Finite Group Databasebeta

← #15766770

Subgroups — #15766770

Order 3328.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic
2#13115798C211yesmaximal, characteristic, complemented
3#13115629C211yesmaximal, characteristic
4#13114837C211yesmaximal, characteristic
5C2×#11718071C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#333C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88061—21no—
13C2×#88060—21no—
14C2×#88060—21no—
15#11718745—22no—
16#11718745—22no—
17C2×#88049—21no—
18C2×#88048—21no—
19#11718596C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22C13×#333—22no—
23#11718143—21no—
24#11718121—21no—
25#11718121—21no—
26#11718071—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055D411yescharacteristic
46C22×#1055D411yescharacteristic
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55#88061—42no—
56#88060—42no—
57#88060—42no—
58#88049—24no—
59#88048—24no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63C4×#1055—21no—
64#10481—131nomaximal, Sylow
65C23×D13—21no—
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×Q8×C13—81no—
69C2×Q8×C13—81no—
70C22×C4×C13—41no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4111yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—41no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52—21no—
80C2×D52—21no—
81C2×D52Q1612yes—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13#4111yescharacteristic
101C42×C13#4111yescharacteristic
102#6103—41no—
103#6103—41no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—81no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055SD1612yes—
120C2×#476—131no—
121#1990—131no—
122#1954—131no—
123#1802—131no—
124C2×#335—131no—
125C2×#333D1311yescharacteristic, complemented
126#1296—131no—
127C23×C13#12111yescharacteristic
128C22×D13—22no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135Q8×C13—82no—
136Q8×C13—82no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—42no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C2×C4×C13#12411yescharacteristic
148C2×C4×C13C2×SD1611yescharacteristic
149C2×C4×C13C2×Q1611yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×C4×C13#13711yescharacteristic
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—81no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162D52—22no—
163D52—22no—
164D52—41no—
165D52—41no—
166C4×D13—81no—
167C4×D13—81no—
168C4×D13—81no—
169C4×D13—81no—
170C8×C13—81no—
171C8×C13—81no—
172#1055—22no—
173#1055—42no—
174#1055—41no—
175C2×C4⋊Q8C2×D1311yescharacteristic
176C2×C4×D4—131no—
177#476—262no—
178#476—262no—
179C2×#106—261no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×C4⋊C8C2×D1311yescharacteristic
183C2×#102—261no—
184C2×#102—261no—
185C2×C22⋊C8—261no—
186C2×C22⋊C8—261no—
187C2×C4×C8—131no—
188#384—131no—
189#340—261no—
190#340—261no—
191#340—261no—
192#335—262no—
193#333—22no—
194C22×C13#39411yescharacteristic
195C22×C13#46111yescharacteristic
196C22×C13#46311yescharacteristic
197C22×C13#46711yescharacteristic
198C22×C13#46811yescharacteristic
199C22×C13#47111yescharacteristic
200C22×C13#47211yescharacteristic
201C2×D13—42no—
202C2×D13—42no—
203C2×D13—42no—
204C2×D13—81no—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—81no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—82no—
211C4×C13#44911yescharacteristic
212C4×C13#45111yescharacteristic
213C4×C13#46011yescharacteristic
214C4×C13#46411yescharacteristic
215C4×C13#46511yescharacteristic
216C4×C13#46811yescharacteristic
217C4×C13#48411yescharacteristic
218C4×C13#48511yescharacteristic
219Dic13—81no—
220Dic13—161no—
221C22×Q8—21no—
222C22×D4—131no—
223C23×C4—261no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—131no—
227C22×C8—131no—
228C22×C8—261no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C22⋊D1312yes—
233C4×D4—261no—
234C4×D4—261no—
235C4×D4—261no—
236C4×D4—261no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C22⋊C4—261no—
244C2×C42C22×D1311yescharacteristic
245#106—264no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—132no—
251C4⋊C8—261no—
252#102—264no—
253#102—522no—
254C22⋊C8—522no—
255C22⋊C8—522no—
256C4×C8—261no—
257C4×C8—261no—
258C2×C13#167511yescharacteristic
259C2×C13#168311yescharacteristic
260C2×C13#169111yescharacteristic
261C2×C13#169711yescharacteristic
262C2×C13#203611yescharacteristic
263C2×C13#205111yescharacteristic
264C2×C13#205511yescharacteristic
265D13—82no—
266C24—261no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×D4—132no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C22×C4—41no—
278C22×C4—261no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4#612711yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—132no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—261no—
299C2×C8—261no—
300C2×C8—261no—
301C2×C8—262no—
302C2×C8—521no—
303C2×C8—521no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C4⋊C4—1041no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C42#612711yescharacteristic
318C42D4×D1311yescharacteristic
319C42#612911yescharacteristic
320C42C2×C22⋊D1311yescharacteristic
321C13#1048111yescharacteristic, complemented, Sylow
322C23—262no—
323C23—521no—
324C23—521no—
325C23—521no—
326C23—521no—
327C23—521no—
328C23—521no—
329C23#8813811yescharacteristic
330Q8—82no—
331Q8—82no—
332D4—262no—
333D4—262no—
334D4—521no—
335D4—521no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—1041no—
345C2×C4—1041no—
346C2×C4—1041no—
347C2×C4—1041no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4—1041no—
351C2×C4#8813711yescharacteristic
352C2×C4#8813811yescharacteristic
353C2×C4#8813911yescharacteristic
354C2×C4SD16×D1311yescharacteristic
355C2×C4#8816811yescharacteristic
356C2×C4#8816811yescharacteristic
357C2×C4#8817011yescharacteristic
358C2×C4Q16×D1311yescharacteristic
359C2×C4#8817211yescharacteristic
360C2×C4#8817211yescharacteristic
361C2×C4#8817311yescharacteristic
362C2×C4#8818311yescharacteristic
363C2×C4#8819111yescharacteristic
364C2×C4#8819311yescharacteristic
365C8—81no—
366C8—81no—
367C8—262no—
368C8—521no—
369C8—522no—
370C22—522no—
371C22—522no—
372C22—522no—
373C22—1041no—
374C22—1041no—
375C22—1041no—
376C22—1041no—
377C22#1171840911yescharacteristic
378C22#1171841011yescharacteristic
379C22#1171847311yescharacteristic
380C22#1171847411yescharacteristic
381C22#1171847911yescharacteristic
382C22#1171848011yescharacteristic
383C22#1171862011yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—1041no—
388C4—2081no—
389C4#1171846811yescharacteristic
390C4#1171847011yescharacteristic
391C4#1171847311yescharacteristic
392C4#1171847611yescharacteristic
393C4#1171882411yescharacteristic
394C4#1171883311yescharacteristic
395C4#1171884611yescharacteristic
396C4#1171884711yescharacteristic
397C2—1042no—
398C2#1311423411yescharacteristic
399C2#1311429011yescharacteristic
400C2#1311433811yescharacteristic
401C2#1311437211yescharacteristic
402C2#1311603711yescharacteristic
403C2#1311612811yescharacteristic
404C2#1311615011yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#333D13
hypocenterC13#10481
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. #13115798C2semidirect
5. C2×#11718071C2semidirect
6. #13112720C2semidirect
7. C2×C13×#333C2semidirect
125. C2×#333D13semidirect
321. C13#10481semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
#131157982
#131156292
#131148372
C2×#117180712
#131127202
C2×C13×#3332
#1048113