Finite Group Databasebeta

← #13074151

Subgroups — #13074151

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#388C211yesmaximal, characteristic
2#10622599C211yesmaximal, characteristic, complemented
3#10622598C211yesmaximal, characteristic, complemented
4#10622566C211yesmaximal, characteristic
5#10622564C211yesmaximal, characteristic
6#10622564C211yesmaximal, characteristic
7#10622562C211yesmaximal, characteristic
8#10622558C211yesmaximal, characteristic
9#10622557C211yesmaximal, characteristic
10C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11#10622546C211yesmaximal, characteristic, complemented
12#10622271C211yesmaximal, characteristic, complemented
13#10622267C211yesmaximal, characteristic, complemented
14#10622266C211yesmaximal, characteristic, complemented
15#10622262C211yesmaximal, 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×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35C2×C4×Dic11C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
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×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C11×C4⋊C4—22no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—22no—
69C11×C22⋊C4—22no—
70C42×C11—22no—
71C22⋊Dic11—22no—
72C22⋊Dic11—22no—
73C22⋊Dic11—41no—
74C22⋊Dic11—41no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79Dic11⋊C4—22no—
80Dic11⋊C4—22no—
81Dic11⋊C4—22no—
82Dic11⋊C4—41no—
83C4×Dic11—22no—
84C4×Dic11—41no—
85C4×Dic11—41no—
86C4×Dic11—41no—
87#2596—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
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#4112yes—
112C2×C4×C11#4112yes—
113C2×C4×C11#4112yes—
114C2×Dic11—21no—
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#4112yes—
137C2×Dic11#4112yes—
138#400—111no—
139#400—111no—
140#399—111no—
141#397—111no—
142#389—111no—
143#388—111no—
144#388—111no—
145#388—111no—
146#388—111no—
147#388D1111yescharacteristic
148#387—111no—
149#387—111no—
150#387—111no—
151C4×C4⋊C4—111no—
152C4×C4⋊C4—111no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C2×#4111yescharacteristic
161C22×C11C2×#4111yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11H(5,𝔽2)11yescharacteristic
166C22×C112−1+411yescharacteristic
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173Dic11—22no—
174Dic11—22no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4C2×D1111yescharacteristic
190C2×C22⋊C4—111no—
191C2×C22⋊C4—111no—
192C2×C22⋊C4—111no—
193C2×C22⋊C4—111no—
194C2×C22⋊C4C2×D1111yescharacteristic
195C2×C22⋊C4C2×D1111yescharacteristic
196C2×C22⋊C4C2×D1111yescharacteristic
197C2×C42—111no—
198C2×C42—111no—
199C2×C42—111no—
200C2×C42—111no—
201C2×C42C2×D1111yescharacteristic
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#95C2×D1111yescharacteristic
215#95C2×D1111yescharacteristic
216C2×C11—81no—
217C2×C11#52911yescharacteristic
218C2×C11#52911yescharacteristic
219C2×C11#53911yescharacteristic
220C2×C11#55211yescharacteristic
221C2×C11#55311yescharacteristic
222C2×C11#55611yescharacteristic
223C2×C11#55911yescharacteristic
224C24C22×D1111yescharacteristic
225C22×C4—111no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236C22×C4C22×D1111yescharacteristic
237C22×C4C22×D1111yescharacteristic
238C22×C4C22×D1111yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—222no—
241C4⋊C4—222no—
242C4⋊C4—222no—
243C4⋊C4—222no—
244C4⋊C4—222no—
245C4⋊C4—222no—
246C4⋊C4—222no—
247C4⋊C4—441no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—222no—
252C22⋊C4—222no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C42—22no—
256C42—222no—
257C42—441no—
258C42—441no—
259C42—441no—
260C11#259611yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D1111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
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—112no—
285C2×C4—112no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
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#433912yes—
309C2×C4#434112yes—
310C2×C4#434112yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#433911yescharacteristic
319C22C2×#434111yescharacteristic
320C22C2×#434111yescharacteristic
321C22#41×D1111yescharacteristic
322C22#41×D1111yescharacteristic
323C22#6704211yescharacteristic
324C22#6704311yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—222no—
332C4—222no—
333C4—441no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4—441no—
339C2—81no—
340C2#1062306111yescharacteristic
341C2#1062307211yescharacteristic
342C2#1062308811yescharacteristic
343C2#1062313111yescharacteristic
344C2#1062319611yescharacteristic
345C2#1062321211yescharacteristic
346C2#1062323311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC24×C11C23
hypercenter#388D11
hypocenterC11#2596
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #10622599C2semidirect
3. #10622598C2semidirect
10. C4×C4⋊Dic11C2semidirect
11. #10622546C2semidirect
12. #10622271C2semidirect
13. #10622267C2semidirect
14. #10622266C2semidirect
15. #10622262C2semidirect
260. C11#2596semidirect

Maximal subgroups

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

subgroupindex
C11×#3882
#106225992
#106225982
#106225662
#106225642
#106225622
#106225582
#106225572
C4×C4⋊Dic112
#106225462
#106222712
#106222672
#106222662
#106222622
#259611