Finite Group Databasebeta

← #15765921

Subgroups — #15765921

Order 3328.

500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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#13114924C212yesmaximal
2#13113105C211yesmaximal, characteristic
3#13112714C212yesmaximal
4#13112679C211yesmaximal, characteristic
5C13×#2646C211yesmaximal, characteristic
6C22×C4⋊Dic13C2211yescharacteristic
7C13×#400—22no—
8C13×#398—22no—
9C13×#385—22no—
10C13×#380C2212yes—
11C2×C13×#95C2211yescharacteristic
12C2×#88071—22no—
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718121—22no—
16#11718121—22no—
17C23×C4×C13D412yes—
18C23×C4×C13C2311yescharacteristic
19C23×Dic13—21no—
20C23×Dic13—21no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D412yes—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C22⋊C4—22no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13—22no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13Q812yes—
30C22×#1055—22no—
31C13×#95—22no—
32C13×#95—22no—
33C13×#95—22no—
34C13×#95—22no—
35#88071—22no—
36#88071—44no—
37C22⋊#1055—22no—
38C22⋊#1055—22no—
39#10347—131nomaximal, Sylow
40C24×C13C2×D411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—42no—
47C22×C4×C13—42no—
48C22×C4×C13—42no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×Q811yescharacteristic
51C22×C4×C13#4112yes—
52C22×C4×C13#4111yescharacteristic
53C22×Dic13—22no—
54C22×Dic13—22no—
55C22×Dic13—42no—
56C22×Dic13—41no—
57C22×Dic13—42no—
58C22×Dic13—42no—
59C22×Dic13—41no—
60C22×Dic13—41no—
61C22×Dic13—41no—
62C22×Dic13—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—82no—
66C13×C4⋊C4—82no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—42no—
69C4⋊Dic13—24no—
70C4⋊Dic13—42no—
71C2×#1055—42no—
72C2×#1055—42no—
73C2×#1055—42no—
74#2646D1311yescharacteristic
75#1824—132no—
76#1445—131no—
77#1294—132no—
78#1280—131no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13#12011yescharacteristic
83C23×C13C22⋊Q811yescharacteristic
84C23×C13#12411yescharacteristic
85C23×C13#13512yes—
86C23×C13#13712yes—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—44no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—82no—
103C2×C4×C13C22⋊Q812yes—
104C2×C4×C13#12412yes—
105C2×Dic13—44no—
106C2×Dic13—42no—
107C2×Dic13—44no—
108C2×Dic13—42no—
109C2×Dic13—82no—
110C2×Dic13—81no—
111C2×Dic13—82no—
112C2×Dic13—81no—
113C2×Dic13—81no—
114C2×Dic13—81no—
115#1055—82no—
116C22×C4⋊C4—131no—
117C2×C22⋊C8—132no—
118#400—22no—
119#398—22no—
120#385—22no—
121#380C2×D1312yes—
122C2×#95—131no—
123C2×#95—262no—
124C2×#95C2×D1311yescharacteristic
125#340—262no—
126#340—262no—
127C22×C13—22no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#39311yescharacteristic
136C22×C13#45212yes—
137C22×C13#45311yescharacteristic
138C22×C13#45411yescharacteristic
139C22×C13#45812yes—
140C22×C13#47912yes—
141C22×C13#48811yescharacteristic
142C22×C13#49111yescharacteristic
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—82no—
146C4×C13—82no—
147C4×C13—82no—
148Dic13—82no—
149Dic13—82no—
150C23×C4—261no—
151C23×C4—261no—
152C23×C4C22⋊D1312yes—
153C23×C4C22×D1311yescharacteristic
154C22×C8—262no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4—262no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4C22⋊D1312yes—
162C2×C4⋊C4C22⋊D1312yes—
163C2×C22⋊C4—22no—
164C22⋊C8—262no—
165C22⋊C8—262no—
166#95—22no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—262no—
171#95—524no—
172C2×C13—21no—
173C2×C13—22no—
174C2×C13—21no—
175C2×C13#161512yes—
176C2×C13#161812yes—
177C2×C13#202611yescharacteristic
178C2×C13#202711yescharacteristic
179C2×C13#203011yescharacteristic
180C24C2×C22⋊D1311yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—522no—
192C22×C4—522no—
193C22×C4—521no—
194C22×C4—522no—
195C22×C4—521no—
196C22×C4—521no—
197C22×C4—522no—
198C22×C4—521no—
199C22×C4Q8×D1311yescharacteristic
200C22×C4#613112yes—
201C22×C4#613111yescharacteristic
202C22×C4C2×C22⋊D1312yes—
203C2×C8—522no—
204C2×C8—522no—
205C2×C8—522no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—264no—
211C4⋊C4—522no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C13#1034711yescharacteristic, complemented, Sylow
215C23—21no—
216C23—22no—
217C23—21no—
218C23#8820011yescharacteristic
219C23#8820111yescharacteristic
220C23#8820412yes—
221C23#8820512yes—
222C23#8820711yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—524no—
240C2×C4—522no—
241C2×C4—524no—
242C2×C4—522no—
243C2×C4—1042no—
244C2×C4—1041no—
245C2×C4—1042no—
246C2×C4—1041no—
247C2×C4—1041no—
248C2×C4—1041no—
249C2×C4#8820012yes—
250C2×C4#8820112yes—
251C8—1042no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1171872412yes—
261C22#1171872911yescharacteristic
262C22#1171873011yescharacteristic
263C22#1171889211yescharacteristic
264C22#1171890012yes—
265C22#1171890211yescharacteristic
266C22#1171890412yes—
267C22#1171890611yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—1042no—
274C4—1042no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1311386712yes—
279C2#1311388412yes—
280C2#1311598411yescharacteristic
281C2#1311598911yescharacteristic
282C2#1311600211yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2646C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#2646D13
hypocenterC13#10347
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
214. C13#10347semidirect

Maximal subgroups

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

subgroupindex
#131149242
#131131052
#131127142
#131126792
C13×#26462
#1034713