Finite Group Databasebeta

← #10826927

Subgroups — #10826927

Order 768.

2596 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#938C211yesmaximal, characteristic, complemented
2C2×D3×#121C211yesmaximal, characteristic, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C2×#5217C211yesmaximal, characteristic, complemented
5C2×#5156C212yesmaximal, complemented
6#72043C212yesmaximal, complemented
7#71677C211yesmaximal, characteristic, complemented
8#70204C212yesmaximal, complemented
9#70200C212yesmaximal, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69932C211yesmaximal, characteristic, complemented
12#23918—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic, complemented
14C23×#67—21no—
15C22×D3×D4—21no—
16C22×D3×D4C2211yescharacteristic, complemented
17C23×C4×D3C2211yescharacteristic
18C22×C3×D8C2212yescomplemented
19C2×C3×#121C2211yescharacteristic
20C22×#217—21no—
21C2×#939—21no—
22C2×#938—21no—
23C2×#938—21no—
24C2×#938—28no—
25C2×#938C2212yes—
26C2×#938C2212yescomplemented
27C2×#938C2211yescharacteristic, complemented
28C22×#213C2212yescomplemented
29C2×#930C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic, complemented
31D3×#121—24no—
32D3×#121—24no—
33C2×#895C2211yescharacteristic, complemented
34C2×D3×C4⋊C4C2211yescharacteristic, complemented
35C2×#884—21no—
36C2×D3×C22⋊C4—21no—
37C3×#447—24no—
38C2×C3×#102C2212yescomplemented
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5217—24no—
41C2×#832C2212yescomplemented
42C2×#832C2212yescomplemented
43C2×#830C2211yescharacteristic, complemented
44#5156—28no—
45C2×#821C2212yescomplemented
46C2×(C2×D3)⋊C8C2212yescomplemented
47C2×(C2×D3)⋊C8C2212yescomplemented
48#4551C2212yescomplemented
49#4529C2212yescomplemented
50C22×#121—31no—
51C22×#121—31no—
52C2×#447—31no—
53C2×#447—32no—
54C2×#447D311yescharacteristic, complemented
55#1999—32no—
56#1999—32no—
57#1874—32no—
58#1874—31no—
59#1874—31no—
60#1779—31no—
61C25×C3—21no—
62C24×D3—21no—
63C24×D3D411yescharacteristic
64C22×C3×D4—21no—
65C22×C3×D4—24no—
66C22×C3×D4—21no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4C2311yescharacteristic
71C22×C3×D4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C22×#67—28no—
74C22×#67—21no—
75C22×#67—21no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—21no—
79C22×#67—44no—
80C22×#67—44no—
81C23×Dic3—21no—
82C23×Dic3D411yescharacteristic
83C2×D3×D4—28no—
84C2×D3×D4—22no—
85C2×D3×D4—22no—
86C2×D3×D4—24no—
87C2×D3×D4—42no—
88C2×D3×D4—44no—
89C2×D3×D4—44no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—24no—
96C22×C4×D3—42no—
97C22×C4×D3D411yescharacteristic
98C22×C4×D3D411yescharacteristic
99C22×C4×D3C2311yescharacteristic
100C22×C4×D3C2311yescharacteristic
101C2×C3×D8—24no—
102C2×C3×D8—24no—
103C2×C3×D8—42no—
104C22×C3×C8C2312yes—
105C3×#121—22no—
106C3×#121D414yescomplemented
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×#217—28no—
110C2×#217—21no—
111C2×#217—22no—
112C2×#217—22no—
113#939—28no—
114#938—28no—
115#938—28no—
116#938—24no—
117#938—22no—
118#938—24no—
119#938—24no—
120#938—22no—
121#938D418yescomplemented
122C2×#213—24no—
123C2×#213—24no—
124C2×#213—42no—
125#930—22no—
126#930D414yescomplemented
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—24no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2312yes—
133C2×Dic3⋊C4—21no—
