Finite Group Databasebeta

← #15758699

Subgroups — #15758699

Order 3328.

692 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 147 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#13123167C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718043C212yesmaximal
4#13112715C212yesmaximal, complemented
5C2×C13×#382C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88184C2211yescharacteristic
9C2×#88183—21no—
10C13×#382—24no—
11C2×C13×#95—21no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718873C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718601—22no—
17#11718600C412yescomplemented
18#11718589C412yescomplemented
19#11718116—22no—
20#11718043—24no—
21C23×C4×C13—22no—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C22⋊D13—21no—
26C22×D52C2×C411yescharacteristic
27C2×C13×C4⋊C4—24no—
28C2×C13×C4⋊C4—42no—
29C2×C13×C4⋊C4—42no—
30C2×C42×C13—22no—
31C2×C42×C13—22no—
32C2×C42×C13C2×C412yes—
33C2×C42×C13D412yes—
34C2×C22⋊Dic13—21no—
35#88184—22no—
36#88184—22no—
37#88183—42no—
38#88183—42no—
39C2×#6103—22no—
40C2×#6103—22no—
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4⋊Dic13C2×C412yes—
44C2×#6101—22no—
45C22×#1055—22no—
46C13×#95—24no—
47C13×#95—22no—
48C13×#95D414yes—
49#88071—22no—
50#88071—21no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#9156—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C23×D13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—44no—
66C22×C4×C13—44no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13D812yes—
72C22×C4×C13SD1612yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D412yes—
76C22×C4×C13#4112yes—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C2×C22⋊D13—41no—
80C2×C22⋊D13—41no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—41no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C2×D52—22no—
86C2×D52—42no—
87C13×C4⋊C4—48no—
88C42×C13—24no—
89C42×C13—24no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92#6103—44no—
93#6103—44no—
94#6103—42no—
95C4⋊Dic13—22no—
96C4⋊Dic13—42no—
97#6101—44no—
98C2×#1055—44no—
99C2×#1055—42no—
100#2854—131no—
101C2×#382D1311yescharacteristic, complemented
102#1817—131no—
103C2×#327—132no—
104#1294—132no—
105C23×C13—22no—
106C23×C13—22no—
107C23×C13C2×C22⋊C411yescharacteristic
108C23×C13#12011yescharacteristic
109C23×C13#12311yescharacteristic
110C23×C13C2×D811yescharacteristic
111C23×C13C2×SD1611yescharacteristic
112C23×C13AGL(1,ℤ/8)11yescharacteristic
113C23×C13#13711yescharacteristic
114C22×D13—41no—
115C22×D13—42no—
116C22×D13—41no—
117C22×D13—41no—
118C22×D13—42no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—44no—
137C2×C4×C13—84no—
138C2×C4×C13—84no—
139C2×C4×C13#10214yes—
140C2×C4×C13C4×D412yes—
141C2×C4×C13#12112yes—
142C22⋊D13—81no—
143C22⋊D13—81no—
144C22⋊D13—81no—
145C22⋊D13—81no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—42no—
152D52—82no—
153#1055—82no—
154C2×#123—261no—
155C2×#121—131no—
156C22×C4⋊C4—21no—
157C22×C42C2×D1311yescharacteristic
158C2×C22⋊C8—132no—
159#390—132no—
160#389—132no—
161#388—262no—
162#386—261no—
163#382—24no—
164#380—131no—
165C2×#95—21no—
166C2×#95C2×D1312yes—
167#336—262no—
168#327—264no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13#38611yescharacteristic
178C22×C13#41012yes—
179C22×C13C2×#10211yescharacteristic
180C22×C13#41711yescharacteristic
181C22×C13#42112yes—
182C22×C13#44711yescharacteristic
183C22×C13#44811yescharacteristic
184C22×C13#48011yescharacteristic
185C22×C13#48111yescharacteristic
186C2×D13—81no—
187C2×D13—81no—
188C2×D13—81no—
189C2×D13—82no—
190C2×D13—82no—
191C4×C13—24no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—42no—
195C4×C13—84no—
196Dic13—81no—
197Dic13—82no—
198C22×D4—131no—
199C22×D4—261no—
200C23×C4—22no—
201C23×C4C22⋊D1311yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C23×C4C22×D1311yescharacteristic
204C22×C8—262no—
205#123—522no—
206#123—522no—
207#121—262no—
208#121—262no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—132no—
214C2×C4⋊C4—262no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—262no—
217C2×C22⋊C4—262no—
218C2×C22⋊C4—261no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C4×D1312yes—
222C2×C42D5212yes—
223C22⋊C8—262no—
224C22⋊C8—262no—
225#95—24no—
226#95—22no—
227#95—262no—
228#95—261no—
229#95C22⋊D1314yes—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13#151212yes—
235C2×C13#151712yes—
236C2×C13#187411yescharacteristic
237C2×C13#189711yescharacteristic
238C2×C13#189911yescharacteristic
239D13—161no—
240C24—261no—
241C24C2×C22⋊D1311yescharacteristic
242C2×D4—262no—
243C2×D4—522no—
244C2×D4—521no—
245C2×D4—521no—
246C2×D4—521no—
247C2×D4—521no—
248C2×D4—521no—
249C2×D4—521no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—262no—
264C22×C4—261no—
265C22×C4#610312yes—
266C22×C4#610312yes—
267C22×C4#610412yes—
268C22×C4#610612yes—
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4#612712yes—
272C22×C4C2×C22⋊D1312yes—
273C2×C8—524no—
274C2×C8—522no—
275C4⋊C4—48no—
276C4⋊C4—262no—
277C4⋊C4—522no—
278C4⋊C4—524no—
279C22⋊C4—524no—
280C22⋊C4—521no—
281C22⋊C4—521no—
282C22⋊C4—522no—
283C22⋊C4—524no—
284C42—24no—
285C42—24no—
286C13#915611yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23—522no—
290C23—522no—
291C23—521no—
292C23—521no—
293C23—521no—
294C23C2×#610311yescharacteristic
295C23#8818311yescharacteristic
296C23C2×#610411yescharacteristic
297C23#8818611yescharacteristic
298C23C2×#610611yescharacteristic
299C23#8819611yescharacteristic
300C23#8820711yescharacteristic
301D4—1042no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305D4—1041no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—522no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4#8804914yes—
333C2×C4C4×C22⋊D1312yes—
334C2×C4#8818412yes—
335C8—1042no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—1041no—
345C22—1042no—
346C22—1042no—
347C22—1041no—
348C22—1041no—
349C22C2×#8804911yescharacteristic
350C22#1171862711yescharacteristic
351C22#1171862811yescharacteristic
352C22#1171862911yescharacteristic
353C22#1171866612yes—
354C22#1171866712yes—
355C22#1171887411yescharacteristic
356C22#1171887811yescharacteristic
357C22#1171888811yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—1041no—
364C4—1042no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—2081no—
370C2#1311337212yes—
371C2#1311339512yes—
372C2#1311515311yescharacteristic
373C2#1311528411yescharacteristic
374C2#1311529411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#382C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×#382D13
hypocenterC13#9156
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #13114904C2semidirect
4. #13112715C2semidirect
5. C2×C13×#382C2semidirect
17. #11718600C4semidirect
18. #11718589C4semidirect
101. C2×#382D13semidirect
286. C13#9156semidirect

Maximal subgroups

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

subgroupindex
#131231672
#131149042
C2×#117180432
#131127152
C2×C13×#3822
#915613