Finite Group Databasebeta

← #15779369

Subgroups — #15779369

Order 3328.

306 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11718085C212yesmaximal
3C2×#11718094C211yesmaximal, characteristic
4#13115006C212yesmaximal
5C2×C13×#368C211yesmaximal, characteristic
6C22×C13×C16C2211yescharacteristic
7C2×C13×#108C2212yes—
8C2×#88062—22no—
9#11718779—22no—
10C2×#88059C2212yes—
11C2×C8×Dic13C2211yescharacteristic
12C22×#6090C2211yescharacteristic
13C13×#368—22no—
14#11718098—22no—
15#11718094C414yes—
16#11718085—24no—
17C2×C13×M16—22no—
18C22×C8×C13C2311yescharacteristic
19C2×C4×Dic13D411yescharacteristic
20C2×#6099—22no—
21C22×#1055D411yescharacteristic
22C2×C13×C16C2×C412yes—
23C2×C13×C16D412yes—
24C2×C13×C16Q812yes—
25C13×#108—22no—
26C13×#108—22no—
27#88062—44no—
28#88059—22no—
29#88059—22no—
30#88054—44no—
31C8×Dic13C2×C412yes—
32C8×Dic13Q812yes—
33C2×#6090C2×C412yes—
34C2×#6090D412yes—
35C2×#6090Q812yes—
36#12910—131nomaximal, Sylow
37C22×C4×C13C2×D411yescharacteristic
38C22×Dic13Q1612yes—
39C13×M16—42no—
40C13×M16—42no—
41C2×C8×C13—42no—
42C2×C8×C13C22×C411yescharacteristic
43C2×C8×C13C2×D411yescharacteristic
44C2×C8×C13C2×D411yescharacteristic
45C2×C8×C13C2×Q811yescharacteristic
46C2×C8×C13C2×Q811yescharacteristic
47C2×C8×C13C2×Q811yescharacteristic
48C4×Dic13C4⋊C412yes—
49C4×Dic13D812yes—
50#6099—42no—
51#6099—42no—
52C2×#1055—42no—
53C2×#1055C4⋊C412yes—
54C2×#1055D812yes—
55C2×#1055Q1612yes—
56C13×C16C4⋊C414yes—
57#6090C4⋊C414yes—
58C2×#368—131no—
59C2×#368—132no—
60C2×#368D1311yescharacteristic
61C2×#346—131no—
62#1848—132no—
63C23×C13C2×Q1611yescharacteristic
64C2×C4×C13C2×C4⋊C411yescharacteristic
65C2×C4×C13#12711yescharacteristic
66C2×C4×C13C4⋊Q811yescharacteristic
67C2×C4×C13C2×D811yescharacteristic
68C2×C4×C13C2×D811yescharacteristic
69C2×C4×C13C2×Q1611yescharacteristic
70C2×Dic13—42no—
71C2×Dic13#10714yes—
72C8×C13—82no—
73C8×C13C2×C4⋊C411yescharacteristic
74C8×C13C2×C4⋊C411yescharacteristic
75C8×C13C4⋊Q811yescharacteristic
76C8×C13C4⋊Q811yescharacteristic
77#1055—82no—
78#1055#10714yes—
79C22×C16—131no—
80C22×C16C2×D1311yescharacteristic
81C2×#108—132no—
82C2×#108—262no—
83C2×#108C2×D1312yes—
84#423—262no—
85C2×C4×C8—131no—
86#368—22no—
87#368—264no—
88#368—262no—
89#346—134no—
90C22×C13—22no—
91C22×C13C2×#10711yescharacteristic
92C22×C13#49411yescharacteristic
93C22×C13#50011yescharacteristic
94C4×C13#38411yescharacteristic
95C4×C13C2×#10711yescharacteristic
96C4×C13#49311yescharacteristic
97C4×C13#50011yescharacteristic
98Dic13—24no—
99C2×M16—22no—
100C2×M16—262no—
101C22×C8—131no—
102C22×C8C22×D1311yescharacteristic
103C2×C42—131no—
104C2×C16—132no—
105C2×C16—132no—
106C2×C16—132no—
107C2×C16Dic2612yes—
108C2×C16C4×D1312yes—
109C2×C16C22⋊D1312yes—
110#108—22no—
111#108—22no—
112#108—262no—
113#108—262no—
114#108—524no—
115C4⋊C8—524no—
116C4×C8—132no—
117C4×C8—132no—
118C2×C13—21no—
119C2×C13—21no—
120C2×C13#184511yescharacteristic
121C2×C13#216112yes—
122C22×C4—132no—
123C22×C4D4×D1311yescharacteristic
124M16—42no—
125M16—42no—
126M16—522no—
127M16—522no—
128C2×C8—42no—
129C2×C8—132no—
130C2×C8—132no—
131C2×C8—132no—
132C2×C8—522no—
133C2×C8C2×Dic2611yescharacteristic
134C2×C8C2×C4×D1311yescharacteristic
135C2×C8D4×D1311yescharacteristic
136C2×C8Q8×D1311yescharacteristic
137C2×C8Q8×D1311yescharacteristic
138C2×C8C2×C22⋊D1311yescharacteristic
139C42—132no—
140C42—132no—
141C16—134no—
142C16#610114yes—
143C13#1291011yescharacteristic, complemented, Sylow
144C23Q16×D1311yescharacteristic
145C2×C4—134no—
146C2×C4—522no—
147C2×C4#8814211yescharacteristic
148C2×C4C4⋊C4×D1311yescharacteristic
149C2×C4D8×D1311yescharacteristic
150C2×C4D8×D1311yescharacteristic
151C2×C4Q16×D1311yescharacteristic
152C2×C4#8819411yescharacteristic
153C8—82no—
154C8—134no—
155C8—1042no—
156C8#8814211yescharacteristic
157C8C4⋊C4×D1311yescharacteristic
158C8C2×#610111yescharacteristic
159C8#8819811yescharacteristic
160C22—22no—
161C22#1171853511yescharacteristic
162C22D13×#10711yescharacteristic
163C22#1171884211yescharacteristic
164C4—264no—
165C4#1171853511yescharacteristic
166C4D13×#10711yescharacteristic
167C4#1171863711yescharacteristic
168C4#1171881211yescharacteristic
169C2—21no—
170C2—21no—
171C2#1311499411yescharacteristic
172C2#1311662912yes—
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#368C2
socleC22×C13C2×#107
prime radicalC23×C13C2×Q16
cosocleC22×C8×C13C23
hypercenterC2×#368D13
hypocenterC13#12910
LCSG ▷ C2×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
143. C13#12910semidirect

Maximal subgroups

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

subgroupindex
C2×#117180982
C2×#117180852
C2×#117180942
#131150062
C2×C13×#3682
#1291013