134C22×C3⋊C8C2312yes—
135#895—22no—
136#895—22no—
137D3×C4⋊C4—22no—
138D3×C4⋊C4—22no—
139#884—28no—
140D3×C22⋊C4—28no—
141C3×#102—24no—
142C3×C22⋊C8—22no—
143#832—24no—
144#832—24no—
145#830—22no—
146#821—24no—
147(C2×D3)⋊C8—24no—
148(C2×D3)⋊C8—42no—
149C23×D4—31no—
150C23×D4—61no—
151C23×D4—61no—
152C23×D4C2×D311yescharacteristic, complemented
153C24×C4—31no—
154C22×D8—32no—
155C22×D8C2×D312yescomplemented
156C2×#121—32no—
157C2×#121—31no—
158C2×#121—32no—
159C2×#121—31no—
160C2×#121—31no—
161C2×#121—61no—
162C2×#121—64no—
163C2×#121—68no—
164C2×#121—61no—
165C2×#121—61no—
166C2×#121—61no—
167C2×#121—64no—
168C2×#121C2×D311yescharacteristic
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C22⋊C4—61no—
172C22×C22⋊C4—61no—
173#447—24no—
174#447—68no—
175#447—64no—
176C2×#102—32no—
177C2×#102—32no—
178C2×#102—32no—
179C2×#102C2×D312yescomplemented
180C2×C22⋊C8—31no—
181C2×C22⋊C8—32no—
182C2×C22⋊C8—32no—
183C2×C22⋊C8C2×D311yescharacteristic, complemented
184#340—32no—
185#340—32no—
186C24×C3—24no—
187C24×C3—22no—
188C24×C3—21no—
189C24×C3—42no—
190C24×C3—42no—
191C24×C3—42no—
192C24×C3—42no—
193C24×C3—42no—
194C24×C3—42no—
195C24×C3C2×D411yescharacteristic
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—24no—
201C23×D3—21no—
202C23×D3—41no—
203C23×D3—41no—
204C23×D3—42no—
205C23×D3—42no—
206C23×D3—42no—
207C23×D3—42no—
208C23×D3—42no—
209C23×D3—42no—
210C23×D3D814yescomplemented
211C23×D3C2×D411yescharacteristic
212C23×D3C2×D411yescharacteristic
213C2×C3×D4—24no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—48no—
224C2×C3×D4—48no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4C2×D414yescomplemented
230C2×C3×D4C2×D412yescomplemented
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—28no—
241C2×#67—24no—
242C2×#67—28no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—432no—
246C2×#67—44no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—44no—
251C2×#67—44no—
252C2×#67—44no—
253C2×#67—42no—
254C22×Dic3—24no—
255C22×Dic3—22no—
256C22×Dic3—21no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—41no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264D3×D4—48no—
265D3×D4—48no—
266D3×D4—432no—
267C2×D12—22no—
268C2×D12—22no—
269C2×D12—24no—
270C2×D12—21no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12C2×D412yescomplemented
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—22no—
277C2×C4×D3—24no—
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—48no—
287C2×C4×D3—48no—
288C2×C4×D3—41no—
289C2×C4×D3—41no—
290C2×C4×D3—42no—
291C2×C4×D3—42no—
292C2×C4×D3C2×D414yes—
293C3×D8—48no—
294C2×C3×C8—22no—
295C2×C3×C8—22no—
296C2×C3×C8—22no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4C2×D412yescomplemented
299C3×C22⋊C4—24no—
300#217—24no—
301#217—28no—
302#217—28no—
303#213—48no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—24no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—22no—
309C4⋊Dic3C2×D414yescomplemented
310C4⋊Dic3C2×D412yescomplemented
311Dic3⋊C4—24no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8—22no—
314C2×C3⋊C8—22no—
315C25—21no—
316C25—31no—
317C25—61no—
318C22×D4—21no—
319C22×D4—24no—
320C22×D4—21no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—31no—
324C22×D4—42no—
325C22×D4—61no—
326C22×D4—64no—
327C22×D4—61no—
328C22×D4—62no—
329C22×D4—68no—
330C22×D4—62no—
