Finite Group Databasebeta

← #14764635

Subgroups — #14764635

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#13071061C211yesmaximal, characteristic
2#13069411C211yesmaximal, characteristic
3#13069339C211yesmaximal, characteristic, complemented
4#13069332C211yesmaximal, characteristic, complemented
5#13069232C211yesmaximal, characteristic, complemented
6#13069226C211yesmaximal, characteristic, complemented
7#13069225C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13068685C211yesmaximal, characteristic, complemented
10#13068682C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068594C211yesmaximal, characteristic, complemented
13#13068475C211yesmaximal, characteristic, complemented
14#13068369C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25#10622833C411yescharacteristic
26#10622833C411yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622594C411yescharacteristic
40#10622594C411yescharacteristic
41#10622564C411yescharacteristic
42#10622564C411yescharacteristic
43#10622563C411yescharacteristic
44#10622563C411yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622545C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2×C411yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80#66979—41no—
81#66979—41no—
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×C4×Dic11—41no—
87C2×C4×Dic11—41no—
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×C4⋊C8—22no—
99C11×C22⋊C8—41no—
100C11×C22⋊C8—41no—
101C11×C22⋊C8—41no—
102C11×C22⋊C8—41no—
103C11×#97—22no—
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C22⋊(C11⋊C8)—41no—
115C22⋊(C11⋊C8)—41no—
116C22⋊(C11⋊C8)—41no—
117C22⋊(C11⋊C8)—41no—
118#66879—41no—
119Dic11⋊C8—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123C8×Dic11—41no—
124C4⋊(C11⋊C8)—22no—
125C4×C11⋊C8—22no—
126#22016—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C24×C11C22×C411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
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×C4⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11#4112yes—
179C42×C11#4112yes—
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C4⋊Dic11—22no—
187C4⋊Dic11—41no—
188C4⋊Dic11—41no—
189C4⋊Dic11—41no—
190C4×Dic11—21no—
191C4×Dic11—21no—
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#2290—111no—
213#1955D1111yescharacteristic
214#1954—111no—
215#1940—111no—
216#1939—111no—
217#1924—111no—
218#1924—111no—
219#1923—111no—
220#1923—111no—
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×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#13112yes—
241C23×C11C23×C411yescharacteristic
242D4×C11—44no—
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—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11#11712yes—
262C2×C4×C11#11712yes—
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
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—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—44no—
293C2×Dic11—44no—
294C2×Dic11#13112yes—
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×D4C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×C22⋊C8C2×D1111yescharacteristic
319C2×C22⋊C8C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97C2×D1111yescharacteristic
322C2×C4×C8—111no—
323C2×C4×C8—111no—
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⋊C4—111no—
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#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#11711yescharacteristic
361C22×C11#51811yescharacteristic
362C22×C11#52011yescharacteristic
363C22×C11C2×#13111yescharacteristic
364C22×C11C2×#13111yescharacteristic
365C22×C11#56811yescharacteristic
366C22×C11#56811yescharacteristic
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11#54011yescharacteristic
372C4×C11#54011yescharacteristic
373C4×C11#54211yescharacteristic
374C4×C11#54211yescharacteristic
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—41no—
380Dic11—41no—
381Dic11—41no—
382Dic11—41no—
383C22×D4C4×D1111yescharacteristic
384C23×C4—111no—
385C23×C4—111no—
386C23×C4C22×D1111yescharacteristic
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—22no—
397C4×D4—22no—
398#117—441no—
399#117—441no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4C4×D1111yescharacteristic
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—111no—
419C2×C42—441no—
420C2×C42—441no—
421C2×C42C22×D1111yescharacteristic
422C4⋊C8—22no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C4⋊C8—441no—
428C22⋊C8—41no—
429C22⋊C8—41no—
430C22⋊C8—41no—
431C22⋊C8—41no—
432C22⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436#97—22no—
437#97—441no—
438C4×C8—222no—
439C4×C8—441no—
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#95—111no—
449#95—111no—
450C2×C11—42no—
451C2×C11—81no—
452C2×C11#231911yescharacteristic
453C2×C11#292411yescharacteristic
454C2×C11#292511yescharacteristic
455C2×C11#297611yescharacteristic
456C2×C11#297611yescharacteristic
457C2×C11#299411yescharacteristic
458C2×C11#299511yescharacteristic
459C24C2×C4×D1111yescharacteristic
460C24C2×C4×D1111yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4—441no—
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—22no—
520C4⋊C4—222no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—441no—
529C22⋊C4—441no—
530C22⋊C4—441no—
531C22⋊C4—441no—
532C42—221no—
533C42—221no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—441no—
541C42—441no—
542C42#434112yes—
543C42#434112yes—
544C11#2201611yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23#6696012yes—
559C23C22×C4×D1111yescharacteristic
560D4—44no—
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—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
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—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4#6693012yes—
606C2×C4#6693012yes—
607C2×C4C2×#434111yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—441no—
618C8—441no—
619C8—441no—
620C8—441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#6693011yescharacteristic
636C22#1062307611yescharacteristic
637C22#1062307711yescharacteristic
638C22C2×#6696011yescharacteristic
639C22#1062327611yescharacteristic
640C22D11×#13111yescharacteristic
641C22#1062328111yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—222no—
647C4—441no—
648C4—441no—
649C4—441no—
650C4—441no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4#1062313411yescharacteristic
655C4#1062315011yescharacteristic
656C4#1062321311yescharacteristic
657C4#1062325011yescharacteristic
658C2—42no—
659C2—81no—
660C2#1307125311yescharacteristic
661C2#1307727611yescharacteristic
662C2#1307727811yescharacteristic
663C2#1307766311yescharacteristic
664C2#1307766511yescharacteristic
665C2#1307776911yescharacteristic
666C2#1307778711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#22016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
3. #13069339C2semidirect
4. #13069332C2semidirect
5. #13069232C2semidirect
6. #13069226C2semidirect
7. #13069225C2semidirect
8. #13069219C2semidirect
9. #13068685C2semidirect
10. #13068682C2semidirect
11. #13068598C2semidirect
12. #13068594C2semidirect
13. #13068475C2semidirect
14. #13068369C2semidirect
544. C11#22016semidirect

Maximal subgroups

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

subgroupindex
#130710612
#130694112
#130693392
#130693322
#130692322
#130692262
#130692252
#130692192
#130686852
#130686822
#130685982
#130685942
#130684752
#130683692
C11×#19552
#2201611