Finite Group Databasebeta

← #13071748

Subgroups — #13071748

Order 1408.

552 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C211yesmaximal, characteristic
2C11×#387C211yesmaximal, characteristic, complemented
3#10622601C211yesmaximal, characteristic
4#10622591C211yesmaximal, characteristic, complemented
5C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#10622283C211yesmaximal, characteristic, complemented
9#10622283C211yesmaximal, characteristic, complemented
10#10622282C211yesmaximal, characteristic, complemented
11#10622282C211yesmaximal, characteristic, complemented
12#10622279C211yesmaximal, characteristic, complemented
13#10622279C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic
15#10622262C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×C4×Dic11C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66947C418yescomplemented
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C23×D11C2311yescharacteristic
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
67C2×D44—41no—
68C2×D44—41no—
69C2×D44C2×C414yes—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11C2×C414yescomplemented
76C11×C4⋊C4—41no—
77C11×C4⋊C4C2×C414yescomplemented
78C42×C11—41no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—22no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4C2×C414yes—
87(C2×D11)⋊C4C2×C414yes—
88(C2×D11)⋊C4C2×C414yescomplemented
89C4⋊Dic11—22no—
90Dic11⋊C4—22no—
91Dic11⋊C4C2×C414yescomplemented
92C4×Dic11—22no—
93C4×Dic11—22no—
94C4×Dic11—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98#2374—111nomaximal, Sylow
99C23×C11C2411yescharacteristic
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—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11C22×C412yes—
113C22×D11C22×C412yes—
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×C4×C11—21no—
131C2×C4×C11C22×C412yes—
132C2×C4×C11C22×C412yes—
133C2×C4×C11C22×C412yes—
134C2×C4×C11#4112yes—
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—21no—
148C2×Dic11C22×C412yes—
149C2×Dic11C22×C412yes—
150C2×Dic11#4112yes—
151C2×Dic11#4112yes—
152C2×Dic11#4112yes—
153D44—44no—
154C4×D11—44no—
155C4×D11—44no—
156C2×#123—111no—
157#390—111no—
158#388—111no—
159#388—111no—
160#388—111no—
161#388—111no—
162#387—111no—
163#387D1111yescharacteristic, complemented
164#386—111no—
165C4×C4⋊C4—111no—
166C4×C4⋊C4—111no—
167C4×C22⋊C4—111no—
168C4×C22⋊C4—111no—
169C4×C22⋊C4—111no—
170C4×C22⋊C4—111no—
171C22×C11C23×C411yescharacteristic
172C22×C11C2×#4111yescharacteristic
173C22×C11C2×#4111yescharacteristic
174C22×C11C2×#4111yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11H(5,𝔽2)11yescharacteristic
177C22×C11H(5,𝔽2)11yescharacteristic
178C2×D11—22no—
179C2×D11—22no—
180C2×D11—22no—
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—22no—
203Dic11—22no—
204Dic11—41no—
205C22×D4—111no—
206C23×C4—111no—
207C23×C4—111no—
208#123—118no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4C2×D1111yescharacteristic
213C2×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42—111no—
228C2×C42—111no—
229C2×C42—111no—
230C2×C42C2×D1111yescharacteristic
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95C2×D1111yescharacteristic
238#95C2×D1111yescharacteristic
239#95C2×D1111yescharacteristic
240#95C2×D1111yescharacteristic
241C2×C11C4×#4111yescharacteristic
242C2×C11C4×#4111yescharacteristic
243C2×C11#51811yescharacteristic
244C2×C11#55111yescharacteristic
245C2×C11#55311yescharacteristic
246C2×C11#55311yescharacteristic
247C2×C11#55911yescharacteristic
248D11—42no—
249D11—42no—
250C24—111no—
251C24—111no—
252C2×D4—114no—
253C2×D4—441no—
254C2×D4—441no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—114no—
261C22×C4—111no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4C22×D1111yescharacteristic
268C22×C4C22×D1111yescharacteristic
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—114no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4C4×D1114yescomplemented
279C22⋊C4—114no—
280C22⋊C4—114no—
281C22⋊C4—114no—
282C22⋊C4—222no—
283C22⋊C4—222no—
284C22⋊C4—222no—
285C22⋊C4—222no—
286C22⋊C4—222no—
287C22⋊C4—222no—
288C22⋊C4—441no—
289C42—41no—
290C42—222no—
291C42—222no—
292C42—441no—
293C42—441no—
294C42—441no—
295C42—441no—
296C11#237411yescharacteristic, complemented, Sylow
297C23—112no—
298C23—112no—
299C23—221no—
300C23—221no—
301C23—221no—
302C23—221no—
303C23—221no—
304C23—221no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—221no—
311C23C23×D1111yescharacteristic
312D4—444no—
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—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—112no—
333C2×C4—112no—
334C2×C4—112no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—444no—
349C2×C4—444no—
350C2×C4C2×C4×D1112yes—
351C2×C4C2×C4×D1112yes—
352C2×C4C2×C4×D1112yes—
353C2×C4#434312yes—
354C22—222no—
355C22—222no—
356C22—222no—
357C22—222no—
358C22—222no—
359C22—222no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22C22×C4×D1111yescharacteristic
369C22#6703711yescharacteristic
370C22C2×#434311yescharacteristic
371C22#41×D1111yescharacteristic
372C22#41×D1111yescharacteristic
373C22#41×D1111yescharacteristic
374C22#6704211yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—222no—
383C4—222no—
384C4—222no—
385C4—222no—
386C4—222no—
387C4—441no—
388C2—442no—
389C2—442no—
390C2#1062305311yescharacteristic
391C2#1062307611yescharacteristic
392C2C4×#434311yescharacteristic
393C2#1062316811yescharacteristic
394C2#1062319511yescharacteristic
395C2#1062322611yescharacteristic
396C2#1062324011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#387C2
socle, cosocleC23×C11C24
prime radicalC22×D44C22
hypercenter#387D11
hypocenterC11#2374
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C11×#387C2semidirect
4. #10622591C2semidirect
5. C4⋊C4×Dic11C2semidirect
6. C4×(C2×D11)⋊C4C2semidirect
7. C4×(C2×D11)⋊C4C2semidirect
8. #10622283C2semidirect
9. #10622283C2semidirect
10. #10622282C2semidirect
11. #10622282C2semidirect
12. #10622279C2semidirect
13. #10622279C2semidirect
15. #10622262C2semidirect
41. #66947C4semidirect
75. C2×C4×D11C2×C4semidirect
77. C11×C4⋊C4C2×C4semidirect
88. (C2×D11)⋊C4C2×C4semidirect
91. Dic11⋊C4C2×C4semidirect
163. #387D11semidirect
278. C4⋊C4C4×D11semidirect
296. C11#2374semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C11×#3872
#106226012
#106225912
C4⋊C4×Dic112
C4×(C2×D11)⋊C42
#106222832
#106222822
#106222792
#106222782
#106222622
#237411