Finite Group Databasebeta

← #14764646

Subgroups — #14764646

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071062C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic
3#13069408C211yesmaximal, characteristic
4#13069336C211yesmaximal, characteristic, complemented
5#13069333C211yesmaximal, characteristic, complemented
6#13069231C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13069222C211yesmaximal, characteristic, complemented
9#13068685C211yesmaximal, characteristic, complemented
10#13068683C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068593C211yesmaximal, characteristic, complemented
13#13068474C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622569C411yescharacteristic
37#10622569C411yescharacteristic
38#10622558C411yescharacteristic
39#10622558C411yescharacteristic
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622545C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622281C411yescharacteristic
46#10622281C411yescharacteristic
47#10622268C411yescharacteristic
48#10622268C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80#66979—41no—
81#66979—41no—
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C42×D11—41no—
97C42×D11—41no—
98C11×C4⋊C8—41no—
99C11×C22⋊C8—41no—
100C11×C22⋊C8—41no—
101C4×C8×C11—41no—
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C22⋊(C11⋊C8)—41no—
113C22⋊(C11⋊C8)—41no—
114(C2×D11)⋊C8—41no—
115(C2×D11)⋊C8—41no—
116(C2×D11)⋊C8—41no—
117(C2×D11)⋊C8—41no—
118#66879—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123C8×Dic11—22no—
124C4⋊(C11⋊C8)—41no—
125#66867—41no—
126#22017—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—41no—
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—41no—
187C4⋊Dic11—41no—
188C4⋊Dic11—41no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—41no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—41no—
197C4×Dic11—41no—
198C4×Dic11#4112yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212#2290—111no—
213#1955—111no—
214#1954—111no—
215#1940—111no—
216#1939—111no—
217#1924—111no—
218#1924—111no—
219#1923—111no—
220#1923D1111yescharacteristic, complemented
221#1818—111no—
222#1817—111no—
223#1798—111no—
224#1797—111no—
225#1768—111no—
226#1746—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11C23×C411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11#13112yes—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11#13112yes—
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C22⋊D11—44no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11#11712yes—
288C2×Dic11#11712yes—
289C4×D11—44no—
290C4×D11—44no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C2×C4×D4—111no—
304C2×#117—111no—
305C22×C42—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8C2×D1111yescharacteristic
319C2×C22⋊C8C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323C2×C4×C8C2×D1111yescharacteristic
324#388—111no—
325#388—111no—
326#387—111no—
327#387—111no—
328#386—111no—
329#386—111no—
330#385—111no—
331#385—111no—
332C4×C4⋊C4—111no—
333C4×C22⋊C4—111no—
334C4×C22⋊C4C2×D1111yescharacteristic
335#376—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336C2×D1111yescharacteristic
345#336C2×D1111yescharacteristic
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11C2×#11711yescharacteristic
354C22×C11#51811yescharacteristic
355C22×C11#52011yescharacteristic
356C22×C11C2×#13111yescharacteristic
357C22×C11C2×#13111yescharacteristic
358C22×C11#56811yescharacteristic
359C22×C11#56811yescharacteristic
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C4×C11—22no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11#54011yescharacteristic
373C4×C11#54011yescharacteristic
374C4×C11#54211yescharacteristic
375C4×C11#54211yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—41no—
379Dic11—41no—
380Dic11—41no—
381Dic11—41no—
382Dic11—41no—
383C22×D4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4×D4—222no—
397C4×D4—222no—
398#117—441no—
399#117—441no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4C4×D1111yescharacteristic
412C2×C22⋊C4C4×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—441no—
419C2×C42—441no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C4⋊C8—41no—
423C4⋊C8—222no—
424C4⋊C8—222no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C4⋊C8—441no—
428C22⋊C8—41no—
429C22⋊C8—41no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432C22⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436#97—222no—
437#97—441no—
438C4×C8—41no—
439C4×C8—222no—
440#95—111no—
441#95—111no—
442#95—111no—
443#95—111no—
444#95—111no—
445#95—111no—
446#95—111no—
447#95—111no—
448#95C4×D1111yescharacteristic
449#95C4×D1111yescharacteristic
450C2×C11—81no—
451C2×C11#231911yescharacteristic
452C2×C11#292411yescharacteristic
453C2×C11#292511yescharacteristic
454C2×C11#297711yescharacteristic
455C2×C11#297811yescharacteristic
456C2×C11#299211yescharacteristic
457C2×C11#299311yescharacteristic
458D11—42no—
459C24—111no—
460C24C2×C4×D1111yescharacteristic
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—441no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4C2×C4×D1111yescharacteristic
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4C2×C4×D1111yescharacteristic
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C22⋊C4—22no—
525C22⋊C4—41no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—441no—
530C22⋊C4—441no—
531C22⋊C4—441no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—112no—
537C42—112no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—441no—
543C42—441no—
544C11#2201711yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—112no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23C22×C4×D1111yescharacteristic
560D4—444no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—444no—
601C2×C4—444no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4#6695412yes—
607C2×C4#6703711yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—441no—
618C8—441no—
619C8—441no—
620C8—441no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22D11×#11711yescharacteristic
636C22#1062307611yescharacteristic
637C22#1062307711yescharacteristic
638C22C2×#6695411yescharacteristic
639C22#1062327611yescharacteristic
640C22D11×#13111yescharacteristic
641C22#1062328111yescharacteristic
642C4—22no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—222no—
648C4—222no—
649C4—441no—
650C4—441no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4#1062314611yescharacteristic
655C4#1062319411yescharacteristic
656C4#1062320011yescharacteristic
657C4#1062324111yescharacteristic
658C2—81no—
659C2—442no—
660C2#1307125711yescharacteristic
661C2#1307727211yescharacteristic
662C2#1307727711yescharacteristic
663C2#1307766911yescharacteristic
664C2#1307767311yescharacteristic
665C2#1307775111yescharacteristic
666C2#1307776611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1923C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1923D11
hypocenterC11#22017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
4. #13069336C2semidirect
5. #13069333C2semidirect
6. #13069231C2semidirect
7. #13069227C2semidirect
8. #13069222C2semidirect
9. #13068685C2semidirect
10. #13068683C2semidirect
11. #13068598C2semidirect
12. #13068593C2semidirect
13. #13068474C2semidirect
14. #13068366C2semidirect
15. C11×#1923C2semidirect
220. #1923D11semidirect
544. C11#22017semidirect

Maximal subgroups

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

subgroupindex
#130710622
#130694122
#130694082
#130693362
#130693332
#130692312
#130692272
#130692222
#130686852
#130686832
#130685982
#130685932
#130684742
#130683662
C11×#19232
#2201711