Finite Group Databasebeta

← #15758342

Subgroups — #15758342

Order 3328.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123860C211yesmaximal, characteristic, complemented
2C2×#11718675C211yesmaximal, characteristic
3#13113226C211yesmaximal, characteristic, complemented
4#13113156C211yesmaximal, characteristic, complemented
5#13112680C211yesmaximal, characteristic, complemented
6#13112666C211yesmaximal, characteristic, complemented
7C13×#1478C211yesmaximal, characteristic, complemented
8C2×C4×D4×C13C2211yescharacteristic
9C22×#6104C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#431C2211yescharacteristic
13C2×#88072C411yescharacteristic
14C2×C22⋊#1055—22no—
15#11718675—22no—
16#11718675—22no—
17D4×#1055—22no—
18D4×#1055—22no—
19C2×#88049C411yescharacteristic
20C2×#88048C411yescharacteristic
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23C2×#88043C2211yescharacteristic
24C13×D4⋊C8—22no—
25#11718075—22no—
26#11718060—22no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13—21no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C4×D4×C13—21no—
32C4×D4×C13—21no—
33C4×D4×C13D412yes—
34C4×D4×C13D412yes—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38C2×#6104—22no—
39C2×#6104—22no—
40C2×#6104C814yescomplemented
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C22×#1055—24no—
44C22×#1055C2×C411yescharacteristic
45C22×#1055C2×C411yescharacteristic
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56#88072—22no—
57C22⋊#1055—24no—
58C22⋊#1055—21no—
59C22⋊#1055D412yes—
60#88049—22no—
61#88048—22no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64#88043—21no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055D412yes—
68#9089—131nomaximal, Sylow
69C24×C13—21no—
70C23×D13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13C22⋊C412yes—
75C2×D4×C13C2×C812yes—
76C2×D4×C13M1612yes—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—82no—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52C2×C812yescomplemented
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—82no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4C22⋊C412yes—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—22no—
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13#4111yescharacteristic
104#6104—28no—
105#6103—41no—
106#6103—41no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C2×#1055—21no—
110C2×#1055—21no—
111C2×#1055—21no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—84no—
117C2×#1055C2×C812yescomplemented
118#2972—131no—
119C2×#442—131no—
120#1478—131no—
121#1478D1311yescharacteristic, complemented
122#1460—131no—
123#1281—131no—
124#1275—131no—
125C23×C13—22no—
126C23×C13—22no—
127C23×C13—22no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13C4×D411yescharacteristic
131C22×D13—22no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—81no—
135C22×D13—81no—
136D4×C13—22no—
137D4×C13—22no—
138D4×C13—22no—
139D4×C13C22⋊C814yes—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—44no—
144C2×C4×C13—82no—
145C2×C4×C13—81no—
146C2×C4×C13C2×C22⋊C411yescharacteristic
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12311yescharacteristic
152C2×C4×C13C22×C811yescharacteristic
153C2×C4×C13C2×M1611yescharacteristic
154C2×C4×C13#13111yescharacteristic
155C2×C4×C13#13111yescharacteristic
156C2×Dic13—41no—
157C2×Dic13—81no—
158D52—22no—
159D52—22no—
160D52—41no—
161D52—41no—
162C4×D13—82no—
163C4×D13—82no—
164C8×C13—81no—
165C8×C13—81no—
166#1055—22no—
167#1055—42no—
168#1055—42no—
169#1055—41no—
170C22×D8—131no—
171C2×C4×D4—131no—
172C2×C4×D4C2×D1311yescharacteristic
173#442—262no—
174#442—262no—
175C8×D4—262no—
176C8×D4—262no—
177#431—131no—
178#431—131no—
179#431C2×D1311yescharacteristic
180#431C2×D1311yescharacteristic
181C2×#106—131no—
182C2×#102—131no—
183C2×#102—131no—
184C2×C22⋊C8—262no—
185C2×#97—131no—
186D4⋊C8—22no—
187D4⋊C8—262no—
188#323—262no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—24no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13#38611yescharacteristic
197C22×C13C8×D411yescharacteristic
198C22×C13#43511yescharacteristic
199C2×D13—42no—
200C2×D13—82no—
201C2×D13—81no—
202C2×D13—81no—
