Finite Group Databasebeta

← #15763497

Subgroups — #15763497

Order 3328.

772 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11718628C212yesmaximal, complemented
2#13120938C211yesmaximal, characteristic
3C2×#11718043C212yesmaximal, complemented
4#13112679C211yesmaximal, characteristic, complemented
5C13×#1445C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184—22no—
8C2×#88184C2212yes—
9C2×C13×#95—22no—
10C2×C13×#95C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12C2×C22⋊#1055C2212yes—
13#11718628—24no—
14#11718628—24no—
15C2×#88049—22no—
16C2×#88047—22no—
17#11718338—22no—
18#11718332—22no—
19#11718043—24no—
20C23×C4×C13—21no—
21C23×C4×C13—21no—
22C23×C4×C13D412yes—
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—22no—
25C22×D52—22no—
26C22×D52D412yes—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D412yescomplemented
31#88184—22no—
32#88184—22no—
33#88184—22no—
34#88184—22no—
35#88184—44no—
36#88184—44no—
37C2×#6103—24no—
38C2×#6103—22no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13D412yes—
41C22×#1055—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—44no—
45C22⋊#1055—22no—
46C22⋊#1055D414yescomplemented
47#88049—28no—
48#88047—28no—
49#9970—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C23×D13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13—41no—
60C22×C4×C13—42no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13D814yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D412yes—
70C22×C4×C13C2×D412yes—
71C22×C4×C13#4111yescharacteristic
72C2×C22⋊D13—42no—
73C2×C22⋊D13—42no—
74C2×C22⋊D13—44no—
75C2×C22⋊D13—44no—
76C22×Dic13—22no—
77C2×D52—22no—
78C2×D52—22no—
79C2×D52—44no—
80C2×D52—44no—
81C2×D52—82no—
82C2×D52—82no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4—42no—
85#6103—48no—
86#6103—42no—
87#6103—42no—
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90C4⋊Dic13—44no—
91C2×#1055—24no—
92C2×#1055—44no—
93C2×#480—132no—
94#2656—131no—
95C2×#327—132no—
96#1445D1311yescharacteristic, complemented
97#1280—131no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—22no—
101C23×C13#12011yescharacteristic
102C23×C13#12111yescharacteristic
103C23×C13#12711yescharacteristic
104C23×C13C2×D812yes—
105C23×C13AGL(1,ℤ/8)12yes—
106C22×D13—42no—
107C22×D13—44no—
108C22×D13—42no—
109C22×D13—42no—
110C22×D13—44no—
111C2×C4×C13—24no—
112C2×C4×C13—24no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—44no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—44no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13—81no—
126C2×C4×C13—82no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#12012yes—
131C2×C4×C13#12112yes—
132C22⋊D13—84no—
133C22⋊D13—82no—
134C22⋊D13—82no—
135C2×Dic13—42no—
136C2×Dic13—44no—
137D52—44no—
138D52—82no—
139D52—88no—
140#1055—44no—
141C2×#121—132no—
142C2×#121—262no—
143C22×C4⋊C4C2×D1311yescharacteristic
144#480—264no—
145#480—264no—
146C2×#107—262no—
147C2×#102—262no—
148C2×C22⋊C8—132no—
149#399—262no—
150#392—262no—
151C2×#95—22no—
152C2×#95C2×D1311yescharacteristic
153C2×#95C2×D1311yescharacteristic
154#327—264no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13#39211yescharacteristic
164C22×C13#44712yes—
165C22×C13#45511yescharacteristic
166C22×C13#45611yescharacteristic
167C22×C13#45812yes—
168C22×C13#45912yes—
169C22×C13#49311yescharacteristic
170C22×C13#49611yescharacteristic
171C2×D13—84no—
172C2×D13—84no—
173C2×D13—82no—
174C2×D13—82no—
175C2×D13—82no—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—44no—
179C4×C13—82no—
180C4×C13—82no—
181Dic13—82no—
182C22×D4—132no—
183C22×D4—262no—
184C22×D4—262no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C22⋊D1312yes—
188C23×C4C22×D1311yescharacteristic
189C22×C8—262no—
190#121—262no—
191#121—262no—
192#121—262no—
193#121—262no—
194#121—524no—
195#121—524no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—132no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4D5212yescomplemented
202C2×C22⋊C4—264no—
203C2×C22⋊C4—262no—
204#107—268no—
205#102—268no—
206C22⋊C8—134no—
207C22⋊C8—262no—
208#95—22no—
209#95—22no—
210#95—44no—
211C2×C13—21no—
212C2×C13—22no—
213C2×C13—21no—
214C2×C13#160712yes—
215C2×C13#161012yes—
216C2×C13#200711yescharacteristic
217C2×C13#201111yescharacteristic
218C2×C13#202211yescharacteristic
219D13—162no—
220C24—262no—
221C24C2×C22⋊D1311yescharacteristic
222C2×D4—262no—
223C2×D4—262no—
224C2×D4—524no—
225C2×D4—524no—
226C2×D4—522no—
227C2×D4—524no—
228C2×D4—522no—
229C2×D4—524no—
230C2×D4—1042no—
231C2×D4—1042no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—262no—
248C22×C4#610414yes—
249C22×C4C2×D5211yescharacteristic
250C22×C4#612711yescharacteristic
251C22×C4D4×D1312yes—
252C22×C4D4×D1312yes—
253C2×C8—264no—
254C2×C8—524no—
255C4⋊C4—24no—
256C4⋊C4—42no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—524no—
260C22⋊C4—528no—
261C22⋊C4—522no—
262C22⋊C4—522no—
263C13#997011yescharacteristic, complemented, Sylow
264C23—22no—
265C23—21no—
266C23—21no—
267C23—524no—
268C23—524no—
269C23—522no—
270C23—522no—
271C23—522no—
272C23#8818411yescharacteristic
273C23C2×#610412yes—
274C23#8819111yescharacteristic
275C23#8819411yescharacteristic
276C23#8820312yes—
277D4—524no—
278D4—1042no—
279D4—1048no—
280D4—1044no—
281D4—1042no—
282D4—1042no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—524no—
303C2×C4—522no—
304C2×C4#8813612yes—
305C2×C4#8813812yes—
306C8—524no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22—1042no—
316C22—1042no—
317C22—1044no—
318C22—1042no—
319C22—1044no—
320C22#1171862111yescharacteristic
321C22#1171867612yes—
322C22#1171869712yes—
323C22#1171871412yes—
324C22#1171871911yescharacteristic
325C22#1171872211yescharacteristic
326C22#1171873411yescharacteristic
327C22#1171875611yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—82no—
333C4—1042no—
334C2—21no—
335C2—22no—
336C2—21no—
337C2—2082no—
338C2#1311382112yes—
339C2#1311383812yes—
340C2#1311588211yescharacteristic
341C2#1311590611yescharacteristic
342C2#1311596711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1445C2
socleC23×C13#120
prime radical#13120938C2
hypercenter#1445D13
hypocenterC13#9970
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C2×#11718628C2semidirect
3. C2×#11718043C2semidirect
4. #13112679C2semidirect
5. C13×#1445C2semidirect
30. C2×C13×C4⋊C4D4semidirect
46. C22⋊#1055D4semidirect
96. #1445D13semidirect
201. C2×C4⋊C4D52semidirect
263. C13#9970semidirect

Maximal subgroups

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

subgroupindex
C2×#117186282
#131209382
C2×#117180432
#131126792
C13×#14452
#997013