Finite Group Databasebeta

← #15761178

Subgroups — #15761178

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115773C211yesmaximal, characteristic
2#13115555C211yesmaximal, characteristic
3C2×Q8⋊#1055C211yesmaximal, characteristic
4C2×C8×#1055C211yesmaximal, characteristic
5#13112677C211yesmaximal, characteristic
6#13112671C211yesmaximal, characteristic
7C4×C13×#103C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×C13×#103C411yescharacteristic
10C2×C13×#103C411yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊#1055—21no—
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C2×C4×#1055C2211yescharacteristic
17C2×C4×#1055C2211yescharacteristic
18C13×#340C411yescharacteristic
19C13×#340C411yescharacteristic
20Q8⋊#1055—22no—
21#11718116—21no—
22#11718116—21no—
23#11718116—21no—
24C8×#1055—22no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C4×Q8×C13—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C22×#1055—21no—
40C22×#1055—21no—
41C22×#1055—21no—
42C22×#1055D411yescharacteristic
43C22×#1055D411yescharacteristic
44C13×#103—22no—
45C13×#103C814yescomplemented
46C4×C8×C13—21no—
47C4×C8×C13—21no—
48C13×#95—21no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—42no—
54C4×#1055—21no—
55C4×#1055—21no—
56C4×#1055—21no—
57C4×#1055D412yes—
58#9553—131nomaximal, Sylow
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—21no—
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13C2×C812yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C2×C8×C13—21no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13—21no—
76C2×C8×C13C2×C812yes—
77C2×C8×C13M1612yes—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4C2×C812yes—
86C42×C13—41no—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C2×#1055—22no—
95C2×#1055—22no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—22no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055SD1612yes—
108C2×#1055Q1612yes—
109#1984—131no—
110#1939—131no—
111C4×#103D1311yescharacteristic
112C2×Q8⋊C8—131no—
113C2×C82—131no—
114#1279—131no—
115#1277—131no—
116C23×C13C4×D411yescharacteristic
117Q8×C13—22no—
118Q8×C13—22no—
119Q8×C13—41no—
120Q8×C13—41no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13#11711yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×C4×C13#12611yescharacteristic
141C2×C4×C13C22×C811yescharacteristic
142C2×C4×C13C2×M1611yescharacteristic
143C2×C4×C13#13111yescharacteristic
144C2×C4×C13#13111yescharacteristic
145C2×C4×C13C2×SD1611yescharacteristic
146C2×C4×C13C2×Q1611yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C8×C13—22no—
150C8×C13—22no—
151#1055—24no—
152#1055—22no—
153#1055—22no—
154#1055—81no—
155#1055—81no—
156C2×C4×Q8C2×D1311yescharacteristic
157C2×C4⋊C8—131no—
158C2×C4⋊C8—131no—
159C2×C4⋊C8—261no—
160C2×#103Dic1311yescharacteristic
161C2×#103Dic1311yescharacteristic
162C2×C4×C8—131no—
163C2×C4×C8—131no—
164C2×C4×C8C2×D1311yescharacteristic
165C4×C4⋊C4C2×D1311yescharacteristic
166#340Dic1311yescharacteristic
167#340Dic1311yescharacteristic
168#336—261no—
169#336—261no—
170#336—261no—
171Q8⋊C8—262no—
172C82—262no—
173C22×C13#38811yescharacteristic
174C22×C13C8×D411yescharacteristic
175C22×C13#43611yescharacteristic
176C22×C13C4×SD1611yescharacteristic
177C22×C13C4×Q1611yescharacteristic
178C22×C13#44311yescharacteristic
179C22×C13#44311yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—42no—
183C4×C13—42no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13#43111yescharacteristic
187C4×C13#43311yescharacteristic
188C4×C13C8×D411yescharacteristic
189C4×C13#43511yescharacteristic
190C4×C13#46511yescharacteristic
191C4×C13#46711yescharacteristic
192C4×C13#48711yescharacteristic
193C4×C13#48811yescharacteristic
194C22×Q8C2×Dic1311yescharacteristic
195C22×C8—131no—
196C22×C8—131no—
197C22×C8—261no—
198C22×C8—261no—
199C22×C8—261no—
200C22×C8C2×Dic1311yescharacteristic
201C22×C8C2×Dic1311yescharacteristic
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C4⋊C4C2×Dic1311yescharacteristic
210C2×C42—21no—
211C2×C42—21no—
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—261no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—522no—
218#103—22no—
219#103#105514yescomplemented
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—132no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8—261no—
226#95—21no—
227C2×C13C8×SD1611yescharacteristic
228C2×C13C8×Q1611yescharacteristic
229C2×C13#159011yescharacteristic
230C2×C13#159111yescharacteristic
231C2×C13#192311yescharacteristic
232C2×C13#193311yescharacteristic
233C2×C13#193711yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8C2×#105512yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4D4×D1311yescharacteristic
245C22×C4#612911yescharacteristic
246C22×C4C22×Dic1311yescharacteristic
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—132no—
252C2×C8—132no—
253C2×C8—262no—
254C2×C8—262no—
255C2×C8—262no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—261no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8C2×#105512yes—
267C2×C8#609912yes—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4C2×#105512yes—
276C42—41no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42#612711yescharacteristic
281C42#612711yescharacteristic
282C42D4×D1311yescharacteristic
283C42#612911yescharacteristic
284C13#955311yescharacteristic, complemented, Sylow
285C23D4×Dic1311yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—41no—
289Q8—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4#8813311yescharacteristic
305C2×C4#8813711yescharacteristic
306C2×C4#8813811yescharacteristic
307C2×C4#8813911yescharacteristic
308C2×C4SD16×D1311yescharacteristic
309C2×C4#8817011yescharacteristic
310C2×C4Q16×D1311yescharacteristic
311C2×C4#8817311yescharacteristic
312C2×C4C22×#105511yescharacteristic
313C2×C4C2×#609911yescharacteristic
314C2×C4#8818011yescharacteristic
315C2×C4D4×Dic1311yescharacteristic
316C2×C4#8820211yescharacteristic
317C2×C4#8820211yescharacteristic
318C8—22no—
319C8—22no—
320C8—264no—
321C8—262no—
322C8—262no—
323C8—1041no—
324C8—1041no—
325C22#1171861211yescharacteristic
326C22D4×#105511yescharacteristic
327C22#1171867311yescharacteristic
328C22SD16×Dic1311yescharacteristic
329C22Q16×Dic1311yescharacteristic
330C22#1171885711yescharacteristic
331C22#1171885711yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—81no—
337C4—81no—
338C4#1171845311yescharacteristic
339C4#1171846111yescharacteristic
340C4#1171846811yescharacteristic
341C4#1171847411yescharacteristic
342C4#1171858611yescharacteristic
343C4#1171866111yescharacteristic
344C4D4×#105511yescharacteristic
345C4#1171867211yescharacteristic
346C2SD16×#105511yescharacteristic
347C2Q16×#105511yescharacteristic
348C2#1311372711yescharacteristic
349C2#1311373311yescharacteristic
350C2#1311544411yescharacteristic
351C2#1311551411yescharacteristic
352C2#1311554211yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC4×C13×#103C2
socle, prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenterC4×#103D13
hypocenterC13#9553
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
45. C13×#103C8semidirect
219. #103#1055semidirect
284. C13#9553semidirect

Maximal subgroups

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

subgroupindex
#131157732
#131155552
C2×Q8⋊#10552
C2×C8×#10552
#131126772
#131126712
C4×C13×#1032
#955313