203C2×D13—82no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—42no—
209C4×C13C2×C22⋊C811yescharacteristic
210C4×C13#40811yescharacteristic
211C4×C13C8×D411yescharacteristic
212C4×C13#43511yescharacteristic
213Dic13—81no—
214C22×D4—131no—
215C22×D4C4×D1311yescharacteristic
216C23×C4—21no—
217C23×C4—261no—
218C2×D8—134no—
219C2×D8—262no—
220C2×D8—262no—
221C22×C8—131no—
222C22×C8—131no—
223C22×C8—264no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—261no—
227C4×D4—261no—
228C4×D4—261no—
229C4×D4—261no—
230C4×D4D5212yes—
231C4×D4C22⋊D1312yes—
232C2×C4⋊C4—131no—
233C2×C4⋊C4C4×D1311yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—261no—
236C2×C42C22×D1311yescharacteristic
237#106—262no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—261no—
241C4⋊C8—261no—
242#102—262no—
243#102—262no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—132no—
247C22⋊C8—264no—
248C22⋊C8—261no—
249#97—261no—
250#97—261no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—132no—
254C4×C8—261no—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13—44no—
258C2×C13#186911yescharacteristic
259C2×C13#190311yescharacteristic
260C2×C13#190411yescharacteristic
261D13—82no—
262C24—21no—
263C24—261no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—132no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4C8×D1312yes—
274C2×D4#609412yes—
275C2×D4#610312yes—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—82no—
280C22×C4—261no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—1042no—
284C22×C4C2×C4×D1311yescharacteristic
285C22×C4D4×D1311yescharacteristic
286C22×C4#612911yescharacteristic
287D8—268no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—132no—
291C2×C8—261no—
292C2×C8—261no—
293C2×C8—262no—
294C2×C8—262no—
295C2×C8—261no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—1044no—
299C4⋊C4—21no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4#610312yes—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C42C2×D5211yescharacteristic
308C42D4×D1311yescharacteristic
309C42#612911yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C13#908911yescharacteristic, complemented, Sylow
312C23—22no—
313C23—22no—
314C23—22no—
315C23—81no—
316C23—81no—
317C23—262no—
318C23—521no—
319C23—521no—
320C23—1041no—
321C23—1041no—
322C23#8813511yescharacteristic
323D4—22no—
324D4—22no—
325D4—22no—
326D4—262no—
327D4—262no—
328D4—521no—
329D4—521no—
330D4#8806014yes—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—521no—
338C2×C4—1042no—
339C2×C4—1042no—
340C2×C4—1041no—
341C2×C4#8813511yescharacteristic
342C2×C4#8813611yescharacteristic
343C2×C4#8814011yescharacteristic
344C2×C4C2×C8×D1311yescharacteristic
345C2×C4C2×#609411yescharacteristic
346C2×C4#8816111yescharacteristic
347C2×C4#8816111yescharacteristic
348C2×C4C2×#610311yescharacteristic
349C2×C4#8819311yescharacteristic
350C2×C4#8819311yescharacteristic
351C8—81no—
352C8—81no—
353C8—262no—
354C8—522no—
355C8—522no—
356C8—521no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—522no—
365C22—1042no—
366C22—1042no—
367C22—1041no—
368C22—1041no—
369C22#1171838611yescharacteristic
370C22#1171839111yescharacteristic
371C22#1171861911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—1041no—
378C4#1171838611yescharacteristic
379C4#1171839111yescharacteristic
380C4C2×#8806011yescharacteristic
381C4#1171879011yescharacteristic
382C2—21no—
383C2—21no—
384C2—44no—
385C2—1042no—
386C2#1311512611yescharacteristic
387C2#1311531411yescharacteristic
388C2#1311532111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1478C2
socleC22×C13#386
prime radicalC22×#6104C4
cosocleC2×C42×C13C23
hypercenter#1478D13
hypocenterC13#9089
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
3. #13113226C2semidirect
4. #13113156C2semidirect
5. #13112680C2semidirect
6. #13112666C2semidirect
7. C13×#1478C2semidirect
40. C2×#6104C8semidirect
90. C2×D52C2×C8semidirect
117. C2×#1055C2×C8semidirect
121. #1478D13semidirect
311. C13#9089semidirect

Maximal subgroups

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

subgroupindex
#131238602
C2×#117186752
#131132262
#131131562
#131126802
#131126662
C13×#14782
#908913