Finite Group Databasebeta

← #15767945

Subgroups — #15767945

Order 3328.

296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115817C211yesmaximal, characteristic
2#13114956C211yesmaximal, characteristic
3#13113611C211yesmaximal, characteristic
4#13113607C211yesmaximal, characteristic
5#13113240C211yesmaximal, characteristic
6#13113240C211yesmaximal, characteristic
7C13×#1274C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#376C2211yescharacteristic
12#11718585C2211yescharacteristic
13C2×C4⋊#1055C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15#11718116—22no—
16#11718115—22no—
17#11718050—22no—
18#11718049—22no—
19#11718048—22no—
20#11718048—22no—
21C2×C42×C13D412yes—
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24#88178—21no—
25#88178—21no—
26C2×#6099—21no—
27C22×#1055—21no—
28C22×#1055—21no—
29#88124—21no—
30#88123Q811yescharacteristic
31#88123Q811yescharacteristic
32C4×Dic26—21no—
33C4×Dic26—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C4×C8×C13D412yes—
39C4×C8×C13D412yes—
40C13×#95—21no—
41C13×#95—21no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48#10669—131nomaximal, Sylow
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C2×Dic26—21no—
54C2×Dic26—21no—
55C2×C8×C13—22no—
56C2×C8×C13—22no—
57C42×C13—22no—
58C42×C13—22no—
59C42×C13C2×D411yescharacteristic
60C42×C13C2×D411yescharacteristic
61C42×C13C2×Q811yescharacteristic
62C42×C13#4111yescharacteristic
63C22⋊Dic13—41no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68#6101—41no—
69#6101—41no—
70C4×Dic13—41no—
71#6099—42no—
72C2×#1055—41no—
73C2×#1055—41no—
74C2×#1055—41no—
75C2×#1055—42no—
76C2×#1055—42no—
77#1995—131no—
78#1832—131no—
79#1571—131no—
80#1570—131no—
81#1481—131no—
82#1481—131no—
83#1274D1311yescharacteristic
84C23×C13#12311yescharacteristic
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13C22⋊Q811yescharacteristic
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13#12311yescharacteristic
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13#12711yescharacteristic
96C2×C4×C13#13512yes—
97C2×C4×C13#13712yes—
98C2×Dic13—41no—
99C2×Dic13—41no—
100Dic26—42no—
101Dic26—42no—
102C8×C13—42no—
103C8×C13—42no—
104#1055—81no—
105#1055—81no—
106#1055—81no—
107#533—131no—
108#431C2×D1311yescharacteristic
109#431C2×D1311yescharacteristic
110#423—131no—
111C2×C4⋊C8—131no—
112C2×C4⋊C8—131no—
113#376C2×D1311yescharacteristic
114#339—262no—
115#336—262no—
116#335—262no—
117#334—262no—
118Q8⋊C8—262no—
119Q8⋊C8—262no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#39911yescharacteristic
123C22×C13#48512yes—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—82no—
129C4×C13#47912yes—
130C4×C13#49511yescharacteristic
131C4×C13#49711yescharacteristic
132Dic13—81no—
133Dic13—81no—
134C2×M16—261no—
135C22×C8—261no—
136C22×C8—261no—
137C4⋊Q8—131no—
138C4⋊Q8—131no—
139#125—261no—
140C22⋊Q8—261no—
141C22⋊Q8—261no—
142C4×Q8—261no—
143C4×Q8—261no—
144#117—261no—
145C2×C42D5212yes—
146C2×C42C22×D1311yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—261no—
150C4⋊C8—261no—
151C4⋊C8—261no—
152C4⋊C8—261no—
153C4⋊C8—261no—
154C4⋊C8—261no—
155C22⋊C8—21no—
156C22⋊C8—21no—
157C4×C8D5212yes—
158C4×C8D5212yes—
159#95—21no—
160#95—21no—
161C2×C13—22no—
162C2×C13#209711yescharacteristic
163C2×C13#209811yescharacteristic
164C2×C13#209811yescharacteristic
165C2×Q8—261no—
166C2×Q8—261no—
167C22×C4—22no—
168C22×C4C2×D5211yescharacteristic
169C22×C4#612911yescharacteristic
170C22×C4#612911yescharacteristic
171M16—522no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—521no—
175C2×C8—521no—
176C2×C8—521no—
177C2×C8—522no—
178C2×C8—522no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4—521no—
184C4⋊C4—521no—
185C22⋊C4—521no—
186C42—22no—
187C42—22no—
188C42—521no—
189C42C2×D5211yescharacteristic
190C42C2×D5211yescharacteristic
191C42#612911yescharacteristic
192C42Q8×D1311yescharacteristic
193C13#1066911yescharacteristic, complemented, Sylow
194C23#8814011yescharacteristic
195Q8—522no—
196Q8—522no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4#8812811yescharacteristic
205C2×C4#8814011yescharacteristic
206C2×C4#8814011yescharacteristic
207C2×C4#8815111yescharacteristic
208C2×C4#8815111yescharacteristic
209C2×C4#8815111yescharacteristic
210C2×C4#8815812yes—
211C2×C4#8816312yes—
212C8—42no—
213C8—42no—
214C8—1041no—
215C8—1041no—
216C8—1041no—
217C22—21no—
218C22—21no—
219C22#1171833811yescharacteristic
220C22#1171838412yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—1041no—
227C4—1041no—
228C4#1171835711yescharacteristic
229C4#1171837611yescharacteristic
230C4#1171849012yes—
231C2—22no—
232C2#1311638311yescharacteristic
233C2#1311639011yescharacteristic
234C2#1311639011yescharacteristic
subgroupG/H
centerC2×C4#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1274C2
socleC22×C13#399
prime radicalC23×C13#123
hypercenter#1274D13
hypocenterC13#10669
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
193. C13#10669semidirect

Maximal subgroups

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

subgroupindex
#131158172
#131149562
#131136112
#131136072
#131132402
C13×#12742
#1066913