Finite Group Databasebeta

← #15765477

Subgroups — #15765477

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718749C211yesmaximal, characteristic
2C2×#11718688C211yesmaximal, characteristic
3#13115773C211yesmaximal, characteristic, complemented
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic, complemented
7C2×C13×#477C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C22×#6106—21no—
11C2×#88128C2211yescharacteristic
12C13×#477—22no—
13C13×#477—22no—
14C2×C13×#107—21no—
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17#11718749—22no—
18#11718749—22no—
19#11718688—22no—
20#11718688—22no—
21C2×#88049—21no—
22C2×#88049—22no—
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4×#1055C2211yescharacteristic
26#11718138—22no—
27#11718116—22no—
28#11718077—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D411yescharacteristic
31C22×D52—21no—
32C22×D52—21no—
33C22×D52—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D412yes—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13C2311yescharacteristic
49C2×#6106—24no—
50C2×#6106—42no—
51C2×#6106—42no—
52C22×#1055—21no—
53C22×#1055—21no—
54C22×#1055D412yes—
55#88128—21no—
56#88128—21no—
57#88128—21no—
58#88128D412yes—
59C13×#107—24no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8D412yes—
62C13×#103—24no—
63#88049—24no—
64#88049—28no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055D412yes—
69C4×#1055—21no—
70C4×#1055—21no—
71#10269—131nomaximal, Sylow
72C23×D13—41no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×Q8×C13—22no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—41no—
80C2×Q8×C13—82no—
81C2×Q8×C13SD1612yes—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C2×D52—22no—
89C2×D52—22no—
90C2×D52—22no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—42no—
94C2×D52—41no—
95C2×D52—41no—
96C2×D52—42no—
97C2×D52—41no—
98C2×D52—41no—
99C2×D52—41no—
100C2×D52—82no—
101C2×C8×C13—22no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C42×C13—41no—
113C42×C13—41no—
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118#6106—48no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—42no—
127C2×#486—131no—
128C2×#477D1311yescharacteristic, complemented
129C2×#460—131no—
130#1984—131no—
131C2×#333—131no—
132C2×#331—131no—
133#1277—131no—
134C23×C13#12111yescharacteristic
135C22×D13—42no—
136C22×D13—82no—
137C22×D13—81no—
138C22×D13—81no—
139C22×D13—82no—
140Q8×C13—22no—
141Q8×C13—22no—
142Q8×C13—41no—
143Q8×C13—41no—
144Q8×C13—82no—
145Q8×C13—82no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—82no—
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12711yescharacteristic
160C2×C4×C13C2×SD1611yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13#13512yes—
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C2×C4×C13#13712yes—
166D52—42no—
167D52—42no—
168D52—44no—
169D52—82no—
170D52—82no—
171D52—81no—
172D52—81no—
173D52—81no—
174D52—81no—
175C8×C13—42no—
176#1055—42no—
177#1055—42no—
178#1055—81no—
179C22×SD16—261no—
180C2×C4⋊Q8C2×D1311yescharacteristic
181C2×#127—131no—
182C2×C4×Q8C2×D1311yescharacteristic
183#486—262no—
184#486—262no—
185#477—22no—
186#477—22no—
187#460—262no—
188#460—262no—
189C2×#107—21no—
190C2×C4⋊C8—131no—
191C2×C4⋊C8—131no—
192C2×C4⋊C8C2×D1311yescharacteristic
193C2×#103—21no—
194C2×#102—262no—
195C2×#102—261no—
196C2×C4×C8—131no—
197#336—262no—
198#333—262no—
199#331—262no—
200C22×C13#39211yescharacteristic
201C22×C13#46412yes—
202C22×C13#46511yescharacteristic
203C22×C13#46811yescharacteristic
204C22×C13#47212yes—
205C2×D13—82no—
206C2×D13—82no—
207C2×D13—82no—
208C2×D13—162no—
209C2×D13—162no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—42no—
213C4×C13—81no—
214C4×C13—82no—
215C4×C13#44811yescharacteristic
216C4×C13#44911yescharacteristic
217C4×C13#45011yescharacteristic
