Finite Group Databasebeta

← #14761628

Subgroups — #14761628

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#13078398C211yesmaximal, characteristic
2#13077557C211yesmaximal, characteristic, complemented
3#13077045C211yesmaximal, characteristic
4#13069391C211yesmaximal, characteristic, complemented
5#13069218C211yesmaximal, characteristic, complemented
6#13069218C211yesmaximal, characteristic, complemented
7#13068892C211yesmaximal, characteristic
8#13068892C211yesmaximal, characteristic
9#13068637C211yesmaximal, characteristic
10#13068499C211yesmaximal, characteristic, complemented
11#13068494C211yesmaximal, characteristic, complemented
12#13068491C211yesmaximal, characteristic, complemented
13#13068457C211yesmaximal, characteristic
14#13068450C211yesmaximal, characteristic
15C11×#1986C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×#66960C2211yescharacteristic
18C2×#66960C2211yescharacteristic
19C4×#4339C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66886C2211yescharacteristic
23C2×#66886C2211yescharacteristic
24#10622735C2211yescharacteristic
25#10622735C2211yescharacteristic
26#10622707C411yescharacteristic, complemented
27#10622704C411yescharacteristic, complemented
28#10622700C411yescharacteristic, complemented
29#10622697C411yescharacteristic, complemented
30#10622679C411yescharacteristic, complemented
31#10622679C411yescharacteristic, complemented
32#10622676C411yescharacteristic, complemented
33#10622676C411yescharacteristic, complemented
34#10622637—21no—
35#10622637—21no—
36#10622637—21no—
37#10622637—21no—
38#10622615C2211yescharacteristic
39#10622615C2211yescharacteristic
40#10622612C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622611C2211yescharacteristic
43#10622611C2211yescharacteristic
44#10622610C2211yescharacteristic
45#10622610C2211yescharacteristic
46C2×#66869C2211yescharacteristic
47C2×#66869C2211yescharacteristic
48#10622537C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622320—21no—
54D11×#97—21no—
55#10622302—21no—
56#10622302—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#339C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×C4⋊Q8C2×C411yescharacteristic
72C11×#125C2×C411yescharacteristic
73C11×#125C2×C411yescharacteristic
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C11×#117C2311yescharacteristic
79C11×#117C2311yescharacteristic
80C2×C11×C4⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86#66979C2311yescharacteristic
87C2×#4318C2311yescharacteristic
88C2×#4318C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66960—22no—
94#66960—22no—
95#66960—22no—
96#66960Q814yescomplemented
97C2×#4313—21no—
98C2×#4313—21no—
99C2×C8×D11—21no—
100C2×C8×D11—21no—
101C4×D44C2×C411yescharacteristic
102C4×D44C2×C411yescharacteristic
103#66925—21no—
104C42×D11—21no—
105C4×Dic22C2×C411yescharacteristic
106C4×Dic22C2×C411yescharacteristic
107C11×#97—21no—
108C4×C8×C11—21no—
109C11×#95—21no—
110#66886—22no—
111#66886—22no—
112#66879—21no—
113#66879—21no—
114C8×Dic11—21no—
115C8×Dic11—21no—
116#66874C2×C411yescharacteristic
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66874C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66873C2×C411yescharacteristic
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66872C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130#66871C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66869—22no—
133#66869—22no—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2×C411yescharacteristic
142C4⋊(C11⋊C8)C2×C411yescharacteristic
143C4⋊(C11⋊C8)C2×C411yescharacteristic
144#66867—21no—
145#66867—21no—
146#66867—22no—
147#66867D411yescharacteristic
148#66867D411yescharacteristic
149#66867D411yescharacteristic
150#66867D411yescharacteristic
151C4×C11⋊C8—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—22no—
154#21629—111nomaximal, Sylow
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—21no—
163#4339—21no—
164#4339—21no—
165#4339C2×Q812yes—
166#4339#4112yes—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×Dic22C22×C411yescharacteristic
172C11×M16—21no—
173C11×M16—21no—
174C11×M16C2×Q812yes—
175C11×M16#4112yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11C22×C411yescharacteristic
198C42×C11C22×C411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C22⋊Dic11—21no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—21no—
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C22×C411yescharacteristic
224C2×C11⋊C8C22×C411yescharacteristic
225C2×C11⋊C8C22×C411yescharacteristic
226C2×C11⋊C8C22×C411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×Q812yes—
232C2×C11⋊C8#4112yes—
233#4313—24no—
234#4313—24no—
235C8×D11—24no—
236C8×D11—24no—
237#3076—111no—
238#2961—111no—
239#2875—111no—
240#1986D1111yescharacteristic, complemented
241#1950—111no—
242#1922—111no—
243#1922—111no—
244#1866—111no—
245#1866—111no—
246#1806—111no—
247#1773—111no—
248#1772—111no—
249#1771—111no—
250#1765—111no—
251#1764—111no—
252C23×C11C2×#4111yescharacteristic
253C22×D11—21no—
254Q8×C11—81no—
255Q8×C11—81no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11C4×D411yescharacteristic
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×Q811yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C22⋊D11—22no—
279C22⋊D11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283D44—21no—
284D44C4×Q812yes—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—81no—
288C4×D11—81no—
289Dic22—21no—
