Finite Group Databasebeta

← #14761622

Subgroups — #14761622

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078400C211yesmaximal, characteristic
2#13077555C211yesmaximal, characteristic, complemented
3#13077042C211yesmaximal, characteristic
4#13069558C211yesmaximal, characteristic, complemented
5#13069388C211yesmaximal, characteristic, complemented
6#13069216C211yesmaximal, characteristic, complemented
7#13069212C211yesmaximal, characteristic, complemented
8#13068891C211yesmaximal, characteristic
9#13068634C211yesmaximal, characteristic
10#13068503C211yesmaximal, characteristic, complemented
11#13068494C211yesmaximal, characteristic, complemented
12#13068487C211yesmaximal, characteristic, complemented
13#13068463C211yesmaximal, characteristic
14#13068454C211yesmaximal, characteristic
15C11×#1866C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17#41×Dic11C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623048C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C11×#424C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#416C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25#10622846C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622735—21no—
28#10622735C2211yescharacteristic
29#10622735C2211yescharacteristic
30#10622731C2211yescharacteristic
31M16×Dic11—21no—
32M16×Dic11C2211yescharacteristic
33#10622719C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622714—21no—
36#10622714C2211yescharacteristic
37C2×#66879—21no—
38C2×#66879C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41#10622611C2211yescharacteristic
42#10622610C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622444—21no—
46#10622444—21no—
47#10622441—21no—
48#10622441—21no—
49#10622412C411yescharacteristic, complemented
50#10622409C411yescharacteristic, complemented
51#10622407C411yescharacteristic, complemented
52#10622404C411yescharacteristic, complemented
53#10622379C411yescharacteristic, complemented
54#10622376C411yescharacteristic, complemented
55#10622374C411yescharacteristic, complemented
56#10622372C411yescharacteristic, complemented
57C11×#339C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622190C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131—22no—
70C2×C11×M16—21no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#67001—22no—
79#67001Q814yescomplemented
80Q8×Dic11C2×C411yescharacteristic
81Q8×Dic11C2×C411yescharacteristic
82D4×Dic11—21no—
83D4×Dic11—21no—
84D4×Dic11C2×C411yescharacteristic
85D4×Dic11C2×C411yescharacteristic
86#66979—21no—
87#66979C2311yescharacteristic
88#66979C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—21no—
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66943C2×C411yescharacteristic
100#66943C2×C411yescharacteristic
101#66941C2×C411yescharacteristic
102#66941C2×C411yescharacteristic
103#66931—21no—
104#66931—21no—
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×#108—22no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×#104—22no—
111C11×#103C2×C411yescharacteristic
112C11×#103C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×#102C2×C411yescharacteristic
115#66901—22no—
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120C11⋊#95—21no—
121#66886—22no—
122#66882C2×C411yescharacteristic
123#66882C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66881C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128#66879—21no—
129#66879—21no—
130#66879—22no—
131#66879D411yescharacteristic
132#66879D411yescharacteristic
133#66879D411yescharacteristic
134#66879D411yescharacteristic
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138Dic11⋊C8—21no—
139Dic11⋊C8C2×C411yescharacteristic
140Dic11⋊C8C2×C411yescharacteristic
141Dic11⋊C8C2×C411yescharacteristic
142Dic11⋊C8C2×C411yescharacteristic
143C8×Dic11—21no—
144C8×Dic11—21no—
145C8×Dic11—21no—
146C8×Dic11—21no—
147#66872C2×C411yescharacteristic
148#66872C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150#66871C2×C411yescharacteristic
151#66867—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—22no—
154#21629—111nomaximal, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11C22×C411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11C22×C411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11#4111yescharacteristic
169C22×Dic11#4111yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—24no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16#4112yes—
177C2×C8×C11—24no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C411yescharacteristic
185C2×C8×C11C22×C411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—21no—
195C22⋊Dic11—21no—
196C22⋊Dic11—21no—
197C22⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209Dic11⋊C4—21no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11C22×C411yescharacteristic
218C4×Dic11C22×C411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221#4318—24no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318C2×Q812yes—
226C2×C11⋊C8—24no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C22×C411yescharacteristic
232C2×C11⋊C8C22×C411yescharacteristic
233C2×C11⋊C8C2×D411yescharacteristic
234C2×C11⋊C8C2×D411yescharacteristic
235C2×C11⋊C8C2×Q812yes—
236C2×C11⋊C8#4112yes—
237#3076—111no—
238#2961—111no—
239#2875—111no—
240#1986—111no—
241#1950—111no—
242#1922—111no—
243#1922—111no—
244#1866—111no—
245#1866D1111yescharacteristic
246#1806—111no—
247#1773—111no—
248#1772—111no—
249#1771—111no—
250#1765—111no—
251#1764—111no—
252C23×C11—21no—
253C23×C11C2×#4111yescharacteristic
254Q8×C11—21no—
255Q8×C11C4×Q812yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—21no—
259D4×C11C4×Q812yes—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—81no—
284C2×Dic11—81no—
285C2×Dic11C4×D411yescharacteristic
286C2×Dic11C4×D411yescharacteristic
287C2×Dic11C4×D411yescharacteristic
