Finite Group Databasebeta

← #35216200

Subgroups — #35216200

Order 20864.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#23781637C212yesmaximal, complemented
3#23781460C211yesmaximal, characteristic, complemented
4#23781457C212yesmaximal, complemented
5#354×C163C211yesmaximal, characteristic, complemented
6C2×#14579700C411yescharacteristic, complemented
7C2×#14579698C2211yescharacteristic
8#19104733C411yescharacteristic, complemented
9#19104731C2211yescharacteristic
10#19104723C411yescharacteristic, complemented
11#19104708—22no—
12(C22⋊D163)⋊C4—22no—
13#19104691—22no—
14C42×D163C411yescharacteristic, complemented
15#19104650C2212yes—
16#19104649—22no—
17#124×C163C2211yescharacteristic
18#99×C163C2212yes—
19#14579700—41no—
20#14579700—41no—
21#14579698—41no—
22#14579698—41no—
23C2×Dic326C2×C411yescharacteristic
24C2×D652—21no—
25C2×D652C2×C411yescharacteristic
26C2×C22⋊D163—22no—
27C2×C22⋊D163D412yes—
28C22×Dic163D412yes—
29C2×C4×D163—21no—
30C2×C4×D163—21no—
31C2×C4×D163C2×C411yescharacteristic
32Dic163⋊C4—22no—
33Dic163⋊C4—42no—
34C22⋊Dic163—22no—
35(C2×D163)⋊C4—22no—
36C4×Dic163—21no—
37C4×Dic163—42no—
38C4×Dic163C2×C411yescharacteristic
39C2×Q8×C163C2×C411yescharacteristic
40C2×D4×C163C2311yescharacteristic
41C22⋊C4×C163—22no—
42C22⋊C4×C163—22no—
43C42×C163C2×C411yescharacteristic
44C22×D163—21no—
45C22×D163C22⋊C411yescharacteristic
46Dic326—41no—
47D652—41no—
48D652—42no—
49C22⋊D163—42no—
50C22⋊D163—44no—
51C2×Dic163—21no—
52C2×Dic163—22no—
53C2×Dic163—22no—
54C2×Dic163—42no—
55C2×Dic163C22⋊C412yes—
56C2×Dic163C22⋊C411yescharacteristic
57C4×D163—21no—
58C4×D163—21no—
59C4×D163—42no—
60C4×D163—41no—
61C4×D163—41no—
62C23×C163C2×D412yes—
63Q8×C163—41no—
64D4×C163—41no—
65C2×C4×C163—21no—
66C2×C4×C163—21no—
67C2×C4×C163—42no—
68C2×C4×C163C22×C411yescharacteristic
69C22×C163—22no—
70C22×C163—42no—
71C22×C163C2×C22⋊C411yescharacteristic
72C2×D163—21no—
73C2×D163—41no—
74C2×D163—42no—
75C2×D163—41no—
76C4×C163—21no—
77C4×C163—41no—
78C4×C163—41no—
79C4×C163—82no—
80Dic163—22no—
81Dic163—22no—
82Dic163—82no—
83Dic163#9911yescharacteristic
84Dic163#9911yescharacteristic
85C2×C163—21no—
86C2×C163—42no—
87C2×C163C2×#9911yescharacteristic
88D163—41no—
89D163—81no—
90C163#212611yescharacteristic, complemented, Sylow
91#2126—1631nomaximal, Sylow
92#532—1631no—
93#410—1632no—
94#354—1631no—
95#354D16311yescharacteristic, complemented
96#353—1632no—
97C2×#41—1631no—
98C2×#41—1631no—
99C4⋊Q8—1631no—
100#127—1631no—
101#124—1631no—
102#124C2×D16311yescharacteristic
103#121—3262no—
104C4×D4—3262no—
105#117—3262no—
106C2×C42—1631no—
107#99—3262no—
108#99—1632no—
109#99C2×D16312yes—
110#41—6521no—
111#41—6521no—
112#41—6521no—
113#41—6521no—
114C2×Q8—1631no—
115C2×Q8C4×D16311yescharacteristic
116C2×D4—3261no—
117C2×D4—3262no—
118C2×D4—1632no—
119C2×D4—1631no—
120C2×D4C22×D16311yescharacteristic
121C22×C4—3261no—
122C22×C4—3261no—
123C22×C4—1632no—
124C22×C4—1631no—
125C4⋊C4—3262no—
126C4⋊C4—6522no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—3262no—
130C22⋊C4—3262no—
131C42—3261no—
132C42—6522no—
133C42—1631no—
134C42C4×D16311yescharacteristic
135C23—3261no—
136C23—1631no—
137C23D4×D16312yes—
138Q8—41no—
139Q8—6521no—
140D4—41no—
141D4—6521no—
142D4—6522no—
143D4—6522no—
144D4—6524no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—3261no—
149C2×C4—3261no—
150C2×C4—3261no—
151C2×C4—3262no—
152C2×C4—3262no—
153C2×C4—6522no—
154C2×C4—6521no—
155C2×C4—6521no—
156C2×C4—6522no—
157C2×C4—1632no—
158C2×C4—1631no—
159C2×C4C2×C4×D16311yescharacteristic
160C22—22no—
161C22—42no—
162C22—3261no—
163C22—6522no—
164C22—6521no—
165C22—6521no—
166C22C22⋊C4×D16311yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—13042no—
172C4—3262no—
173C4—3262no—
174C4—1631no—
175C4—1631no—
176C2—21no—
177C2—42no—
178C2—13041no—
179C2—6521no—
180C2#99×D16311yescharacteristic
subgroupG/H
centerC2#99×D163
commutatorC2×C4×C163C22×C4
FrattiniC2×D4C22×D163
Fitting#354×C163C2
socleC2×C163C2×#99
prime radical#23782214C2
cosocleC2×D4×C163C23
hypercenter#354D163
hypocenterC163#2126
LCSG ▷ C2×C4×C163 ▷ C22×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #23781637C2semidirect
3. #23781460C2semidirect
4. #23781457C2semidirect
5. #354×C163C2semidirect
6. C2×#14579700C4semidirect
8. #19104733C4semidirect
10. #19104723C4semidirect
14. C42×D163C4semidirect
90. C163#2126semidirect
95. #354D163semidirect

Maximal subgroups

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

subgroupindex
#237822142
#237816372
#237814602
#237814572
#354×C1632
#2126163