Finite Group Databasebeta

← #15762097

Subgroups — #15762097

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#13115781C211yesmaximal, characteristic, complemented
2#13115756C211yesmaximal, characteristic
3C4×#88058C211yesmaximal, characteristic, complemented
4#13113335C211yesmaximal, characteristic, complemented
5#13113331C211yesmaximal, characteristic
6#13113125C211yesmaximal, characteristic, complemented
7C13×#3167C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C13×#498C411yescharacteristic, complemented
11C13×#492C411yescharacteristic, complemented
12C13×#487C411yescharacteristic, complemented
13C13×#486C411yescharacteristic, complemented
14C13×#465—21no—
15C13×#465—21no—
16C4×C13×SD16—21no—
17C4×C13×SD16—21no—
18C2×C4×C8×C13C2211yescharacteristic
19C2×#88077—22no—
20C2×#88058—21no—
21C4×C4⋊Dic13C2211yescharacteristic
22C4×C4⋊Dic13C2211yescharacteristic
23#11718586C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25#11718143—21no—
26#11718130—22no—
27#11718129—22no—
28#11718124—22no—
29#11718047—21no—
30#11718046—21no—
31C2×C13×#41—21no—
32C2×C13×SD16—21no—
33C2×C13×SD16—21no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C4⋊Q8C2×C411yescharacteristic
37C13×C4⋊Q8C2×C411yescharacteristic
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×#127C2×C411yescharacteristic
40C13×#125—21no—
41C13×#124—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#121—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×D4×C13—21no—
49C4×D4×C13—21no—
50C13×#117—21no—
51C2×C42×C13C2311yescharacteristic
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4×Dic13—21no—
55C2×C4×Dic13—21no—
56C2×#6099D412yes—
57C13×#106—21no—
58C13×#106—21no—
59C13×#103—21no—
60C13×#103—21no—
61C13×#102—21no—
62C13×#102—21no—
63C4×C8×C13C2×C411yescharacteristic
64C4×C8×C13C2×C411yescharacteristic
65C4×C8×C13D411yescharacteristic
66C4×C8×C13D411yescharacteristic
67#88077—44no—
68#88071—21no—
69#88071—21no—
70C22⋊#1055D412yes—
71#88058—24no—
72C4⋊#1055—21no—
73#88043—21no—
74C4×#1055—21no—
75C4×#1055—21no—
76#9722—131nomaximal, Sylow
77C13×#41—42no—
78C13×#41—42no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×Dic13—41no—
91C22×Dic13—41no—
92C13×SD16—42no—
93C13×SD16—42no—
94C2×C8×C13—22no—
95C2×C8×C13—41no—
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22⋊C411yescharacteristic
99C2×C8×C13C22⋊C411yescharacteristic
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C42×C13—41no—
112C42×C13C22×C411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13#4111yescharacteristic
115C42×C13#4111yescharacteristic
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4×Dic13—42no—
121C4×Dic13—42no—
122#6099—22no—
123#6099—22no—
124C2×#1055—22no—
125C2×#1055—22no—
126#3167D1311yescharacteristic
127#1986—131no—
128#1980—131no—
129C4×#107—131no—
130#1503—131no—
131#1502—131no—
132#1451—131no—
133C23×C13—41no—
134C23×C13#12711yescharacteristic
135Q8×C13—41no—
136Q8×C13—41no—
137Q8×C13—42no—
138Q8×C13—81no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—42no—
142D4×C13—81no—
143D4×C13—81no—
144D4×C13—81no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—82no—
152C2×C4×C13C2×C22⋊C411yescharacteristic
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13C4×D411yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12411yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)12yes—
159C2×C4×C13#13712yes—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—81no—
163C2×Dic13—81no—
164C2×Dic13—81no—
165C2×Dic13—81no—
166C8×C13—21no—
167C8×C13—21no—
168C8×C13—21no—
169C8×C13#10412yescomplemented
170#1055—42no—
171#1055—42no—
172#533C2×D1311yescharacteristic
173#532C2×D1311yescharacteristic
174#498Dic1311yescharacteristic, complemented
175#492Dic1311yescharacteristic, complemented
176#487Dic1311yescharacteristic, complemented
177#486Dic1311yescharacteristic, complemented
178#465—21no—
179#465—21no—
180C4×SD16—21no—
181C4×SD16—21no—
182#431—131no—
183C2×#107—261no—
184C2×#104—262no—
185C4×M16—131no—
186C2×C4×C8C2×D1311yescharacteristic
