Finite Group Databasebeta

← #15758163

Subgroups — #15758163

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123785C211yesmaximal, characteristic
2#13115781C211yesmaximal, characteristic
3#13113335C211yesmaximal, characteristic
4#13113239C211yesmaximal, characteristic
5#13112676C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C13×#3170C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#533C2211yescharacteristic
10C13×#500C411yescharacteristic, complemented
11C13×#494C411yescharacteristic, complemented
12C13×#487C411yescharacteristic, complemented
13C13×#487C411yescharacteristic, complemented
14C13×#467—22no—
15C4×C13×Q16—22no—
16C2×C4×C8×C13C2211yescharacteristic
17#11718685—21no—
18#11718685—22no—
19Q8×#1055—21no—
20#11718660—21no—
21#11718658—21no—
22C4×C4⋊Dic13C2211yescharacteristic
23#11718586C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718130—22no—
27Q8⋊#1055—21no—
28Q8⋊#1055—21no—
29#11718124—21no—
30#11718124—21no—
31C2×C13×Q16—22no—
32C22×C8×C13—21no—
33C13×C4⋊Q8C2×C411yescharacteristic
34C13×C4⋊Q8C2×C411yescharacteristic
35C13×C4⋊Q8C2×C411yescharacteristic
36C13×C4⋊Q8C2×C411yescharacteristic
37C13×#125—21no—
38C13×#125—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8D412yes—
43C4×Q8×C13—21no—
44C4×Q8×C13—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13D412yes—
47C13×#117—21no—
48C13×#117—21no—
49C2×C42×C13C2311yescharacteristic
50C2×C4⋊Dic13—21no—
51C2×C4×Dic13—21no—
52C2×#6099D411yescharacteristic
53C2×#6099D411yescharacteristic
54C22×#1055—21no—
55C13×#107—22no—
56C13×#103—22no—
57C13×#103—22no—
58C4×C8×C13—21no—
59C4×C8×C13C2×C411yescharacteristic
60C4×C8×C13C2×C411yescharacteristic
61#88071—21no—
62C22⋊#1055—21no—
63C4⋊#1055—22no—
64C4⋊#1055—22no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D411yescharacteristic
68C4⋊#1055D411yescharacteristic
69#88043—22no—
70#88043—21no—
71C4×#1055—22no—
72C4×#1055—21no—
73C4×#1055—21no—
74#9056—131nomaximal, Sylow
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13C22⋊C412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—41no—
83C13×Q16—44no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—42no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4C22⋊C412yes—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—41no—
101C42×C13—22no—
102C42×C13—41no—
103C42×C13C22×C411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C4⋊Dic13—22no—
108C4⋊Dic13—41no—
109C4×Dic13—41no—
110C4×Dic13—41no—
111#6099—21no—
112#6099—21no—
113#6099—21no—
114#6099Q1612yescomplemented
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—21no—
118C2×#1055—21no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—41no—
122#3170D1311yescharacteristic
123#2962—131no—
124#1986—131no—
125#1503—131no—
126#1481—131no—
127#1279—131no—
128#1278—131no—
129C23×C13#12111yescharacteristic
130Q8×C13—42no—
131Q8×C13—42no—
132Q8×C13—41no—
133Q8×C13—41no—
134Q8×C13—41no—
135Q8×C13—41no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13C2×C22⋊C411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12311yescharacteristic
149C2×C4×C13C2×Q1611yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×Dic13—42no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156C8×C13—22no—
157C8×C13—41no—
158#1055—22no—
159#1055—41no—
160#1055—41no—
161#1055—41no—
162#1055—81no—
163#533C2×D1311yescharacteristic
164#533C2×D1311yescharacteristic
165#500Dic1311yescharacteristic, complemented
166#494Dic1311yescharacteristic, complemented
167#487Dic1311yescharacteristic, complemented
168#487Dic1311yescharacteristic, complemented
169#467—22no—
170#446—261no—
171#446—262no—
172C8×Q8—261no—
173C4×Q16—22no—
174#431—131no—
175#424—261no—
176C2×C4⋊C8—131no—
177#405—261no—
178C4×M16—131no—
179C2×C4×C8C2×D1311yescharacteristic
180C4×C4⋊C4—131no—
181#339—261no—
182#339—261no—
183#328—262no—
184Q8⋊C8—261no—
