Finite Group Databasebeta

← #15757224

Subgroups — #15757224

Order 3328.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123502C211yesmaximal, characteristic
2#13113608C211yesmaximal, characteristic, complemented
3#13113594C211yesmaximal, characteristic, complemented
4#13113218C211yesmaximal, characteristic
5#13112739C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1806C211yesmaximal, characteristic
8C4×C13×#41C2211yescharacteristic
9C13×#423C2211yescharacteristic
10C2×C13×#104—21no—
11C4×C13×C4⋊C4C2211yescharacteristic
12#11718895—21no—
13#11718661—22no—
14#11718658—21no—
15#11718587—21no—
16#11718586—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C13×#339—21no—
22Q8⋊#1055C411yescharacteristic, complemented
23Q8⋊#1055C411yescharacteristic, complemented
24D4⋊#1055C411yescharacteristic, complemented
25D4⋊#1055C411yescharacteristic, complemented
26#11718072—21no—
27#11718072—21no—
28#11718071—22no—
29C2×C13×#41D411yescharacteristic
30C2×C13×M16—21no—
31C4×Q8×C13C2×C411yescharacteristic
32C4×Q8×C13Q811yescharacteristic
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13C2×C411yescharacteristic
36C4×D4×C13Q811yescharacteristic
37C13×#117—21no—
38C13×#117D411yescharacteristic
39C2×C13×C4⋊C4—21no—
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2311yescharacteristic
43C2×#6099—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×#104—42no—
49C13×#95—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055C2×C411yescharacteristic
56C4⋊#1055C2×C411yescharacteristic
57C4⋊#1055D412yes—
58C4⋊#1055D411yescharacteristic
59C4⋊#1055D411yescharacteristic
60#88043—22no—
61C4×#1055—22no—
62C4×#1055—21no—
63C4×#1055—21no—
64C4×#1055C2×C411yescharacteristic
65C4×#1055C2×C411yescharacteristic
66#8903—131nomaximal, Sylow
67C13×#41—21no—
68C13×#41—21no—
69C13×#41—21no—
70C13×#41—21no—
71C2×Q8×C13C4⋊C411yescharacteristic
72C2×D4×C13—21no—
73C2×D4×C13C4⋊C411yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4C4⋊C411yescharacteristic
89C13×C4⋊C4C4⋊C411yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—41no—
97C42×C13—41no—
98C42×C13C22×C411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×Q811yescharacteristic
102#6099—41no—
103#6099—41no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—22no—
111C2×#1055—42no—
112C2×#1055—41no—
113C2×#1055—41no—
114#2925—131no—
115#1806D1311yescharacteristic
116#1570—131no—
117#1567—131no—
118#1476—131no—
119#1303—131no—
120#1279—131no—
121C23×C13—21no—
122C23×C13#12311yescharacteristic
123Q8×C13—21no—
124Q8×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—41no—
128D4×C13—41no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13C2×C4⋊C411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13C22⋊Q811yescharacteristic
148C2×C4×C13C22⋊Q811yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C8×C13—81no—
154#1055—22no—
155#1055—41no—
156#1055—41no—
157#1055—41no—
158#1055—42no—
159#1055—41no—
160#1055—41no—
161C4×#41C2×D1311yescharacteristic
162#433—262no—
163#432—261no—
164#431—131no—
165#431—261no—
166#423—131no—
167#423C2×D1311yescharacteristic
168C2×C4⋊C8—131no—
169C2×#104—21no—
170#408—261no—
171#405—261no—
172C2×C4×C8—131no—
173C4×C4⋊C4C2×D1311yescharacteristic
174#339—21no—
175#335—262no—
176#334—261no—
177#334—261no—
178Q8⋊C8—131no—
179Q8⋊C8—131no—
180D4⋊C8—131no—
181D4⋊C8—131no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13#38511yescharacteristic
188C22×C13#48211yescharacteristic
189C22×C13#48511yescharacteristic
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—82no—
197C4×C13#42711yescharacteristic
198C4×C13#42811yescharacteristic
