Finite Group Databasebeta

← #14764559

Subgroups — #14764559

Order 2816.

752 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#13071075C211yesmaximal, characteristic
2#13069232C211yesmaximal, characteristic, complemented
3#13069225C211yesmaximal, characteristic, complemented
4#13069177C211yesmaximal, characteristic, complemented
5#13069170C211yesmaximal, characteristic, complemented
6#13068910C211yesmaximal, characteristic
7#13068905C211yesmaximal, characteristic
8#13068797C211yesmaximal, characteristic, complemented
9#13068792C211yesmaximal, characteristic, complemented
10#13068758C211yesmaximal, characteristic, complemented
11#13068731C211yesmaximal, characteristic, complemented
12#13068687C211yesmaximal, characteristic, complemented
13#13068381C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622603C411yescharacteristic
35#10622603C411yescharacteristic
36#10622585C411yescharacteristic
37#10622585C411yescharacteristic
38#10622570C411yescharacteristic
39#10622570C411yescharacteristic
40#10622558C411yescharacteristic
41#10622558C411yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C42×Dic11C2211yescharacteristic
45C11×#336C2211yescharacteristic
46C11×#336C2211yescharacteristic
47#10622188C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117—41no—
67C11×#117—41no—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4313—22no—
101C2×#4313—41no—
102C2×#4313—41no—
103C2×C8×D11—22no—
104C2×C8×D11—41no—
105C2×C8×D11—41no—
106#66925—41no—
107#66925—41no—
108C11×C4⋊C8—41no—
109C11×C4⋊C8—41no—
110C11×C22⋊C8—41no—
111C11×C22⋊C8—41no—
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—22no—
122#66879—41no—
123Dic11⋊C8—41no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#22007—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—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11#4112yes—
156C2×C4×D11#4112yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—41no—
180(C2×D11)⋊C4—22no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185Dic11⋊C4—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—41no—
199C4×Dic11—41no—
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#4313—44no—
213C8×D11—44no—
214#2293—111no—
215#1924—111no—
216#1923—111no—
217#1917—111no—
218#1916—111no—
219#1870—111no—
220#1869—111no—
221#1851—111no—
222#1850—111no—
223#1839—111no—
224#1831—111no—
225#1818—111no—
226#1798D1111yescharacteristic, complemented
227#1750—111no—
228#1729—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11C23×C411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11#11712yes—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C22⋊D11—44no—
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—21no—
288C2×Dic11#11712yes—
289C2×Dic11#13112yes—
290C2×Dic11#13112yes—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×M16—111no—
304C23×C8—111no—
305C2×C4×D4—111no—
306C2×#117—111no—
307C2×#117C2×D1111yescharacteristic
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8C2×D1111yescharacteristic
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—111no—
319C2×C4×C8—111no—
320#390—111no—
321#390—111no—
322#389—111no—
323#389—111no—
324#388—111no—
325#388—111no—
326#388—111no—
327#388—111no—
328C4×C4⋊C4—111no—
329C4×C22⋊C4—111no—
330C4×C22⋊C4—111no—
331C43—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—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—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11#53811yescharacteristic
373C4×C11#53811yescharacteristic
374C4×C11#53911yescharacteristic
375C4×C11#53911yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—22no—
379Dic11—41no—
380Dic11—41no—
381Dic11—41no—
382Dic11—41no—
383C22×D4—111no—
384C23×C4—111no—
385C23×C4C22×D1111yescharacteristic
386C2×M16—222no—
387C2×M16—441no—
388C2×M16—441no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—222no—
394C22×C8—441no—
395C22×C8—441no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4×D4—222no—
401C4×D4—222no—
402#117—41no—
403#117—41no—
404#117—441no—
405#117—441no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4C4×D1111yescharacteristic
412C2×C4⋊C4C4×D1111yescharacteristic
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—111no—
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4C4×D1111yescharacteristic
422C2×C22⋊C4C4×D1111yescharacteristic
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432C4⋊C8—41no—
433C4⋊C8—41no—
434C4⋊C8—441no—
435C4⋊C8—441no—
436C22⋊C8—41no—
437C22⋊C8—41no—
438C22⋊C8—222no—
439C22⋊C8—222no—
440C22⋊C8—441no—
441C22⋊C8—441no—
442#97—441no—
443C4×C8—441no—
444#95—111no—
445#95—111no—
446#95—111no—
447#95—111no—
448#95—111no—
449#95—111no—
450C2×C11—81no—
451C2×C11#231811yescharacteristic
452C2×C11#292411yescharacteristic
453C2×C11#292511yescharacteristic
454C2×C11#298111yescharacteristic
455C2×C11#298111yescharacteristic
456C2×C11#299411yescharacteristic
457C2×C11#299511yescharacteristic
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—112no—
474C22×C4—112no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—444no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—441no—
520C4⋊C4—441no—
521C4⋊C4—441no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—441no—
529C22⋊C4—441no—
530C22⋊C4—441no—
531C22⋊C4—441no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—222no—
537C42—222no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—221no—
544C42—441no—
545C42—441no—
546C11#2200711yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—112no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23C22×C4×D1111yescharacteristic
562D4—444no—
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—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4#6703711yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6704011yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#41×D1111yescharacteristic
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—
635C22#1062301711yescharacteristic
636C22#1062303511yescharacteristic
637C22D11×#11711yescharacteristic
638C22D11×#13111yescharacteristic
639C22D11×#13111yescharacteristic
640C22#1062328111yescharacteristic
641C22#1062328111yescharacteristic
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—222no—
648C4—222no—
649C4—222no—
650C4—441no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4#1062314411yescharacteristic
655C4#1062314411yescharacteristic
656C4#1062316911yescharacteristic
657C4#1062316911yescharacteristic
658C2—81no—
659C2—442no—
660C2#1307125111yescharacteristic
661C2#1307727211yescharacteristic
662C2#1307727911yescharacteristic
663C2#1307768911yescharacteristic
664C2#1307768911yescharacteristic
665C2#1307777411yescharacteristic
666C2#1307778411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#22007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #13069232C2semidirect
3. #13069225C2semidirect
4. #13069177C2semidirect
5. #13069170C2semidirect
8. #13068797C2semidirect
9. #13068792C2semidirect
10. #13068758C2semidirect
11. #13068731C2semidirect
12. #13068687C2semidirect
13. #13068381C2semidirect
14. #13068311C2semidirect
15. C11×#1798C2semidirect
226. #1798D11semidirect
546. C11#22007semidirect

Maximal subgroups

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

subgroupindex
#130710752
#130692322
#130692252
#130691772
#130691702
#130689102
#130689052
#130687972
#130687922
#130687582
#130687312
#130686872
#130683812
#130683112
C11×#17982
#2200711