331C22×D4—61no—
332C22×D4—62no—
333C22×D4—68no—
334C22×D4—61no—
335C22×D4—62no—
336C22×D4—122no—
337C22×D4—124no—
338C22×D4—124no—
339C22×D4—124no—
340C22×D4—124no—
341C22×D4C22×D312yes—
342C22×D4C22×D311yescharacteristic
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—64no—
349C23×C4—61no—
350C23×C4—61no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—122no—
354C23×C4C22×D311yescharacteristic
355C2×D8—24no—
356C2×D8—24no—
357C2×D8—42no—
358C2×D8—64no—
359C2×D8—64no—
360C2×D8—122no—
361C22×C8—32no—
362C22×C8C22×D312yes—
363#121—22no—
364#121—38no—
365#121—34no—
366#121—68no—
367#121—62no—
368#121—62no—
369#121—64no—
370#121—64no—
371#121—68no—
372#121—68no—
373#121—68no—
374#121—64no—
375#121—62no—
376#121—62no—
377#121—62no—
378#121#6714yescomplemented
379C2×C4⋊C4—32no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—64no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—68no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—68no—
394C2×C22⋊C4—61no—
395#102—24no—
396#102—64no—
397#102—64no—
398#102—64no—
399C22⋊C8—22no—
400C22⋊C8—64no—
401C22⋊C8—62no—
402C22⋊C8—122no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—24no—
408C23×C3—22no—
409C23×C3—48no—
410C23×C3—48no—
411C23×C3—48no—
412C23×C3—41no—
413C23×C3—42no—
414C23×C3—41no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3—41no—
418C23×C3—42no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—42no—
422C23×C3—41no—
423C23×C3—42no—
424C23×C3—84no—
425C23×C3—84no—
426C23×C3—84no—
427C23×C3—84no—
428C23×C3#12012yes—
429C23×C3C2×D812yes—
430C23×C3AGL(1,ℤ/8)12yes—
431C23×C3C22×D411yescharacteristic
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—28no—
443C22×D3—28no—
444C22×D3—22no—
445C22×D3—44no—
446C22×D3—44no—
447C22×D3—44no—
448C22×D3—44no—
449C22×D3—44no—
450C22×D3—48no—
451C22×D3—48no—
452C22×D3—48no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—84no—
460C22×D3—84no—
461C22×D3—84no—
462C22×D3—84no—
463C22×D3#12012yes—
464C22×D3C2×D812yes—
465C22×D3C2×D812yes—
466C22×D3AGL(1,ℤ/8)12yes—
467C3×D4—24no—
468C3×D4—24no—
469C3×D4—24no—
470C3×D4—48no—
471C3×D4—48no—
472C3×D4—42no—
473C3×D4—42no—
474C3×D4—42no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4#12012yes—
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4H(5,𝔽2)12yes—
487#67—48no—
488#67—48no—
489#67—416no—
490#67—48no—
491#67—416no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—44no—
500C2×Dic3—48no—
501C2×Dic3—41no—
502C2×Dic3—42no—
503C2×Dic3—41no—
504C2×Dic3—42no—
505C2×Dic3#12012yes—
506D12—24no—
507D12—48no—
508D12—42no—
509C4×D3—24no—
510C4×D3—24no—
511C4×D3—44no—
512C4×D3—44no—
513C4×D3—48no—
514C4×D3—42no—
515C4×D3—42no—
516C3×C8—42no—
517C3⋊C8—42no—
518C24—24no—
519C24—21no—
520C24—22no—
521C24—31no—
522C24—31no—
523C24—34no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—62no—
531C24—62no—
532C24—64no—
533C24—62no—
534C24—62no—
535C24—61no—
536C24—121no—
537C24—121no—
538C24—122no—
539C24—122no—
540C24—122no—
541C24—122no—
542C24—122no—
543C24—122no—
544C24D3×D411yescharacteristic
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—32no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—64no—
563C2×D4—68no—
564C2×D4—64no—
565C2×D4—64no—
566C2×D4—68no—
567C2×D4—64no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—61no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4—122no—
