Finite Group Databasebeta

← #13076837

Subgroups — #13076837

Order 1408.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#400C211yesmaximal, characteristic, complemented
2#10622607C211yesmaximal, characteristic, complemented
3#10622607C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622603C211yesmaximal, characteristic, complemented
6#10622290C211yesmaximal, characteristic, complemented
7#10622288C211yesmaximal, characteristic, complemented
8#10622288C211yesmaximal, characteristic, complemented
9#10622285C211yesmaximal, characteristic
10#10622285C211yesmaximal, characteristic
11#10622285C211yesmaximal, characteristic
12#10622283C211yesmaximal, characteristic, complemented
13#10622270C211yesmaximal, characteristic, complemented
14#10622270C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊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×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C23×D11C2311yescharacteristic
52C23×D11C2311yescharacteristic
53C22×C4×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
66C2×D44—41no—
67C2×D44—41no—
68C2×D44—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—41no—
74(C2×D11)⋊C4—41no—
75(C2×D11)⋊C4—41no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—22no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92C4×Dic11—41no—
93#2837—111nomaximal, Sylow
94C23×C11C2411yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—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×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—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×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11#4112yes—
148D44—44no—
149#400D1111yescharacteristic, complemented
150#399—111no—
151#399—111no—
152#398—111no—
153#398—111no—
154#397—111no—
155#397—111no—
156#396—111no—
157#396—111no—
158#394—111no—
159#394—111no—
160#394—111no—
161#389—111no—
162#388—111no—
163#388—111no—
164C22×C11C2×#4111yescharacteristic
165C22×C11H(5,𝔽2)11yescharacteristic
166C22×C11H(5,𝔽2)11yescharacteristic
167C22×C11H(5,𝔽2)11yescharacteristic
168C22×C11H(5,𝔽2)11yescharacteristic
169C22×C112−1+411yescharacteristic
170C22×C112−1+411yescharacteristic
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—22no—
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198C22×D4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4C2×D1111yescharacteristic
209C2×C4⋊C4C2×D1111yescharacteristic
210C2×C22⋊C4—111no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—111no—
218C2×C22⋊C4—111no—
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—111no—
222C2×C42—111no—
223#95—111no—
224#95—111no—
225#95—111no—
226#95—111no—
227#95—111no—
228#95C2×D1111yescharacteristic
229#95C2×D1111yescharacteristic
230#95C2×D1111yescharacteristic
231#95C2×D1111yescharacteristic
232#95C2×D1111yescharacteristic
233C2×C11#53911yescharacteristic
234C2×C11#54011yescharacteristic
235C2×C11#54211yescharacteristic
236C2×C11#56011yescharacteristic
237C2×C11#56211yescharacteristic
238C2×C11#56211yescharacteristic
239C2×C11#56311yescharacteristic
240D11—81no—
241D11—81no—
242C24—111no—
243C24—111no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—441no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255C22×C4C22×D1111yescharacteristic
256C22×C4C22×D1111yescharacteristic
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1111yescharacteristic
259C22×C4C22×D1111yescharacteristic
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—222no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—222no—
272C22⋊C4—222no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C22⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C42—441no—
284C11#283711yescharacteristic, complemented, Sylow
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—221no—
290C23—221no—
291C23—221no—
292C23—221no—
293C23—221no—
294C23—221no—
295C23—221no—
296C23—221no—
297C23—221no—
298C23—221no—
299C23C23×D1111yescharacteristic
300D4—444no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—112no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22#6703711yescharacteristic
355C22#6704011yescharacteristic
356C22#41×D1111yescharacteristic
357C22#6704211yescharacteristic
358C22#6704211yescharacteristic
359C22#6704211yescharacteristic
360C22#6704311yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—222no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4—441no—
374C2—881no—
375C2—881no—
376C2#1062317811yescharacteristic
377C2#1062319411yescharacteristic
378C2#1062321511yescharacteristic
379C2#1062322311yescharacteristic
380C2#1062323011yescharacteristic
381C2#1062324111yescharacteristic
382C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2837
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C11×#400C2semidirect
2. #10622607C2semidirect
3. #10622607C2semidirect
4. #10622605C2semidirect
5. #10622603C2semidirect
6. #10622290C2semidirect
7. #10622288C2semidirect
8. #10622288C2semidirect
12. #10622283C2semidirect
13. #10622270C2semidirect
14. #10622270C2semidirect
15. #10622260C2semidirect
149. #400D11semidirect
284. C11#2837semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106226072
#106226052
#106226032
#106222902
#106222882
#106222852
#106222832
#106222702
#106222602
#283711