Finite Group Databasebeta

← #15778337

Subgroups — #15778337

Order 3328.

306 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11718098C211yesmaximal, characteristic
2C2×#11718094C211yesmaximal, characteristic
3#108×Dic13C212yesmaximal
4#13112929C212yesmaximal
5C2×C13×#368C211yesmaximal, characteristic
6C22×C13×C16C2211yescharacteristic
7C2×C13×#108C2212yes—
8M16×Dic13—22no—
9C2×#88059C2212yes—
10C2×C8×Dic13C2211yescharacteristic
11C22×#6090C2211yescharacteristic
12C13×#368C414yescomplemented
13#11718150—22no—
14#11718098C414yescomplemented
15#11718094C414yes—
16C2×C13×M16—22no—
17C22×C8×C13C2311yescharacteristic
18C2×C4×Dic13D411yescharacteristic
19C2×#6099—22no—
20C22×#1055D411yescharacteristic
21C2×C13×C16C2×C412yes—
22C2×C13×C16C2×C412yes—
23C2×C13×C16C2×C412yes—
24C13×#108—22no—
25C13×#108C2×C414yes—
26#88059—22no—
27#88059C2×C414yes—
28#88055—42no—
29C8×Dic13—42no—
30C8×Dic13C2×C412yes—
31C8×Dic13Q812yes—
32C2×#6090—21no—
33C2×#6090—21no—
34C2×#6090C2×C412yes—
35#12676—131nomaximal, Sylow
36C22×C4×C13C2×D411yescharacteristic
37C22×Dic13Q1612yes—
38C13×M16—24no—
39C13×M16—42no—
40C2×C8×C13—42no—
41C2×C8×C13C22×C411yescharacteristic
42C2×C8×C13C22×C411yescharacteristic
43C2×C8×C13C22×C411yescharacteristic
44C2×C8×C13C2×Q811yescharacteristic
45C2×C8×C13#4111yescharacteristic
46C2×C8×C13#4111yescharacteristic
47C4×Dic13C4⋊C412yes—
48C4×Dic13D812yes—
49#6099—24no—
50#6099—42no—
51C2×#1055—21no—
52C2×#1055—21no—
53C2×#1055—42no—
54C2×#1055C4⋊C412yes—
55C13×C16C4214yes—
56#6090—22no—
57C2×#368—131no—
58C2×#368D1311yescharacteristic
59C2×#346—131no—
60C4×#108—132no—
61#1381—132no—
62C23×C13C2×Q1611yescharacteristic
63C2×C4×C13C2×C4⋊C411yescharacteristic
64C2×C4×C13C4×D411yescharacteristic
65C2×C4×C13C4×D411yescharacteristic
66C2×C4×C13C2×D811yescharacteristic
67C2×C4×C13#13511yescharacteristic
68C2×C4×C13#13511yescharacteristic
69C2×Dic13—42no—
70C2×Dic13#10714yes—
71C8×C13—44no—
72C8×C13C2×C4211yescharacteristic
73C8×C13#11711yescharacteristic
74C8×C13C4×Q811yescharacteristic
75C8×C13C4×Q811yescharacteristic
76#1055—22no—
77#1055—44no—
78C22×C16—131no—
79C22×C16C2×D1311yescharacteristic
80C2×#108—132no—
81C2×#108C2×D1312yes—
82C4×M16—262no—
83C2×C4×C8—131no—
84#368—134no—
85#368Dic1314yescomplemented
86#346—134no—
87#341—262no—
88C22×C13—22no—
89C22×C13C2×#10711yescharacteristic
90C22×C13C4×Q1611yescharacteristic
91C22×C13C4×Q1611yescharacteristic
92C4×C13C4×C4⋊C411yescharacteristic
93C4×C13#42711yescharacteristic
94C4×C13C4×D811yescharacteristic
95C4×C13C4×D811yescharacteristic
96Dic13—24no—
97C2×M16—22no—
98C2×M16—262no—
99C22×C8—131no—
100C22×C8C22×D1311yescharacteristic
101C2×C42—131no—
102C2×C16—132no—
103C2×C16—261no—
104C2×C16—261no—
105C2×C16C4×D1312yes—
106C2×C16C4×D1312yes—
107C2×C16C2×Dic1312yes—
108#108—22no—
109#108—134no—
110#108—262no—
111#108C2×Dic1314yes—
112#97—522no—
113C4×C8—132no—
114C4×C8—132no—
115C4×C8—522no—
116C2×C13—21no—
117C2×C13—21no—
118C2×C13C4×#10711yescharacteristic
119C2×C13#216112yes—
120C22×C4—132no—
121C22×C4D4×D1311yescharacteristic
122M16—24no—
123M16—42no—
124M16—264no—
125M16—522no—
126C2×C8—42no—
127C2×C8—132no—
128C2×C8—261no—
129C2×C8—261no—
130C2×C8—522no—
131C2×C8C2×C4×D1311yescharacteristic
132C2×C8C2×C4×D1311yescharacteristic
133C2×C8#612911yescharacteristic
134C2×C8Q8×D1311yescharacteristic
135C2×C8#613111yescharacteristic
136C2×C8C22×Dic1311yescharacteristic
137C42—132no—
138C42—132no—
139C16—262no—
140C16C4×Dic1314yes—
141C13#1267611yescharacteristic, complemented, Sylow
142C23Q16×D1311yescharacteristic
143C2×C4—134no—
144C2×C4—522no—
145C2×C4C4⋊C4×D1311yescharacteristic
146C2×C4#8814711yescharacteristic
147C2×C4D8×D1311yescharacteristic
148C2×C4#8816611yescharacteristic
149C2×C4#8817311yescharacteristic
150C2×C4D4×Dic1311yescharacteristic
151C8—44no—
152C8—262no—
153C8—524no—
154C8#8814111yescharacteristic
155C8#8814611yescharacteristic
156C8C2×C4×Dic1311yescharacteristic
157C8Q8×Dic1311yescharacteristic
158C22—22no—
159C22#1171853411yescharacteristic
160C22D13×#10711yescharacteristic
161C22Q16×Dic1311yescharacteristic
162C4—264no—
163C4#1171853311yescharacteristic
164C4#1171854111yescharacteristic
165C4C4⋊C4×Dic1311yescharacteristic
166C4D8×Dic1311yescharacteristic
167C2—21no—
168C2—21no—
169C2#107×Dic1311yescharacteristic
170C2#1311662912yes—
subgroupG/H
centerC2×C4D8×D13
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#368C2
socleC22×C13C2×#107
prime radicalC23×C13C2×Q16
cosocleC22×C8×C13C23
hypercenterC2×#368D13
hypocenterC13#12676
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

Complements

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

NH ≅ G/Ntype
12. C13×#368C4semidirect
14. #11718098C4semidirect
85. #368Dic13semidirect
141. C13#12676semidirect

Maximal subgroups

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

subgroupindex
C2×#117180982
C2×#117180942
#108×Dic132
#131129292
C2×C13×#3682
#1267613