Finite Group Databasebeta

← #15775998

Subgroups — #15775998

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#13116186C211yesmaximal, characteristic
2#13113809C212yesmaximal
3#13112866C212yesmaximal
4#13112780C211yesmaximal, characteristic
5C13×#2844C211yesmaximal, characteristic
6#11719205C2211yescharacteristic
7C13×#400—21no—
8C13×#400—22no—
9C13×#395—22no—
10C13×#395C2212yes—
11C13×#382—21no—
12C13×#382C2211yescharacteristic
13#11718889—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13D412yes—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×#6107—42no—
28#88180—21no—
29#88178—22no—
30C2×#6099—21no—
31#88144—41no—
32#88142—41no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95D412yes—
39#88075—42no—
40C22⋊#1055—22no—
41#88048—41no—
42#88047—41no—
43#12260—131nomaximal, Sylow
44C2×Q8×C13—42no—
45C2×Q8×C13—82no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D412yes—
52C2×Dic26—22no—
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—81no—
56C13×C4⋊C4—81no—
57C13×C4⋊C4—82no—
58C13×C4⋊C4—81no—
59C42×C13—21no—
60C42×C13Q1612yescomplemented
61C22⋊Dic13—41no—
62#6107—84no—
63C4⋊Dic13—22no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66#6101—42no—
67C4×Dic13—41no—
68#6099—22no—
69#6099—41no—
70C2×#1055—41no—
71C2×#1055—42no—
72#2844D1311yescharacteristic
73#2061—131no—
74#1605—132no—
75#1354—132no—
76#1324—131no—
77C23×C13#12011yescharacteristic
78Q8×C13—44no—
79Q8×C13—82no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13C2×Q1611yescharacteristic
96C2×C4×C13#13711yescharacteristic
97C2×Dic13—41no—
98C2×Dic13—41no—
99Dic26—82no—
100#1055—42no—
101#1055—82no—
102#544—131no—
103#451—262no—
104#428—261no—
105#400—21no—
106#400—22no—
107#395—22no—
108#395C2×D1312yes—
109#382—21no—
110#382C2×D1311yescharacteristic
111#343—131no—
112#339—261no—
113#328—262no—
114#324—132no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#45111yescharacteristic
118C22×C13#45611yescharacteristic
119C22×C13B(4,𝔽2)11yescharacteristic
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—82no—
125C4×C13—82no—
126C4×C13—81no—
127Dic13—81no—
128Dic13—81no—
129C22×Q8C22⋊D1312yes—
130C2×Q16—522no—
131C2×M16—261no—
132C4⋊Q8—521no—
133#125—521no—
134C22⋊Q8—262no—
135#117—261no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4C22⋊D1311yescharacteristic
141C2×C4⋊C4C22×D1311yescharacteristic
142C2×C42C22⋊D1311yescharacteristic
143#107—521no—
144#106—521no—
145#103—522no—
146C22⋊C8—262no—
147#95—22no—
148#95—22no—
149#95—21no—
150#95—22no—
151#95—22no—
152#95C22⋊D1312yes—
153C2×C13—21no—
154C2×C13—21no—
155C2×C13#160511yescharacteristic
156C2×C13#219911yescharacteristic
157C2×C13#220311yescharacteristic
158C2×Q8—42no—
159C2×Q8—82no—
160C2×Q8—262no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4C2×C22⋊D1311yescharacteristic
166C22×C4C2×C22⋊D1312yes—
167Q16—1044no—
168M16—262no—
169M16—521no—
170C2×C8—521no—
171C2×C8—522no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C4⋊C4—82no—
177C4⋊C4—81no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4—522no—
182C22⋊C4—521no—
183C42—21no—
184C42—521no—
185C42#610712yescomplemented
186C13#1226011yescharacteristic, complemented, Sylow
187C23#8820711yescharacteristic
188Q8—44no—
189Q8—82no—
190Q8—1042no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—521no—
207C2×C4—521no—
208C2×C4#8819611yescharacteristic
209C2×C4C2×#610711yescharacteristic
210C8—522no—
211C8—1042no—
212C22—21no—
213C22—21no—
214C22#1171888911yescharacteristic
215C22#1171890511yescharacteristic
216C22#1171890711yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C4—81no—
224C4—1041no—
225C4—1041no—
226C2—21no—
227C2—21no—
228C2#1311381011yescharacteristic
229C2#1311683711yescharacteristic
230C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2844C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2844D13
hypocenterC13#12260
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
60. C42×C13Q16semidirect
185. C42#6107semidirect
186. C13#12260semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138092
#131128662
#131127802
C13×#28442
#1226013