187C4×C4⋊C4—131no—
188C4×C4⋊C4—131no—
189#340—261no—
190#339—262no—
191#328—262no—
192#327—262no—
193#322—261no—
194#322—261no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13#39011yescharacteristic
201C22×C13#49611yescharacteristic
202C22×C13#49711yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209C4×C13C2×#10411yescharacteristic
210C4×C13#42111yescharacteristic
211C4×C13#44012yes—
212C4×C13#46812yes—
213Dic13—82no—
214Dic13—82no—
215C2×#41—21no—
216C2×SD16—21no—
217C2×SD16—21no—
218C2×M16—132no—
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22⋊D1311yescharacteristic
221C4⋊Q8C2×Dic1311yescharacteristic
222C4⋊Q8C2×Dic1311yescharacteristic
223C4⋊Q8C2×Dic1311yescharacteristic
224#127C2×Dic1311yescharacteristic
225#125—21no—
226#124—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229#121—21no—
230#121—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×D4—21no—
234C4×D4—21no—
235#117—21no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C42—261no—
239C2×C42—261no—
240C2×C42C22×D1311yescharacteristic
241#107—264no—
242#106—21no—
243#106—21no—
244C4⋊C8—261no—
245#104—524no—
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250C22⋊C8—132no—
251#97—261no—
252C4×C8—261no—
253C4×C8—261no—
254C4×C8C2×Dic1311yescharacteristic
255C4×C8C2×Dic1311yescharacteristic
256C4×C8C22⋊D1311yescharacteristic
257C4×C8C22⋊D1311yescharacteristic
258#95—261no—
259#95—261no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—161no—
263C2×C13#197311yescharacteristic
264C2×C13#197611yescharacteristic
265C2×C13#198011yescharacteristic
266#41—42no—
267#41—42no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—521no—
277C22×C4—521no—
278C22×C4D4×D1311yescharacteristic
279C22×C4D4×D1311yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281SD16—42no—
282SD16—42no—
283M16—262no—
284M16—262no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8C22⋊Dic1311yescharacteristic
290C2×C8C22⋊Dic1311yescharacteristic
291C2×C8C22⋊Dic1311yescharacteristic
292C2×C8C22⋊Dic1311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—522no—
310C42—522no—
311C42#612911yescharacteristic
312C42#612911yescharacteristic
313C42C22×Dic1311yescharacteristic
314C42C2×C22⋊D1311yescharacteristic
315C13#972211yescharacteristic, complemented, Sylow
316C23—41no—
317C23#8819411yescharacteristic
318Q8—42no—
319Q8—41no—
320Q8—41no—
321Q8—81no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4—1041no—
341C2×C4#8816812yes—
342C2×C4#8816912yes—
343C2×C4D4×Dic1311yescharacteristic
344C2×C4D4×Dic1311yescharacteristic
345C2×C4#8819011yescharacteristic
346C2×C4#8819211yescharacteristic
347C2×C4#8819211yescharacteristic
348C2×C4C2×C22⋊Dic1311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—522no—
353C8—522no—
354C8#8807712yescomplemented
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1171882811yescharacteristic
361C22#1171883711yescharacteristic
362C22#1171888211yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—1042no—
370C4—1042no—
371C4#1171882512yes—
372C4#1171883512yes—
373C4C2×#8807711yescharacteristic
374C4#1171889711yescharacteristic
375C2—21no—
376C2—21no—
377C2—161no—
378C2#1311571911yescharacteristic
379C2#1311573511yescharacteristic
380C2#1311575611yescharacteristic
subgroupG/H
centerC2×C4#88192
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3167C2
socleC22×C13#390
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#3167D13
hypocenterC13#9722
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13115781C2semidirect
3. C4×#88058C2semidirect
4. #13113335C2semidirect
6. #13113125C2semidirect
10. C13×#498C4semidirect
11. C13×#492C4semidirect
12. C13×#487C4semidirect
13. C13×#486C4semidirect
169. C8×C13#104semidirect
174. #498Dic13semidirect
175. #492Dic13semidirect
176. #487Dic13semidirect
177. #486Dic13semidirect
315. C13#9722semidirect
354. C8#88077semidirect

Maximal subgroups

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

subgroupindex
#131157812
#131157562
C4×#880582
#131133352
#131133312
#131131252
C13×#31672
#972213