Finite Group Databasebeta

← #15750144

Subgroups — #15750144

Order 3328.

202 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 103 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#13116635C211yesmaximal, characteristic
2#13113595C211yesmaximal, characteristic
3C2×C13×#335C211yesmaximal, characteristic
4C2×C13×C4⋊C8—21no—
5C2×C4×C8×C13C2211yescharacteristic
6#11718585—21no—
7C13×#335—21no—
8C13×#335C412yes—
9C22⋊#6090C412yes—
10C4⋊#6090—21no—
11C4×#6090—21no—
12#11718050—21no—
13#11718050C412yes—
14C22×C8×C13—41no—
15C22×C8×C13C2×C411yescharacteristic
16C22×C8×C13Q811yescharacteristic
17C2×C42×C13D411yescharacteristic
18C2×#6099—41no—
19C13×C4⋊C8—22no—
20C13×C4⋊C8—41no—
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13C2×C411yescharacteristic
23C4×C8×C13D411yescharacteristic
24C4×C8×C13D411yescharacteristic
25C2×#6090—22no—
26C4⋊#1055—22no—
27C4⋊#1055—41no—
28#7288—131nomaximal, Sylow
29C22×C4×C13C4⋊C411yescharacteristic
30C22×C4×C13D811yescharacteristic
31C22×C4×C13Q1611yescharacteristic
32C2×C8×C13—22no—
33C2×C8×C13—41no—
34C2×C8×C13—42no—
35C2×C8×C13—81no—
36C2×C8×C13—81no—
37C2×C8×C13C4211yescharacteristic
38C2×C8×C13C22⋊C411yescharacteristic
39C2×C8×C13C4⋊C411yescharacteristic
40C2×C8×C13C4⋊C411yescharacteristic
41C42×C13C22⋊C411yescharacteristic
42C42×C13C22⋊C411yescharacteristic
43C42×C13SD1611yescharacteristic
44C42×C13SD1611yescharacteristic
45#6099—81no—
46#6099—81no—
47C2×#1055—42no—
48#6090—42no—
49#2162—131no—
50#1567—131no—
51C2×#335D1311yescharacteristic
52C23×C13#10711yescharacteristic
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—41no—
56C2×C4×C13#9511yescharacteristic
57C2×C4×C13#10211yescharacteristic
58C2×C4×C13#10211yescharacteristic
59C2×C4×C13#10311yescharacteristic
60C2×C4×C13#10311yescharacteristic
61C2×C4×C13#10611yescharacteristic
62C2×C4×C13D1611yescharacteristic
63C2×C4×C13SD3211yescharacteristic
64C2×C4×C13SD3211yescharacteristic
65C2×C4×C13Q3211yescharacteristic
66C8×C13—21no—
67C8×C13—21no—
68C8×C13—21no—
69C8×C13—82no—
70C8×C13#10812yes—
71#1055—82no—
72#423—261no—
73C2×C4⋊C8—21no—
74C2×C4×C8C2×D1311yescharacteristic
75C4⋊C16—261no—
76C22⋊C16—132no—
77C4×C16—261no—
78#335—21no—
79#335—132no—
80#335—261no—
81#335Dic1312yes—
82C22×C13—21no—
83C22×C13—21no—
84C22×C13#34011yescharacteristic
85C22×C13#36611yescharacteristic
86C22×C13#36711yescharacteristic
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13#34111yescharacteristic
91C4×C13#34411yescharacteristic
92C4×C13#35711yescharacteristic
93C4×C13#35711yescharacteristic
94C4×C13#35811yescharacteristic
95C4×C13#35811yescharacteristic
96C2×M16—521no—
97C22×C8—41no—
98C22×C8Dic2611yescharacteristic
99C22×C8C4×D1311yescharacteristic
100C2×C42C22⋊D1311yescharacteristic
101C2×C16—262no—
102C4⋊C8—22no—
103C4⋊C8—41no—
104C4⋊C8—262no—
105C4⋊C8—521no—
106C4×C8C4×D1311yescharacteristic
107C4×C8D5211yescharacteristic
108C4×C8C2×Dic1311yescharacteristic
109C4×C8C22⋊D1311yescharacteristic
110C2×C13—21no—
111C2×C13—21no—
112C2×C13#130111yescharacteristic
113C2×C13#138011yescharacteristic
114C2×C13#138811yescharacteristic
115C22×C4#610111yescharacteristic
116C22×C4#610411yescharacteristic
117C22×C4#610711yescharacteristic
118M16—1041no—
119M16—1041no—
120C2×C8—22no—
121C2×C8—41no—
122C2×C8—42no—
123C2×C8—81no—
124C2×C8—81no—
125C2×C8—522no—
126C2×C8C4×Dic1311yescharacteristic
127C2×C8#610111yescharacteristic
128C2×C8C4⋊Dic1311yescharacteristic
129C2×C8#610311yescharacteristic
130C42#610311yescharacteristic
131C42#610511yescharacteristic
132C42#610611yescharacteristic
133C42C22⋊Dic1311yescharacteristic
134C16—522no—
135C13#728811yescharacteristic, complemented, Sylow
136C23#8804711yescharacteristic
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4#8804811yescharacteristic
141C2×C4#8804911yescharacteristic
142C2×C4#8805011yescharacteristic
143C2×C4#8806611yescharacteristic
144C2×C4#8806711yescharacteristic
145C2×C4#8806811yescharacteristic
146C2×C4#8806911yescharacteristic
147C2×C4#8807111yescharacteristic
148C2×C4#8807211yescharacteristic
149C2×C4#8807511yescharacteristic
150C8—21no—
151C8—21no—
152C8—21no—
153C8—82no—
154C8—1042no—
155C8#8805912yes—
156C22—21no—
157C22—21no—
158C22#1171808111yescharacteristic
159C22#1171808211yescharacteristic
160C22#1171812111yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4#1171808311yescharacteristic
165C4#1171808411yescharacteristic
166C4#1171814411yescharacteristic
167C4#1171815111yescharacteristic
168C4#1171815411yescharacteristic
169C4#1171815611yescharacteristic
170C2—21no—
171C2—21no—
172C2#1311273311yescharacteristic
173C2#1311292711yescharacteristic
174C2#1311294911yescharacteristic
subgroupG/H
centerC2×C4#88049
commutatorC2×C8×C13C42
FrattiniC2×C4×C8C2×D13
FittingC2×C13×#335C2
socleC22×C13#340
prime radicalC23×C13#107
cosocleC2×C4×C8×C13C22
hypercenterC2×#335D13
hypocenterC13#7288
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
135. C13#7288semidirect

Maximal subgroups

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

subgroupindex
#131166352
#131135952
C2×C13×#3352
#728813