Finite Group Databasebeta

← #14784771

Subgroups — #14784771

Order 2816.

2414 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4323C211yesmaximal, characteristic, complemented
2C2×#10622830C212yesmaximal, complemented
3C2×#10622649C211yesmaximal, characteristic, complemented
4#13071972C211yesmaximal, characteristic, complemented
5#13069687C212yesmaximal, complemented
6#13069612C212yesmaximal, complemented
7#13069045C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068547C211yesmaximal, characteristic, complemented
11C2×D42×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11—21no—
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic, complemented
15C23×D44C2211yescharacteristic, complemented
16D42×C11—24no—
17D42×C11—24no—
18C2×C11×#127C2211yescharacteristic, complemented
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic, complemented
22C2×C11×#120—21no—
23C2×C11×#120—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic, complemented
26C2×#66990—21no—
27C22×#4323—24no—
28C22×#4323—28no—
29C22×#4323C2212yes—
30C22×#4323C2212yescomplemented
31C22×#4323C2212yescomplemented
32C2×#66983C2212yescomplemented
33C23×C11⋊C8C2211yescharacteristic, complemented
34#10622830—28no—
35C2×#66896C2212yescomplemented
36C2×#66896C2212yescomplemented
37C2×#66896C2212yescomplemented
38#10622825C2211yescharacteristic, complemented
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C11⋊C8)C2212yescomplemented
41#10622649—24no—
42#10622604—21no—
43C2×#66873C2212yescomplemented
44#10622573—21no—
45#10622568—21no—
46#10622552C2212yescomplemented
47#10622167C2212yescomplemented
48#10622162C2212yescomplemented
49C25×C11—21no—
50C25×C11—21no—
51C24×D11—21no—
52C22×D4×C11—24no—
53C22×D4×C11—28no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—24no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—42no—
65C22×D4×C11—42no—
66C22×D4×C11—44no—
67C22×D4×C11—44no—
68C22×D4×C11D411yescharacteristic
69C22×D4×C11D414yescomplemented
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—22no—
77C22×D44—22no—
78C22×D44—24no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—42no—
82C22×D44C2312yes—
83C11×#127—22no—
84C11×#127—22no—
85C11×#121—28no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121D414yescomplemented
90C11×#120—28no—
91C11×#120—28no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105#66990—44no—
106C2×#4323—232no—
107C2×#4323—24no—
108C2×#4323—24no—
109C2×#4323—24no—
110C2×#4323—24no—
111C2×#4323—24no—
112C2×#4323—24no—
113C2×#4323—24no—
114C2×#4323—42no—
115C2×#4323D418yescomplemented
116#66983—24no—
117#66983—42no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×C4⋊Dic11C2312yes—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—24no—
124C22×C11⋊C8C2312yes—
125C22×C11⋊C8C2312yes—
126#66896—24no—
127#66896—24no—
128#66896—42no—
129C11⋊#95—21no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—24no—
132#66873—24no—
133#23848—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11—24no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—24no—
139C24×C11—44no—
140C24×C11—44no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—82no—
146C24×C11—82no—
147C24×C11C2×D411yescharacteristic
148C24×C11C2×D411yescharacteristic
149C23×D11—22no—
150C23×D11—44no—
151C23×D11—42no—
152C23×D11—42no—
153C23×D11—42no—
154C23×D11—82no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—28no—
158C2×D4×C11—24no—
159C2×D4×C11—24no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—24no—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—44no—
173C2×D4×C11—48no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C2×D4×C11—42no—
177C2×D4×C11—48no—
178C2×D4×C11—432no—
