Finite Group Databasebeta

← #10727934

Subgroups — #10727934

Order 768.

3350 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#217C211yesmaximal, characteristic
2C2×C3×#379C211yesmaximal, characteristic
3C2×#5247C211yesmaximal, characteristic
4C2×#4952C212yesmaximal, complemented
5C2×#4942C211yesmaximal, characteristic, complemented
6#71549C212yesmaximal, complemented
7#71548C212yesmaximal, complemented
8#71547C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14820—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×#217—24no—
21C22×#217—28no—
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2212yes—
26C22×#217C2212yes—
27C22×#217C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic, complemented
29C22×Dic3⋊C4C2211yescharacteristic, complemented
30C3×#379—24no—
31#5247—24no—
32C2×C3⋊#95C2212yescomplemented
33C2×C3⋊#95C2212yescomplemented
34C2×C3⋊#95C2212yescomplemented
35C2×C3⋊#95C2211yescharacteristic, complemented
36C2×C3⋊#95C2211yescharacteristic, complemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40#4952—28no—
41#4942—24no—
42C23×C22⋊C4—31no—
43C2×#397—32no—
44C2×#380—31no—
45C2×#379—31no—
46C2×#379D311yescharacteristic
47#1440—32no—
48#1440—32no—
49#1439—32no—
50C22⋊#95—31no—
51C22⋊#95—31no—
52C22⋊#95—31no—
53C25×C3—24no—
54C25×C3—22no—
55C25×C3—24no—
56C25×C3—22no—
57C25×C3—22no—
58C25×C3—22no—
59C25×C3—22no—
60C25×C3—22no—
61C25×C3—42no—
62C25×C3—42no—
63C25×C3D414yes—
64C25×C3C2312yes—
65C25×C3C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×Dic3—22no—
70C23×Dic3—22no—
71C23×Dic3—22no—
72C23×Dic3—24no—
73C23×Dic3—24no—
74C23×Dic3—22no—
75C23×Dic3—22no—
76C23×Dic3—42no—
77C23×Dic3—42no—
78C23×Dic3D414yes—
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2312yes—
84C23×Dic3C2311yescharacteristic
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×#217—232no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—22no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—24no—
112C2×#217—22no—
113C2×#217—42no—
114C2×#217—42no—
115C2×#217D418yes—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—42no—
120C3⋊#95—22no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—42no—
126C3⋊#95—42no—
127C3⋊#95—42no—
128C26C2×D311yescharacteristic
129C24×C4—31no—
130C24×C4—31no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4—31no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—68no—
140C22×C22⋊C4—64no—
141C22×C22⋊C4C2×D312yes—
142C22×C22⋊C4C2×D311yescharacteristic
143C22×C22⋊C4C2×D311yescharacteristic
144C22×C22⋊C4C2×D312yes—
145#397—68no—
146#380—64no—
147#379—24no—
148#379—64no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—28no—
162C24×C3—216no—
163C24×C3—28no—
164C24×C3—216no—
165C24×C3—28no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—28no—
179C24×C3—28no—
180C24×C3—48no—
181C24×C3—48no—
182C24×C3—48no—
183C24×C3—48no—
184C24×C3—48no—
185C24×C3—48no—
186C24×C3—48no—
187C24×C3—48no—
188C24×C3—48no—
189C24×C3—44no—
190C24×C3—44no—
191C24×C3—48no—
192C24×C3—44no—
193C24×C3—44no—
194C24×C3—44no—
195C24×C3—44no—
196C24×C3C2×D414yes—
197C24×C3C2×D412yes—
198C24×C3C2×D414yes—
199C24×C3C2×D412yes—
200C24×C3#4112yes—
201C24×C3#4112yes—
202C24×C3#4114yes—
203C24×C3#4112yes—
204C24×C3#4112yes—
205C24×C3#4112yes—
206C24×C3C2411yescharacteristic
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—28no—
228C22×Dic3—28no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—28no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—21no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—44no—
258C22×Dic3—48no—
259C22×Dic3—48no—
260C22×Dic3—48no—
261C22×Dic3—48no—
262C22×Dic3—44no—
263C22×Dic3—44no—
264C22×Dic3C2×D412yes—
265C22×Dic3C2×D414yes—
266C22×Dic3C2×D414yes—
267C22×Dic3C2×D412yes—
268C3×C22⋊C4—48no—
269C3×C22⋊C4—48no—
270C3×C22⋊C4—44no—
271C3×C22⋊C4—44no—
272#217—216no—
273#217—216no—
274#217—48no—
275#217—48no—
276#217—44no—
277#217—44no—
278Dic3⋊C4—44no—
279Dic3⋊C4—44no—
280C25—24no—
281C25—22no—
282C25—24no—
283C25—22no—
284C25—22no—
285C25—22no—
286C25—22no—
287C25—22no—
288C25—42no—
289C25—42no—
290C25#6714yes—
291C25C22×D312yes—
292C25C22×D311yescharacteristic
293C23×C4—31no—
294C23×C4—32no—
295C23×C4—31no—
