Finite Group Databasebeta

← #16777536

Subgroups — #16777536

Order 3328.

222 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D13⋊(C4⋊C16)C211yesmaximal, characteristic
2#13130776C211yesmaximal, characteristic
3#13113581C211yesmaximal, characteristic
4C2×#88104C412yes—
5C2×#88103—21no—
6C2×D13⋊C16—21no—
7#11719053—21no—
8#11718494—21no—
9C4×C8×D13C2211yescharacteristic
10#11718260C412yes—
11C4⋊#6092—21no—
12C13×#334C411yescharacteristic
13#11718071—21no—
14#11718049C411yescharacteristic
15C2×#6118—22no—
16C2×C8×D13C2×C411yescharacteristic
17C2×C8×D13D411yescharacteristic
18C42×D13D411yescharacteristic
19#88112—41no—
20#88112—41no—
21C2×#6092—22no—
22#88104—42no—
23#88103—41no—
24#88103—41no—
25D13⋊C16—41no—
26D13⋊C16—41no—
27C13×C4⋊C8—21no—
28C4×C8×C13C2×C411yescharacteristic
29#88060—41no—
30C8×Dic13—41no—
31C8×Dic13C2×C411yescharacteristic
32C8×Dic13Q811yescharacteristic
33C4⋊#1055—21no—
34C4×#1055D411yescharacteristic
35#7276—131nomaximal, Sylow
36C2×C4×D13C22⋊C411yescharacteristic
37C2×C4×D13SD1611yescharacteristic
38C2×C4×D13Q1611yescharacteristic
39C2×#1057—42no—
40#6118—42no—
41#6118—42no—
42C2×C8×C13—41no—
43C2×C8×C13C4211yescharacteristic
44C2×C8×C13C4⋊C411yescharacteristic
45C42×C13C22⋊C411yescharacteristic
46C4×Dic13C4⋊C411yescharacteristic
47C4×Dic13D811yescharacteristic
48C4×Dic13SD1611yescharacteristic
49C2×#1055—41no—
50C2×#1055C22⋊C411yescharacteristic
51C2×#1055C4⋊C411yescharacteristic
52C8×D13—21no—
53C8×D13—21no—
54C8×D13D811yescharacteristic
55C8×D13SD1611yescharacteristic
56C8×D13SD1611yescharacteristic
57C8×D13Q1611yescharacteristic
58#6092—42no—
59C2×C4⋊C16—131no—
60#1848—131no—
61#1564—131no—
62C22×D13#10311yescharacteristic
63C2×C4×C13#9511yescharacteristic
64C2×C4×C13#10211yescharacteristic
65C2×C4×C13#10311yescharacteristic
66C2×Dic13#10211yescharacteristic
67C2×Dic13#10611yescharacteristic
68C2×Dic13#10711yescharacteristic
69C4×D13—22no—
70C4×D13—41no—
71C4×D13#10011yescharacteristic
72C4×D13#10111yescharacteristic
73C4×D13#10211yescharacteristic
74C4×D13#10311yescharacteristic
75#1057—82no—
76C8×C13—21no—
77C8×C13—81no—
78C8×C13#10611yescharacteristic
79C8×C13#10711yescharacteristic
80#1055—21no—
81#1055—81no—
82#1055#10211yescharacteristic
83#1055#10311yescharacteristic
84C22×C16—261no—
85#431—261no—
86C2×#108—132no—
87C2×#108—261no—
88#423—261no—
89C2×C4×C8—131no—
90C4⋊C16—132no—
91C4⋊C16—261no—
92#335—261no—
93#334—131no—
94#334#26111yescharacteristic
95C22×C13#34011yescharacteristic
96C2×D13—21no—
97C2×D13—21no—
98C2×D13#33211yescharacteristic
99C2×D13#33311yescharacteristic
100C4×C13—21no—
101C4×C13—21no—
102C4×C13#34011yescharacteristic
103C4×C13#34311yescharacteristic
104Dic13—21no—
105Dic13#33111yescharacteristic
106Dic13#33211yescharacteristic
107Dic13#36812yes—
108C2×M16—262no—
109C22×C8—131no—
110C22×C8—131no—
111C2×C42—131no—
112C2×C16—262no—
113C2×C16—521no—
114C2×C16—521no—
115#108—521no—
116#108—521no—
117#108—522no—
118C4⋊C8—21no—
119C4⋊C8—261no—
120C4⋊C8—521no—
121C4⋊C8—521no—
122C22⋊C8—521no—
123C4×C8—131no—
124C4×C8—131no—
125C4×C8—131no—
126C4×C8—521no—
127C4×C8C2×#26111yescharacteristic
128C2×C13#129611yescharacteristic
129C2×C13#138111yescharacteristic
130C2×C13#138911yescharacteristic
131D13—21no—
132D13—21no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136M16—522no—
137M16—522no—
138C2×C8—41no—
139C2×C8—131no—
140C2×C8—131no—
141C2×C8—131no—
142C2×C8—131no—
143C2×C8—131no—
144C2×C8—131no—
145C2×C8—261no—
146C2×C8—261no—
147C2×C8—522no—
148C2×C8—521no—
149C2×C8C4×#26111yescharacteristic
150C2×C8C4⋊#26111yescharacteristic
151C42—131no—
152C42—131no—
153C42—131no—
154C42C22⋊#26111yescharacteristic
155C16—522no—
156C13#727611yescharacteristic, complemented, Sylow
157C23—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—131no—
165C2×C4—262no—
166C2×C4—521no—
167C2×C4(C2×#261)⋊C411yescharacteristic
168C2×C4#8811511yescharacteristic
169C2×C4#8811711yescharacteristic
170C8—21no—
171C8—81no—
172C8—131no—
173C8—131no—
174C8—261no—
175C8—1041no—
176C8—1042no—
177C8#8810111yescharacteristic
178C8#8810211yescharacteristic
179C22—131no—
180C22—131no—
181C22—261no—
182C22—261no—
183C22#1171824611yescharacteristic
184C4—21no—
185C4—21no—
186C4—132no—
187C4—131no—
188C4—131no—
189C4—261no—
190C4#1171826511yescharacteristic
191C4#1171827111yescharacteristic
192C2—261no—
193C2—261no—
194C2#1312971511yescharacteristic
195C2#1312989511yescharacteristic
196C2#1312991811yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×#334C4
socleC22×C13#340
prime radicalC22×D13#103
cosocleC4×C8×D13C22
hypercenter#334#261
hypocenterC13#7276
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #334

Complements

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

NH ≅ G/Ntype
156. C13#7276semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
#131307762
#131135812
#727613