Finite Group Databasebeta

← #15767485

Subgroups — #15767485

Order 3328.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115798C211yesmaximal, characteristic
2#13115594C211yesmaximal, characteristic
3#13115555C211yesmaximal, characteristic
4C2×#11718071C211yesmaximal, characteristic
5C2×#11718139C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic
7C13×#1981C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×#103—21no—
11C2×C13×#103—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88047—21no—
14#11718596C2211yescharacteristic
15C2×C4⋊#1055—21no—
16C2×C4⋊#1055C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718139—22no—
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718116—21no—
24#11718071—22no—
25C22×Q8×C13—21no—
26C22×C8×C13—21no—
27C13×C4⋊Q8—21no—
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8Q812yes—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C22×#1055—21no—
41C22×#1055—21no—
42C22×#1055D411yescharacteristic
43C22×#1055D411yescharacteristic
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×#103—42no—
47C13×#103—42no—
48C13×#95—21no—
49#88047—42no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—42no—
54C4⋊#1055D412yes—
55C4×#1055—21no—
56C4×#1055—21no—
57#10594—131nomaximal, Sylow
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×Dic13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4D812yes—
82C42×C13—41no—
83C42×C13—41no—
84C42×C13C2×D411yescharacteristic
85C42×C13C2×Q811yescharacteristic
86C42×C13#4111yescharacteristic
87C42×C13#4111yescharacteristic
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—81no—
93C2×#1055—21no—
94C2×#1055—21no—
95C2×#1055—22no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055Q1612yes—
105#1990—131no—
106#1981D1311yescharacteristic
107#1947—131no—
108#1939—131no—
109C2×#335—131no—
110C2×#332—131no—
111#1296—131no—
112C23×C13#12111yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115Q8×C13—81no—
116Q8×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13C22⋊Q811yescharacteristic
132C2×C4×C13C22⋊Q811yescharacteristic
133C2×C4×C13#12611yescharacteristic
134C2×C4×C13C2×D811yescharacteristic
135C2×C4×C13C2×Q1611yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C8×C13—81no—
146#1055—22no—
147#1055—42no—
148#1055—41no—
149#1055—81no—
150C2×C4⋊Q8C2×D1311yescharacteristic
151C2×#107—261no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8—131no—
154C2×C4⋊C8—261no—
155C2×C4⋊C8C2×D1311yescharacteristic
156C2×#103—21no—
157C2×#103—21no—
158C2×C4×C8—131no—
159#384—131no—
160C4×C4⋊C4C2×D1311yescharacteristic
161#340—261no—
162#340—261no—
163#340—261no—
164#336—261no—
165#335—262no—
166#332—262no—
167C22×C13#39611yescharacteristic
168C22×C13#46211yescharacteristic
169C22×C13#46311yescharacteristic
170C22×C13#46611yescharacteristic
171C22×C13#46811yescharacteristic
172C22×C13#47111yescharacteristic
173C22×C13#47311yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—42no—
177C4×C13—82no—
178C4×C13—81no—
179C4×C13#45911yescharacteristic
180C4×C13#46411yescharacteristic
181C4×C13#46711yescharacteristic
182C4×C13#46811yescharacteristic
183C4×C13#47411yescharacteristic
184C4×C13#47711yescharacteristic
185C4×C13#47811yescharacteristic
186C4×C13#47911yescharacteristic
187Dic13—161no—
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—131no—
191C22×C8—131no—
192C22×C8—261no—
193C22×C8—261no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8Dic2612yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C4⋊C4C22⋊D1311yescharacteristic
205C2×C42—21no—
206C2×C42C22×D1311yescharacteristic
207#107—522no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—132no—
211C4⋊C8—261no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214C4⋊C8—522no—
215#103—42no—
216#103—42no—
217C4×C8—261no—
218C4×C8—261no—
219#95—21no—
220C2×C13#167411yescharacteristic
221C2×C13#168111yescharacteristic
222C2×C13#169211yescharacteristic
223C2×C13#169911yescharacteristic
224C2×C13#206411yescharacteristic
225C2×C13#206711yescharacteristic
226C2×C13#206811yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—521no—
237C22×C4D4×D1311yescharacteristic
238C22×C4#612911yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—132no—
244C2×C8—261no—
245C2×C8—261no—
246C2×C8—261no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—262no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—1041no—
267C4⋊C4#610412yes—
268C42—41no—
269C42—41no—
270C42C2×Dic2611yescharacteristic
271C42#612711yescharacteristic
272C42D4×D1311yescharacteristic
273C42#612911yescharacteristic
274C13#1059411yescharacteristic, complemented, Sylow
275C23#8819311yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4#8813211yescharacteristic
295C2×C4#8813211yescharacteristic
296C2×C4#8813311yescharacteristic
297C2×C4#8813811yescharacteristic
298C2×C4#8816811yescharacteristic
299C2×C4#8817011yescharacteristic
300C2×C4Q16×D1311yescharacteristic
301C2×C4#8817211yescharacteristic
302C2×C4#8817811yescharacteristic
303C2×C4C2×#610411yescharacteristic
304C2×C4#8818611yescharacteristic
305C2×C4#8819211yescharacteristic
306C2×C4#8820411yescharacteristic
307C2×C4#8820511yescharacteristic
308C8—81no—
309C8—262no—
310C8—521no—
311C8—522no—
312C8—1041no—
313C22#1171860911yescharacteristic
314C22#1171869911yescharacteristic
315C22#1171870311yescharacteristic
316C22#1171882611yescharacteristic
317C22#1171884311yescharacteristic
318C22#1171886411yescharacteristic
319C22#1171886511yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—82no—
325C4—2081no—
326C4#1171845511yescharacteristic
327C4#1171846011yescharacteristic
328C4#1171847311yescharacteristic
329C4#1171847411yescharacteristic
330C4#1171866811yescharacteristic
331C4#1171867011yescharacteristic
332C4#1171871511yescharacteristic
333C4#1171873311yescharacteristic
334C2#1311422811yescharacteristic
335C2#1311427511yescharacteristic
336C2#1311434011yescharacteristic
337C2#1311438511yescharacteristic
338C2#1311620311yescharacteristic
339C2#1311622411yescharacteristic
340C2#1311622711yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1981C2
socle, prime radicalC23×C13#121
hypercenter#1981D13
hypocenterC13#10594
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
274. C13#10594semidirect

Maximal subgroups

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

subgroupindex
#131157982
#131155942
#131155552
C2×#117180712
C2×#117181392
#131127202
C13×#19812
#1059413