179C2×D4×C11—44no—
180C2×D4×C11—42no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—44no—
185C2×D4×C11—42no—
186C2×D4×C11—82no—
187C2×D4×C11D814yescomplemented
188C2×D4×C11C2×D412yes—
189C2×D4×C11C2×D412yes—
190C2×D4×C11C2×D414yes—
191C2×D4×C11C2×D412yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—24no—
195C22×C4×C11—21no—
196C22×C4×C11—22no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—22no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—82no—
212C22×Dic11—22no—
213C2×D44—28no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—44no—
220C2×D44—48no—
221C2×D44—44no—
222C2×D44—42no—
223C2×D44C2×D414yescomplemented
224C11×C4⋊C4—22no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—22no—
232C42×C11—21no—
233C42×C11—21no—
234C22⋊Dic11—42no—
235#4323—216no—
236#4323—216no—
237#4323—48no—
238(C2×D11)⋊C4—44no—
239(C2×D11)⋊C4—44no—
240(C2×D11)⋊C4—82no—
241C4⋊Dic11—22no—
242C4⋊Dic11—22no—
243C2×C11⋊C8—28no—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8C2×D414yescomplemented
250C23×D8—111no—
251C2×D42D1111yescharacteristic, complemented
252C2×#447—112no—
253C2×#447—111no—
254#2408—111no—
255#2011—112no—
256#1999—112no—
257#1893—111no—
258#1879—112no—
259#1869—111no—
260#1786—111no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—24no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—48no—
272C23×C11—48no—
273C23×C11—48no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11—48no—
286C23×C11—84no—
287C23×C11—88no—
288C23×C11—88no—
289C23×C11—88no—
290C23×C11—84no—
291C23×C11—88no—
292C23×C11#12012yes—
293C23×C11C2×D812yes—
294C23×C11C2×D812yescomplemented
295C23×C11AGL(1,ℤ/8)12yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—24no—
298C22×D11—48no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—88no—
306C22×D11—88no—
307C22×D11—84no—
308C22×D11—84no—
309D4×C11—28no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—24no—
314D4×C11—24no—
315D4×C11—48no—
316D4×C11—48no—
317D4×C11—48no—
318D4×C11—48no—
319D4×C11—48no—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—42no—
323D4×C11—84no—
324D4×C11#12014yescomplemented
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—48no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—42no—
342C2×C4×C11#12012yes—
343C2×C4×C11C2×D812yescomplemented
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11H(5,𝔽2)12yes—
348C22⋊D11—88no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352D44—24no—
353D44—24no—
354D44—48no—
355D44—42no—
356D44—42no—
357C11⋊C8—24no—
358C11⋊C8—42no—
359C23×D4—21no—
360C23×D4—111no—
361C23×D4C2×D1111yescharacteristic
362C23×D4C2×D1111yescharacteristic, complemented
363C22×D8—112no—
364C22×D8—112no—
365C22×D8—112no—
366C22×D8—228no—
367C22×D8—224no—
368C23×C8—111no—
369D42—24no—
370D42—24no—
371C2×#127C2×D1111yescharacteristic, complemented
372C2×#121—21no—
373C2×#121—112no—
374C2×#121C2×D1111yescharacteristic
375C2×#121C2×D1111yescharacteristic, complemented
376C2×#120—21no—
377C2×#120—21no—
378C2×#120—221no—
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic, complemented
381#447—228no—
382#447—224no—
383C2×#102—112no—
384C2×#102—112no—
385C2×#102—112no—
386C2×#102—112no—
387C2×C22⋊C8—112no—
388C2×C22⋊C8—111no—
389#394—221no—
390#392—221no—
391#390—112no—
392#380—111no—
393#379—221no—
394#340—112no—
395#336—112no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—22no—
402C22×C11—24no—
403C22×C11—41no—
404C22×C11—42no—
405C22×C11—41no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—44no—
409C22×C11—44no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—816no—
417C22×C11—816no—
418C22×C11—82no—
419C22×C11—82no—
420C22×C11—82no—
421C22×C11—82no—
