Finite Group Databasebeta

← #15765920

Subgroups — #15765920

Order 3328.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#13120806C211yesmaximal, characteristic
2#13114923C212yesmaximal
3#13113103C211yesmaximal, characteristic
4#13112716C212yesmaximal
5C13×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic13C2211yescharacteristic
7C2×C13×C22⋊C8C2212yes—
8C2×C13×#95C2211yescharacteristic
9#11718873C2212yes—
10#11718871—22no—
11C2×#88071—22no—
12C2×#88071C2211yescharacteristic
13#11718321—22no—
14#11718318—22no—
15#11718143—22no—
16#11718143—22no—
17C23×C4×C13D412yes—
18C23×C4×C13C2311yescharacteristic
19C23×Dic13—21no—
20C23×Dic13—21no—
21C22×C8×C13—22no—
22C2×C22⋊Dic13—22no—
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13Q812yes—
29C2×#6101—22no—
30C2×#6101—22no—
31C13×C22⋊C8—22no—
32C13×C22⋊C8—22no—
33C13×#95—22no—
34#88071—22no—
35#88071—22no—
36#88071—22no—
37#88071—22no—
38#88071—44no—
39#10346—131nomaximal, Sylow
40C24×C13C2×D411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—42no—
45C22×C4×C13—42no—
46C22×C4×C13—42no—
47C22×C4×C13C2×D412yes—
48C22×C4×C13C2×Q811yescharacteristic
49C22×C4×C13#4112yes—
50C22×C4×C13#4111yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—22no—
55C22×Dic13—41no—
56C22×Dic13—42no—
57C22×Dic13—41no—
58C22×Dic13—41no—
59C22×Dic13—41no—
60C22×Dic13—42no—
61C22×Dic13—42no—
62C22×Dic13—42no—
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C22⋊Dic13—42no—
67C22⋊Dic13—42no—
68C4⋊Dic13—24no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72#6101—82no—
73#6101—82no—
74#2646—131no—
75#1823—132no—
76#1445—131no—
77#1294—132no—
78#1280D1311yescharacteristic
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13#12011yescharacteristic
83C23×C13C22⋊Q811yescharacteristic
84C23×C13#12411yescharacteristic
85C23×C13#13512yes—
86C23×C13AGL(1,ℤ/8)12yes—
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—82no—
97C2×C4×C13C22⋊Q812yes—
98C2×C4×C13#12412yes—
99C2×Dic13—44no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—44no—
109C2×Dic13—82no—
110C2×Dic13—81no—
111C2×Dic13—82no—
112C2×Dic13—81no—
113C2×Dic13—81no—
114C2×Dic13—81no—
115C8×C13—82no—
116C22×C4⋊C4—131no—
117C2×C22⋊C8C2×D1312yes—
118#400—262no—
119#398—262no—
120#385—262no—
121#380—132no—
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#44912yes—
137C22×C13#45511yescharacteristic
138C22×C13#45611yescharacteristic
139C22×C13#45812yes—
140C22×C13#47812yes—
141C22×C13#48811yescharacteristic
142C22×C13#49011yescharacteristic
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—82no—
146Dic13—82no—
147Dic13—82no—
148Dic13—82no—
149Dic13—82no—
150C23×C4—261no—
151C23×C4—261no—
152C23×C4D5212yes—
153C23×C4C22×D1311yescharacteristic
154C22×C8—22no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4—262no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4—262no—
162C2×C4⋊C4—262no—
163C2×C22⋊C4—262no—
164C22⋊C8—22no—
165C22⋊C8—22no—
166#95—22no—
167#95—262no—
168#95—262no—
169#95—262no—
170#95—262no—
171#95—524no—
172C2×C13—21no—
173C2×C13—22no—
174C2×C13—21no—
175C2×C13#160912yes—
176C2×C13#161212yes—
177C2×C13#202511yescharacteristic
178C2×C13#202811yescharacteristic
179C2×C13#203011yescharacteristic
180C24C2×D5211yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—262no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—522no—
192C22×C4—521no—
193C22×C4—521no—
194C22×C4—521no—
195C22×C4—521no—
196C22×C4—522no—
197C22×C4—522no—
198C22×C4—522no—
199C22×C4#612712yes—
200C22×C4D4×D1312yes—
201C22×C4#612911yescharacteristic
202C22×C4Q8×D1311yescharacteristic
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C4⋊C4—264no—
207C4⋊C4—522no—
208C4⋊C4—522no—
209C4⋊C4—522no—
210C4⋊C4—1042no—
211C4⋊C4—1042no—
212C22⋊C4—522no—
213C22⋊C4—522no—
214C13#1034611yescharacteristic, complemented, Sylow
215C23—22no—
216C23—21no—
217C23—21no—
218C23#8812911yescharacteristic
219C23#8813611yescharacteristic
220C23#8815111yescharacteristic
221C23#8815812yes—
222C23#8816212yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—522no—
234C2×C4—524no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4—524no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—1041no—
244C2×C4—1042no—
245C2×C4—1041no—
246C2×C4—1041no—
247C2×C4—1041no—
248C2×C4—1042no—
249C2×C4#8813912yes—
250C2×C4#8815012yes—
251C8—82no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—22no—
260C22#1171833411yescharacteristic
261C22#1171835811yescharacteristic
262C22#1171837411yescharacteristic
263C22#1171839512yes—
264C22#1171840312yes—
265C22#1171840711yescharacteristic
266C22#1171841311yescharacteristic
267C22#1171850812yes—
268C4—22no—
269C4—22no—
270C4—82no—
271C4—1042no—
272C4—1042no—
273C4—1042no—
274C4—1042no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1311383512yes—
279C2#1311385212yes—
280C2#1311598311yescharacteristic
281C2#1311599811yescharacteristic
282C2#1311600411yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1280D13
hypocenterC13#10346
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
214. C13#10346semidirect

Maximal subgroups

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

subgroupindex
#131208062
#131149232
#131131032
#131127162
C13×#12802
#1034613