288C2×Dic11C4×D411yescharacteristic
289Dic22—81no—
290Dic22—81no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—22no—
295C8×C11—21no—
296C8×C11—41no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C11⋊C8C22⋊Q812yes—
302C11⋊C8C22⋊Q812yes—
303C2×#131—111no—
304C2×#131C2×D1111yescharacteristic
305#533—111no—
306C4×#41—111no—
307#479—111no—
308#479—111no—
309#478—111no—
310#478—111no—
311#477—111no—
312#476—111no—
313#475—111no—
314#474—111no—
315#446—221no—
316#446—221no—
317#446—221no—
318#446—221no—
319C2×#108—111no—
320C2×#108C2×D1111yescharacteristic
321#427—111no—
322#427—111no—
323#424—111no—
324#424C2×D1111yescharacteristic
325#423—111no—
326C2×C4⋊C8—111no—
327C2×#104—111no—
328C2×#104C2×D1111yescharacteristic
329#416—111no—
330#416C2×D1111yescharacteristic
331#405—111no—
332#405—111no—
333#405—111no—
334#405—111no—
335#405—221no—
336#405—221no—
337C4×M16—111no—
338C4×M16—221no—
339C2×#97—111no—
340C2×#97—111no—
341C2×#97—221no—
342C2×C4×C8—111no—
343C4×C4⋊C4—111no—
344#341—111no—
345#341—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#339C2×D1111yescharacteristic
352#336—111no—
353#336C2×D1111yescharacteristic
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11#52911yescharacteristic
361C22×C11#53311yescharacteristic
362C4×C11—22no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C2×C4×Q811yescharacteristic
367C4×C11C4×#4111yescharacteristic
368C4×C11C2×C22⋊Q811yescharacteristic
369C4×C11#52511yescharacteristic
370Dic11—21no—
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379C2×#41C22×D1111yescharacteristic
380#131—22no—
381#131—22no—
382#131—114no—
383#131—222no—
384C2×M16—21no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—221no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—21no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—221no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—111no—
397C4⋊Q8—111no—
398#125—111no—
399#125—111no—
400C22⋊Q8—221no—
401C22⋊Q8—221no—
402C4×Q8—111no—
403C4×Q8—111no—
404C4×Q8—221no—
405C4×Q8—221no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410#117—111no—
411#117—111no—
412#117—221no—
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—221no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#108—22no—
420#108—222no—
421#107—111no—
422#107—111no—
423#107—111no—
424#107—111no—
425#106—111no—
426#106—111no—
427#106—111no—
428#106—111no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439#104—22no—
440#104—222no—
441#103—111no—
442#103—111no—
443#103C4×D1111yescharacteristic
444#103C4×D1111yescharacteristic
445#102—111no—
446#102—111no—
447#102C4×D1111yescharacteristic
448#102C4×D1111yescharacteristic
449#97—111no—
450#97—111no—
451#97—111no—
452#97—111no—
453#97—221no—
454#97—221no—
455#97—222no—
456#97—221no—
457#97—221no—
458#97—221no—
459C4×C8—222no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—221no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—42no—
469C2×C11C4×C22⋊Q811yescharacteristic
470C2×C11#295611yescharacteristic
471C2×C11#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41#434112yes—
475#41Q8×D1112yes—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8C2×C4×D1111yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4C23×D1111yescharacteristic
489M16—24no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—112no—
494M16—224no—
495M16—221no—
496M16—221no—
497M16—221no—
498M16#434112yes—
499C2×C8—24no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—112no—
509C2×C8—112no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—224no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8C2×C4×D1111yescharacteristic
518C2×C8C2×C4×D1111yescharacteristic
519C2×C8D4×D1111yescharacteristic
520C2×C8D4×D1111yescharacteristic
521C4⋊C4—111no—
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—111no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C11#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23#41×D1111yescharacteristic
557Q8—21no—
558Q8—881no—
559Q8—881no—
560Q8#6694012yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4#6694012yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—881no—
587C2×C4—881no—
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4C2×#434111yescharacteristic
592C2×C4C2×Q8×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—22no—
598C8—21no—
599C8—41no—
600C8—112no—
601C8—112no—
602C8—221no—
603C8—221no—
604C8—222no—
605C8—441no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C4×D4×D1111yescharacteristic
612C22#1062315311yescharacteristic
613C22#1062318011yescharacteristic
614C4—22no—
615C4—42no—
616C4—41no—
617C4—41no—
618C4—221no—
619C4—221no—
620C4—221no—
621C4—221no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—441no—
626C4—881no—
627C4C2×#6694011yescharacteristic
628C4C4×#434111yescharacteristic
629C4#1062311711yescharacteristic
630C4D11×C22⋊Q811yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2#1307114811yescharacteristic
635C2#1307752111yescharacteristic
636C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1866C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1866D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #13077555C2semidirect
4. #13069558C2semidirect
5. #13069388C2semidirect
6. #13069216C2semidirect
7. #13069212C2semidirect
10. #13068503C2semidirect
11. #13068494C2semidirect
12. #13068487C2semidirect
49. #10622412C4semidirect
50. #10622409C4semidirect
51. #10622407C4semidirect
52. #10622404C4semidirect
53. #10622379C4semidirect
54. #10622376C4semidirect
55. #10622374C4semidirect
56. #10622372C4semidirect
79. #67001Q8semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130784002
#130775552
#130770422
#130695582
#130693882
#130692162
#130692122
#130688912
#130686342
#130685032
#130684942
#130684872
#130684632
#130684542
C11×#18662
#2162911