422C22×C11#44714yescomplemented
423C22×C11C2×#12011yescharacteristic
424C22×C11D4212yes—
425C22×C11C22×D811yescharacteristic
426C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
427C22×C11#57612yes—
428C2×D11—44no—
429C2×D11—44no—
430C2×D11—44no—
431C2×D11—816no—
432C2×D11—82no—
433C2×D11—82no—
434C2×D11—82no—
435C2×D11—82no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—41no—
439C4×C11—42no—
440C4×C11—41no—
441C4×C11C2×#12011yescharacteristic
442C4×C11#53411yescharacteristic
443C4×C11D4212yes—
444Dic11—82no—
445C25—21no—
446C25—21no—
447C25—221no—
448C22×D4—24no—
449C22×D4—28no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—24no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—22no—
459C22×D4—21no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4—44no—
463C22×D4—44no—
464C22×D4—112no—
465C22×D4—224no—
466C22×D4—222no—
467C22×D4—222no—
468C22×D4—222no—
469C22×D4—221no—
470C22×D4—442no—
471C22×D4C22⋊D1111yescharacteristic
472C22×D4C22⋊D1114yescomplemented
473C22×D4C22×D1111yescharacteristic
474C22×D4C22×D1111yescharacteristic
475C22×D4C22×D1111yescharacteristic
476C23×C4—21no—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C2×D8—118no—
480C2×D8—224no—
481C2×D8—224no—
482C2×D8—2232no—
483C2×D8—224no—
484C2×D8—224no—
485C2×D8—224no—
486C2×D8—224no—
487C2×D8—224no—
488C2×D8—442no—
489C22×C8—112no—
490C22×C8—112no—
491C22×C8—224no—
492C22×C8—222no—
493#127—22no—
494#127—22no—
495#121—28no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—224no—
500#121—442no—
501#121C22⋊D1114yescomplemented
502#120—28no—
503#120—28no—
504#120—444no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4C22⋊D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42C22×D1111yescharacteristic
522#102—224no—
523#102—224no—
524#102—224no—
525#102—442no—
526C22⋊C8—224no—
527C22⋊C8—222no—
528#95—221no—
529C2×C11—24no—
530C2×C11—42no—
531C2×C11—44no—
532C2×C11—82no—
533C2×C11—82no—
534C2×C11#240311yescharacteristic
535C2×C11C2×#44711yescharacteristic
536C2×C11#300811yescharacteristic
537C2×C11#326412yes—
538C2×C11D4×D812yes—
539D11—84no—
540C24—21no—
541C24—24no—
542C24—21no—
543C24—21no—
544C24—24no—
545C24—44no—
546C24—44no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—82no—
552C24—82no—
553C24—222no—
554C24—444no—
555C24—442no—
556C24—442no—
557C24—442no—
558C24—882no—
559C24C2×C22⋊D1111yescharacteristic
560C24C2×C22⋊D1111yescharacteristic
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—28no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—44no—
579C2×D4—48no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—48no—
584C2×D4—432no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—44no—
591C2×D4—42no—
592C2×D4—82no—
593C2×D4—114no—
594C2×D4—228no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—448no—
601C2×D4—444no—
602C2×D4—444no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—442no—
606C2×D4—882no—
607C2×D4#432314yescomplemented
608C2×D4D4×D1114yes—
609C2×D4C2×C22⋊D1112yes—
610C2×D4C2×C22⋊D1112yes—
611C2×D4C2×C22⋊D1112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—222no—
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1112yes—
628C22×C4C2×C22⋊D1112yes—
629C22×C4C23×D1111yescharacteristic
630D8—2216no—
631D8—2216no—
632D8—448no—
633C2×C8—114no—
634C2×C8—228no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8—222no—
639C2×C8—222no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—222no—
643C4⋊C4—222no—
644C4⋊C4C2×C22⋊D1112yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—22no—
648C22⋊C4—24no—
649C22⋊C4—22no—
650C22⋊C4—444no—
651C22⋊C4—442no—
652C22⋊C4—444no—
653C22⋊C4—882no—
654C42—21no—
655C42—21no—
