Finite Group Databasebeta

← #10729053

Subgroups — #10729053

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#4956C212yesmaximal, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#72134C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71549C212yesmaximal, complemented
10#71545C212yesmaximal, complemented
11#71534C211yesmaximal, characteristic, complemented
12#14915—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×#67C2212yes—
16C23×C4×D3C2211yescharacteristic
17C2×C3×#124—28no—
18C2×C3×#124—24no—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C42C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2212yes—
24C22×#217C2212yes—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29#5231—24no—
30#5223—24no—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40#4956—28no—
41C4×(C2×D3)⋊C4—24no—
42C22×#124D311yescharacteristic, complemented
43C2×#393—31no—
44C2×#392—31no—
45C2×#386—32no—
46C2×C4×C22⋊C4—31no—
47#1446—31no—
48#1440—32no—
49#1438—31no—
50#1438—32no—
51#1437—32no—
52#1434—31no—
53C25×C3C2312yes—
54C24×D3C2311yescharacteristic
55C22×C3×Q8—24no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—42no—
60C22×C3×D4—24no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—42no—
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—42no—
75C22×#67—42no—
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—24no—
85C22×C4×D3—42no—
86C3×#124—232no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4D418yescomplemented
93C2×C3×C42—24no—
94C2×C3×C42D414yescomplemented
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—42no—
101C2×#217—42no—
102C2×#217—42no—
103C2×#217—42no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4D414yes—
113C2×C4×Dic3—22no—
114C2×C4×Dic3—42no—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—22no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
124C23×Q8C2×D311yescharacteristic
125C23×D4—32no—
126C23×D4C2×D311yescharacteristic
127C24×C4—31no—
128C2×#124—28no—
129C2×#124—24no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D312yes—
137C22×C22⋊C4C2×D312yes—
138C22×C42—31no—
139C22×C42C2×D311yescharacteristic
140#393—64no—
141#392—64no—
142#386—68no—
143C4×C22⋊C4—64no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—32no—
152C2×#95—32no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3C2×D414yes—
168C24×C3C2411yescharacteristic
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3C2×D412yes—
178C23×D3#4112yes—
179C23×D3#4112yes—
180C2×C3×Q8—28no—
181C2×C3×Q8—48no—
182C2×C3×Q8—48no—
183C2×C3×Q8—44no—
184C2×C3×Q8—44no—
185C2×C3×D4—28no—
186C2×C3×D4—48no—
187C2×C3×D4—48no—
188C2×C3×D4—44no—
189C2×C3×D4—44no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D414yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4#4112yes—
212C2×#67—216no—
213C2×#67—48no—
214C2×#67—48no—
215C2×#67—48no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
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×Dic3C2×D412yes—
245C22×Dic3#4114yes—
246C22×Dic3#4112yes—
247C22×Dic3#4112yes—
248C2×C4×D3—28no—
249C2×C4×D3—48no—
250C2×C4×D3—48no—
251C2×C4×D3—44no—
252C2×C4×D3—44no—
253C3×C22⋊C4—216no—
254C3×C22⋊C4—216no—
255C3×C42—28no—
256#217—48no—
257#217—48no—
258#217—48no—
259(C2×D3)⋊C4—28no—
260(C2×D3)⋊C4—28no—
261(C2×D3)⋊C4—48no—
262C4×Dic3—44no—
263C25—31no—
264C25C22×D312yes—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—24no—
268C22×Q8—22no—
269C22×Q8—42no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—42no—
275C22×D4—64no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—64no—
280C22×D4—122no—
281C22×D4—122no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—32no—
286C23×C4—32no—
287C23×C4—62no—
288C23×C4—62no—
289C23×C4—62no—
290C23×C4—64no—
291C23×C4—122no—
292C23×C4C22×D312yes—
293C23×C4C22×D311yescharacteristic
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296#124—232no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—34no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4—122no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4#6718yescomplemented