574C2×D4—128no—
575C2×D4—128no—
576C2×D4—122no—
577C2×D4—1232no—
578C2×D4—124no—
579C2×D4—122no—
580C2×D4—124no—
581C2×D4—124no—
582C2×D4—1232no—
583C2×D4—122no—
584C2×D4—124no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4D3×D414yescomplemented
588C2×D4C2×#6712yescomplemented
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—34no—
594C22×C4—31no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—64no—
598C22×C4—62no—
599C22×C4—61no—
600C22×C4—62no—
601C22×C4—61no—
602C22×C4—64no—
603C22×C4—62no—
604C22×C4—61no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—61no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—61no—
612C22×C4—121no—
613C22×C4—121no—
614C22×C4—128no—
615C22×C4—128no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—121no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D412yes—
623C22×C4C2×#6712yes—
624C22×C4C23×D311yescharacteristic
625D8—48no—
626D8—128no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—62no—
631C2×C8—62no—
632C2×C8—62no—
633C4⋊C4—21no—
634C4⋊C4—32no—
635C4⋊C4—34no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—62no—
639C4⋊C4—61no—
640C4⋊C4C2×#6712yescomplemented
641C22⋊C4—24no—
642C22⋊C4—64no—
643C22⋊C4—68no—
644C22⋊C4—64no—
645C22⋊C4—68no—
646C22⋊C4—64no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—44no—
659C22×C3—816no—
660C22×C3—81no—
661C22×C3—82no—
662C22×C3—81no—
663C22×C3—82no—
664C22×C3—81no—
665C22×C3—82no—
666C22×C3—81no—
667C22×C3—82no—
668C22×C3#44714yescomplemented
669C22×C3C2×#12011yescharacteristic
670C22×C3C2×#12011yescharacteristic
671C22×C3#53411yescharacteristic
672C22×C3C22×D811yescharacteristic
673C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
674C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
675C22×C3#57511yescharacteristic
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—416no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—816no—
694C2×D3—81no—
695C2×D3—81no—
696C2×D3—81no—
697C2×D3—81no—
698C2×D3#44714yescomplemented
699C3×C4—22no—
700C3×C4—42no—
701C3×C4D4212yes—
702C3×C4D4212yes—
703Dic3—22no—
704Dic3—41no—
705Dic3—42no—
706Dic3—44no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—24no—
713C23—32no—
714C23—32no—
715C23—32no—
716C23—32no—
717C23—48no—
718C23—48no—
719C23—48no—
720C23—41no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—68no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—68no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—62no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—84no—
749C23—124no—
750C23—124no—
751C23—124no—
752C23—124no—
753C23—124no—
754C23—128no—
755C23—128no—
756C23—128no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—244no—
764C23—244no—
765C23—244no—
766C23—244no—
767C23D3×D812yes—
768C23#91112yes—
769C23#93712yes—
770C23C2×D3×D411yescharacteristic
771D4—24no—
772D4—24no—
773D4—24no—
774D4—48no—
775D4—48no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—64no—
780D4—128no—
781D4—128no—
782D4—1216no—
783D4—128no—
784D4—1216no—
785D4—128no—
786D4—122no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—32no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—64no—
798C2×C4—64no—
799C2×C4—61no—
800C2×C4—62no—
801C2×C4—61no—
802C2×C4—64no—
803C2×C4—61no—
804C2×C4—124no—
805C2×C4—124no—
806C2×C4—128no—
807C2×C4—124no—
