Finite Group Databasebeta

← #15762093

Subgroups — #15762093

Order 3328.

460 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
1#13125395C211yesmaximal, characteristic
2#13115779C211yesmaximal, characteristic, complemented
3#13115754C211yesmaximal, characteristic
4#13113334C211yesmaximal, characteristic, complemented
5#13113330C211yesmaximal, characteristic
6#13113125C211yesmaximal, characteristic, complemented
7C4×C13×#107C211yesmaximal, characteristic, complemented
8#11719182C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×#107—21no—
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14#11718775—21no—
15#11718775—21no—
16C2×#88045—22no—
17#11718586C2211yescharacteristic
18C4×#6099C2211yescharacteristic
19#11718355C411yescharacteristic, complemented
20#11718354C411yescharacteristic, complemented
21C4×#6095—21no—
22C4×#6095—21no—
23#11718342C411yescharacteristic, complemented
24#11718341C411yescharacteristic, complemented
25C13×#340—21no—
26#11718115—22no—
27#11718047—21no—
28#11718046—21no—
29#11718044—22no—
30#11718043—22no—
31C2×#6127—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39#88184—21no—
40#88184—21no—
41#88180—21no—
42#88178—21no—
43#88178—21no—
44C2×#6099D412yes—
45C2×#6095—21no—
46C2×#6095—21no—
47#88129—21no—
48#88128C2×C411yescharacteristic
49C4×D52—21no—
50C4×D52—21no—
51#88124—21no—
52#88123C2×C411yescharacteristic
53#88123C2×C411yescharacteristic
54#88123C2×C411yescharacteristic
55C4×Dic26—21no—
56C4×Dic26—21no—
57C13×#107—24no—
58C4×C8×C13C2×C411yescharacteristic
59C4×C8×C13C2×C411yescharacteristic
60C4×C8×C13D411yescharacteristic
61C4×C8×C13D411yescharacteristic
62C13×#95—21no—
63C13×#95—21no—
64C22⋊#1055D412yes—
65#88061—21no—
66#88061—21no—
67#88057—21no—
68#88057—21no—
69#88056—21no—
70#88056—21no—
71#88045—44no—
72C4⋊#1055—21no—
73#88043—21no—
74C4×#1055—21no—
75C4×#1055—21no—
76#9722—131nomaximal, Sylow
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C2×C22⋊D13—41no—
83#6127—42no—
84#6127—42no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×C4×D13—41no—
89C2×Dic26—21no—
90C2×Dic26—21no—
91C2×Dic26—21no—
92C2×C8×C13—22no—
93C2×C8×C13—41no—
94C2×C8×C13C22⋊C411yescharacteristic
95C2×C8×C13C22⋊C411yescharacteristic
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C42×C13—42no—
103C42×C13—42no—
104C42×C13C22×C411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108C22⋊Dic13—41no—
109#6103—41no—
110#6103—41no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117#6101—41no—
118#6101—41no—
119C4×Dic13—41no—
120#6099—22no—
121#6099—22no—
122C2×#1055—22no—
123C2×#1055—22no—
124#6095—42no—
125#6095—42no—
126#3167—131no—
127#1986—131no—
128#1980—131no—
129C4×#107D1311yescharacteristic, complemented
130#1503—131no—
131#1502—131no—
132#1451—131no—
133C23×C13#12711yescharacteristic
134C22×D13—41no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12411yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)12yes—
151C2×C4×C13#13712yes—
152C22⋊D13—81no—
153C22⋊D13—81no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157D52—41no—
158D52—41no—
159D52—42no—
160D52—81no—
161C4×D13—82no—
162Dic26—41no—
163Dic26—41no—
164Dic26—42no—
165Dic26—81no—
166C8×C13—21no—
167C8×C13—21no—
168C8×C13—21no—
169C8×C13#10412yescomplemented
170#1055—42no—
171#1055—42no—
172#533—131no—
173#532—131no—
174#498—131no—
175#492—131no—
176#487—131no—
177#486—131no—
178#465—261no—
179#465—261no—
180C4×SD16—261no—
181C4×SD16—261no—
182#431—131no—
183C2×#107—21no—
184C2×#104—262no—
185C4×M16—131no—
186C2×C4×C8C2×D1311yescharacteristic
187C4×C4⋊C4C2×D1311yescharacteristic
188C4×C4⋊C4C2×D1311yescharacteristic
189#340—21no—
190#339—262no—
191#328—262no—
192#327—262no—
193#322—261no—
194#322—261no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13#39011yescharacteristic
198C22×C13#49611yescharacteristic
