Finite Group Databasebeta

← #10742715

Subgroups — #10742715

Order 768.

2678 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C22×#935C211yesmaximal, characteristic, complemented
3C2×#5220C211yesmaximal, characteristic, complemented
4C2×#5210C212yesmaximal, complemented
5C2×#4946C211yesmaximal, characteristic, complemented
6#72131C212yesmaximal, complemented
7#72131C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#71566C212yesmaximal, complemented
10#71548C211yesmaximal, characteristic, complemented
11#71547C212yesmaximal, complemented
12#15950—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C2×C3×#121—24no—
19C2×C3×#121—24no—
20C2×C3×#121—24no—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2212yes—
29C22×#217C2211yescharacteristic
30C22×#217C2212yes—
31C2×#935—24no—
32C2×#935—28no—
33C22×Dic3⋊C4C2212yes—
34C22×Dic3⋊C4C2212yes—
35#5220—24no—
36#5210—28no—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4946—24no—
44C22×#123—31no—
45C22×#121D311yescharacteristic
46C2×#386—31no—
47C2×#385—32no—
48C2×#385—31no—
49#1441—32no—
50#1440—31no—
51#1439—32no—
52#1438—32no—
53#1438—31no—
54#1438—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—24no—
66C22×C3×D4—24no—
67C22×C3×D4—22no—
68C22×C3×D4—42no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4D414yes—
72C22×C3×D4D414yes—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—24no—
77C23×C3×C4—42no—
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3—22no—
83C23×Dic3—24no—
84C23×Dic3—22no—
85C23×Dic3—22no—
86C23×Dic3—42no—
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C23×Dic3C2312yes—
91C3×#121—232no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4D414yes—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—24no—
108C2×#217—24no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—24no—
112C2×#217—22no—
113C2×#217—24no—
114C2×#217—24no—
115C2×#217—42no—
116C2×#217—42no—
117C2×#217—42no—
118C2×#217—42no—
119#935—232no—
120C2×Dic3⋊C4—24no—
121C2×Dic3⋊C4—24no—
122C2×Dic3⋊C4—24no—
123C2×Dic3⋊C4—24no—
124C2×Dic3⋊C4—42no—
125C2×Dic3⋊C4D418yescomplemented
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—42no—
131C3⋊#95—42no—
132C23×D4C2×D311yescharacteristic
133C23×D4C2×D311yescharacteristic
134C23×D4C2×D311yescharacteristic
135C24×C4—31no—
136C24×C4C2×D311yescharacteristic
137C2×#123—68no—
138C2×#123—64no—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C22×C4⋊C4—32no—
143C22×C4⋊C4—32no—
144C22×C4⋊C4C2×D311yescharacteristic
145C22×C22⋊C4—32no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—31no—
152C22×C22⋊C4C2×D311yescharacteristic
153C22×C22⋊C4C2×D311yescharacteristic
154#386—64no—
155#385—68no—
156#385—64no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
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—21no—
178C24×C3—21no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3C2×D412yes—
187C24×C3C2×D412yes—
188C24×C3C2×D412yes—
189C24×C3#4114yes—
190C24×C3C2411yescharacteristic
191C2×C3×D4—28no—
192C2×C3×D4—28no—
193C2×C3×D4—28no—
194C2×C3×D4—28no—
195C2×C3×D4—28no—
196C2×C3×D4—44no—
197C2×C3×D4—44no—
198C2×C3×D4—48no—
199C2×C3×D4—48no—
200C2×C3×D4—48no—
201C2×C3×D4—48no—
202C2×C3×D4—48no—
203C2×C3×D4—48no—
204C2×C3×D4—44no—
205C2×C3×D4—44no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—28no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
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—48no—
223C22×C3×C4—48no—
224C22×C3×C4—44no—
225C22×C3×C4—44no—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D412yes—
231C22×Dic3—28no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—48no—
258C22×Dic3—48no—
259C22×Dic3—44no—
260C22×Dic3—44no—
261C22×Dic3C2×D414yes—
262C22×Dic3C2×D414yes—
263C22×Dic3#4114yes—
264C3×C4⋊C4—28no—
265C3×C22⋊C4—28no—
266C3×C22⋊C4—28no—
267#217—28no—
268#217—216no—
269#217—216no—
270#217—28no—
271#217—48no—
272#217—48no—
273#217—44no—
274Dic3⋊C4—216no—
275Dic3⋊C4—48no—
276C25C22×D311yescharacteristic
277C25C22×D311yescharacteristic
278C25C22×D311yescharacteristic
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—24no—
287C22×D4—24no—
288C22×D4—22no—
289C22×D4—42no—
290C22×D4—42no—
291C22×D4—42no—
292C22×D4#6714yes—
293C22×D4#6714yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—24no—
298C23×C4—32no—
299C23×C4—32no—
300C23×C4—32no—
301C23×C4—32no—
302C23×C4—42no—
303C23×C4—64no—
304C23×C4—62no—
305C23×C4—62no—
306C23×C4—62no—
307C23×C4—122no—
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D311yescharacteristic
312#123—632no—
313#121—232no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—38no—
318C2×C4⋊C4—64no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C4⋊C4—64no—
322C2×C4⋊C4—122no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—62no—
342C2×C22⋊C4—122no—
343C2×C22⋊C4—122no—
344C2×C22⋊C4—122no—
345C2×C22⋊C4—122no—
346C2×C22⋊C4#6714yes—
