Finite Group Databasebeta

← #15765727

Subgroups — #15765727

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718754C211yesmaximal, characteristic, complemented
2C2×#11718749C211yesmaximal, characteristic
3C2×#11718355C211yesmaximal, characteristic
4#13115796C211yesmaximal, characteristic, complemented
5#13115641C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic, complemented
7C13×#1956C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88128C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×#103—22no—
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C2×#88061—22no—
15#11718754—22no—
16#11718754—22no—
17#11718749—22no—
18#11718749—22no—
19C2×#88050—22no—
20C2×#88049—22no—
21C2×#88049—22no—
22C2×C4×#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24#11718355—22no—
25#11718355—22no—
26#11718121—22no—
27C22×Q8×C13—21no—
28C22×D52—21no—
29C22×D52—21no—
30C22×D52—21no—
31C22×Dic26—21no—
32C22×C8×C13D412yes—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8D412yes—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C42×C13C2311yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C22×#1055D412yes—
46C22×#1055D412yes—
47#88128—21no—
48#88128—21no—
49#88128—21no—
50#88128D412yes—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123D412yes—
55C13×#103—44no—
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58#88061—28no—
59#88050—28no—
60#88049—28no—
61#88049—44no—
62C4×#1055—21no—
63C4×#1055—21no—
64C4×#1055—21no—
65C4×#1055—21no—
66#10311—131nomaximal, Sylow
67C23×D13—41no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—42no—
71C2×Q8×C13—42no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—41no—
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—22no—
81C2×D52—42no—
82C2×D52—42no—
83C2×D52—42no—
84C2×D52—42no—
85C2×D52—42no—
86C2×D52—42no—
87C2×D52—41no—
88C2×D52—41no—
89C2×D52—41no—
90C2×Dic26—22no—
91C2×Dic26—42no—
92C2×Dic26—42no—
93C2×Dic26—41no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—42no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—42no—
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C42×C13#4111yescharacteristic
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#487—131no—
119C2×#486—131no—
120C2×#486—131no—
121#1990—131no—
122#1957—131no—
123#1956D1311yescharacteristic, complemented
124#1273—131no—
125C23×C13#12711yescharacteristic
126C22×D13—42no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—81no—
130C22×D13—81no—
131C22×D13—81no—
132C22×D13—81no—
133Q8×C13—44no—
134Q8×C13—82no—
135C2×C4×C13—42no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#13512yes—
148C2×C4×C13#13512yes—
149C2×C4×C13#13512yes—
150C2×C4×C13AGL(1,ℤ/8)12yes—
151C2×C4×C13AGL(1,ℤ/8)12yes—
152C2×C4×C13#13712yes—
153C2×Dic13—42no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156D52—44no—
157D52—44no—
158D52—44no—
159D52—82no—
160D52—82no—
161D52—82no—
162Dic26—44no—
163Dic26—82no—
164C8×C13—42no—
165#1055—42no—
166#1055—42no—
167C2×C4⋊Q8—131no—
168C2×C4⋊Q8C2×D1311yescharacteristic
169C2×#127—131no—
170#487—262no—
171#487—262no—
172#486—262no—
173#486—262no—
174#486—262no—
175#486—262no—
176C2×#103—22no—
177C2×#103—262no—
178C2×#102—262no—
179C2×#102—262no—
180C2×#102—262no—
181C2×C4×C8—131no—
182C2×C4×C8—131no—
183C2×C4×C8C2×D1311yescharacteristic
184#384C2×D1311yescharacteristic
185#340—262no—
186C22×C13#39211yescharacteristic
187C22×C13#49511yescharacteristic
188C22×C13#49511yescharacteristic
189C22×C13#49511yescharacteristic
190C22×C13#49611yescharacteristic
191C22×C13#49611yescharacteristic
192C22×C13#49711yescharacteristic
193C2×D13—82no—
194C2×D13—82no—
195C2×D13—82no—
196C2×D13—161no—
197C2×D13—161no—
198C2×D13—161no—
199C2×D13—161no—
200C4×C13—82no—
201C4×C13—161no—