199C22×C13#49711yescharacteristic
200C2×D13—81no—
201C2×D13—81no—
202C2×D13—81no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13—82no—
208C4×C13C2×#10411yescharacteristic
209C4×C13#42111yescharacteristic
210C4×C13#44012yes—
211C4×C13#46812yes—
212Dic13—81no—
213Dic13—81no—
214Dic13—81no—
215C2×#41—261no—
216C2×SD16—261no—
217C2×SD16—261no—
218C2×M16—132no—
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22⋊D1311yescharacteristic
221C4⋊Q8—131no—
222C4⋊Q8—131no—
223C4⋊Q8—131no—
224#127—131no—
225#125—261no—
226#124—261no—
227C22⋊Q8—261no—
228C22⋊Q8—261no—
229#121—261no—
230#121—261no—
231C4×Q8—261no—
232C4×Q8—261no—
233C4×D4—261no—
234C4×D4—261no—
235#117—261no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42C22×D1311yescharacteristic
241#107—24no—
242#106—261no—
243#106—261no—
244C4⋊C8—261no—
245#104—524no—
246#103—261no—
247#103—261no—
248#102—261no—
249#102—261no—
250C22⋊C8—132no—
251#97—261no—
252C4×C8—261no—
253C4×C8—261no—
254C4×C8C4×D1311yescharacteristic
255C4×C8C4×D1311yescharacteristic
256C4×C8D5211yescharacteristic
257C4×C8D5211yescharacteristic
258#95—21no—
259#95—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13#197311yescharacteristic
263C2×C13#197611yescharacteristic
264C2×C13#198011yescharacteristic
265D13—161no—
266#41—522no—
267#41—522no—
268C2×Q8—261no—
269C2×Q8—261no—
270C2×Q8—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—521no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—521no—
278C22×C4D4×D1311yescharacteristic
279C22×C4D4×D1311yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281SD16—522no—
282SD16—522no—
283M16—262no—
284M16—262no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8#610311yescharacteristic
290C2×C8#610311yescharacteristic
291C2×C8#610311yescharacteristic
292C2×C8#610311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C42—42no—
309C42—42no—
310C42—521no—
311C42C2×C4×D1311yescharacteristic
312C42C2×D5211yescharacteristic
313C42#613111yescharacteristic
314C42#613111yescharacteristic
315C13#972211yescharacteristic, complemented, Sylow
316C23—521no—
317C23#8819411yescharacteristic
318Q8—521no—
319Q8—522no—
320Q8—521no—
321Q8—1041no—
322D4—521no—
323D4—522no—
324D4—521no—
325D4—1041no—
326D4—1041no—
327D4—1041no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—1042no—
341C2×C4#8814711yescharacteristic
342C2×C4#8814711yescharacteristic
343C2×C4#8814911yescharacteristic
344C2×C4#8814911yescharacteristic
345C2×C4#8816512yes—
346C2×C4#8817212yes—
347C2×C4C2×#610311yescharacteristic
348C2×C4#8820111yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—522no—
353C8—522no—
354C8#8804512yescomplemented
355C22—21no—
356C22—21no—
357C22—1041no—
358C22—1041no—
359C22—1041no—
360C22#1171864911yescharacteristic
361C22#1171881511yescharacteristic
362C22#1171885111yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—1041no—
369C4—1041no—
370C4—1041no—
371C4#1171854712yes—
372C4#1171855012yes—
373C4C2×#8804511yescharacteristic
374C4#1171866611yescharacteristic
375C2—21no—
376C2—21no—
377C2—2081no—
378C2#1311571511yescharacteristic
379C2#1311573211yescharacteristic
380C2#1311575411yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#107C2
socleC22×C13#390
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenterC4×#107D13
hypocenterC13#9722
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #13115779C2semidirect
4. #13113334C2semidirect
6. #13113125C2semidirect
7. C4×C13×#107C2semidirect
19. #11718355C4semidirect
20. #11718354C4semidirect
23. #11718342C4semidirect
24. #11718341C4semidirect
129. C4×#107D13semidirect
169. C8×C13#104semidirect
315. C13#9722semidirect
354. C8#88045semidirect

Maximal subgroups

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

subgroupindex
#131253952
#131157792
#131157542
#131133342
#131133302
#131131252
C4×C13×#1072
#972213