Finite Group Databasebeta

← #15761523

Subgroups — #15761523

Order 3328.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114953C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic
3C2×#11718071C211yesmaximal, characteristic
4C2×#11718072C211yesmaximal, characteristic
5#13112670C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1767C211yesmaximal, characteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×#97—21no—
11C43×C13C2211yescharacteristic
12C2×C4⋊#1055C411yescharacteristic
13C2×C4⋊#1055C411yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C2×C4×#1055C2211yescharacteristic
17C2×C4×#1055C2211yescharacteristic
18C13×#336—21no—
19#11718116—21no—
20#11718116—21no—
21#11718116C411yescharacteristic
22#11718116C411yescharacteristic
23#11718072—22no—
24#11718071—22no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13Q811yescharacteristic
32C2×C42×C13Q811yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C22×#1055—21no—
35C22×#1055—21no—
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2×C411yescharacteristic
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8D412yes—
43C13×C4⋊C8Q812yes—
44C13×#97—42no—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4×#1055—21no—
52C4×#1055—21no—
53C4×#1055—21no—
54C4×#1055—21no—
55#9606—131nomaximal, Sylow
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C4⋊C411yescharacteristic
58C22×C4×C13C4⋊C411yescharacteristic
59C22×C4×C13C4⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×Q811yescharacteristic
63C2×C8×C13—22no—
64C2×C8×C13—22no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C42×C13—22no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—41no—
79C42×C13C2×D411yescharacteristic
80C42×C13C2×Q811yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C2×#1055—21no—
84C2×#1055—21no—
85C2×#1055—21no—
86C2×#1055—21no—
87C2×#1055—21no—
88C2×#1055—21no—
89C2×#1055—21no—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055M1612yes—
100C2×#1055M1612yes—
101#1831—131no—
102#1767D1311yescharacteristic
103C4×C4⋊C8—131no—
104C2×#335—131no—
105C2×#334—131no—
106#1277—131no—
107#1277—131no—
108C23×C13C2×C4⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13#10812yes—
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13C4×Q811yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13#12511yescharacteristic
128C2×C4×C13C4⋊Q811yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13#13111yescharacteristic
132C2×C4×C13#13111yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C8×C13—42no—
138C8×C13—42no—
139#1055—22no—
140#1055—22no—
141#1055—41no—
142#1055—41no—
143#1055—81no—
144#1055—81no—
145C2×C4⋊C8—131no—
146C2×C4⋊C8—131no—
147C2×C4⋊C8—131no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8C2×D1311yescharacteristic
150C2×C4⋊C8C2×D1311yescharacteristic
151C2×#97—21no—
152C2×C4×C8—131no—
153C2×C4×C8—131no—
154C43C2×D1311yescharacteristic
155#336—21no—
156#336—131no—
157#336—131no—
158#336—261no—
159#336—261no—
160#335—262no—
161#334—262no—
162C22×C13#38911yescharacteristic
163C22×C13#42311yescharacteristic
164C22×C13#42411yescharacteristic
165C22×C13#42711yescharacteristic
166C22×C13#42811yescharacteristic
167C22×C13C2×#10811yescharacteristic
168C22×C13#43011yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13#43511yescharacteristic
176C4×C13#43511yescharacteristic
177C4×C13#44611yescharacteristic
178C4×C13#44611yescharacteristic
179C4×C13#46311yescharacteristic
180C4×C13#46411yescharacteristic
181C4×C13#47811yescharacteristic
182C4×C13#47911yescharacteristic
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—131no—
186C22×C8—131no—
187C22×C8—131no—
188C22×C8—131no—
189C22×C8—261no—
190C22×C8—261no—
191C2×C42Dic2611yescharacteristic
192C2×C42Dic2611yescharacteristic
193C2×C42C4×D1311yescharacteristic
194C2×C42C4×D1311yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C2×C42C22⋊D1311yescharacteristic
197C2×C42C22×D1311yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—262no—
201C4⋊C8—262no—
202C4⋊C8—261no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C4⋊C8Dic2612yes—
207C4⋊C8D5212yes—
208#97—42no—
209C4×C8—261no—
210C4×C8—261no—
211C4×C8—261no—
212C4×C8—261no—
213C2×C13#156811yescharacteristic
214C2×C13#156911yescharacteristic
215C2×C13#157211yescharacteristic
216C2×C13#157411yescharacteristic
217C2×C13#194011yescharacteristic
218C2×C13#194911yescharacteristic
219C2×C13#195011yescharacteristic
220C22×C4#610111yescharacteristic
221C22×C4#610111yescharacteristic
222C22×C4#610111yescharacteristic
223C22×C4#610111yescharacteristic
224C22×C4C2×Dic2611yescharacteristic
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—132no—
234C2×C8—132no—
235C2×C8—261no—
236C2×C8—261no—
237C2×C8—261no—
238C2×C8—261no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—261no—
242C2×C8—261no—
243C2×C8—261no—
244C2×C8—261no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—22no—
260C42—41no—
261C42C2×Dic2611yescharacteristic
262C42C2×D5211yescharacteristic
263C42#612711yescharacteristic
264C42#612711yescharacteristic
265C13#960611yescharacteristic, complemented, Sylow
266C23C2×#610111yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4#8806212yes—
281C2×C4C4×Dic2611yescharacteristic
282C2×C4#8812311yescharacteristic
283C2×C4#8812411yescharacteristic
284C2×C4C4×D5211yescharacteristic
285C2×C4M16×D1311yescharacteristic
286C2×C4M16×D1311yescharacteristic
287C2×C4#8816111yescharacteristic
288C2×C4#8816111yescharacteristic
289C2×C4#8817811yescharacteristic
290C2×C4#8818411yescharacteristic
291C2×C4#8818611yescharacteristic
292C2×C4#8819611yescharacteristic
293C2×C4#8820411yescharacteristic
294C2×C4#8820411yescharacteristic
295C8—42no—
296C8—42no—
297C8—262no—
298C8—262no—
299C8—521no—
300C8—521no—
301C8—1041no—
302C8—1041no—
303C22#1171858911yescharacteristic
304C22#1171862511yescharacteristic
305C22#1171865911yescharacteristic
306C22#1171877911yescharacteristic
307C22#1171878011yescharacteristic
308C22C2×#8806211yescharacteristic
309C22#1171878511yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1171836211yescharacteristic
317C4#1171836211yescharacteristic
318C4#1171836711yescharacteristic
319C4#1171836711yescharacteristic
320C4#1171867011yescharacteristic
321C4#1171867711yescharacteristic
322C4#1171868311yescharacteristic
323C4#1171868911yescharacteristic
324C2#1311359711yescharacteristic
325C2#1311360111yescharacteristic
326C2#1311361711yescharacteristic
327C2#1311362711yescharacteristic
328C2#1311555911yescharacteristic
329C2#1311560411yescharacteristic
330C2#1311561111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1767C2
socle, prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1767D13
hypocenterC13#9606
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
265. C13#9606semidirect

Maximal subgroups

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

subgroupindex
#131149532
C4×C4⋊#10552
C2×#117180712
C2×#117180722
#131126702
C13×#17672
#960613