Finite Group Databasebeta

← #15774870

Subgroups — #15774870

Order 3328.

220 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 71 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#13116700C211yesmaximal, characteristic
2#13113746C211yesmaximal, characteristic, complemented
3#13112901C211yesmaximal, characteristic, complemented
4#13112805C211yesmaximal, characteristic, complemented
5#13112803C211yesmaximal, characteristic
6#13112757C211yesmaximal, characteristic, complemented
7C13×#1580C211yesmaximal, characteristic
8C4×C13×D8C2211yescharacteristic
9C8×D4×C13—21no—
10C2×#88067C411yescharacteristic
11C4×Dic52C2211yescharacteristic
12#11718340—21no—
13C13×#334C2211yescharacteristic
14C13×D4⋊C8—21no—
15C13×#322C2211yescharacteristic
16#11718154C411yescharacteristic
17#11718084C411yescharacteristic
18#11718081C411yescharacteristic
19#11718053C2211yescharacteristic
20#11718053C2211yescharacteristic
21#11718049C2211yescharacteristic
22#11718048—21no—
23C2×C13×D8C2×C411yescharacteristic
24C22×C8×C13—41no—
25C4×D4×C13—21no—
26C2×Dic52C2×C411yescharacteristic
27C4×Dic26—21no—
28C13×#107C2×C411yescharacteristic
29C13×C4⋊C8—21no—
30C13×#102—21no—
31C13×C22⋊C8—41no—
32C4×C8×C13D411yescharacteristic
33C4×C8×C13D411yescharacteristic
34C4×C8×C13C2311yescharacteristic
35#88067—22no—
36#88058C2×C411yescharacteristic
37#88056—21no—
38#88055—41no—
39#88054—41no—
40C2×#6090—21no—
41C2×#6090C2×C411yescharacteristic
42C2×#6090C2×C411yescharacteristic
43C4⋊#1055—21no—
44#12077—131nomaximal, Sylow
45C2×D4×C13—21no—
46C22×C4×C13—41no—
47C2×Dic26—21no—
48C13×D8—21no—
49C13×D8M1612yes—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13—82no—
54C2×C8×C13C22×C411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C13×C4⋊C4—21no—
57C13×C22⋊C4—41no—
58C42×C13C2×D411yescharacteristic
59C4⋊Dic13—21no—
60#6101—41no—
61C4×Dic13—41no—
62C2×#1055—41no—
63Dic52—21no—
64Dic52—21no—
65#6090—22no—
66#6090—21no—
67#6090—21no—
68#2175—131no—
69#1593—131no—
70#1580D1311yescharacteristic
71#1368—131no—
72#1334—131no—
73#1333—131no—
74#1313—131no—
75C23×C13—41no—
76D4×C13—22no—
77D4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—81no—
80C2×C4×C13—81no—
81C2×C4×C13C4×D411yescharacteristic
82C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
84C2×Dic13—41no—
85C2×Dic13—41no—
86Dic26—41no—
87Dic26—41no—
88C8×C13—21no—
89C8×C13—41no—
90C8×C13—41no—
91C8×C13—81no—
92C8×C13C2×M1611yescharacteristic
93C8×C13#13111yescharacteristic
94#1055—81no—
95C2×SD32—131no—
96#446—261no—
97C4×Q16—131no—
98C4×D8C2×D1311yescharacteristic
99C8×D4—21no—
100#366—131no—
101#358—131no—
102#357—131no—
103#346—131no—
104#346—131no—
105#334—131no—
106#334C2×D1311yescharacteristic
107Q8⋊C8—261no—
108D4⋊C8—21no—
109#322C2×D1311yescharacteristic
110C22×C13—42no—
111C22×C13—81no—
112C22×C13—81no—
113C22×C13#44211yescharacteristic
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—81no—
117C4×C13#43511yescharacteristic
118C4×C13#44311yescharacteristic
119Dic13—81no—
120Dic13—81no—
121C2×Q16—131no—
122C2×D8C4×D1311yescharacteristic
123C22×C8—41no—
124C4×Q8—261no—
125C4×D4—21no—
126SD32—262no—
127C2×C16—131no—
128C2×C16—131no—
129C2×C16—261no—
130#107—131no—
131#107C4×D1311yescharacteristic
132C4⋊C8—21no—
133C4⋊C8—261no—
134C4⋊C8—521no—
135#103—261no—
136#102—21no—
137C22⋊C8—41no—
138#97—521no—
139C4×C8C22⋊D1311yescharacteristic
140C4×C8C22⋊D1311yescharacteristic
141C4×C8C22×D1311yescharacteristic
142C2×C13—82no—
143C2×C13#158611yescharacteristic
144C2×C13#218011yescharacteristic
145C2×C13AGL(1,ℤ/16)11yescharacteristic
146C2×Q8—261no—
147C2×D4—21no—
148C22×C4—41no—
149Q16—261no—
150Q16—261no—
151D8—21no—
152D8#609412yes—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—82no—
157C2×C8—521no—
158C2×C8C2×C4×D1311yescharacteristic
159C2×C8#612711yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—261no—
162C4⋊C4—521no—
163C22⋊C4—41no—
164C42—521no—
165C42C2×C22⋊D1311yescharacteristic
166C16—262no—
167C16—261no—
168C16—261no—
169C13#1207711yescharacteristic, complemented, Sylow
170C23—41no—
171Q8—521no—
172Q8—521no—
173D4—22no—
174D4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4C4×C22⋊D1311yescharacteristic
181C2×C4#8818611yescharacteristic
182C2×C4#8820311yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—81no—
187C8—1041no—
188C8C2×#609411yescharacteristic
189C8#8815511yescharacteristic
190C22—42no—
191C22—81no—
192C22—81no—
193C22#1171867511yescharacteristic
194C4—21no—
195C4—21no—
196C4—81no—
197C4—1041no—
198C4—1041no—
199C4#1171877211yescharacteristic
200C4#1171880511yescharacteristic
201C2—82no—
202C2#1311370011yescharacteristic
203C2#1311672711yescharacteristic
204C2#1311673211yescharacteristic
subgroupG/H
centerC22#11718675
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1580C2
socleC22×C13#442
prime radicalC2×C13×D8C2×C4
cosocleC4×C8×C13C23
hypercenter#1580D13
hypocenterC13#12077
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #13113746C2semidirect
3. #13112901C2semidirect
4. #13112805C2semidirect
6. #13112757C2semidirect
169. C13#12077semidirect

Maximal subgroups

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

subgroupindex
#131167002
#131137462
#131129012
#131128052
#131128032
#131127572
C13×#15802
#1207713