Finite Group Databasebeta

← #15779718

Subgroups — #15779718

Order 3328.

536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11718133C211yesmaximal, characteristic
2#13115225C211yesmaximal, characteristic
3#13115116C212yesmaximal
4#13112954C212yesmaximal
5C13×#2372C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7#11719503C2211yescharacteristic
8C13×#391—21no—
9C13×#388—22no—
10C13×#386C2212yes—
11C4×C13×C22⋊C4—22no—
12C13×#376—21no—
13#11718886—21no—
14C2×#88074C2212yes—
15C2×#88073C2211yescharacteristic
16#11718871—22no—
17#11718133C414yescomplemented
18#11718119—22no—
19#11718115—21no—
20C22×Q8×C13D411yescharacteristic
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13D412yes—
23C13×#124—22no—
24C13×#124C2×C412yes—
25C13×#124Q812yes—
26C2×C13×C4⋊C4—21no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4D412yes—
30C2×C42×C13—22no—
31C2×C42×C13—21no—
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35D4×Dic13—42no—
36#88180—21no—
37C2×#6101—42no—
38C2×#6099—21no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95—22no—
43#88075—42no—
44#88074—22no—
45#88074C2×C414yes—
46#88073—22no—
47#88071—42no—
48#12965—131nomaximal, Sylow
49C24×C13C2×D412yes—
50C2×Q8×C13—21no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13C4⋊C412yescomplemented
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13C22×C411yescharacteristic
57C2×D4×C13C2×Q811yescharacteristic
58C2×D4×C13#4112yes—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—44no—
64C22×C4×C13—42no—
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—42no—
69C13×C4⋊C4—81no—
70C13×C22⋊C4—24no—
71C13×C22⋊C4—24no—
72C13×C22⋊C4—44no—
73C13×C22⋊C4—42no—
74C42×C13—21no—
75C42×C13—44no—
76C42×C13—81no—
77C42×C13C4⋊C412yescomplemented
78C22⋊Dic13—24no—
79C22⋊Dic13—42no—
80C22⋊Dic13—42no—
81C22⋊Dic13—41no—
82C4⋊Dic13—22no—
83#6101—84no—
84C4×Dic13—41no—
85#6099—41no—
86#6099—41no—
87C2×#1055—41no—
88#2372D1311yescharacteristic
89C2×#354—131no—
90#1885—131no—
91#1867—132no—
92#1390—132no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C4×D412yes—
98C23×C13#12011yescharacteristic
99C23×C13C22⋊Q812yes—
100Q8×C13—42no—
101Q8×C13—81no—
102D4×C13—41no—
103D4×C13—41no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—24no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—44no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—82no—
120C2×C4×C13C2×C4⋊C411yescharacteristic
121C2×C4×C13#12311yescharacteristic
122C2×Dic13—44no—
123C2×Dic13—42no—
124C2×Dic13—82no—
125C2×Dic13—82no—
126C2×Dic13—82no—
127C2×Dic13—82no—
128#1055—81no—
129C2×#124C2×D1311yescharacteristic
130#518—131no—
131#419—261no—
132C2×#100—131no—
133C2×#99—132no—
134#391—21no—
135#388—22no—
136#386C2×D1312yes—
137#385—262no—
138C4×C22⋊C4—22no—
139#376—21no—
140#354—134no—
141#342—262no—
142#339—261no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—82no—
151C22×C13#38511yescharacteristic
152C22×C13B(4,𝔽2)11yescharacteristic
153C22×C13#45811yescharacteristic
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—42no—
157C4×C13—42no—
158C4×C13—44no—
159C4×C13—82no—
160Dic13—84no—
161Dic13—82no—
162C22×Q8C22⋊D1311yescharacteristic
163C22×D4C22×D1311yescharacteristic
164C23×C4C22⋊D1312yes—
165C2×M16—261no—
166#124—22no—
167#124Dic2612yes—
168#124C4×D1312yes—
169C4×D4—522no—
170#117—261no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—522no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—262no—
176C2×C22⋊C4—262no—
177C2×C22⋊C4C22⋊D1312yes—
178C2×C42—22no—
179C2×C42—21no—
180C2×C42C22⋊D1311yescharacteristic
181#103—522no—
182#100—262no—
183#99—134no—
184#99—262no—
185#95—21no—
186#95—21no—
187#95—22no—
188#95—22no—
189#95—522no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13—42no—
194C2×C13#186711yescharacteristic
195C2×C13#219712yes—
196C24C2×C22⋊D1312yes—
197C2×Q8—21no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8#610112yescomplemented
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C2×Dic2611yescharacteristic
204C2×D4C2×C4×D1311yescharacteristic
205C2×D4#612712yes—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—262no—
213C22×C4—262no—
214C22×C4—522no—
215C22×C4C2×C22⋊D1311yescharacteristic
216M16—521no—
217M16—521no—
218C2×C8—521no—
219C4⋊C4—81no—
220C4⋊C4—262no—
221C4⋊C4—1044no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—264no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—521no—
230C42—21no—
231C42—44no—
232C42—81no—
233C42—521no—
234C42#610112yescomplemented
235C13#1296511yescharacteristic, complemented, Sylow
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23#8817812yes—
241C23C4×C22⋊D1312yes—
242C23#8820711yescharacteristic
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—82no—
263C2×C4—524no—
264C2×C4—522no—
265C2×C4—1042no—
266C2×C4—1042no—
267C2×C4—1042no—
268C2×C4—1042no—
269C2×C4C2×#610111yescharacteristic
270C2×C4#8818311yescharacteristic
271C8—1041no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22#1171887111yescharacteristic
281C22#1171890411yescharacteristic
282C22#1171890511yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—44no—
287C4—42no—
288C4—82no—
289C4—1044no—
290C4—1042no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2#1311511711yescharacteristic
296C2#1311682612yes—
subgroupG/H
centerC22#11718905
commutatorC2×D4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2372C2
socleC22×C13B(4,𝔽2)
prime radical, cosocleC22×D4×C13C23
hypercenter#2372D13
hypocenterC13#12965
LCSG ▷ C2×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2372

Complements

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

NH ≅ G/Ntype
17. #11718133C4semidirect
53. C2×Q8×C13C4⋊C4semidirect
77. C42×C13C4⋊C4semidirect
200. C2×Q8#6101semidirect
234. C42#6101semidirect
235. C13#12965semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
#131152252
#131151162
#131129542
C13×#23722
#1296513