Finite Group Databasebeta

← #15776278

Subgroups — #15776278

Order 3328.

286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117048C212yesmaximal, complemented
2#13116416C211yesmaximal, characteristic, complemented
3#13112827C212yesmaximal, complemented
4#13112789C211yesmaximal, characteristic, complemented
5C13×#3259C211yesmaximal, characteristic
6C13×#540—21no—
7C13×#478—22no—
8C13×#469C2212yes—
9C13×#466—21no—
10C13×#459—22no—
11C13×#424C2211yescharacteristic
12#11718786C2211yescharacteristic
13#11718155—22no—
14#11718152C2211yescharacteristic
15#11718145C2212yes—
16#11718144—21no—
17#11718125—21no—
18#11718079—22no—
19C2×C13×D8—21no—
20C2×C13×D8D412yes—
21C2×C13×M16C2311yescharacteristic
22C22×C8×C13D411yescharacteristic
23C13×#127—21no—
24C13×#125—21no—
25C13×#123—42no—
26C13×#121—22no—
27C13×#121—42no—
28C4×D4×C13—22no—
29C13×#117D411yescharacteristic
30C2×#6099—21no—
31C2×#6099—21no—
32C13×#107—21no—
33C13×#106D412yes—
34C13×C4⋊C8—22no—
35C13×#102—22no—
36C13×#102—22no—
37#88059—22no—
38#88052—22no—
39#12304—131nomaximal, Sylow
40C2×D4×C13—22no—
41C2×D4×C13—42no—
42C2×D4×C13—42no—
43C22×C4×C13—42no—
44C22×C4×C13C2×D411yescharacteristic
45C13×D8—42no—
46C13×D8—81no—
47C13×M16—41no—
48C2×C8×C13—21no—
49C2×C8×C13—41no—
50C2×C8×C13C2×D412yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C13×C22⋊C4—42no—
55C13×C22⋊C4—42no—
56C13×C22⋊C4SD1612yes—
57C42×C13—21no—
58#6099—41no—
59#6099—41no—
60#6099—41no—
61#6099—41no—
62C2×#1055—41no—
63C2×#1055—41no—
64#6090—42no—
65#3259D1311yescharacteristic
66#2238—132no—
67#2103—131no—
68#1341—132no—
69#1328—131no—
70C23×C13—42no—
71C23×C13C2×SD1611yescharacteristic
72D4×C13—42no—
73D4×C13—42no—
74D4×C13—162no—
75D4×C13—162no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—42no—
80C2×C4×C13—162no—
81C2×C4×C13#12011yescharacteristic
82C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
83C8×C13—22no—
84C8×C13—41no—
85#1055—81no—
86#1055—81no—
87#540—21no—
88#478—22no—
89#469C2×D1312yes—
90#466—21no—
91#459—22no—
92#430—131no—
93#424C2×D1311yescharacteristic
94#365—262no—
95#361—262no—
96#349—132no—
97#344—261no—
98#341—261no—
99#338—131no—
100C22×C13—21no—
101C22×C13—41no—
102C22×C13—82no—
103C22×C13—82no—
104C22×C13—82no—
105C22×C13#45011yescharacteristic
106C4×C13—21no—
107C4×C13—42no—
108C4×C13—82no—
109C4×C13#45411yescharacteristic
110C4×C13#45811yescharacteristic
111C2×D8—21no—
112C2×D8C22⋊D1312yes—
113C2×M16—261no—
114C2×M16—261no—
115C2×M16C22×D1311yescharacteristic
116C22×C8C22⋊D1311yescharacteristic
117#127—21no—
118#125—21no—
119#123—42no—
120#121—22no—
121#121—42no—
122C4×D4—22no—
123#117C22⋊D1311yescharacteristic
124M32—262no—
125#108—262no—
126#107—21no—
127#106C22⋊D1312yes—
128C4⋊C8—22no—
129#102—22no—
130#102—22no—
131C2×C13—21no—
132C2×C13—41no—
133C2×C13—162no—
134C2×C13#161611yescharacteristic
135C2×D4—22no—
136C2×D4—42no—
137C2×D4—42no—
138C22×C4—42no—
139C22×C4C2×C22⋊D1311yescharacteristic
140D8—42no—
141D8—81no—
142M16—41no—
143M16—521no—
144M16—521no—
145M16—521no—
146M16—521no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—521no—
150C2×C8—521no—
151C2×C8C2×C22⋊D1312yes—
152C4⋊C4—21no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C22⋊C4—42no—
156C22⋊C4—42no—
157C22⋊C4#610512yes—
158C42—21no—
159C16—522no—
160C13#1230411yescharacteristic, complemented, Sylow
161C23—42no—
162C23C2×#610511yescharacteristic
163D4—42no—
164D4—42no—
165D4—162no—
166D4—162no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—162no—
172C2×C4#8818611yescharacteristic
173C2×C4#8820711yescharacteristic
174C8—22no—
175C8—41no—
176C8—1041no—
177C8—1041no—
178C22—21no—
179C22—41no—
180C22—82no—
181C22—82no—
182C22—82no—
183C22#1171887911yescharacteristic
184C4—21no—
185C4—42no—
186C4—82no—
187C4#1171890411yescharacteristic
188C4#1171890611yescharacteristic
189C2—21no—
190C2—41no—
191C2—162no—
192C2#1311387311yescharacteristic
subgroupG/H
centerC2#13113873
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
Fitting, prime radicalC13×#3259C2
socleC2×C13#1616
hypercenter#3259D13
hypocenterC13#12304
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3259

Complements

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

NH ≅ G/Ntype
1. #13117048C2semidirect
2. #13116416C2semidirect
3. #13112827C2semidirect
4. #13112789C2semidirect
160. C13#12304semidirect

Maximal subgroups

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

subgroupindex
#131170482
#131164162
#131128272
#131127892
C13×#32592
#1230413