Finite Group Databasebeta

← #13075439

Subgroups — #13075439

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66941C211yesmaximal, characteristic, complemented
2C2×#66932C211yesmaximal, characteristic
3C11×#388C211yesmaximal, characteristic
4#10622596C211yesmaximal, characteristic, complemented
5#10622565C211yesmaximal, characteristic
6#10622561C211yesmaximal, characteristic
7#10622560C211yesmaximal, characteristic
8#10622560C211yesmaximal, characteristic
9#10622558C211yesmaximal, characteristic
10#10622546C211yesmaximal, characteristic, complemented
11#10622542C211yesmaximal, characteristic, complemented
12#10622271C211yesmaximal, characteristic, complemented
13#10622268C211yesmaximal, characteristic, complemented
14#10622265C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×Dic22C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×C4×Dic11C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37#66941—24no—
38#66932—24no—
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×Dic22—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C11×C4⋊C4—22no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—41no—
78C42×C11—41no—
79C22⋊Dic11—22no—
80C22⋊Dic11—22no—
81C22⋊Dic11—22no—
82C22⋊Dic11—41no—
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85Dic11⋊C4—22no—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88Dic11⋊C4—22no—
89Dic11⋊C4—41no—
90Dic11⋊C4D414yes—
91C4×Dic11—22no—
92C4×Dic11—22no—
93#2716—111nomaximal, Sylow
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11C2411yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D412yes—
119C2×C4×C11#4112yes—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11C2×D412yes—
142C2×Dic11C2×D412yes—
143C2×Dic11#4112yes—
144Dic22—44no—
145Dic22—44no—
146C2×C4⋊Q8—111no—
147C2×#126—111no—
148#400—111no—
149#398—111no—
150#397—111no—
151#396—111no—
152#393—111no—
153#393—111no—
154#391—111no—
155#391—111no—
156#388—111no—
157#388D1111yescharacteristic
158#387—111no—
159#387—111no—
160#387—111no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C22×C11C2×#4111yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C11H(5,𝔽2)11yescharacteristic
172C22×C112−1+411yescharacteristic
173C22×C112−1+411yescharacteristic
174C22×C112−1+411yescharacteristic
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181Dic11—22no—
182Dic11—22no—
183Dic11—22no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189C22×Q8—111no—
190C22×Q8—111no—
191C4⋊Q8—224no—
192#126—224no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4C2×D1111yescharacteristic
202C2×C22⋊C4—111no—
203C2×C22⋊C4—111no—
204C2×C22⋊C4—111no—
205C2×C22⋊C4—111no—
206C2×C22⋊C4C2×D1111yescharacteristic
207C2×C22⋊C4C2×D1111yescharacteristic
208C2×C22⋊C4C2×D1111yescharacteristic
209C2×C42—111no—
210C2×C42—111no—
211C2×C42C2×D1111yescharacteristic
212#95—111no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95—111no—
218#95—111no—
219#95—111no—
220#95—111no—
221#95—111no—
222#95—111no—
223#95—111no—
224#95C2×D1111yescharacteristic
225#95C2×D1111yescharacteristic
226C2×C11—81no—
227C2×C11#53611yescharacteristic
228C2×C11#54111yescharacteristic
229C2×C11#54211yescharacteristic
230C2×C11#54611yescharacteristic
231C2×C11#54811yescharacteristic
232C2×C11#55611yescharacteristic
233C2×C11#56311yescharacteristic
234C24C22×D1111yescharacteristic
235C2×Q8—222no—
236C2×Q8—222no—
237C2×Q8—222no—
238C2×Q8—222no—
239C2×Q8—441no—
240C2×Q8—441no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251C22×C4C22×D1111yescharacteristic
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—114no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—222no—
262C4⋊C4—222no—
263C4⋊C4—441no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—222no—
268C22⋊C4—222no—
269C22⋊C4—222no—
270C22⋊C4—441no—
271C42—41no—
272C42—222no—
273C42—222no—
274C11#271611yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23C23×D1111yescharacteristic
283Q8—444no—
284Q8—444no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—112no—
302C2×C4—112no—
303C2×C4—112no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4#433912yes—
326C2×C4D4×D1112yes—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×#433911yescharacteristic
335C22C2×D4×D1111yescharacteristic
336C22#6703711yescharacteristic
337C22#41×D1111yescharacteristic
338C22#6704311yescharacteristic
339C22#6704311yescharacteristic
340C22#6704311yescharacteristic
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—222no—
348C4—222no—
349C4—222no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4—441no—
354C4—441no—
355C2—81no—
356C2#1062306411yescharacteristic
357C2#1062308311yescharacteristic
358C2#1062309211yescharacteristic
359C2#1062314111yescharacteristic
360C2#1062318211yescharacteristic
361C2#1062320611yescharacteristic
362C2#1062323211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC24×C11C23
hypercenter#388D11
hypocenterC11#2716
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
4. #10622596C2semidirect
10. #10622546C2semidirect
11. #10622542C2semidirect
12. #10622271C2semidirect
13. #10622268C2semidirect
14. #10622265C2semidirect
15. #10622259C2semidirect
274. C11#2716semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#669322
C11×#3882
#106225962
#106225652
#106225612
#106225602
#106225582
#106225462
#106225422
#106222712
#106222682
#106222652
#106222592
#271611