Finite Group Databasebeta

← #35213169

Subgroups — #35213169

Order 20864.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#23782214C211yesmaximal, characteristic
2#23781720C212yesmaximal, complemented
3#23781405C211yesmaximal, characteristic, complemented
4#23781404C212yesmaximal, complemented
5#329×C163C211yesmaximal, characteristic, complemented
6C2×#14579700C411yescharacteristic
7C2×#14579698C411yescharacteristic
8#19104733C411yescharacteristic
9#19104731C411yescharacteristic
10#19104723C2211yescharacteristic
11#19104708—22no—
12(C22⋊D163)⋊C4—22no—
13C42×D163C2211yescharacteristic
14Dic163⋊C8—22no—
15(C2×D163)⋊C8—22no—
16#19104646C2212yes—
17#124×C163C2211yescharacteristic
18#97×C163C2212yes—
19#14579700—42no—
20#14579698—42no—
21C2×Dic326C2×C411yescharacteristic
22C2×D652—21no—
23C2×D652C2×C411yescharacteristic
24C2×C22⋊D163—21no—
25C2×C22⋊D163—22no—
26C22×Dic163—21no—
27C2×C4×D163—21no—
28C2×C4×D163C2×C411yescharacteristic
29C2×C4×D163D412yes—
30C2×C163⋊C8—22no—
31Dic163⋊C4—22no—
32(C2×D163)⋊C4—22no—
33C4×Dic163C2×C411yescharacteristic
34C4×Dic163D412yes—
35C2×Q8×C163C2×C411yescharacteristic
36C2×D4×C163C2×C411yescharacteristic
37C2×C8×C163—22no—
38C22⋊C4×C163—22no—
39C42×C163C2311yescharacteristic
40C22×D163—21no—
41C22×D163C22⋊C411yescharacteristic
42Dic326—41no—
43D652—41no—
44D652—42no—
45C22⋊D163—44no—
46C22⋊D163—42no—
47C2×Dic163—21no—
48C2×Dic163—42no—
49C2×Dic163C22⋊C412yes—
50C2×Dic163C22⋊C411yescharacteristic
51C4×D163—22no—
52C4×D163—42no—
53C4×D163—42no—
54C163⋊C8—42no—
55C23×C163—21no—
56Q8×C163—41no—
57D4×C163—41no—
58C2×C4×C163—21no—
59C2×C4×C163C22×C411yescharacteristic
60C2×C4×C163C2×D412yes—
61C8×C163—42no—
62C22×C163—41no—
63C22×C163—42no—
64C22×C163C2×C22⋊C411yescharacteristic
65C2×D163—21no—
66C2×D163—22no—
67C2×D163—41no—
68C2×D163—42no—
69C4×C163—21no—
70C4×C163—22no—
71C4×C163—41no—
72Dic163—22no—
73Dic163—41no—
74Dic163#10012yes—
75C2×C163—81no—
76C2×C163C2×#10011yescharacteristic
77C2×C163#42112yes—
78D163—41no—
79D163—81no—
80C163#153611yescharacteristic, complemented, Sylow
81#1536—1631nomaximal, Sylow
82#532—1631no—
83#432—1632no—
84#329—1631no—
85#329—1632no—
86#329D16311yescharacteristic, complemented
87C2×#41—1631no—
88C2×#41—1631no—
89C4⋊Q8—1631no—
90#127—1631no—
91#124—1631no—
92#124C2×D16311yescharacteristic
93#121—3262no—
94C4×D4—3262no—
95C2×C42—1631no—
96C4⋊C8—3262no—
97C22⋊C8—3262no—
98#97—1632no—
99#97C2×D16312yes—
100#41—6522no—
101#41—6522no—
102C2×Q8—1631no—
103C2×Q8C4×D16311yescharacteristic
104C2×D4—3261no—
105C2×D4—3261no—
106C2×D4—3262no—
107C2×D4—1631no—
108C2×D4C4×D16311yescharacteristic
109C22×C4—3261no—
110C22×C4—3261no—
111C22×C4—1631no—
112C22×C4—1632no—
113C2×C8—22no—
114C2×C8—3262no—
115C4⋊C4—3262no—
116C22⋊C4—22no—
117C22⋊C4—3262no—
118C42—1631no—
119C42—1632no—
120C42C22×D16311yescharacteristic
121C23—21no—
122C23—3261no—
123C23—1631no—
124Q8—41no—
125Q8—6521no—
126D4—41no—
127D4—6521no—
128D4—6522no—
129D4—6524no—
130D4—6522no—
131C2×C4—21no—
132C2×C4—3262no—
133C2×C4—3261no—
134C2×C4—6522no—
135C2×C4—6522no—
136C2×C4—6522no—
137C2×C4—1632no—
138C2×C4—1631no—
139C2×C4C2×C4×D16311yescharacteristic
140C2×C4D4×D16312yes—
141C8—42no—
142C8—6522no—
143C22—41no—
144C22—42no—
145C22—3261no—
146C22—3262no—
147C22—6521no—
148C22—6522no—
149C22C22⋊C4×D16311yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—3262no—
154C4—6521no—
155C4—1632no—
156C2—81no—
157C2—13041no—
158C2—6521no—
159C2#100×D16311yescharacteristic
160C2#2378168012yes—
subgroupG/H
centerC22C22⋊C4×D163
commutatorC2×C4×C163C22×C4
FrattiniC42C22×D163
Fitting#329×C163C2
socleC22×C163C2×C22⋊C4
prime radical#23782214C2
cosocleC42×C163C23
hypercenter#329D163
hypocenterC163#1536
LCSG ▷ C2×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23781720C2semidirect
3. #23781405C2semidirect
4. #23781404C2semidirect
5. #329×C163C2semidirect
80. C163#1536semidirect
86. #329D163semidirect

Maximal subgroups

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

subgroupindex
#237822142
#237817202
#237814052
#237814042
#329×C1632
#1536163