Finite Group Databasebeta

← #27170429

Subgroups — #27170429

Order 12928.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#20265931C211yesmaximal, characteristic, complemented
2#20265564C211yesmaximal, characteristic
3#20265541C211yesmaximal, characteristic, complemented
4#20264919C211yesmaximal, characteristic, complemented
5#20264918C211yesmaximal, characteristic, complemented
6#20264916C211yesmaximal, characteristic, complemented
7#490×C101C211yesmaximal, characteristic, complemented
8C2×#13108062—21no—
9C2×#13108059—21no—
10#15692254—21no—
11#15692250—21no—
12#15692250—21no—
13#15692247C2211yescharacteristic
14#15692243C2211yescharacteristic
15#15692240—21no—
16#15692235—21no—
17#15692233—21no—
18#15692176—21no—
19#15692176—21no—
20#15692166C2211yescharacteristic
21#15692166C2211yescharacteristic
22#127×C101C2211yescharacteristic
23#125×C101C2211yescharacteristic
24#102×C101—21no—
25#102×C101—21no—
26#97×C101C2211yescharacteristic
27C2×Dic202—21no—
28C2×Dic202D411yescharacteristic
29C2×D404D411yescharacteristic
30C2×C4×D101—21no—
31#13108062—42no—
32#13108059—42no—
33C2×#11717579—21no—
34C2×#11717579—21no—
35C4⋊Dic101—21no—
36C4⋊Dic101D411yescharacteristic
37C4⋊Dic101D411yescharacteristic
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108051—21no—
42#13108051—21no—
43#13108051—21no—
44#13108051—21no—
45#13108051—21no—
46C4×Dic101—21no—
47C2×D4×C101—21no—
48C2×D4×C101—21no—
49C2×D4×C101—21no—
50C2×C8×C101—21no—
51C4⋊C4×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101D411yescharacteristic
54C4⋊C4×C101D411yescharacteristic
55C42×C101C2311yescharacteristic
56C23×C101—41no—
57C22×D101—21no—
58D4×C101—42no—
59D4×C101—42no—
60D4×C101—41no—
61D4×C101—41no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101C2×D411yescharacteristic
65C2×C4×C101C2×D411yescharacteristic
66C2×C4×C101C2×D411yescharacteristic
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101—21no—
70D404—41no—
71C4×D101—81no—
72Dic202—41no—
73Dic202—81no—
74C8×C101—41no—
75#11717579—22no—
76#11717579—41no—
77C22×C101—81no—
78C22×C101—81no—
79C22×C101—81no—
80C22×C101#12011yescharacteristic
81C2×D101—41no—
82C2×D101—41no—
83C2×D101—41no—
84C4×C101—21no—
85C4×C101—21no—
86C4×C101—21no—
87C4×C101—41no—
88C4×C101—41no—
89Dic101—41no—
90Dic101—41no—
91Dic101—41no—
92C2×C101—161no—
93C2×C101#45311yescharacteristic
94C2×C101#45411yescharacteristic
95C2×C101#45411yescharacteristic
96D101—81no—
97#1657—1011nomaximal, Sylow
98C101#165711yescharacteristic, complemented, Sylow
99#563—1011no—
100#496—1011no—
101#490—1011no—
102#490D10111yescharacteristic, complemented
103#330—1011no—
104#330—1011no—
105#329—1011no—
106C2×SD16—2021no—
107C2×D8—2021no—
108C4⋊Q8—2021no—
109#127C2×D10111yescharacteristic
110#126—2021no—
111#126—2021no—
112#125—1011no—
113#125C2×D10111yescharacteristic
114#124—1011no—
115#123—2021no—
116C22⋊Q8—2021no—
117C22⋊Q8—2021no—
118#102—21no—
119#102—21no—
120#102—2021no—
121#102—2021no—
122#97—1011no—
123#97—1011no—
124#97C2×D10111yescharacteristic
125C2×Q8—1011no—
126C2×Q8—2021no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1011no—
131C22×C4—2021no—
132SD16—4042no—
133D8—4042no—
134C2×C8—21no—
135C2×C8—2021no—
136C2×C8—2021no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—1011no—
140C4⋊C4—1011no—
141C4⋊C4—2021no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2021no—
145C4⋊C4C22⋊D10111yescharacteristic
146C4⋊C4C22⋊D10111yescharacteristic
147C22⋊C4—2021no—
148C22⋊C4—2021no—
149C22⋊C4—2021no—
150C22⋊C4—2021no—
151C22⋊C4—2021no—
152C42—2021no—
153C42C22×D10111yescharacteristic
154C23—41no—
155C23—2021no—
156Q8—8081no—
157Q8—4041no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—4041no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—8081no—
166C2×C4—2021no—
167C2×C4—2021no—
168C2×C4—2021no—
169C2×C4D4×D10111yescharacteristic
170C2×C4D4×D10111yescharacteristic
171C2×C4C2×C22⋊D10111yescharacteristic
172C8—41no—
173C8—4041no—
174C8—2022no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—4041no—
179C22—4041no—
180C22—4041no—
181C22#1569222311yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—4041no—
188C4—4041no—
189C4—4041no—
190C2—161no—
191C2—8081no—
192C2#2026534311yescharacteristic
193C2#2026534811yescharacteristic
194C2#2026534911yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#490×C101C2
socleC22×C101#120
prime radical#20265564C2
hypercenter#490D101
hypocenterC101#1657
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20265931C2semidirect
3. #20265541C2semidirect
4. #20264919C2semidirect
5. #20264918C2semidirect
6. #20264916C2semidirect
7. #490×C101C2semidirect
98. C101#1657semidirect
102. #490D101semidirect

Maximal subgroups

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

subgroupindex
#202659312
#202655642
#202655412
#202649192
#202649182
#202649162
#490×C1012
#1657101