656C11#2384811yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—48no—
669C23—48no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—48no—
680C23—42no—
681C23—42no—
682C23—84no—
683C23—88no—
684C23—88no—
685C23—88no—
686C23—84no—
687C23—88no—
688C23—224no—
689C23—448no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—888no—
697C23—888no—
698C23—884no—
699C23—884no—
700C23C2×#432312yes—
701C23C2×#432312yescomplemented
702C23#6698512yes—
703C23#6700612yes—
704C23C22×C22⋊D1111yescharacteristic
705D4—28no—
706D4—22no—
707D4—24no—
708D4—24no—
709D4—22no—
710D4—22no—
711D4—48no—
712D4—48no—
713D4—48no—
714D4—48no—
715D4—48no—
716D4—41no—
717D4—42no—
718D4—41no—
719D4—84no—
720D4—224no—
721D4—224no—
722D4—448no—
723D4—442no—
724D4—442no—
725D4—888no—
726D4#6699014yescomplemented
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4C2×#432312yescomplemented
748C2×C4#6700612yes—
749C2×C4C2×D4×D1112yes—
750C2×C4#6703712yes—
751C2×C4C22×C22⋊D1111yescharacteristic
752C2×C4C22×C22⋊D1111yescharacteristic
753C8—224no—
754C8—442no—
755C22—24no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—24no—
761C22—24no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—816no—
776C22—816no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—444no—
782C22—444no—
783C22—444no—
784C22—8816no—
785C22—882no—
786C22—882no—
787C22—882no—
788C22—882no—
789C22#1062283014yescomplemented
790C22C22×#432311yescharacteristic
791C22C2×#6698511yescharacteristic
792C22D4×C22⋊D1112yes—
793C22#1062336612yes—
794C22C2×#6700611yescharacteristic
795C4—22no—
796C4—22no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—882no—
801C4C2×#6699011yescharacteristic
802C4D4×C22⋊D1112yes—
803C4#1062333511yescharacteristic
804C2—24no—
805C2—42no—
806C2—44no—
807C2—82no—
808C2—82no—
809C2—884no—
810C2#1307192611yescharacteristic
811C2C2×#1062283011yescharacteristic
812C2#1307788411yescharacteristic
813C2#1308009212yes—
814C2D4×#432312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11#23848
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C23×#4323C2semidirect
2. C2×#10622830C2semidirect
3. C2×#10622649C2semidirect
4. #13071972C2semidirect
5. #13069687C2semidirect
6. #13069612C2semidirect
7. #13069045C2semidirect
8. #13068964C2semidirect
9. #13068909C2semidirect
10. #13068547C2semidirect
11. C2×D42×C11C2semidirect
14. C23×D4×C11C22semidirect
15. C23×D44C22semidirect
18. C2×C11×#127C22semidirect
21. C2×C11×#121C22semidirect
25. C2×C4×D4×C11C22semidirect
30. C22×#4323C22semidirect
31. C22×#4323C22semidirect
32. C2×#66983C22semidirect
33. C23×C11⋊C8C22semidirect
35. C2×#66896C22semidirect
36. C2×#66896C22semidirect
37. C2×#66896C22semidirect
38. #10622825C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
43. C2×#66873C22semidirect
46. #10622552C22semidirect
47. #10622167C22semidirect
48. #10622162C22semidirect
69. C22×D4×C11D4semidirect
89. C11×#121D4semidirect
115. C2×#4323D4semidirect
187. C2×D4×C11D8semidirect
223. C2×D44C2×D4semidirect
249. C2×C11⋊C8C2×D4semidirect
251. C2×D42D11semidirect
294. C23×C11C2×D8semidirect
324. D4×C11#120semidirect
343. C2×C4×C11C2×D8semidirect
362. C23×D4C2×D11semidirect
371. C2×#127C2×D11semidirect
375. C2×#121C2×D11semidirect
380. C2×C4×D4C2×D11semidirect
422. C22×C11#447semidirect
472. C22×D4C22⋊D11semidirect
501. #121C22⋊D11semidirect
607. C2×D4#4323semidirect
656. C11#23848semidirect
701. C23C2×#4323semidirect
726. D4#66990semidirect
747. C2×C4C2×#4323semidirect
789. C22#10622830semidirect

Maximal subgroups

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

subgroupindex
C23×#43232
C2×#106228302
C2×#106226492
#130719722
#130696872
#130696122
#130690452
#130689642
#130689092
#130685472
C2×D42×C112
#2384811