Finite Group Databasebeta

← #15775979

Subgroups — #15775979

Order 3328.

342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116181C211yesmaximal, characteristic
2#13113877C212yesmaximal
3#13112863C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2571C211yesmaximal, characteristic
6#11719205C2211yescharacteristic
7C13×#400—21no—
8C13×#400C2212yes—
9C13×#389—22no—
10C13×#384C2211yescharacteristic
11C13×#382—22no—
12C4×C13×C4⋊C4—21no—
13#11718631—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13—22no—
27C2×C42×C13D411yescharacteristic
28#88180—21no—
29#88178—22no—
30C2×#6099—21no—
31#88144—41no—
32#88142—41no—
33C13×#95—21no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95D412yes—
38C22⋊#1055—22no—
39#88050—42no—
40#88048—41no—
41#88047—41no—
42#88047—42no—
43#12257—131nomaximal, Sylow
44C22×C4×C13—21no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—21no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13C2×D412yes—
50C2×Dic26—22no—
51C13×C4⋊C4—41no—
52C13×C4⋊C4—41no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—44no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—81no—
58C42×C13—21no—
59C42×C13—44no—
60C42×C13Q1612yes—
61C22⋊Dic13—41no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13—21no—
65#6101—42no—
66C4×Dic13—41no—
67#6099—22no—
68#6099—41no—
69C2×#1055—41no—
70C2×#1055—42no—
71#2571D1311yescharacteristic
72#2060—131no—
73#1617—132no—
74#1353—132no—
75#1325—131no—
76C23×C13#12011yescharacteristic
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13C2×Q1611yescharacteristic
93C2×C4×C13#13711yescharacteristic
94C2×Dic13—41no—
95C2×Dic13—41no—
96Dic26—82no—
97#1055—42no—
98#1055—82no—
99#544—131no—
100#484—262no—
101#428—261no—
102#400—21no—
103#400C2×D1312yes—
104#389—22no—
105#384C2×D1311yescharacteristic
106#382—22no—
107C4×C4⋊C4—21no—
108#343—131no—
109#339—261no—
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—82no—
122C4×C13—81no—
123C4×C13—82no—
124Dic13—81no—
125Dic13—81no—
126C2×M16—261no—
127C4⋊Q8—521no—
128#125—521no—
129C22⋊Q8—262no—
130#117—261no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4C22⋊D1311yescharacteristic
136C2×C4⋊C4C22⋊D1312yes—
137C2×C4⋊C4C22×D1311yescharacteristic
138C2×C42—22no—
139C2×C42C22⋊D1311yescharacteristic
140#107—521no—
141#107—522no—
142#106—521no—
143#103—522no—
144C22⋊C8—262no—
145#95—21no—
146#95—22no—
147#95—22no—
148#95—22no—
149#95C22⋊D1312yes—
150C2×C13—21no—
151C2×C13—21no—
152C2×C13#160511yescharacteristic
153C2×C13#219811yescharacteristic
154C2×C13#220411yescharacteristic
155C2×Q8—262no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—21no—
160C22×C4C2×C22⋊D1311yescharacteristic
161C22×C4C2×C22⋊D1312yes—
162M16—262no—
163M16—521no—
164C2×C8—521no—
165C2×C8—522no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C4⋊C4—42no—
170C4⋊C4—44no—
171C4⋊C4—42no—
172C4⋊C4—81no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—262no—
176C4⋊C4—522no—
177C22⋊C4—521no—
178C42—21no—
179C42—44no—
180C42—521no—
181C42#610712yes—
182C13#1225711yescharacteristic, complemented, Sylow
183C23#8820711yescharacteristic
184Q8—1042no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4#8819611yescharacteristic
203C2×C4C2×#610711yescharacteristic
204C8—522no—
205C8—1042no—
206C22—21no—
207C22—21no—
208C22#1171888911yescharacteristic
209C22#1171890511yescharacteristic
210C22#1171890711yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—82no—
218C4—1041no—
219C4—1041no—
220C2—21no—
221C2—21no—
222C2#1311381011yescharacteristic
223C2#1311683211yescharacteristic
224C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2571C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2571D13
hypocenterC13#12257
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

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
#131161812
#131138772
#131128632
#131127822
C13×#25712
#1225713