Finite Group Databasebeta

← #14821973

Subgroups — #14821973

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072984C211yesmaximal, characteristic, complemented
2#13071653C211yesmaximal, characteristic
3#13069935C211yesmaximal, characteristic, complemented
4#13069800C211yesmaximal, characteristic
5#13069751C211yesmaximal, characteristic, complemented
6#13069622C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069291C211yesmaximal, characteristic, complemented
9#13069256C211yesmaximal, characteristic, complemented
10#13069220C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068927C211yesmaximal, characteristic, complemented
13#13068709C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622603—21no—
31#10622601—21no—
32#10622601C2211yescharacteristic
33#10622600C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622587C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40#10622553—21no—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42#10622542—21no—
43#10622542C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622286—21no—
46#10622279—21no—
47#10622278—21no—
48#10622272—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×#4314—22no—
93C2×#4314—41no—
94C2×#4314—41no—
95#66950—22no—
96#66950—41no—
97#66948—22no—
98#66948—22no—
99#66945—22no—
100#66945—41no—
101#66941—22no—
102#66941—41no—
103C4×D44—22no—
104C4×D44—41no—
105C11×#107—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116#66885—41no—
117(C2×D11)⋊C8—41no—
118(C2×D11)⋊C8—41no—
119#66880—22no—
120Dic11⋊C8—41no—
121#66874—22no—
122#66874—41no—
123#66873—22no—
124#66873—22no—
125C4×C11⋊C8—41no—
126#26731—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—24no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—81no—
149C2×D44—81no—
150C2×D44#4112yes—
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—42no—
158C2×C4×D11—42no—
159C2×C4×D11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
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—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4#4112yes—
183C11×C4⋊C4#4112yes—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—81no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—81no—
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#4314—44no—
213#2492—111no—
214#2363—111no—
215#2055—111no—
216#2033—111no—
217#2023—111no—
218#2000—111no—
219#1988—111no—
220#1933—111no—
221#1928—111no—
222#1923—111no—
223#1921D1111yescharacteristic, complemented
224#1877—111no—
225#1873—111no—
226#1825—111no—
227C4×#102—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
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#13712yes—
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11#13512yes—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289D44—84no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—84no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—84no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C2×C4⋊Q8—111no—
306C2×C22⋊Q8—111no—
307C2×#121—111no—
308C2×C4×D4—111no—
309C2×#117—111no—
310C2×#107C2×D1111yescharacteristic
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×C4×C8—111no—
321#400—221no—
322#393—221no—
323#391—111no—
324#391—111no—
325#391—221no—
326#390—111no—
327#390—221no—
328#389C2×D1111yescharacteristic
329#388—221no—
330#388—221no—
331#386—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4C2×D1111yescharacteristic
335C4×C22⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11#52511yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—42no—
357C2×D11—41no—
358C2×D11—42no—
359C2×D11—41no—
360C2×D11—42no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C4×C11—22no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55511yescharacteristic
377C4×C11#55911yescharacteristic
378Dic11—22no—
379Dic11—41no—
380Dic11—41no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—111no—
385C22×Q8—221no—
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—111no—
389C23×C4—221no—
390C2×SD16—222no—
391C2×SD16—441no—
392C2×SD16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—222no—
398C4⋊Q8—441no—
399C22⋊Q8—222no—
400C22⋊Q8—441no—
401#121—222no—
402#121—222no—
403C4×D4—222no—
404C4×D4—441no—
405#117—222no—
406#117—441no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—111no—
417C2×C22⋊C4—111no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—21no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430#107—22no—
431C4⋊C8—441no—
432#103—222no—
433#103—222no—
434#103—441no—
435#102—222no—
436#102—222no—
437#102—441no—
438C22⋊C8—441no—
439C22⋊C8—441no—
440C4×C8—441no—
441#95—21no—
442#95—21no—
443#95—111no—
444#95—111no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11#245911yescharacteristic
452C2×C11#310711yescharacteristic
453C2×C11#311811yescharacteristic
454C2×C11#329711yescharacteristic
455C2×C11#330411yescharacteristic
456C2×C11#331411yescharacteristic
457C2×C11#332911yescharacteristic
458D11—81no—
459D11—82no—
460C24—111no—
461C24—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—442no—
469C2×Q8—442no—
470C2×Q8—881no—
471C2×D4—112no—
472C2×D4—224no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—881no—
479C2×D4—881no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502SD16—444no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—81no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4#433912yes—
529C4⋊C4#434312yes—
530C22⋊C4—222no—
531C22⋊C4—224no—
532C22⋊C4—222no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C22⋊C4—881no—
539C42—21no—
540C42—21no—
541C42—81no—
542C42—221no—
543C42—221no—
544C42—442no—
545C42—881no—
546C11#2673111yescharacteristic, complemented, Sylow
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—222no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C2×D4×D1111yescharacteristic
562Q8—441no—
563Q8—441no—
564Q8—441no—
565Q8—441no—
566Q8—884no—
567D4—222no—
568D4—222no—
569D4—441no—
570D4—441no—
571D4—884no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
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—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—884no—
612C2×C4#6697112yes—
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×#434311yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#6704211yescharacteristic
618C2×C4#6704211yescharacteristic
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C22—441no—
624C22—442no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—442no—
630C22—441no—
631C22—442no—
632C22—441no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22#1062307811yescharacteristic
638C22#1062316111yescharacteristic
639C22#1062318511yescharacteristic
640C22C2×#6697111yescharacteristic
641C22D11×#13511yescharacteristic
642C22#1062330511yescharacteristic
643C22#1062330611yescharacteristic
644C4—22no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—222no—
651C4—441no—
652C4—442no—
653C4—441no—
654C4—881no—
655C4—881no—
656C4#1062306311yescharacteristic
657C4#1062311611yescharacteristic
658C4#1062322211yescharacteristic
659C4#1062323511yescharacteristic
660C2—881no—
661C2—882no—
662C2#1307255711yescharacteristic
663C2#1307868511yescharacteristic
664C2#1307879811yescharacteristic
665C2#1308046311yescharacteristic
666C2#1308055311yescharacteristic
667C2#1308069511yescharacteristic
668C2#1308090711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1921D11
hypocenterC11#26731
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #13072984C2semidirect
3. #13069935C2semidirect
5. #13069751C2semidirect
7. #13069566C2semidirect
8. #13069291C2semidirect
9. #13069256C2semidirect
10. #13069220C2semidirect
11. #13068949C2semidirect
12. #13068927C2semidirect
13. #13068709C2semidirect
14. C4×#66873C2semidirect
15. C11×#1921C2semidirect
223. #1921D11semidirect
546. C11#26731semidirect

Maximal subgroups

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

subgroupindex
#130729842
#130716532
#130699352
#130698002
#130697512
#130696222
#130695662
#130692912
#130692562
#130692202
#130689492
#130689272
#130687092
C4×#668732
C11×#19212
#2673111