Finite Group Databasebeta

← #27170138

Subgroups — #27170138

Order 12928.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#20265806C211yesmaximal, characteristic
2#20265507C211yesmaximal, characteristic
3#20265108C211yesmaximal, characteristic
4#20264915C211yesmaximal, characteristic
5#20264914C211yesmaximal, characteristic
6#20264902C211yesmaximal, characteristic
7#483×C101C211yesmaximal, characteristic
8#15692254—21no—
9#15692253—21no—
10#15692245—21no—
11#15692245—21no—
12#15692234C2211yescharacteristic
13#15692232—21no—
14#15692211—21no—
15C2×#13108053—21no—
16C2×#13108053C2211yescharacteristic
17#15692186—21no—
18#15692178—21no—
19C22⋊#11717579C2211yescharacteristic
20#15692162—21no—
21#15692162C2211yescharacteristic
22C22⋊Q8×C101C2211yescharacteristic
23C2×C4⋊C4×C101C2211yescharacteristic
24#106×C101—21no—
25#103×C101—21no—
26C22⋊C8×C101C2211yescharacteristic
27C2×Dic202—21no—
28C2×Dic202D411yescharacteristic
29C22×Dic101—21no—
30C22×Dic101D411yescharacteristic
31C22×Dic101D411yescharacteristic
32C2×#11717579—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101D411yescharacteristic
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—42no—
43C22⋊Dic101—21no—
44C4×Dic101—21no—
45C4×Dic101—21no—
46C2×Q8×C101D411yescharacteristic
47C22×C4×C101—21no—
48C22×C4×C101C2311yescharacteristic
49C2×C8×C101—21no—
50C4⋊C4×C101—21no—
51C4⋊C4×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101D411yescharacteristic
54C22⋊C4×C101—21no—
55C23×C101C2×D411yescharacteristic
56Q8×C101—41no—
57C2×C4×C101—21no—
58C2×C4×C101—21no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101—41no—
63C2×C4×C101C2×D411yescharacteristic
64C2×C4×C101C2×D411yescharacteristic
65C2×Dic101—21no—
66C2×Dic101—21no—
67C2×Dic101—22no—
68C2×Dic101—21no—
69C2×Dic101—21no—
70C2×Dic101—21no—
71C2×Dic101—41no—
72C2×Dic101—41no—
73C2×Dic101—41no—
74C2×Dic101SD1612yes—
75Dic202—41no—
76Dic202—81no—
77C8×C101—41no—
78#11717579—41no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101#12011yescharacteristic
82C22×C101C2×SD1611yescharacteristic
83C22×C101#13711yescharacteristic
84C4×C101—21no—
85C4×C101—21no—
86C4×C101—41no—
87C4×C101—41no—
88C4×C101—81no—
89Dic101—22no—
90Dic101—42no—
91Dic101—41no—
92Dic101—41no—
93Dic101—41no—
94C2×C101—21no—
95C2×C101—21no—
96C2×C101#44811yescharacteristic
97C2×C101#45611yescharacteristic
98C2×C101#45811yescharacteristic
99#1611—1011nomaximal, Sylow
100C101#161111yescharacteristic, complemented, Sylow
101#544—1011no—
102#483—1011no—
103#483D10111yescharacteristic
104#398—1011no—
105#328—1011no—
106#328—1011no—
107#324—1011no—
108C4⋊Q8—2021no—
109C4⋊Q8—2021no—
110#125—2021no—
111#125—2021no—
112C22⋊Q8—1011no—
113C22⋊Q8—2021no—
114C22⋊Q8C2×D10111yescharacteristic
115#117—2021no—
116C2×C4⋊C4—1011no—
117C2×C4⋊C4—2021no—
118C2×C4⋊C4C2×D10111yescharacteristic
119#106—21no—
120#106—2021no—
121#103—21no—
122#103—2021no—
123C22⋊C8—1011no—
124C22⋊C8C2×D10111yescharacteristic
125#95—1011no—
126#95—2021no—
127C2×Q8—1011no—
128C2×Q8—2021no—
129C2×Q8C22⋊D10111yescharacteristic
130C22×C4—21no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—2021no—
134C22×C4C22×D10111yescharacteristic
135C2×C8—21no—
136C2×C8—2021no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1011no—
141C4⋊C4—4042no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4—2021no—
150C4⋊C4C22⋊D10111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2021no—
153C42—2021no—
154C42—2021no—
155C23D4×D10111yescharacteristic
156Q8—41no—
157Q8—8081no—
158Q8—4041no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—1012no—
166C2×C4—4041no—
167C2×C4—4041no—
168C2×C4—4041no—
169C2×C4—2022no—
170C2×C4—2021no—
171C2×C4—2021no—
172C2×C4—2021no—
173C2×C4—2021no—
174C2×C4—2021no—
175C2×C4D4×D10111yescharacteristic
176C2×C4C2×C22⋊D10111yescharacteristic
177C8—41no—
178C8—4041no—
179C22—21no—
180C22—21no—
181C22#1569222311yescharacteristic
182C22SD16×D10111yescharacteristic
183C22#1569228411yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—4042no—
190C4—4041no—
191C4—4041no—
192C4—4041no—
193C4—2022no—
194C2—21no—
195C2—21no—
196C2#2026531411yescharacteristic
197C2#2026535811yescharacteristic
198C2#2026536611yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#483×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#483D101
hypocenterC101#1611
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
100. C101#1611semidirect

Maximal subgroups

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

subgroupindex
#202658062
#202655072
#202651082
#202649152
#202649142
#202649022
#483×C1012
#1611101