Finite Group Databasebeta

← #15749549

Subgroups — #15749549

Order 3328.

240 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 47 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#13115633C211yesmaximal, characteristic
2#13112776C211yesmaximal, characteristic, complemented
3C13×#1322C211yesmaximal, characteristic, complemented
4C2×C4×D52C411yescharacteristic
5C2×C13×C4⋊C8C2211yescharacteristic
6C2×#88060—21no—
7C2×#88060—21no—
8C2×#88043C411yescharacteristic
9C13×C22⋊C16—21no—
10C22⋊#6090—21no—
11C22×D52C811yescharacteristic
12C22×C4×D13—21no—
13C22×C8×C13D411yescharacteristic
14C22×C8×C13D411yescharacteristic
15C2×C42×C13C2×C411yescharacteristic
16C2×#6103—21no—
17C2×C4⋊Dic13C811yescharacteristic
18C22×#1055—21no—
19C4×D52—41no—
20C4×D52—41no—
21C2×C13×C16—41no—
22C13×C4⋊C8—41no—
23#88060—42no—
24#88060—42no—
25C2×#6090—41no—
26#88043—41no—
27#7060—131nomaximal, Sylow
28C23×D13—21no—
29C22×C4×C13C22⋊C411yescharacteristic
30C22×C4×C13C2×C811yescharacteristic
31C22×C4×C13M1611yescharacteristic
32C22×Dic13—21no—
33C2×D52—41no—
34C2×D52—42no—
35C2×C4×D13—41no—
36C2×C4×D13—41no—
37C2×C4×D13—41no—
38C2×C4×D13—41no—
39C2×C4×D13—41no—
40C2×C4×D13—41no—
41C2×C8×C13—21no—
42C2×C8×C13—21no—
43C2×C8×C13—41no—
44C2×C8×C13—41no—
45C42×C13—21no—
46C42×C13—21no—
47#6103—42no—
48C4⋊Dic13—41no—
49C2×#1055—22no—
50C2×#1055—41no—
51C2×#1055—41no—
52C13×C16—81no—
53#6090—81no—
54#1955—131no—
55#1322—131no—
56#1322D1311yescharacteristic, complemented
57C23×C13C22⋊C811yescharacteristic
58C22×D13—22no—
59C22×D13—41no—
60C22×D13—41no—
61C22×D13—41no—
62C22×D13—41no—
63C22×D13—41no—
64C22×D13—41no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—41no—
72C2×C4×C13#9911yescharacteristic
73C2×C4×C13#10011yescharacteristic
74C2×Dic13—41no—
75C2×Dic13—41no—
76C2×Dic13—41no—
77D52—42no—
78D52—42no—
79C4×D13—81no—
80C4×D13—81no—
81C4×D13—81no—
82C4×D13—81no—
83C8×C13—41no—
84C8×C13—41no—
85#1055—42no—
86C2×C4×D4—131no—
87C2×C4⋊C8C2×D1311yescharacteristic
88C2×C22⋊C8—261no—
89C2×C22⋊C8—261no—
90C2×#97—131no—
91C22⋊C16—21no—
92C22⋊C16—261no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13#32311yescharacteristic
96C22×C13#35011yescharacteristic
97C22×C13#35011yescharacteristic
98C2×D13—42no—
99C2×D13—42no—
100C2×D13—42no—
101C2×D13—81no—
102C2×D13—81no—
103C2×D13—81no—
104C2×D13—81no—
105C4×C13—21no—
106C4×C13—41no—
107C4×C13—41no—
108C4×C13#35311yescharacteristic
109C4×C13#35511yescharacteristic
110Dic13—81no—
111C22×D4—131no—
112C23×C4—261no—
113C22×C8—261no—
114C22×C8D5211yescharacteristic
115C22×C8C22⋊D1311yescharacteristic
116C4×D4—521no—
117C4×D4—521no—
118C2×C4⋊C4—131no—
119C2×C22⋊C4—261no—
120C2×C42C4×D1311yescharacteristic
121C2×C16—41no—
122C2×C16—521no—
123C4⋊C8—41no—
124C22⋊C8—522no—
125C22⋊C8—522no—
126#97—521no—
127C2×C13—21no—
128C2×C13—21no—
129C2×C13#131511yescharacteristic
130C2×C13#131811yescharacteristic
131C2×C13#132011yescharacteristic
132D13—82no—
133C24—261no—
134C2×D4—521no—
135C2×D4—522no—
136C22×C4—261no—
137C22×C4—521no—
138C22×C4—521no—
139C22×C4—521no—
140C22×C4—521no—
141C22×C4—521no—
142C22×C4—521no—
143C22×C4C8×D1311yescharacteristic
144C22×C4#609411yescharacteristic
145C22×C4#610311yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—262no—
151C2×C8—521no—
152C2×C8—521no—
153C4⋊C4—521no—
154C22⋊C4—522no—
155C42—21no—
156C42—21no—
157C16—81no—
158C16—1041no—
159C13#706011yescharacteristic, complemented, Sylow
160C23—262no—
161C23—521no—
162C23—521no—
163C23—521no—
164C23—521no—
165C23—521no—
166C23—521no—
167C23#8806011yescharacteristic
168D4—522no—
169D4—522no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—1041no—
181C2×C4—1041no—
182C2×C4—1041no—
183C2×C4—1041no—
184C2×C4#8804611yescharacteristic
185C2×C4#8806311yescharacteristic
186C8—41no—
187C8—41no—
188C8—522no—
189C22—21no—
190C22—21no—
191C22—522no—
192C22—522no—
193C22—522no—
194C22—1041no—
195C22—1041no—
196C22—1041no—
197C22—1041no—
198C22#1171806011yescharacteristic
199C22#1171810011yescharacteristic
200C22#1171810711yescharacteristic
201C4—21no—
202C4—41no—
203C4—41no—
204C4—1041no—
205C4#1171806611yescharacteristic
206C4#1171806911yescharacteristic
207C2—21no—
208C2—21no—
209C2—1042no—
210C2#1311276111yescharacteristic
211C2#1311276711yescharacteristic
212C2#1311277111yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C2×C8
FrattiniC2×C4⋊C8C2×D13
FittingC13×#1322C2
socleC22×C13#323
prime radicalC22×D52C8
cosocleC2×C13×C4⋊C8C22
hypercenter#1322D13
hypocenterC13#7060
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #13112776C2semidirect
3. C13×#1322C2semidirect
56. #1322D13semidirect
159. C13#7060semidirect

Maximal subgroups

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

subgroupindex
#131156332
#131127762
C13×#13222
#706013