199C4×C13#44311yescharacteristic
200C4×C13#44411yescharacteristic
201C4×C13#44911yescharacteristic
202C4×C13#45211yescharacteristic
203C2×#41C22⋊D1311yescharacteristic
204C2×M16—21no—
205C2×M16—261no—
206C22×C8—261no—
207C22×C8—261no—
208C4×Q8Dic2611yescharacteristic
209C4×Q8C4×D1311yescharacteristic
210C4×D4—21no—
211C4×D4—21no—
212C4×D4Dic2611yescharacteristic
213C4×D4C4×D1311yescharacteristic
214#117—21no—
215#117C22⋊D1311yescharacteristic
216C2×C4⋊C4—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42C22×D1311yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—131no—
223C4⋊C8—131no—
224C4⋊C8—131no—
225C4⋊C8—131no—
226C4⋊C8—132no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229#104—42no—
230C22⋊C8—262no—
231C22⋊C8—262no—
232C22⋊C8—261no—
233#97—262no—
234C4×C8—131no—
235C4×C8—131no—
236C4×C8—262no—
237C4×C8—261no—
238C4×C8—261no—
239#95—21no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—81no—
243C2×C13#185411yescharacteristic
244C2×C13#186111yescharacteristic
245C2×C13#186611yescharacteristic
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250C2×Q8#610111yescharacteristic
251C2×D4—21no—
252C2×D4#610111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4#612911yescharacteristic
258C22×C4#612911yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260M16—41no—
261M16—41no—
262M16—521no—
263M16—521no—
264C2×C8—41no—
265C2×C8—261no—
266C2×C8—261no—
267C2×C8—261no—
268C2×C8—261no—
269C2×C8—261no—
270C2×C8—262no—
271C2×C8—261no—
272C2×C8—522no—
273C2×C8—521no—
274C2×C8—521no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4#610111yescharacteristic
280C4⋊C4#610111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—41no—
288C42—41no—
289C42C2×Dic2611yescharacteristic
290C42C2×C4×D1311yescharacteristic
291C42D4×D1311yescharacteristic
292C42D4×D1311yescharacteristic
293C13#890311yescharacteristic, complemented, Sylow
294C23—21no—
295C23#8818911yescharacteristic
296Q8—21no—
297Q8—21no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4#8813211yescharacteristic
317C2×C4#8813211yescharacteristic
318C2×C4#8813511yescharacteristic
319C2×C4#8813511yescharacteristic
320C2×C4C2×#610111yescharacteristic
321C2×C4#8818611yescharacteristic
322C2×C4#8819111yescharacteristic
323C2×C4#8819611yescharacteristic
324C2×C4#8820411yescharacteristic
325C2×C4#8820411yescharacteristic
326C8—81no—
327C8—262no—
328C8—521no—
329C8—522no—
330C8—521no—
331C8—521no—
332C8—521no—
333C8—521no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#1171860711yescharacteristic
340C22#1171869611yescharacteristic
341C22#1171870611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4#1171848411yescharacteristic
350C4#1171848511yescharacteristic
351C4#1171862511yescharacteristic
352C4#1171865911yescharacteristic
353C4#1171869811yescharacteristic
354C4#1171870811yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1311503311yescharacteristic
359C2#1311507411yescharacteristic
360C2#1311510911yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1806C2
socleC22×C13#385
prime radicalC2×C13×#41D4
cosocleC2×C42×C13C23
hypercenter#1806D13
hypocenterC13#8903
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #13113608C2semidirect
3. #13113594C2semidirect
5. #13112739C2semidirect
6. #13112677C2semidirect
22. Q8⋊#1055C4semidirect
23. Q8⋊#1055C4semidirect
24. D4⋊#1055C4semidirect
25. D4⋊#1055C4semidirect
293. C13#8903semidirect

Maximal subgroups

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

subgroupindex
#131235022
#131136082
#131135942
#131132182
#131127392
#131126772
C13×#18062
#890313