296C23×C4—34no—
297C23×C4—31no—
298C23×C4—31no—
299C23×C4—32no—
300C23×C4—64no—
301C23×C4—64no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—62no—
305C23×C4—62no—
306C23×C4—62no—
307C23×C4—122no—
308C23×C4—122no—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D312yes—
312C2×C4⋊C4—62no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—122no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—38no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—632no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—62no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—62no—
345C2×C22⋊C4—122no—
346C2×C22⋊C4—122no—
347#95—62no—
348#95—62no—
349#95—64no—
350#95—64no—
351#95—64no—
352#95—122no—
353#95—122no—
354#95—122no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—24no—
361C23×C3—22no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—232no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—432no—
391C23×C3—432no—
392C23×C3—416no—
393C23×C3—416no—
394C23×C3—416no—
395C23×C3—416no—
396C23×C3—432no—
397C23×C3—432no—
398C23×C3—416no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—416no—
416C23×C3#12118yes—
417C23×C3#12114yes—
418C23×C3#12314yes—
419C23×C3#12314yes—
420C23×C3#12314yes—
421C23×C3#12414yes—
422C23×C3#12614yes—
423C23×C3#12614yes—
424C23×C3C22×D411yescharacteristic
425C23×C3C22×D412yes—
426C23×C3C22×D411yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4112yes—
431C23×C3C2×#4111yescharacteristic
432C23×C3C2×#4111yescharacteristic
433C23×C3H(5,𝔽2)12yes—
434C23×C3H(5,𝔽2)12yes—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—41no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—41no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—24no—
455C2×Dic3—24no—
456C2×Dic3—22no—
457C2×Dic3—24no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—416no—
463C2×Dic3—416no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—42no—
473C2×Dic3—41no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—41no—
477C2×Dic3—42no—
478C2×Dic3—41no—
479C2×Dic3—42no—
480C2×Dic3—42no—
481C2×Dic3—41no—
482C2×Dic3—42no—
483C2×Dic3—42no—
484C2×Dic3—42no—
485C2×Dic3—42no—
486C2×Dic3—42no—
487C2×Dic3#12014yes—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—28no—
493C24—28no—
494C24—216no—
495C24—216no—
496C24—28no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—28no—
510C24—28no—
511C24—48no—
512C24—48no—
513C24—48no—
514C24—48no—
515C24—48no—
516C24—48no—
517C24—48no—
518C24—48no—
519C24—48no—
520C24—44no—
521C24—44no—
522C24—48no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24#23512yes—
528C24#23512yes—
529C24D3×D414yes—
530C24D3×D412yes—
531C24#23714yes—
532C24#23712yes—
533C24#23712yes—
534C24#23712yes—
535C24C2×#6714yes—
536C24C2×#6712yes—
537C24C23×D311yescharacteristic
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—34no—
556C22×C4—32no—
557C22×C4—34no—
558C22×C4—32no—
559C22×C4—68no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—62no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—61no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—61no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—61no—
579C22×C4—62no—
580C22×C4—61no—
581C22×C4—62no—
582C22×C4—61no—
583C22×C4—62no—
584C22×C4—61no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—124no—
593C22×C4—128no—
594C22×C4—128no—
595C22×C4—128no—
596C22×C4—128no—
597C22×C4—124no—
598C22×C4—124no—
599C4⋊C4—124no—
600C4⋊C4—124no—
601C22⋊C4—48no—
602C22⋊C4—44no—
603C22⋊C4—48no—
604C22⋊C4—44no—
605C22⋊C4—616no—
606C22⋊C4—616no—
607C22⋊C4—128no—
608C22⋊C4—124no—
609C22⋊C4—128no—
610C22⋊C4—124no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—28no—
616C22×C3—28no—
617C22×C3—24no—
618C22×C3—28no—
619C22×C3—28no—
620C22×C3—24no—
621C22×C3—28no—
622C22×C3—28no—
623C22×C3—28no—
624C22×C3—464no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3#39718yescomplemented
638C22×C3C2×#12011yescharacteristic
639C22×C3C2×#12111yescharacteristic
640C22×C3C2×#12112yes—
641C22×C3C2×#12311yescharacteristic
642C22×C3C2×#12311yescharacteristic
643C22×C3C2×#12311yescharacteristic
644C22×C3#52511yescharacteristic
645C22×C3#52512yes—
646C22×C3C2×#12411yescharacteristic