202C4×C13#44912yes—
203C4×C13#44912yes—
204C4×C13#45212yes—
205C4×C13#46312yes—
206C4×C13#46312yes—
207C4×C13#46412yes—
208Dic13—82no—
209C22×Q8—21no—
210C22×Q8—261no—
211C22×D4—261no—
212C22×D4—261no—
213C22×D4—261no—
214C22×C8—132no—
215C22×C8—132no—
216C22×C8C22⋊D1312yes—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—132no—
221C4⋊Q8—261no—
222C4⋊Q8—261no—
223C4⋊Q8—261no—
224C4⋊Q8D5212yes—
225#127—132no—
226#127—261no—
227#127—261no—
228#127—261no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C42C22×D1311yescharacteristic
237#103—44no—
238#103—268no—
239#102—268no—
240#102—268no—
241#102—524no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—261no—
245C4×C8—261no—
246C4×C8—261no—
247C4×C8—261no—
248C2×C13#171111yescharacteristic
249C2×C13#171711yescharacteristic
250C2×C13#171911yescharacteristic
251C2×C13#172011yescharacteristic
252C2×C13#201211yescharacteristic
253C2×C13#201211yescharacteristic
254C2×C13#201511yescharacteristic
255D13—162no—
256C24—521no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—262no—
262C2×Q8—521no—
263C2×Q8—522no—
264C2×Q8—522no—
265C2×D4—262no—
266C2×D4—262no—
267C2×D4—262no—
268C2×D4—521no—
269C2×D4—521no—
270C2×D4—522no—
271C2×D4—522no—
272C2×D4—522no—
273C2×D4—522no—
274C2×D4—521no—
275C2×D4—522no—
276C2×D4—522no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—521no—
280C22×C4D4×D1311yescharacteristic
281C22×C4D4×D1311yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8—262no—
291C2×C8—262no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C42C2×D5211yescharacteristic
304C42#612711yescharacteristic
305C42D4×D1311yescharacteristic
306C42D4×D1311yescharacteristic
307C13#1031111yescharacteristic, complemented, Sylow
308C23—522no—
309C23—1041no—
310C23—1041no—
311C23—1041no—
312C23—1041no—
313C23—1041no—
314C23—1041no—
315C23#8819411yescharacteristic
316Q8—44no—
317Q8—82no—
318Q8—524no—
319Q8—1042no—
320D4—524no—
321D4—524no—
322D4—524no—
323D4—1042no—
324D4—1042no—
325D4—1042no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—522no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4#8813611yescharacteristic
336C2×C4#8813611yescharacteristic
337C2×C4#8813811yescharacteristic
338C2×C4#8813811yescharacteristic
339C2×C4#8816812yes—
340C2×C4#8817012yes—
341C2×C4#8817212yes—
342C2×C4#8817312yes—
343C2×C4#8818411yescharacteristic
344C2×C4#8818612yes—
345C2×C4#8819111yescharacteristic
346C2×C4#8820412yes—
347C8—42no—
348C8—522no—
349C8—522no—
350C22—1042no—
351C22—1042no—
352C22—1042no—
353C22—2081no—
354C22—2081no—
355C22—2081no—
356C22—2081no—
357C22#1171862111yescharacteristic
358C22#1171872011yescharacteristic
359C22#1171873511yescharacteristic
360C22#1171882911yescharacteristic
361C22#1171883711yescharacteristic
362C22#1171885111yescharacteristic
363C22#1171885211yescharacteristic
364C4—82no—
365C4—161no—
366C4—1042no—
367C4#1171845912yes—
368C4#1171847112yes—
369C4#1171847212yes—
370C4#1171848012yes—
371C4#1171867712yes—
372C4#1171869812yes—
373C2—2082no—
374C2#1311444911yescharacteristic
375C2#1311447311yescharacteristic
376C2#1311449011yescharacteristic
377C2#1311449911yescharacteristic
378C2#1311591211yescharacteristic
379C2#1311591411yescharacteristic
380C2#1311593111yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socleC23×C13#127
prime radicalC2×#88128C22
hypercenter#1956D13
hypocenterC13#10311
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#11718754C2semidirect
4. #13115796C2semidirect
6. #13112663C2semidirect
7. C13×#1956C2semidirect
123. #1956D13semidirect
307. C13#10311semidirect

Maximal subgroups

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

subgroupindex
C2×#117187542
C2×#117187492
C2×#117183552
#131157962
#131156412
#131126632
C13×#19562
#1031113