290Dic22C4×Q812yes—
291C8×C11—22no—
292C8×C11—22no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8C22⋊Q812yes—
302C11⋊C8C22⋊Q812yes—
303C2×#131—111no—
304C2×#131—111no—
305#533C2×D1111yescharacteristic
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×#108—111no—
321#427—111no—
322#427—111no—
323#424—111no—
324#424—111no—
325#423—111no—
326C2×C4⋊C8—111no—
327C2×#104—111no—
328C2×#104—111no—
329#416—111no—
330#416—111no—
331#405—111no—
332#405—111no—
333#405—111no—
334#405—111no—
335#405—221no—
336#405—221no—
337C4×M16—221no—
338C4×M16C2×D1111yescharacteristic
339C2×#97—111no—
340C2×#97—111no—
341C2×#97—221no—
342C2×C4×C8—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#341—111no—
345#341—111no—
346#339—111no—
347#339—111no—
348#339C2×D1111yescharacteristic
349#339C2×D1111yescharacteristic
350#339C2×D1111yescharacteristic
351#339C2×D1111yescharacteristic
352#336—111no—
353#336—111no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11#52911yescharacteristic
358C22×C11#53311yescharacteristic
359C2×D11—22no—
360C2×D11—41no—
361C2×D11—41no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11C2×C4×Q811yescharacteristic
373C4×C11C4×#4111yescharacteristic
374C4×C11C2×C22⋊Q811yescharacteristic
375C4×C11#52511yescharacteristic
376Dic11—22no—
377Dic11—41no—
378Dic11—41no—
379C2×#41—111no—
380#131—114no—
381#131—222no—
382#131—222no—
383#131—222no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—221no—
395C22×C8—221no—
396C4⋊Q8C4×D1111yescharacteristic
397C4⋊Q8C4×D1111yescharacteristic
398#125C4×D1111yescharacteristic
399#125C4×D1111yescharacteristic
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—111no—
405C4×Q8—111no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410#117—111no—
411#117—221no—
412#117C22×D1111yescharacteristic
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—21no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#108—222no—
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—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439#104—222no—
440#104—222no—
441#103—111no—
442#103—111no—
443#103—111no—
444#103—111no—
445#102—111no—
446#102—111no—
447#102—111no—
448#102—111no—
449#97—21no—
450#97—111no—
451#97—111no—
452#97—111no—
453#97—111no—
454#97—222no—
455#97—221no—
456#97—221no—
457#97—221no—
458#97—221no—
459C4×C8—21no—
460C4×C8—222no—
461C4×C8—221no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—21no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11C4×C22⋊Q811yescharacteristic
469C2×C11#295611yescharacteristic
470C2×C11#295711yescharacteristic
471D11—42no—
472#41—112no—
473#41—112no—
474#41—221no—
475#41—221no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—111no—
479C2×D4—111no—
480C2×D4—221no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4#434111yescharacteristic
487C22×C4#434111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—21no—
490M16—21no—
491M16—224no—
492M16—224no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16Q8×D1112yes—
498M16#434312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—224no—
512C2×C8—224no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—111no—
529C4⋊C4—111no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42C2×C4×D1111yescharacteristic
551C42C2×C4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42D4×D1111yescharacteristic
554C11#2162911yescharacteristic, complemented, Sylow
555C23—221no—
556C23C2×#434111yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—112no—
560Q8—221no—
561D4—112no—
562D4—222no—
563D4—222no—
564D4—221no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—221no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—881no—
583C2×C4—881no—
584C2×C4(C22⋊D11)⋊C411yescharacteristic
585C2×C4(C22⋊D11)⋊C411yescharacteristic
586C2×C4(C22⋊D11)⋊C411yescharacteristic
587C2×C4(C22⋊D11)⋊C411yescharacteristic
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×Q8×D1111yescharacteristic
591C2×C4C2×#434311yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—22no—
595C8—22no—
596C8—112no—
597C8—112no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—221no—
604C8—441no—
605C8—441no—
606C22—21no—
607C22—21no—
608C22—222no—
609C22—441no—
610C22—441no—
611C22C2×(C22⋊D11)⋊C411yescharacteristic
612C22#1062321111yescharacteristic
613C22#1062325911yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—222no—
625C4—441no—
626C4—441no—
627C4C4×Q8×D1111yescharacteristic
628C4C4×#434311yescharacteristic
629C4D11×C22⋊Q811yescharacteristic
630C4#1062315811yescharacteristic
631C2—21no—
632C2—21no—
633C2—442no—
634C2#1307115411yescharacteristic
635C2#1307752211yescharacteristic
636C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1986C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1986D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13077557C2semidirect
4. #13069391C2semidirect
5. #13069218C2semidirect
6. #13069218C2semidirect
10. #13068499C2semidirect
11. #13068494C2semidirect
12. #13068491C2semidirect
15. C11×#1986C2semidirect
26. #10622707C4semidirect
27. #10622704C4semidirect
28. #10622700C4semidirect
29. #10622697C4semidirect
30. #10622679C4semidirect
31. #10622679C4semidirect
32. #10622676C4semidirect
33. #10622676C4semidirect
96. #66960Q8semidirect
240. #1986D11semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130775572
#130770452
#130693912
#130692182
#130688922
#130686372
#130684992
#130684942
#130684912
#130684572
#130684502
C11×#19862
#2162911