218C4×C13#45211yescharacteristic
219C4×C13#45212yes—
220C4×C13#49511yescharacteristic
221C4×C13#49711yescharacteristic
222C22×Q8—21no—
223C22×Q8C22⋊D1311yescharacteristic
224C22×D4—261no—
225C22×D4—261no—
226C22×D4—261no—
227C2×SD16—264no—
228C2×SD16—522no—
229C2×SD16—522no—
230C22×C8—21no—
231C22×C8—132no—
232C22×C8—261no—
233C22×C8—261no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C22⋊D1312yes—
238#127—132no—
239#127—261no—
240#127—261no—
241#127—261no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C22⋊D1311yescharacteristic
250C2×C42—21no—
251C2×C42C22×D1311yescharacteristic
252#107—24no—
253C4⋊C8—21no—
254C4⋊C8—132no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258C4⋊C8C22⋊D1312yes—
259#103—24no—
260#102—264no—
261#102—268no—
262C4×C8—261no—
263C4×C8—261no—
264C2×C13#167812yes—
265C2×C13#169812yes—
266C2×C13#200011yescharacteristic
267C2×C13#201511yescharacteristic
268C2×C13#201811yescharacteristic
269D13—162no—
270C24—521no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×Q8#610612yes—
280C2×D4—262no—
281C2×D4—262no—
282C2×D4—262no—
283C2×D4—522no—
284C2×D4—522no—
285C2×D4—521no—
286C2×D4—521no—
287C2×D4—521no—
288C2×D4—521no—
289C2×D4—521no—
290C2×D4—521no—
291C2×D4—521no—
292C2×D4—1042no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4D4×D1311yescharacteristic
297C22×C4#612911yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299SD16—528no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—262no—
304C2×C8—262no—
305C2×C8—262no—
306C2×C8—262no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—522no—
310C2×C8—521no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C42—41no—
320C42—41no—
321C42D4×D1311yescharacteristic
322C42D4×D1311yescharacteristic
323C42C2×C22⋊D1311yescharacteristic
324C42C2×C22⋊D1311yescharacteristic
325C13#1026911yescharacteristic, complemented, Sylow
326C23—522no—
327C23—1041no—
328C23—1041no—
329C23—1042no—
330C23—1042no—
331C23#8819311yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—82no—
337Q8—82no—
338D4—522no—
339D4—522no—
340D4—524no—
341D4—1042no—
342D4—1042no—
343D4—1041no—
344D4—1041no—
345D4—1041no—
346D4—1041no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4#8817212yes—
356C2×C4#8817312yes—
357C2×C4#8819111yescharacteristic
358C2×C4#8819111yescharacteristic
359C2×C4#8819211yescharacteristic
360C2×C4#8819311yescharacteristic
361C2×C4#8819411yescharacteristic
362C2×C4C2×#610611yescharacteristic
363C2×C4#8819611yescharacteristic
364C2×C4#8820311yescharacteristic
365C2×C4#8820411yescharacteristic
366C2×C4#8820711yescharacteristic
367C8—42no—
368C8—522no—
369C8—522no—
370C8—1041no—
371C22—1042no—
372C22—1042no—
373C22—1042no—
374C22—2082no—
375C22—2082no—
376C22#1171870911yescharacteristic
377C22#1171871011yescharacteristic
378C22#1171884612yes—
379C22#1171886012yes—
380C22#1171888411yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—81no—
385C4—82no—
386C4#1171870711yescharacteristic
387C4#1171870811yescharacteristic
388C4#1171884812yes—
389C4#1171885111yescharacteristic
390C4#1171885211yescharacteristic
391C4#1171888811yescharacteristic
392C4#1171889911yescharacteristic
393C2—2082no—
394C2#1311425412yes—
395C2#1311437812yes—
396C2#1311583711yescharacteristic
397C2#1311592711yescharacteristic
398C2#1311594211yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#477C2
socleC23×C13#121
prime radicalC2×#88128C22
hypercenterC2×#477D13
hypocenterC13#10269
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13115773C2semidirect
4. C2×#11718138C2semidirect
6. #13112670C2semidirect
7. C2×C13×#477C2semidirect
128. C2×#477D13semidirect
325. C13#10269semidirect

Maximal subgroups

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

subgroupindex
C2×#117187492
C2×#117186882
#131157732
C2×#117181382
C2×#117180772
#131126702
C2×C13×#4772
#1026913