Finite Group Databasebeta

← #15750628

Subgroups — #15750628

Order 3328.

174 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718091C211yesmaximal, characteristic
2C2×#11718097C211yesmaximal, characteristic
3C2×C13×#368C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5C2×C13×#108—21no—
6C2×#88058—21no—
7C13×#368—21no—
8C13×#368C412yescomplemented
9#11718097—21no—
10#11718097C412yes—
11#11718091—21no—
12#11718091—21no—
13C2×#88034C412yescomplemented
14C2×C13×M16—41no—
15C22×C8×C13D411yescharacteristic
16C2×C4⋊Dic13—41no—
17C2×C13×C16C2×C411yescharacteristic
18C2×C13×C16C2×C411yescharacteristic
19C2×C13×C16C2×C411yescharacteristic
20C2×C13×C16D411yescharacteristic
21C2×C13×C16D411yescharacteristic
22C2×C13×C16Q811yescharacteristic
23C13×#108—22no—
24C13×#108—41no—
25#88058—22no—
26#88058—41no—
27#88034—22no—
28#7474—131nomaximal, Sylow
29C22×C4×C13D811yescharacteristic
30C22×Dic13—81no—
31C13×M16—42no—
32C13×M16—81no—
33C2×C8×C13—81no—
34C2×C8×C13C22⋊C411yescharacteristic
35C2×C8×C13C22⋊C411yescharacteristic
36C2×C8×C13C4⋊C411yescharacteristic
37C2×C8×C13SD1611yescharacteristic
38C2×C8×C13SD1611yescharacteristic
39C2×C8×C13Q1611yescharacteristic
40C4⋊Dic13—42no—
41C4⋊Dic13—81no—
42C13×C16C4211yescharacteristic
43C13×C16C22⋊C411yescharacteristic
44C13×C16C4⋊C411yescharacteristic
45C13×C16C4⋊C411yescharacteristic
46C2×M64—131no—
47C2×#368D1311yescharacteristic
48C2×#367—131no—
49C23×C13SD3211yescharacteristic
50C2×C4×C13#10211yescharacteristic
51C2×C4×C13#10211yescharacteristic
52C2×C4×C13#10711yescharacteristic
53C2×C4×C13D1611yescharacteristic
54C2×C4×C13SD3211yescharacteristic
55C2×C4×C13Q3211yescharacteristic
56C2×Dic13—82no—
57C2×Dic13—162no—
58C8×C13—82no—
59C8×C13#9511yescharacteristic
60C8×C13#10311yescharacteristic
61C8×C13#10311yescharacteristic
62C8×C13#10611yescharacteristic
63C22×C16C2×D1311yescharacteristic
64C2×#108—21no—
65C2×#107—261no—
66M64—261no—
67M64—261no—
68C2×C32—132no—
69#368—21no—
70#368Dic1312yescomplemented
71#367—132no—
72#367—261no—
73C22×C13—22no—
74C22×C13#35711yescharacteristic
75C22×C13#35811yescharacteristic
76C22×C13#36711yescharacteristic
77C4×C13#34011yescharacteristic
78C4×C13#35711yescharacteristic
79C4×C13#35811yescharacteristic
80C4×C13#36611yescharacteristic
81Dic13—162no—
82C2×M16—41no—
83C22×C8C22⋊D1311yescharacteristic
84C2×C4⋊C4—521no—
85C2×C16Dic2611yescharacteristic
86C2×C16C4×D1311yescharacteristic
87C2×C16C4×D1311yescharacteristic
88C2×C16D5211yescharacteristic
89C2×C16C2×Dic1311yescharacteristic
90C2×C16C22⋊D1311yescharacteristic
91#108—22no—
92#108—41no—
93#107—262no—
94#107—521no—
95C32—262no—
96C2×C13—21no—
97C2×C13—21no—
98C2×C13#138011yescharacteristic
99C2×C13#142612yes—
100C22×C4—1041no—
101C22×C4#610411yescharacteristic
102M16—42no—
103M16—81no—
104C2×C8—81no—
105C2×C8#610111yescharacteristic
106C2×C8#610311yescharacteristic
107C2×C8#610511yescharacteristic
108C2×C8#610611yescharacteristic
109C2×C8#610711yescharacteristic
110C2×C8C22⋊Dic1311yescharacteristic
111C4⋊C4—522no—
112C4⋊C4—1041no—
113C16C4×Dic1311yescharacteristic
114C16#610111yescharacteristic
115C16C4⋊Dic1311yescharacteristic
116C16#610311yescharacteristic
117C13#747411yescharacteristic, complemented, Sylow
118C23#8806811yescharacteristic
119C2×C4—1042no—
120C2×C4—2082no—
121C2×C4#8804711yescharacteristic
122C2×C4#8804911yescharacteristic
123C2×C4#8806611yescharacteristic
124C2×C4#8806711yescharacteristic
125C2×C4#8806911yescharacteristic
126C2×C4#8807211yescharacteristic
127C8—82no—
128C8#8804811yescharacteristic
129C8#8805011yescharacteristic
130C8#8807111yescharacteristic
131C8#8807511yescharacteristic
132C22—22no—
133C22#1171808211yescharacteristic
134C22#1171808311yescharacteristic
135C22#1171815611yescharacteristic
136C4—2082no—
137C4#1171808111yescharacteristic
138C4#1171808411yescharacteristic
139C4#1171812111yescharacteristic
140C4#1171815411yescharacteristic
141C2—21no—
142C2—21no—
143C2#1311292711yescharacteristic
144C2#1311304312yes—
subgroupG/H
centerC22#11718082
commutatorC13×C16C42
FrattiniC22×C16C2×D13
FittingC2×C13×#368C2
socleC22×C13#367
prime radicalC23×C13SD32
cosocleC22×C13×C16C22
hypercenterC2×#368D13
hypocenterC13#7474
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#368

Complements

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

NH ≅ G/Ntype
8. C13×#368C4semidirect
13. C2×#88034C4semidirect
70. #368Dic13semidirect
117. C13#7474semidirect

Maximal subgroups

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

subgroupindex
C2×#117180912
C2×#117180972
C2×C13×#3682
#747413