Finite Group Databasebeta

← #14764623

Subgroups — #14764623

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071079C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic
3#13069412C211yesmaximal, characteristic
4#13069338C211yesmaximal, characteristic, complemented
5#13069336C211yesmaximal, characteristic, complemented
6#13069231C211yesmaximal, characteristic, complemented
7#13069229C211yesmaximal, characteristic, complemented
8#13069227C211yesmaximal, characteristic, complemented
9#13068686C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068597C211yesmaximal, characteristic, complemented
13#13068470C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
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×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622570C411yescharacteristic
37#10622570C411yescharacteristic
38#10622557C411yescharacteristic
39#10622557C411yescharacteristic
40C4×(C2×D11)⋊C4C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C42×Dic11C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622283C411yescharacteristic
46#10622283C411yescharacteristic
47#10622260C411yescharacteristic
48#10622260C411yescharacteristic
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×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11C2×C411yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×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
100#66925—41no—
101#66925—41no—
102C11×C4⋊C8—41no—
103C11×C22⋊C8—41no—
104C11×C22⋊C8—41no—
105C11×#97—41no—
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—
119#66879—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124C4⋊(C11⋊C8)—41no—
125#66867—41no—
126#22015—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—41no—
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—21no—
156C2×C4×D11—21no—
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×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C22⋊Dic11—22no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185Dic11⋊C4—22no—
186Dic11⋊C4—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—41no—
195C4×Dic11—41no—
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#2293—111no—
213#1955—111no—
214#1955—111no—
215#1940—111no—
216#1940—111no—
217#1924—111no—
218#1924—111no—
219#1924—111no—
220#1924D1111yescharacteristic, complemented
221#1818—111no—
222#1818—111no—
223#1798—111no—
224#1798—111no—
225#1767—111no—
226#1745—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—21no—
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—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
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—41no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C8×C11—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C2×C4×D4—111no—
302C2×#117—111no—
303C2×#117—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
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×#97—111no—
320C2×#97—111no—
321C2×#97C2×D1111yescharacteristic
322#390—111no—
323#390—111no—
324#389—111no—
325#389—111no—
326#388—111no—
327#388—111no—
328#388—111no—
329#388—111no—
330C4×C4⋊C4—111no—
331C4×C22⋊C4—111no—
332C4×C22⋊C4C2×D1111yescharacteristic
333C43—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#336C2×D1111yescharacteristic
343#336C2×D1111yescharacteristic
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×#11711yescharacteristic
352C22×C11#51811yescharacteristic
353C22×C11#52011yescharacteristic
354C22×C11#56811yescharacteristic
355C22×C11#56811yescharacteristic
356C22×C11#56811yescharacteristic
357C22×C11#56811yescharacteristic
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11#54011yescharacteristic
371C4×C11#54011yescharacteristic
372C4×C11#54211yescharacteristic
373C4×C11#54211yescharacteristic
374Dic11—22no—
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—41no—
380Dic11—41no—
381C22×D4—111no—
382C23×C4—111no—
383C23×C4C22×D1111yescharacteristic
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×D4—222no—
393C4×D4—222no—
394#117—441no—
395#117—441no—
396#117—441no—
397#117—441no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
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⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4C4×D1111yescharacteristic
414C2×C22⋊C4C4×D1111yescharacteristic
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C4⋊C8—41no—
425C4⋊C8—222no—
426C4⋊C8—222no—
427C4⋊C8—441no—
428C4⋊C8—441no—
429C4⋊C8—441no—
430C22⋊C8—41no—
431C22⋊C8—41no—
432C22⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436C22⋊C8—441no—
437C22⋊C8—441no—
438#97—41no—
439#97—222no—
440#97—222no—
441#97—441no—
442#95—111no—
443#95—111no—
444#95—111no—
445#95—111no—
446#95C4×D1111yescharacteristic
447#95C4×D1111yescharacteristic
448C2×C11—81no—
449C2×C11#231911yescharacteristic
450C2×C11#292111yescharacteristic
451C2×C11#292311yescharacteristic
452C2×C11#298011yescharacteristic
453C2×C11#298011yescharacteristic
454C2×C11#299511yescharacteristic
455C2×C11#299511yescharacteristic
456D11—81no—
457C24—111no—
458C24C2×C4×D1111yescharacteristic
459C2×D4—222no—
460C2×D4—441no—
461C2×D4—441no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
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—221no—
500C2×C8—221no—
501C2×C8—221no—
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—
511C4⋊C4—222no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C4⋊C4—441no—
517C4⋊C4—441no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C22⋊C4—441no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—112no—
533C42—112no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—441no—
539C42—441no—
540C42—441no—
541C42—441no—
542C11#2201511yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23C22×C4×D1111yescharacteristic
558D4—444no—
559C2×C4—21no—
560C2×C4—21no—
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—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—221no—
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—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4#6703711yescharacteristic
604C2×C4#6703711yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C2×C4#6704211yescharacteristic
608C2×C4#6704311yescharacteristic
609C8—41no—
610C8—41no—
611C8—41no—
612C8—41no—
613C8—441no—
614C8—441no—
615C8—441no—
616C8—441no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22D11×#11711yescharacteristic
632C22#1062307611yescharacteristic
633C22#1062307711yescharacteristic
634C22#1062327611yescharacteristic
635C22#1062327611yescharacteristic
636C22#1062328111yescharacteristic
637C22#1062328111yescharacteristic
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—222no—
644C4—222no—
645C4—441no—
646C4—441no—
647C4—441no—
648C4—441no—
649C4—441no—
650C4#1062314611yescharacteristic
651C4#1062319411yescharacteristic
652C4#1062320011yescharacteristic
653C4#1062324111yescharacteristic
654C2—81no—
655C2—881no—
656C2#1307125711yescharacteristic
657C2#1307725011yescharacteristic
658C2#1307726211yescharacteristic
659C2#1307768411yescharacteristic
660C2#1307768411yescharacteristic
661C2#1307778011yescharacteristic
662C2#1307778711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#22015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
4. #13069338C2semidirect
5. #13069336C2semidirect
6. #13069231C2semidirect
7. #13069229C2semidirect
8. #13069227C2semidirect
9. #13068686C2semidirect
10. #13068685C2semidirect
11. #13068598C2semidirect
12. #13068597C2semidirect
13. #13068470C2semidirect
14. #13068363C2semidirect
15. C11×#1924C2semidirect
220. #1924D11semidirect
542. C11#22015semidirect

Maximal subgroups

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

subgroupindex
#130710792
#130694122
#130693382
#130693362
#130692312
#130692292
#130692272
#130686862
#130686852
#130685982
#130685972
#130684702
#130683632
C11×#19242
#2201511