Finite Group Databasebeta

← #15749513

Subgroups — #15749513

Order 3328.

278 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 103 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#13114979C211yesmaximal, characteristic
2#13114689C211yesmaximal, characteristic
3C13×#1831C211yesmaximal, characteristic
4C2×C13×C4⋊C8—21no—
5C43×C13C2211yescharacteristic
6C2×C4⋊#1055—21no—
7C2×#88043—21no—
8C13×#336—21no—
9C13×#336C412yes—
10#11718116—21no—
11#11718116—21no—
12#11718116C412yes—
13#11718116C412yes—
14C22×C8×C13—22no—
15C2×C42×C13C2×C411yescharacteristic
16C2×C42×C13C2×C411yescharacteristic
17C2×C42×C13C2×C411yescharacteristic
18C2×C42×C13D411yescharacteristic
19C2×C42×C13D411yescharacteristic
20C2×C42×C13D411yescharacteristic
21C2×C42×C13Q811yescharacteristic
22C22×#1055—22no—
23C22×#1055—22no—
24C13×C4⋊C8—41no—
25C13×C4⋊C8—41no—
26C4⋊#1055—24no—
27#88043—41no—
28#88043—41no—
29#7041—131nomaximal, Sylow
30C22×C4×C13C4211yescharacteristic
31C22×C4×C13C22⋊C411yescharacteristic
32C22×C4×C13C22⋊C411yescharacteristic
33C22×C4×C13C22⋊C411yescharacteristic
34C22×C4×C13C4⋊C411yescharacteristic
35C22×C4×C13C4⋊C411yescharacteristic
36C22×C4×C13C4⋊C411yescharacteristic
37C2×C8×C13—42no—
38C2×C8×C13—42no—
39C2×C8×C13—42no—
40C42×C13—22no—
41C42×C13—22no—
42C42×C13—41no—
43C42×C13—41no—
44C42×C13—41no—
45C42×C13—41no—
46C42×C13D811yescharacteristic
47C42×C13SD1611yescharacteristic
48C42×C13SD1611yescharacteristic
49C42×C13Q1611yescharacteristic
50C2×#1055—24no—
51C2×#1055—42no—
52C2×#1055—42no—
53C2×#1055—42no—
54C2×#1055—42no—
55C2×#1055—42no—
56#1839—131no—
57#1831D1311yescharacteristic
58#1767—131no—
59C23×C13#9511yescharacteristic
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
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—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13#10211yescharacteristic
77C2×C4×C13#10211yescharacteristic
78C2×C4×C13#10311yescharacteristic
79C2×C4×C13#10311yescharacteristic
80C2×C4×C13#10412yes—
81C2×C4×C13#10611yescharacteristic
82C2×C4×C13#10711yescharacteristic
83C2×C4×C13#10812yes—
84C8×C13—82no—
85#1055—44no—
86#1055—82no—
87C2×C4⋊C8—21no—
88C2×C4⋊C8—261no—
89C2×#97—261no—
90C43C2×D1311yescharacteristic
91#336—21no—
92#336—132no—
93#336—132no—
94#336—261no—
95#336—261no—
96#336Dic1312yes—
97C22×C13H(3,ℤ/4)11yescharacteristic
98C22×C13#33911yescharacteristic
99C22×C13#34011yescharacteristic
100C22×C13#34111yescharacteristic
101C22×C13#34411yescharacteristic
102C22×C13#34411yescharacteristic
103C22×C13#34411yescharacteristic
104C4×C13—21no—
105C4×C13—21no—
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—22no—
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—41no—
113C4×C13—41no—
114C22×C8—22no—
115C22×C8—262no—
116C22×C8—262no—
117C2×C42Dic2611yescharacteristic
118C2×C42C4×D1311yescharacteristic
119C2×C42C4×D1311yescharacteristic
120C2×C42D5211yescharacteristic
121C2×C42C2×Dic1311yescharacteristic
122C2×C42C22⋊D1311yescharacteristic
123C2×C42C22⋊D1311yescharacteristic
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—264no—
127#97—521no—
128#97—521no—
129C2×C13#128611yescharacteristic
130C2×C13#128711yescharacteristic
131C2×C13#128811yescharacteristic
132C2×C13#130111yescharacteristic
133C2×C13#130211yescharacteristic
134C2×C13#130311yescharacteristic
135C2×C13#130811yescharacteristic
136C22×C4C4×Dic1311yescharacteristic
137C22×C4#610111yescharacteristic
138C22×C4#610111yescharacteristic
139C22×C4C4⋊Dic1311yescharacteristic
140C22×C4#610311yescharacteristic
141C22×C4#610311yescharacteristic
142C22×C4C22⋊Dic1311yescharacteristic
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—42no—
146C2×C8—264no—
147C2×C8—522no—
148C2×C8—522no—
149C2×C8—522no—
150C2×C8—522no—
151C2×C8—522no—
152C42—22no—
153C42—22no—
154C42—41no—
155C42—41no—
156C42—41no—
157C42—41no—
158C42#610411yescharacteristic
159C42#610511yescharacteristic
160C42#610611yescharacteristic
161C42#610711yescharacteristic
162C13#704111yescharacteristic, complemented, Sylow
163C23#8807111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4#8804711yescharacteristic
181C2×C4#8804811yescharacteristic
182C2×C4#8804911yescharacteristic
183C2×C4#8805011yescharacteristic
184C2×C4#8805912yes—
185C2×C4#8806512yes—
186C2×C4#8807211yescharacteristic
187C2×C4#8807511yescharacteristic
188C8—82no—
189C8—524no—
190C8—1042no—
191C22#1171812111yescharacteristic
192C22#1171812311yescharacteristic
193C22#1171812511yescharacteristic
194C22#1171814411yescharacteristic
195C22#1171814711yescharacteristic
196C22#1171814811yescharacteristic
197C22#1171815111yescharacteristic
198C4—21no—
199C4—21no—
200C4—22no—
201C4—21no—
202C4—21no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C2#1311269411yescharacteristic
209C2#1311269811yescharacteristic
210C2#1311270211yescharacteristic
211C2#1311273311yescharacteristic
212C2#1311273611yescharacteristic
213C2#1311273711yescharacteristic
214C2#1311274811yescharacteristic
subgroupG/H
centerC23#88071
commutatorC22×C4×C13C42
FrattiniC43C2×D13
FittingC13×#1831C2
socle, prime radicalC23×C13#95
cosocleC43×C13C22
hypercenter#1831D13
hypocenterC13#7041
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
162. C13#7041semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131146892
C13×#18312
#704113