Finite Group Databasebeta

← #13073293

Subgroups — #13073293

Order 1408.

454 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66943C211yesmaximal, characteristic, complemented
2C2×#66932C211yesmaximal, characteristic
3C11×#388C211yesmaximal, characteristic
4#10622596C211yesmaximal, characteristic, complemented
5#10622564C211yesmaximal, characteristic
6#10622562C211yesmaximal, characteristic
7#10622561C211yesmaximal, characteristic
8#10622558C211yesmaximal, characteristic
9#10622557C211yesmaximal, characteristic
10#10622549C211yesmaximal, characteristic, complemented
11C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12#10622270C211yesmaximal, characteristic, complemented
13#10622265C211yesmaximal, characteristic, complemented
14#10622262C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C42×C11C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊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×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66943—24no—
42#66932—24no—
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
68C11×C4⋊C4—22no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—22no—
71C11×C22⋊C4—22no—
72C42×C11—22no—
73C22⋊Dic11—22no—
74C22⋊Dic11—22no—
75C22⋊Dic11—22no—
76C22⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81Dic11⋊C4—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—22no—
84Dic11⋊C4—22no—
85Dic11⋊C4—22no—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88Dic11⋊C4D414yes—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—22no—
92C4×Dic11—22no—
93#2519—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×C11C2×D412yes—
118C2×C4×C11#4112yes—
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×Dic11C2×D412yes—
141C2×Dic11C2×D412yes—
142C2×Dic11#4112yes—
143C2×Dic11#4112yes—
144C2×#126—111no—
145C2×#125—111no—
146#399—111no—
147#398—111no—
148#398—111no—
149#396—111no—
150#389—111no—
151#388—111no—
152#388—111no—
153#388—111no—
154#388D1111yescharacteristic
155#387—111no—
156#382—111no—
157C4×C4⋊C4—111no—
158C4×C4⋊C4—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11C2×#4111yescharacteristic
169C22×C11C2×#4111yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C112−1+411yescharacteristic
172C22×C112−1+411yescharacteristic
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179Dic11—22no—
180Dic11—22no—
181Dic11—22no—
182Dic11—22no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187#126—224no—
188#125—224no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
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×C42—111no—
212C2×C42—111no—
213C2×C42C2×D1111yescharacteristic
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#95C2×D1111yescharacteristic
223#95C2×D1111yescharacteristic
224C2×C11—81no—
225C2×C11#52911yescharacteristic
226C2×C11#53211yescharacteristic
227C2×C11#54111yescharacteristic
228C2×C11#54711yescharacteristic
229C2×C11#54811yescharacteristic
230C2×C11#55211yescharacteristic
231C2×C11#55211yescharacteristic
232C24C22×D1111yescharacteristic
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—114no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—222no—
264C22⋊C4—222no—
265C22⋊C4—222no—
266C22⋊C4—222no—
267C42—22no—
268C42—222no—
269C42—222no—
270C42—222no—
271C42—222no—
272C11#251911yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23C23×D1111yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
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—112no—
297C2×C4—112no—
298C2×C4—112no—
299C2×C4—112no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
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#433912yes—
321C2×C4D4×D1112yes—
322C2×C4#434112yes—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×#433911yescharacteristic
331C22C2×D4×D1111yescharacteristic
332C22C2×#434111yescharacteristic
333C22#41×D1111yescharacteristic
334C22#41×D1111yescharacteristic
335C22#6704311yescharacteristic
336C22#6704311yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—222no—
344C4—222no—
345C4—222no—
346C4—222no—
347C4—441no—
348C4—441no—
349C4—441no—
350C4—441no—
351C2—81no—
352C2#1062306011yescharacteristic
353C2#1062308311yescharacteristic
354C2#1062308811yescharacteristic
355C2#1062314211yescharacteristic
356C2#1062318111yescharacteristic
357C2#1062319911yescharacteristic
358C2#1062323211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC24×C11C23
hypercenter#388D11
hypocenterC11#2519
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66943C2semidirect
4. #10622596C2semidirect
10. #10622549C2semidirect
11. C4×Dic11⋊C4C2semidirect
12. #10622270C2semidirect
13. #10622265C2semidirect
14. #10622262C2semidirect
15. #10622260C2semidirect
272. C11#2519semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669322
C11×#3882
#106225962
#106225642
#106225622
#106225612
#106225582
#106225572
#106225492
C4×Dic11⋊C42
#106222702
#106222652
#106222622
#106222602
#251911