Finite Group Databasebeta

← #14764651

Subgroups — #14764651

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#13071060C211yesmaximal, characteristic
2#13069414C211yesmaximal, characteristic
3#13069410C211yesmaximal, characteristic
4#13069339C211yesmaximal, characteristic, complemented
5#13069334C211yesmaximal, characteristic, complemented
6#13069227C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13069220C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13068686C211yesmaximal, characteristic, complemented
11#13068683C211yesmaximal, characteristic, complemented
12#13068599C211yesmaximal, characteristic, complemented
13#13068595C211yesmaximal, characteristic, complemented
14#13068473C211yesmaximal, characteristic, complemented
15C11×#1746C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C4×(C2×D11)⋊C4C2211yescharacteristic
35C4×(C2×D11)⋊C4C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622283C411yescharacteristic
42#10622283C411yescharacteristic
43#10622281C411yescharacteristic
44#10622281C411yescharacteristic
45#10622278C411yescharacteristic
46#10622278C411yescharacteristic
47#10622266C411yescharacteristic
48#10622266C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C4×D44—22no—
93C4×D44—22no—
94#66925—41no—
95#66925—41no—
96C42×D11—41no—
97C42×D11—41no—
98C11×#97—22no—
99C4×C8×C11—22no—
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110(C2×D11)⋊C8—41no—
111(C2×D11)⋊C8—41no—
112(C2×D11)⋊C8—41no—
113(C2×D11)⋊C8—41no—
114(C2×D11)⋊C8—41no—
115(C2×D11)⋊C8—41no—
116(C2×D11)⋊C8—41no—
117(C2×D11)⋊C8—41no—
118Dic11⋊C8—41no—
119Dic11⋊C8—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)—22no—
124#66867—41no—
125C4×C11⋊C8—41no—
126#22017—111nomaximal, Sylow
127C23×D11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—41no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
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×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—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11#4112yes—
180C42×C11#4112yes—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
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#1955—111no—
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#1746D1111yescharacteristic, complemented
227C23×C11C23×C411yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11#11712yes—
259C2×C4×C11#11712yes—
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
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#13112yes—
284D44—44no—
285C4×D11—44no—
286C4×D11—44no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
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⋊C8—111no—
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⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×#97—111no—
321C2×#97C2×D1111yescharacteristic
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⋊C4—111no—
335#376C2×D1111yescharacteristic
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336C2×D1111yescharacteristic
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345#336C2×D1111yescharacteristic
346C22×C11C2×#11711yescharacteristic
347C22×C11#51811yescharacteristic
348C22×C11#52011yescharacteristic
349C22×C11C2×#13111yescharacteristic
350C22×C11C2×#13111yescharacteristic
351C22×C11#56811yescharacteristic
352C22×C11#56811yescharacteristic
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11#54011yescharacteristic
374C4×C11#54011yescharacteristic
375C4×C11#54211yescharacteristic
376C4×C11#54211yescharacteristic
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×C4—111no—
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⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—441no—
418C2×C42—441no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C4⋊C8—222no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C4⋊C8—441no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432C22⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436#97—22no—
437#97—441no—
438C4×C8—22no—
439C4×C8—441no—
440#95—111no—
441#95—111no—
442#95—111no—
443#95—111no—
444#95—111no—
445#95—111no—
446#95C4×D1111yescharacteristic
447#95C4×D1111yescharacteristic
448#95C4×D1111yescharacteristic
449#95C4×D1111yescharacteristic
450C2×C11#231911yescharacteristic
451C2×C11#292411yescharacteristic
452C2×C11#292511yescharacteristic
453C2×C11#297711yescharacteristic
454C2×C11#297811yescharacteristic
455C2×C11#299211yescharacteristic
456C2×C11#299311yescharacteristic
457D11—42no—
458D11—81no—
459C24—111no—
460C24—111no—
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—441no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—441no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4C2×C4×D1111yescharacteristic
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—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—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—441no—
541C42—441no—
542C42#433912yes—
543C42#433912yes—
544C11#2201711yescharacteristic, complemented, Sylow
545C23—112no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
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—21no—
576C2×C4—21no—
577C2×C4—112no—
578C2×C4—221no—
579C2×C4—221no—
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—444no—
596C2×C4—444no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4#6692512yes—
606C2×C4#6692512yes—
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4#6704211yescharacteristic
610C2×C4#6704211yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—441no—
618C8—441no—
619C8—441no—
620C8—441no—
621C22—222no—
622C22—222no—
623C22—222no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22C2×#6692511yescharacteristic
636C22#1062305211yescharacteristic
637C22#1062305411yescharacteristic
638C22D11×#13111yescharacteristic
639C22D11×#13111yescharacteristic
640C22#1062328111yescharacteristic
641C22#1062328111yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—222no—
649C4—441no—
650C4—441no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4#1062306511yescharacteristic
655C4#1062306511yescharacteristic
656C4#1062306611yescharacteristic
657C4#1062306611yescharacteristic
658C2—442no—
659C2—881no—
660C2#1307126011yescharacteristic
661C2#1307727111yescharacteristic
662C2#1307728011yescharacteristic
663C2#1307767111yescharacteristic
664C2#1307767711yescharacteristic
665C2#1307775011yescharacteristic
666C2#1307775911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1746C2
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1746

Complements

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

NH ≅ G/Ntype
4. #13069339C2semidirect
5. #13069334C2semidirect
6. #13069227C2semidirect
7. #13069227C2semidirect
8. #13069220C2semidirect
9. #13069220C2semidirect
10. #13068686C2semidirect
11. #13068683C2semidirect
12. #13068599C2semidirect
13. #13068595C2semidirect
14. #13068473C2semidirect
15. C11×#1746C2semidirect
226. #1746D11semidirect
544. C11#22017semidirect

Maximal subgroups

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

subgroupindex
#130710602
#130694142
#130694102
#130693392
#130693342
#130692272
#130692202
#130686862
#130686832
#130685992
#130685952
#130684732
C11×#17462
#2201711