Finite Group Databasebeta

← #13075527

Subgroups — #13075527

Order 1408.

448 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
1C2×#66951C211yesmaximal, characteristic
2C2×#66951C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic, complemented
4#10622602C211yesmaximal, characteristic
5#10622600C211yesmaximal, characteristic
6#10622598C211yesmaximal, characteristic, complemented
7#10622596C211yesmaximal, characteristic, complemented
8#10622594C211yesmaximal, characteristic, complemented
9#10622591C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic
11#10622287C211yesmaximal, characteristic
12#10622280C211yesmaximal, characteristic
13#10622270C211yesmaximal, characteristic, complemented
14#10622270C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39#66951—24no—
40#66951—24no—
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×C4×D11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—22no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4D414yes—
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85Dic11⋊C4—22no—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88Dic11⋊C4—22no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—22no—
92C4×Dic11—22no—
93#2722—111nomaximal, Sylow
94C23×C11C2411yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—21no—
100C22×D11—21no—
101C22×D11C2×D412yes—
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×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D412yes—
122C2×C4×C11#4112yes—
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×Dic11—21no—
142C2×Dic11C2×D412yes—
143C2×Dic11#4112yes—
144C4×D11—44no—
145C2×#126—111no—
146C2×#126—111no—
147#398—111no—
148#398—111no—
149#398—111no—
150#398D1111yescharacteristic, complemented
151#397—111no—
152#397—111no—
153#389—111no—
154#389—111no—
155#387—111no—
156#387—111no—
157#385—111no—
158#380—111no—
159#380—111no—
160C22×C11C22×D411yescharacteristic
161C22×C11C2×#4111yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11H(5,𝔽2)11yescharacteristic
164C22×C112−1+411yescharacteristic
165C22×C112−1+411yescharacteristic
166C22×C112−1+411yescharacteristic
167C2×D11—22no—
168C2×D11—22no—
169C2×D11—22no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181Dic11—22no—
182Dic11—22no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C23×C4—111no—
189#126—224no—
190#126—224no—
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×C4⋊C4C2×D1111yescharacteristic
203C2×C4⋊C4C2×D1111yescharacteristic
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—111no—
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—111no—
211C2×C42—111no—
212C2×C42—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#95C2×D1111yescharacteristic
223#95C2×D1111yescharacteristic
224#95C2×D1111yescharacteristic
225C2×C11#53711yescharacteristic
226C2×C11#54111yescharacteristic
227C2×C11#54111yescharacteristic
228C2×C11#54711yescharacteristic
229C2×C11#54711yescharacteristic
230C2×C11#55111yescharacteristic
231C2×C11#56311yescharacteristic
232D11—42no—
233C24—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—441no—
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C22×C4C22×D1111yescharacteristic
248C22×C4C22×D1111yescharacteristic
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—114no—
266C22⋊C4—222no—
267C22⋊C4—222no—
268C22⋊C4—222no—
269C22⋊C4—222no—
270C22⋊C4—441no—
271C42—222no—
272C42—222no—
273C11#272211yescharacteristic, complemented, Sylow
274C23—112no—
275C23—221no—
276C23—221no—
277C23—221no—
278C23—221no—
279C23—221no—
280C23—221no—
281C23C23×D1111yescharacteristic
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—112no—
302C2×C4—112no—
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—221no—
321C2×C4—221no—
322C2×C4—444no—
323C2×C4D4×D1112yes—
324C2×C4#434112yes—
325C22—222no—
326C22—222no—
327C22—222no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22C2×D4×D1111yescharacteristic
333C22C2×#434111yescharacteristic
334C22#6704011yescharacteristic
335C22#6704011yescharacteristic
336C22#41×D1111yescharacteristic
337C22#6704211yescharacteristic
338C22#6704311yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—222no—
347C4—222no—
348C4—441no—
349C4—441no—
350C4—441no—
351C4—441no—
352C4—441no—
353C2—442no—
354C2#1062314211yescharacteristic
355C2#1062316011yescharacteristic
356C2#1062316211yescharacteristic
357C2#1062318911yescharacteristic
358C2#1062322711yescharacteristic
359C2#1062323011yescharacteristic
360C2#1062326211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC23×D11C23
hypercenter#398D11
hypocenterC11#2722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C11×#398C2semidirect
6. #10622598C2semidirect
7. #10622596C2semidirect
8. #10622594C2semidirect
9. #10622591C2semidirect
13. #10622270C2semidirect
14. #10622270C2semidirect
15. #10622260C2semidirect
150. #398D11semidirect
273. C11#2722semidirect

Maximal subgroups

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

subgroupindex
C2×#669512
C11×#3982
#106226022
#106226002
#106225982
#106225962
#106225942
#106225912
#106222882
#106222872
#106222802
#106222702
#106222602
#272211