Finite Group Databasebeta

← #13073005

Subgroups — #13073005

Order 1408.

440 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
1C11×#381C211yesmaximal, characteristic
2#10622824C211yesmaximal, characteristic
3C2×C11⋊#95C211yesmaximal, characteristic
4#10622563C211yesmaximal, characteristic
5#10622559C211yesmaximal, characteristic
6#10622555C211yesmaximal, characteristic
7C22⋊C4×Dic11C211yesmaximal, characteristic
8C11⋊#401C211yesmaximal, characteristic, complemented
9#10622273C211yesmaximal, characteristic, complemented
10#10622272C211yesmaximal, characteristic, complemented
11#10622271C211yesmaximal, characteristic, complemented
12#10622268C211yesmaximal, characteristic, complemented
13#10622266C211yesmaximal, characteristic, complemented
14#10622265C211yesmaximal, characteristic, complemented
15#10622264C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11—22no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C11×C22⋊C4—22no—
76C11×C22⋊C4—22no—
77C22⋊Dic11—22no—
78C22⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—41no—
81Dic11⋊C4—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85C4×Dic11—22no—
86C4×Dic11—41no—
87#2493—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11#4112yes—
93C23×C11#4112yes—
94C23×C11#4112yes—
95C23×C11C2411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
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—44no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
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—44no—
138C2×Dic11—44no—
139C2×Dic11#4112yes—
140C2×Dic11#4112yes—
141#401—111no—
142#400—111no—
143#400—111no—
144#400—111no—
145#387—111no—
146#387—111no—
147#387—111no—
148#385—111no—
149#385—111no—
150#383—111no—
151#381—111no—
152#381D1111yescharacteristic
153#380—111no—
154C4×C22⋊C4—111no—
155C2×#95—111no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11#12614yes—
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11C2×#4111yescharacteristic
166C22×C11C2×#4111yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11H(5,𝔽2)11yescharacteristic
169C22×C112−1+411yescharacteristic
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176Dic11—22no—
177Dic11—22no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C23×C4—111no—
185C23×C4—111no—
186C23×C4C2×D1111yescharacteristic
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C22⋊C4—111no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4C2×D1111yescharacteristic
196C2×C22⋊C4C2×D1111yescharacteristic
197C2×C42—111no—
198C2×C42—111no—
199#95—111no—
200#95—111no—
201#95—111no—
202#95—111no—
203#95—111no—
204#95—111no—
205#95—111no—
206#95—111no—
207#95—111no—
208#95—111no—
209#95—111no—
210#95—111no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95C2×D1111yescharacteristic
216#95C2×D1111yescharacteristic
217#95C2×D1111yescharacteristic
218#95C2×D1111yescharacteristic
219C2×C11—24no—
220C2×C11C2×#12611yescharacteristic
221C2×C11#52911yescharacteristic
222C2×C11#53911yescharacteristic
223C2×C11#55111yescharacteristic
224C2×C11#55111yescharacteristic
225C2×C11#55211yescharacteristic
226C2×C11#55211yescharacteristic
227C24C22×D1111yescharacteristic
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—222no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—441no—
244C22×C4—441no—
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C22×C4C22×D1111yescharacteristic
248C22×C4C22×D1111yescharacteristic
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—222no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—222no—
260C22⋊C4—222no—
261C42—222no—
262C42—441no—
263C11#249311yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#433912yes—
269C23#434112yes—
270C23#434112yes—
271C23C23×D1111yescharacteristic
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—21no—
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—44no—
291C2×C4—112no—
292C2×C4—112no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
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—444no—
316C2×C4—444no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22#6693214yes—
324C22C2×#433911yescharacteristic
325C22C2×#434111yescharacteristic
326C22C2×#434111yescharacteristic
327C22#41×D1111yescharacteristic
328C22#41×D1111yescharacteristic
329C22#6704211yescharacteristic
330C22#6704311yescharacteristic
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—222no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4—441no—
345C2—24no—
346C2C2×#6693211yescharacteristic
347C2#1062305811yescharacteristic
348C2#1062306211yescharacteristic
349C2#1062318011yescharacteristic
350C2#1062318111yescharacteristic
351C2#1062318911yescharacteristic
352C2#1062319611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC24×C11C23
hypercenter#381D11
hypocenterC11#2493
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
8. C11⋊#401C2semidirect
9. #10622273C2semidirect
10. #10622272C2semidirect
11. #10622271C2semidirect
12. #10622268C2semidirect
13. #10622266C2semidirect
14. #10622265C2semidirect
15. #10622264C2semidirect
263. C11#2493semidirect

Maximal subgroups

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

subgroupindex
C11×#3812
#106228242
C2×C11⋊#952
#106225632
#106225592
#106225552
C22⋊C4×Dic112
C11⋊#4012
#106222732
#106222722
#106222712
#106222682
#106222662
#106222652
#106222642
#249311