647C22×C3C2×#12611yescharacteristic
648C22×C3C2×#12611yescharacteristic
649C22×C3#53412yes—
650C22×C3#53411yescharacteristic
651C22×C3#53511yescharacteristic
652C22×C3#53812yes—
653C22×C3#54612yes—
654C22×C3#54612yes—
655C22×C3#54612yes—
656C22×C3#54612yes—
657C22×C3#55112yes—
658C22×C3#55112yes—
659C22×C3#55112yes—
660C22×C3#55112yes—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—82no—
664Dic3—24no—
665Dic3—42no—
666Dic3—44no—
667Dic3—81no—
668Dic3—81no—
669Dic3—82no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—24no—
686C23—232no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—432no—
706C23—432no—
707C23—416no—
708C23—432no—
709C23—432no—
710C23—416no—
711C23—416no—
712C23—416no—
713C23—416no—
714C23—416no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23#87914yes—
732C23#87914yes—
733C23#88314yes—
734C23#88514yes—
735C23#92914yes—
736C23#93514yes—
737C23#93918yes—
738C23#93914yes—
739C23C2×#23511yescharacteristic
740C23C2×#23511yescharacteristic
741C23C2×D3×D411yescharacteristic
742C23C2×D3×D412yes—
743C23C2×#23711yescharacteristic
744C23C2×#23711yescharacteristic
745C23C2×#23711yescharacteristic
746C23C2×#23712yes—
747C23#100412yes—
748C23#100412yes—
749C23C22×#6711yescharacteristic
750C2×C4—34no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—62no—
769C2×C4—64no—
770C2×C4—62no—
771C2×C4—64no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—64no—
778C2×C4—1216no—
779C2×C4—1216no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4—122no—
787C2×C4—122no—
788C2×C4—122no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—121no—
792C2×C4—122no—
793C2×C4—121no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—122no—
803C2×C3—28no—
804C2×C3—48no—
805C2×C3C2×#39711yescharacteristic
806C2×C3#240511yescharacteristic
807C2×C3#241212yes—
808C2×C3#241212yes—
809C2×C3#243511yescharacteristic
810C2×C3#248012yes—
811C2×C3#248012yes—
812C2×C3#248211yescharacteristic
813C2×C3#256111yescharacteristic
814C2×C3#261711yescharacteristic
815C2×C3#284711yescharacteristic
816C22—24no—
817C22—28no—
818C22—28no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—28no—
823C22—24no—
824C22—24no—
825C22—28no—
826C22—28no—
827C22—28no—
828C22—28no—
829C22—464no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22#495218yescomplemented
843C22C2×#87911yescharacteristic
844C22C2×#87911yescharacteristic
845C22C2×#88311yescharacteristic
846C22#549012yes—
847C22#549012yes—
848C22C2×#88511yescharacteristic
849C22#549512yes—
850C22#549512yes—
851C22#558612yes—
852C22#558611yescharacteristic
853C22#558712yes—
854C22#558712yes—
855C22D3×#12011yescharacteristic
856C22#558911yescharacteristic
857C22#559112yes—
858C22#559112yes—
859C22#559211yescharacteristic
860C22#559312yes—
861C22C2×#92911yescharacteristic
862C22C2×#93511yescharacteristic
863C22C2×#93912yes—
864C22C2×#93911yescharacteristic
865C22#580412yes—
866C4—64no—
867C4—82no—
868C4—81no—
869C4—81no—
870C4—124no—
871C4—122no—
872C4—241no—
873C4—241no—
874C4—242no—
875C3#1482011yescharacteristic, complemented, Sylow
876C2—28no—
877C2—48no—
878C2#7382711yescharacteristic
879C2#7383012yes—
880C2#7383112yes—
881C2#7383211yescharacteristic
882C2#7383511yescharacteristic
883C2#7385311yescharacteristic
884C2C2×#495211yescharacteristic
885C2#8210712yes—
886C2#8258412yes—
887C2#8259211yescharacteristic
888C2#8260111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#379C2
prime radicalC26×C3C22
hypercenterC2×#379D3
hypocenterC3#14820
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
4. C2×#4952C2semidirect
5. C2×#4942C2semidirect
6. #71549C2semidirect
7. #71548C2semidirect
8. #71547C2semidirect
9. #71544C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
28. C22×Dic3⋊C4C22semidirect
29. C22×Dic3⋊C4C22semidirect
32. C2×C3⋊#95C22semidirect
33. C2×C3⋊#95C22semidirect
34. C2×C3⋊#95C22semidirect
35. C2×C3⋊#95C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
637. C22×C3#397semidirect
842. C22#4952semidirect
875. C3#14820semidirect

Maximal subgroups

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

subgroupindex
C23×#2172
C2×C3×#3792
C2×#52472
C2×#49522
C2×#49422
#715492
#715482
#715472
#715442
#148203