347#95—64no—
348#95—64no—
349#95—64no—
350#95—64no—
351#95—122no—
352#95—122no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
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—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—42no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—42no—
401C23×C3—41no—
402C23×C3—41no—
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#12014yes—
415C23×C3#12314yescomplemented
416C23×C3C22×D412yes—
417C23×C3C22×D411yescharacteristic
418C23×C3C22×D411yescharacteristic
419C23×C3C22×D411yescharacteristic
420C23×C3C2×#4112yes—
421C23×C3C2×#4112yes—
422C23×C3H(5,𝔽2)12yes—
423C23×C3H(5,𝔽2)12yes—
424C23×C32−1+412yes—
425C3×D4—416no—
426C3×D4—416no—
427C3×D4—416no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—416no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4#12014yes—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—24no—
455C2×Dic3—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—416no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—42no—
477C2×Dic3—42no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24#23714yes—
500C24C2×#6712yes—
501C24C2×#6712yes—
502C24C2×#6712yes—
503C24C2×#6712yes—
504C24C2×#6712yes—
505C24C23×D311yescharacteristic
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—44no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—68no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—128no—
571C22×C4—128no—
572C22×C4—124no—
573C22×C4—124no—
574C22×C4D3×D414yes—
575C22×C4C2×#6712yes—
576C22×C4C2×#6712yes—
577C22×C4C2×#6712yes—
578C22×C4C2×#6712yes—
579C4⋊C4—28no—
580C4⋊C4—616no—
581C4⋊C4—128no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—68no—
585C22⋊C4—616no—
586C22⋊C4—68no—
587C22⋊C4—616no—
588C22⋊C4—128no—
589C22⋊C4—128no—
590C22⋊C4—124no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—28no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—44no—
613C22×C3—44no—
614C22×C3—82no—
615C22×C3—82no—
616C22×C3—82no—
617C22×C3—82no—
618C22×C3C2×#12011yescharacteristic
619C22×C3C2×#12011yescharacteristic
620C22×C3C2×#12311yescharacteristic
621C22×C3#52511yescharacteristic
622C22×C3#52512yes—
623C22×C3#53411yescharacteristic
624C22×C3#53411yescharacteristic
625C22×C3#53611yescharacteristic
626C22×C3#53712yes—
627C22×C3#53812yes—
628C22×C3#53912yes—
629C22×C3D4212yes—
630C22×C3D4212yes—
631C22×C3#54612yes—
632C22×C3#54612yes—
633C22×C3#54712yes—
634C22×C3#54712yes—
635C22×C3#54812yes—
636C22×C3#55012yes—
637C22×C3#55312yes—
638C22×C3#56212yes—
639C3×C4—24no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643Dic3—44no—
644Dic3—44no—
645Dic3—44no—
646Dic3—82no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23#93514yescomplemented
709C23#95314yes—
710C23C2×D3×D412yes—
711C23C2×#23712yes—
712C23#100412yes—
713C23#100412yes—
714C23D3×#4112yes—
715C23#101012yes—
716C23C22×#6711yescharacteristic
717C23C22×#6711yescharacteristic
718C23C22×#6711yescharacteristic
719D4—416no—
720D4—416no—
721D4—416no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—1216no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4#93714yes—
772C2×C3—44no—
773C2×C3—44no—
774C2×C3—82no—
775C2×C3#240311yescharacteristic
776C2×C3#240511yescharacteristic
777C2×C3#240611yescharacteristic
778C2×C3#240712yes—
779C2×C3#244312yes—
780C2×C3#245612yes—
781C2×C3#268112yes—
782C2×C3#268212yes—
783C2×C3#270812yes—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22#559812yes—
812C22#559912yes—
813C22#560112yes—
814C22#560212yes—
815C22#560612yes—
816C22#560812yes—
817C22#561312yes—
818C22#562112yes—
819C22C2×#93511yescharacteristic
820C22C2×#93711yescharacteristic
821C22D4×#6712yes—
822C22D4×#6712yes—
823C22#580411yescharacteristic
824C22#580411yescharacteristic
825C22#580612yes—
826C22#580612yes—
827C22#582412yes—
828C22#582412yes—
829C22#582511yescharacteristic
830C22#582811yescharacteristic
831C22C2×#95311yescharacteristic
832C4—24no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—124no—
837C4—124no—
838C4—124no—
839C4—242no—
840C3#1595011yescharacteristic, complemented, Sylow
841C2—44no—
842C2—44no—
843C2—82no—
844C2#8265512yes—
845C2#8265712yes—
846C2#8268512yes—
847C2#8268612yes—
848C2#8269412yes—
849C2#8270112yes—
850C2#8404711yescharacteristic
851C2#8405211yescharacteristic
852C2#8409011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15950
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#935C2semidirect
3. C2×#5220C2semidirect
4. C2×#5210C2semidirect
5. C2×#4946C2semidirect
6. #72131C2semidirect
7. #72131C2semidirect
8. #72131C2semidirect
9. #71566C2semidirect
10. #71548C2semidirect
11. #71547C2semidirect
125. C2×Dic3⋊C4D4semidirect
415. C23×C3#123semidirect
708. C23#935semidirect
840. C3#15950semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9352
C2×#52202
C2×#52102
C2×#49462
#721312
#715662
#715482
#715472
#159503