Finite Group Databasebeta

← #15774790

Subgroups — #15774790

Order 3328.

230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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#13116698C211yesmaximal, characteristic
2#13113661C211yesmaximal, characteristic
3#13112901C211yesmaximal, characteristic, complemented
4#13112806C211yesmaximal, characteristic, complemented
5#13112802C211yesmaximal, characteristic
6#13112757C211yesmaximal, characteristic, complemented
7C13×#1579C211yesmaximal, characteristic, complemented
8C8×Q8×C13—21no—
9C4×C13×Q16C2211yescharacteristic
10C2×#88068C411yescharacteristic
11C4×D104C2211yescharacteristic
12C8×D52—21no—
13C13×#334C2211yescharacteristic
14C13×Q8⋊C8—21no—
15C13×#322C2211yescharacteristic
16#11718156C411yescharacteristic
17#11718083C411yescharacteristic
18#11718081C411yescharacteristic
19#11718053C2211yescharacteristic
20#11718053C2211yescharacteristic
21#11718051—21no—
22#11718049C2211yescharacteristic
23C2×C13×Q16C2×C411yescharacteristic
24C4×Q8×C13—21no—
25C2×D104C2×C411yescharacteristic
26C2×C8×D13—41no—
27C4×D52—21no—
28C13×#107C2×C411yescharacteristic
29C13×C4⋊C8—21no—
30C13×C4⋊C8—41no—
31C13×#103—21no—
32C4×C8×C13—41no—
33C4×C8×C13D411yescharacteristic
34C4×C8×C13D411yescharacteristic
35C4×C8×C13C2311yescharacteristic
36#88068C814yescomplemented
37#88061—21no—
38#88060—41no—
39#88058C2×C411yescharacteristic
40C2×#6090—21no—
41C2×#6090C2×C411yescharacteristic
42C2×#6090C2×C411yescharacteristic
43C4⋊#1055—21no—
44#12065—131nomaximal, Sylow
45C2×Q8×C13—21no—
46C2×D52—21no—
47C2×C4×D13—41no—
48C13×Q16—21no—
49C13×Q16C2×C812yescomplemented
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13C22×C411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C13×C4⋊C4—21no—
56C13×C4⋊C4—41no—
57C42×C13—41no—
58C42×C13C2×D411yescharacteristic
59#6103—41no—
60C4⋊Dic13—21no—
61C2×#1055—41no—
62D104—21no—
63D104C2×C812yes—
64C8×D13—82no—
65#6090—21no—
66#6090—41no—
67#6090C2×C812yescomplemented
68#2175—131no—
69#1580—131no—
70#1579D1311yescharacteristic, complemented
71#1368—131no—
72#1334—131no—
73#1333—131no—
74#1313—131no—
75C22×D13—41no—
76Q8×C13—22no—
77Q8×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13C4×D411yescharacteristic
81C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
83C2×Dic13—41no—
84D52—22no—
85D52—41no—
86C4×D13—81no—
87C4×D13—81no—
88C8×C13—21no—
89C8×C13—41no—
90C8×C13—41no—
91C8×C13—81no—
92C8×C13C22×C811yescharacteristic
93C8×C13#13111yescharacteristic
94#1055—81no—
95C2×SD32—131no—
96C8×Q8—21no—
97C4×Q16C2×D1311yescharacteristic
98C4×D8—131no—
99C8×D4—261no—
100#366—131no—
101#358—131no—
102#357—131no—
103#346—131no—
104#346—131no—
105#334—131no—
106#334C2×D1311yescharacteristic
107Q8⋊C8—21no—
108D4⋊C8—261no—
109#322C2×D1311yescharacteristic
110C22×C13#44211yescharacteristic
111C2×D13—42no—
112C2×D13—81no—
113C2×D13—81no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—42no—
117C4×C13—81no—
118C4×C13C8×D411yescharacteristic
119C4×C13#44411yescharacteristic
120Dic13—81no—
121C2×Q16C4×D1311yescharacteristic
122C2×D8—131no—
123C22×C8—521no—
124C4×Q8—21no—
125C4×D4—261no—
126SD32—134no—
127C2×C16—131no—
128C2×C16—131no—
129C2×C16—261no—
130#107—131no—
131#107C4×D1311yescharacteristic
132C4⋊C8—21no—
133C4⋊C8—41no—
134C4⋊C8—261no—
135#103—21no—
136#102—261no—
137C22⋊C8—521no—
138C4×C8—41no—
139C4×C8C22⋊D1311yescharacteristic
140C4×C8C22⋊D1311yescharacteristic
141C4×C8C22×D1311yescharacteristic
142C2×C13#158011yescharacteristic
143C2×C13#218011yescharacteristic
144C2×C13AGL(1,ℤ/16)11yescharacteristic
145D13—82no—
146C2×Q8—21no—
147C2×D4—261no—
148C22×C4—521no—
149Q16—21no—
150Q16C8×D1312yescomplemented
151D8—132no—
152D8—261no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—521no—
157C2×C8—1042no—
158C2×C8C2×C4×D1311yescharacteristic
159C2×C8#612711yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—41no—
162C4⋊C4—261no—
163C22⋊C4—521no—
164C42—41no—
165C42C2×C22⋊D1311yescharacteristic
166C16—132no—
167C16—261no—
168C16—521no—
169C13#1206511yescharacteristic, complemented, Sylow
170C23—521no—
171Q8—22no—
172Q8—41no—
173D4—262no—
174D4—521no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—521no—
178C2×C4—1041no—
179C2×C4—1041no—
180C2×C4C4×C22⋊D1311yescharacteristic
181C2×C4#8818611yescharacteristic
182C2×C4#8820311yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—81no—
187C8—1041no—
188C8C2×C8×D1311yescharacteristic
189C8#8815511yescharacteristic
190C22—522no—
191C22—1041no—
192C22—1041no—
193C22#1171867511yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—81no—
198C4—1041no—
199C4C8×C22⋊D1311yescharacteristic
200C4#1171880611yescharacteristic
201C2—1042no—
202C2#1311365811yescharacteristic
203C2#1311672511yescharacteristic
204C2#1311673411yescharacteristic
subgroupG/H
centerC22#11718675
commutatorC8×C13C22×C8
FrattiniC4×C8C22×D13
FittingC13×#1579C2
socleC22×C13#442
prime radicalC2×D104C2×C4
cosocleC4×C8×C13C23
hypercenter#1579D13
hypocenterC13#12065
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #13112901C2semidirect
4. #13112806C2semidirect
6. #13112757C2semidirect
7. C13×#1579C2semidirect
36. #88068C8semidirect
49. C13×Q16C2×C8semidirect
67. #6090C2×C8semidirect
70. #1579D13semidirect
150. Q16C8×D13semidirect
169. C13#12065semidirect

Maximal subgroups

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

subgroupindex
#131166982
#131136612
#131129012
#131128062
#131128022
#131127572
C13×#15792
#1206513