808C2×C4—128no—
809C2×C4—121no—
810C2×C4—122no—
811C2×C4—121no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4#93712yes—
816C2×C4C2×D3×D412yes—
817C2×C4C2×D3×D411yescharacteristic
818C2×C4#100412yes—
819C2×C4C22×#6711yescharacteristic
820C8—42no—
821C8—122no—
822C2×C3—24no—
823C2×C3—82no—
824C2×C3—84no—
825C2×C3#240311yescharacteristic
826C2×C3C2×#44711yescharacteristic
827C2×C3C2×#44711yescharacteristic
828C2×C3#300611yescharacteristic
829C2×C3#300611yescharacteristic
830C2×C3#318611yescharacteristic
831C2×C3#319211yescharacteristic
832D3—24no—
833D3—42no—
834D3—82no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—34no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—816no—
858C22—82no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—82no—
864C22—81no—
865C22—82no—
866C22—1216no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—2416no—
875C22—241no—
876C22—241no—
877C22—241no—
878C22—241no—
879C22#515614yescomplemented
880C22D3×#12011yescharacteristic
881C22#558911yescharacteristic
882C22C2×D3×D811yescharacteristic
883C22C2×#91111yescharacteristic
884C22D3×AGL(1,ℤ/8)11yescharacteristic
885C22#577311yescharacteristic
886C22C2×#93711yescharacteristic
887C4—22no—
888C4—42no—
889C4—62no—
890C4—122no—
891C4—124no—
892C4—121no—
893C4#559012yes—
894C4D4×#6712yes—
895C3#2391811yescharacteristic, complemented, Sylow
896C2—24no—
897C2—64no—
898C2—84no—
899C2—82no—
900C2—122no—
901C2—242no—
902C2D3×#44711yescharacteristic
903C2#8000311yescharacteristic
904C2#8000611yescharacteristic
905C2#8000811yescharacteristic
906C2#8260411yescharacteristic
907C2C2×#515611yescharacteristic
908C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#447C2
socleC23×C3C22×D4
hypercenterC2×#447D3
hypocenterC3#23918
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C2×D3×#121C2semidirect
3. C2×C3×#447C2semidirect
4. C2×#5217C2semidirect
5. C2×#5156C2semidirect
6. #72043C2semidirect
7. #71677C2semidirect
8. #70204C2semidirect
9. #70200C2semidirect
10. #69955C2semidirect
11. #69932C2semidirect
13. C23×C3×D4C22semidirect
16. C22×D3×D4C22semidirect
18. C22×C3×D8C22semidirect
26. C2×#938C22semidirect
27. C2×#938C22semidirect
28. C22×#213C22semidirect
30. C22×C4⋊Dic3C22semidirect
33. C2×#895C22semidirect
34. C2×D3×C4⋊C4C22semidirect
38. C2×C3×#102C22semidirect
39. C2×C3×C22⋊C8C22semidirect
41. C2×#832C22semidirect
42. C2×#832C22semidirect
43. C2×#830C22semidirect
45. C2×#821C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. #4551C22semidirect
49. #4529C22semidirect
54. C2×#447D3semidirect
106. C3×#121D4semidirect
121. #938D4semidirect
126. #930D4semidirect
152. C23×D4C2×D3semidirect
155. C22×D8C2×D3semidirect
179. C2×#102C2×D3semidirect
183. C2×C22⋊C8C2×D3semidirect
210. C23×D3D8semidirect
229. C2×C3×D4C2×D4semidirect
230. C2×C3×D4C2×D4semidirect
273. C2×D12C2×D4semidirect
298. C3×C4⋊C4C2×D4semidirect
309. C4⋊Dic3C2×D4semidirect
310. C4⋊Dic3C2×D4semidirect
378. #121#67semidirect
587. C2×D4D3×D4semidirect
588. C2×D4C2×#67semidirect
640. C4⋊C4C2×#67semidirect
668. C22×C3#447semidirect
698. C2×D3#447semidirect
879. C22#5156semidirect
895. C3#23918semidirect

Maximal subgroups

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

subgroupindex
C22×#9382
C2×D3×#1212
C2×C3×#4472
C2×#52172
C2×#51562
#720432
#716772
#702042
#702002
#699552
#699322
#239183