8C2×C4⋊Dic101C2211yescharacteristic
9C2×#13108053—21no—
10#15692188—21no—
11#15692186—21no—
12#15692179—21no—
13#15692176—21no—
14C22⋊#11717579C2211yescharacteristic
15C22⋊#11717579C2211yescharacteristic
16#15692162—21no—
17#15692162C2211yescharacteristic
18#126×C101—21no—
19#125×C101—21no—
20#123×C101—21no—
21#123×C101—21no—
22C22⋊Q8×C101—21no—
23C22⋊Q8×C101C2211yescharacteristic
24#121×C101C2211yescharacteristic
25C4×D4×C101—21no—
26C2×C4⋊C4×C101C2211yescharacteristic
27C22×Dic101—21no—
28C22×Dic101—21no—
29C2×#11717579—21no—
30C2×#11717579—21no—
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33#13108053—42no—
34C2×Q8×C101D411yescharacteristic
35C2×D4×C101—21no—
36C2×D4×C101D411yescharacteristic
37C22×C4×C101—21no—
38C22×C4×C101D411yescharacteristic
39C22×C4×C101D411yescharacteristic
40C22×C4×C101C2311yescharacteristic
41C4⋊C4×C101—21no—
42C4⋊C4×C101—21no—
43C4⋊C4×C101—21no—
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101—21no—
47C4⋊C4×C101D411yescharacteristic
48C4⋊C4×C101D411yescharacteristic
49C22⋊C4×C101—21no—
50C22⋊C4×C101—21no—
51C22⋊C4×C101—21no—
52C22⋊C4×C101—21no—
53C22⋊C4×C101—21no—
54C42×C101—21no—
55C23×C101—21no—
56C23×C101C2×D411yescharacteristic
57Q8×C101—41no—
58D4×C101—41no—
59D4×C101—41no—
60D4×C101—41no—
61C2×C4×C101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—21no—
65C2×C4×C101—21no—
66C2×C4×C101—21no—
67C2×C4×C101—21no—
68C2×C4×C101—41no—
69C2×C4×C101—41no—
70C2×C4×C101—81no—
71C2×C4×C101C2×D411yescharacteristic
72C2×C4×C101C2×D411yescharacteristic
73C2×Dic101—22no—
74C2×Dic101—41no—
75C2×Dic101—41no—
76C2×Dic101—41no—
77C2×Dic101—41no—
78C2×Dic101—41no—
79#11717579—41no—
80#11717579—41no—
81C22×C101—21no—
82C22×C101—21no—
83C22×C101—41no—
84C22×C101—41no—
85C22×C101—41no—
86C22×C101#12011yescharacteristic
87C22×C101#13511yescharacteristic
88C22×C101AGL(1,ℤ/8)11yescharacteristic
89C4×C101—21no—
90C4×C101—21no—
91C4×C101—41no—
92C4×C101—41no—
93C4×C101—41no—
94C4×C101—41no—
95C4×C101—41no—
96Dic101—42no—
97Dic101—81no—
98C2×C101—21no—
99C2×C101—21no—
100C2×C101—81no—
101C2×C101#44911yescharacteristic
102C2×C101#45611yescharacteristic
103C2×C101#45811yescharacteristic
104#1609—1011nomaximal, Sylow
105C101#160911yescharacteristic, complemented, Sylow
106#539D10111yescharacteristic
107#483—1011no—
108#480—1011no—
109#398—1011no—
110#328—1011no—
111#327—1011no—
112#324—1011no—
113#126—21no—
114#125—21no—
115#123—21no—
116#123—21no—
117C22⋊Q8—21no—
118C22⋊Q8C2×D10111yescharacteristic
119#121C2×D10111yescharacteristic
120C4×D4—21no—
121C2×C4⋊C4—1011no—
122C2×C4⋊C4—2021no—
123C2×C4⋊C4C2×D10111yescharacteristic
124#107—2021no—
125#106—2021no—
126#103—2021no—
127#102—2021no—
128C22⋊C8—1011no—
129C22⋊C8—1011no—
130#95—1011no—
131#95—2021no—
132C2×Q8C22⋊D10111yescharacteristic
133C2×D4—21no—
134C2×D4C22⋊D10111yescharacteristic
135C22×C4—21no—
136C22×C4—2021no—
137C22×C4—2021no—
138C22×C4C22⋊D10111yescharacteristic
139C22×C4C22⋊D10111yescharacteristic
140C22×C4C22×D10111yescharacteristic
141C2×C8—2021no—
142C2×C8—2021no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—4042no—
150C4⋊C4—2021no—
151C4⋊C4—2021no—
152C4⋊C4C22⋊D10111yescharacteristic
153C4⋊C4C22⋊D10111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×C22⋊D10111yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—81no—
176C2×C4—4041no—
177C2×C4—4041no—
178C2×C4—4041no—
179C2×C4—4041no—
180C2×C4—4041no—
181C2×C4—2022no—
182C2×C4C2×C22⋊D10111yescharacteristic
183C2×C4C2×C22⋊D10111yescharacteristic
184C8—4041no—
185C8—4041no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1569222411yescharacteristic
192C22#1569227511yescharacteristic
193C22#1569228011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—8081no—
202C4—4042no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2026532211yescharacteristic
207C2#2026536011yescharacteristic
208C2#2026536711yescharacteristic
subgroupG/H
centerC22#15692224
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#539×C101C2
socleC22×C101#120
prime radical#121×C101C22
hypercenter#539D101
hypocenterC101#1609
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #20265505C2semidirect
3. #20265107C2semidirect
4. #20264914C2semidirect
6. #20264903C2semidirect
105. C101#1609semidirect

Maximal subgroups

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

subgroupindex
#202655052
#202654882
#202651072
#202649142
#202649112
#202649032
#539×C1012
#1609101