185Q8⋊C8—261no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#38611yescharacteristic
189C22×C13#46211yescharacteristic
190C22×C13#46411yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13C4×Q1611yescharacteristic
199C4×C13#44111yescharacteristic
200C4×C13#44311yescharacteristic
201C4×C13#44411yescharacteristic
202C4×C13#45111yescharacteristic
203C4×C13#45211yescharacteristic
204Dic13—82no—
205C2×Q16—22no—
206C2×M16—131no—
207C2×M16—131no—
208C22×C8—21no—
209C22×C8—261no—
210C4⋊Q8C2×Dic1311yescharacteristic
211C4⋊Q8C2×Dic1311yescharacteristic
212C4⋊Q8C2×Dic1311yescharacteristic
213C4⋊Q8C2×Dic1311yescharacteristic
214#125—21no—
215#125—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8C22⋊D1312yes—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8C22⋊D1312yes—
224#117—21no—
225#117—21no—
226C2×C4⋊C4—261no—
227C2×C42—261no—
228C2×C42C22×D1311yescharacteristic
229#107—22no—
230C4⋊C8—131no—
231C4⋊C8—131no—
232C4⋊C8—262no—
233C4⋊C8—262no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236#103—22no—
237#103—22no—
238C22⋊C8—261no—
239#97—262no—
240#97—261no—
241C4×C8—21no—
242C4×C8—262no—
243C4×C8—261no—
244C4×C8—261no—
245C4×C8C2×Dic1311yescharacteristic
246C4×C8C2×Dic1311yescharacteristic
247#95—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13#187611yescharacteristic
251C2×C13#187811yescharacteristic
252C2×C13#188411yescharacteristic
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8C22⋊Dic1312yes—
257C22×C4—521no—
258C22×C4D4×D1311yescharacteristic
259C22×C4#612911yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261Q16—44no—
262M16—132no—
263M16—261no—
264M16—261no—
265M16—261no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—42no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—261no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—262no—
288C4⋊C4—521no—
289C4⋊C4C22⋊Dic1312yes—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C42—22no—
293C42—41no—
294C42—521no—
295C42—521no—
296C42D4×D1311yescharacteristic
297C42#612911yescharacteristic
298C42C22×Dic1311yescharacteristic
299C42C2×C22⋊D1311yescharacteristic
300C13#905611yescharacteristic, complemented, Sylow
301C23#8819311yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—522no—
316C2×C4—1041no—
317C2×C4—1041no—
318C2×C4Q16×D1311yescharacteristic
319C2×C4#8817211yescharacteristic
320C2×C4#8817211yescharacteristic
321C2×C4#8817311yescharacteristic
322C2×C4D4×Dic1311yescharacteristic
323C2×C4D4×Dic1311yescharacteristic
324C2×C4#8818911yescharacteristic
325C2×C4#8819111yescharacteristic
326C2×C4#8819311yescharacteristic
327C2×C4C2×C22⋊Dic1311yescharacteristic
328C8—22no—
329C8—41no—
330C8—262no—
331C8—521no—
332C8—521no—
333C8—521no—
334C8—1041no—
335C22—21no—
336C22—21no—
337C22#1171884311yescharacteristic
338C22#1171884611yescharacteristic
339C22#1171888111yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—42no—
345C4—81no—
346C4—81no—
347C4—1042no—
348C4Q16×Dic1311yescharacteristic
349C4#1171884511yescharacteristic
350C4#1171884711yescharacteristic
351C4#1171884811yescharacteristic
352C4#1171885711yescharacteristic
353C4#1171885811yescharacteristic
354C2—21no—
355C2—21no—
356C2#1311516511yescharacteristic
357C2#1311517911yescharacteristic
358C2#1311522011yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3170C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#3170D13
hypocenterC13#9056
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
10. C13×#500C4semidirect
11. C13×#494C4semidirect
12. C13×#487C4semidirect
13. C13×#487C4semidirect
114. #6099Q16semidirect
165. #500Dic13semidirect
166. #494Dic13semidirect
167. #487Dic13semidirect
168. #487Dic13semidirect
300. C13#9056semidirect

Maximal subgroups

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

subgroupindex
#131237852
#131157812
#131133352
#131132392
#131126762
#131126732
C13×#31702
#905613