Finite Group Databasebeta

← #15775978

Subgroups — #15775978

Order 3328.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#13120078C211yesmaximal, characteristic
2#13113878C212yesmaximal
3#13112862C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2060C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C13×#428—21no—
8C13×#384C2211yescharacteristic
9#11718705—22no—
10#11718647—21no—
11#11718647C2212yes—
12#11718646—22no—
13#11718638—22no—
14C4×C4⋊Dic13—21no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C2×C13×M16—21no—
20C13×C4⋊Q8—41no—
21C13×#125—41no—
22C13×C22⋊Q8—22no—
23C13×#117—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13D412yes—
32C2×C4×Dic13—22no—
33C13×#107—41no—
34C13×#106—41no—
35#88075—42no—
36#88071—21no—
37#88071—22no—
38#88071—22no—
39#88071—22no—
40#88071D412yes—
41C22⋊#1055—22no—
42#88047—42no—
43#12257—131nomaximal, Sylow
44C2×Q8×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2×D412yes—
48C22×C4×C13C2×D411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13—22no—
51C13×M16—22no—
52C13×M16—41no—
53C2×C8×C13—41no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—44no—
60C13×C4⋊C4—42no—
61C13×C22⋊C4—41no—
62C42×C13—21no—
63C42×C13—41no—
64C42×C13Q1612yes—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—81no—
69C4×Dic13—44no—
70C2×#1055—42no—
71#2571—131no—
72#2060D1311yescharacteristic
73#1617—132no—
74#1353—132no—
75#1325—131no—
76C23×C13#12011yescharacteristic
77Q8×C13—82no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13C2×Q1611yescharacteristic
90C2×C4×C13#13711yescharacteristic
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C8×C13—42no—
98#1055—82no—
99#544C2×D1311yescharacteristic
100#484—262no—
101#428—21no—
102#400—132no—
103#400—261no—
104#389—262no—
105#384C2×D1311yescharacteristic
106#382—262no—
107C4×C4⋊C4—261no—
108#343C2×D1311yescharacteristic
109#339—21no—
110#328—262no—
111#324—132no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13#45111yescharacteristic
115C22×C13#45611yescharacteristic
116C22×C13B(4,𝔽2)11yescharacteristic
117C4×C13—24no—
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—81no—
122C4×C13—81no—
123C4×C13—81no—
124Dic13—82no—
125Dic13—82no—
126C2×M16—21no—
127C4⋊Q8—41no—
128#125—41no—
129C22⋊Q8—22no—
130#117—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—261no—
134C2×C4⋊C4—261no—
135C2×C4⋊C4—261no—
136C2×C4⋊C4C22⋊D1311yescharacteristic
137C2×C4⋊C4C22×D1311yescharacteristic
138C2×C42—262no—
139C2×C42C22⋊D1311yescharacteristic
140#107—41no—
141#107—522no—
142#106—41no—
143#103—522no—
144C22⋊C8—262no—
145#95—132no—
146#95—261no—
147#95—262no—
148#95—262no—
149#95—262no—
150C2×C13—21no—
151C2×C13—21no—
152C2×C13#160511yescharacteristic
153C2×C13#219811yescharacteristic
154C2×C13#220411yescharacteristic
155C2×Q8—22no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—262no—
159C22×C4—262no—
160C22×C4D4×D1312yes—
161C22×C4C2×C22⋊D1311yescharacteristic
162M16—22no—
163M16—41no—
164C2×C8—41no—
165C2×C8—522no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—522no—
174C4⋊C4—522no—
175C4⋊C4—522no—
176C4⋊C4—1041no—
177C22⋊C4—41no—
178C42—21no—
179C42—41no—
180C42—524no—
181C42#610712yes—
182C13#1225711yescharacteristic, complemented, Sylow
183C23#8819111yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4C2×#610711yescharacteristic
203C2×C4#8820511yescharacteristic
204C8—42no—
205C8—1042no—
206C22—21no—
207C22—21no—
208C22#1171869311yescharacteristic
209C22#1171871111yescharacteristic
210C22#1171875611yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—81no—
218C4—1042no—
219C4—1042no—
220C2—21no—
221C2—21no—
222C2#1311380911yescharacteristic
223C2#1311683111yescharacteristic
224C2#1311686111yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2060C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2060D13
hypocenterC13#12257
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
182. C13#12257semidirect

Maximal subgroups

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

subgroupindex
#131200782
#131138782
#131128622
#131127822
C13×#20602
#1225713