321C2×C42—24no—
322C2×C42—62no—
323C2×C42—122no—
324C2×C42#6714yescomplemented
325#95—64no—
326#95—64no—
327#95—62no—
328#95—62no—
329#95—62no—
330#95—62no—
331#95—64no—
332#95—64no—
333#95—122no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3C22×D411yescharacteristic
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D412yes—
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4111yescharacteristic
374C23×C3C2×#4111yescharacteristic
375C23×C3C2×#4111yescharacteristic
376C23×C3C2×#4111yescharacteristic
377C23×C3C2×#4112yes—
378C23×C3H(5,𝔽2)12yes—
379C23×C3H(5,𝔽2)12yes—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—24no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—42no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3#12414yescomplemented
403C3×Q8—416no—
404C3×D4—416no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4#12014yes—
426C2×C3×C4#12114yes—
427#67—432no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—41no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C4×D3—416no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—32no—
473C24—32no—
474C24—32no—
475C24—61no—
476C24—62no—
477C24—61no—
478C24—61no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24—62no—
483C24C2×#6714yes—
484C24C23×D311yescharacteristic
485C2×Q8—28no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×D4—28no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—616no—
496C2×D4—128no—
497C2×D4—128no—
498C2×D4—128no—
499C2×D4—128no—
500C2×D4—128no—
501C2×D4—128no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—32no—
518C22×C4—34no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—68no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4D3×D412yes—
552C22×C4#23712yes—
553C22×C4C2×#6712yes—
554C22×C4C2×#6714yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6714yes—
557C22×C4C2×#6712yes—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C22⋊C4—68no—
561C22⋊C4—68no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C22⋊C4—128no—
565C22⋊C4—128no—
566C42—28no—
567C42—124no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—82no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3C2×#12011yescharacteristic
584C22×C3C2×#12111yescharacteristic
585C22×C3#52511yescharacteristic
586C22×C3#52511yescharacteristic
587C22×C3#52512yes—
588C22×C3C2×#12411yescharacteristic
589C22×C3#52911yescharacteristic
590C22×C3#52911yescharacteristic
591C22×C3#53211yescharacteristic
592C22×C3#53211yescharacteristic
593C22×C3#53212yes—
594C22×C3#53511yescharacteristic
595C22×C3#53511yescharacteristic
596C22×C3#53812yes—
597C22×C3#53812yes—
598C22×C3D4212yes—
599C22×C3#54612yes—
600C22×C3#54612yes—
601C22×C3#54612yes—
602C22×C3#54612yes—
603C22×C3#55112yes—
604C22×C3#55512yes—
605C22×C3#55912yes—
606C2×D3—24no—
607C2×D3—28no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—44no—
614C2×D3—42no—
615C2×D3—44no—
616C2×D3—44no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—44no—
621Dic3—42no—
622Dic3—42no—
623Dic3—44no—
624Dic3—42no—
625Dic3—82no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—34no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—62no—
663C23—64no—
664C23—64no—
665C23—64no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23—64no—
670C23—62no—
671C23—62no—
672C23—64no—
673C23—64no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—121no—
678C23—122no—
679C23—122no—
680C23—121no—
681C23—121no—
682C23—122no—
683C23—121no—
684C23C2×D3×D411yescharacteristic
685C23C2×#23711yescharacteristic
686C23#100412yes—
687C23D3×#4111yescharacteristic
688C23D3×#4111yescharacteristic
689C23D3×#4112yes—
690C23D3×#4111yescharacteristic
691C23D3×#4111yescharacteristic
692C23#100912yes—
693C23C22×#6711yescharacteristic
694C23C22×#6712yes—
695Q8—416no—
696D4—416no—
697D4—1232no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—1216no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4#93814yes—
749C2×C4#95314yes—
750C2×C3—84no—
751C2×C3#238811yescharacteristic
752C2×C3#240411yescharacteristic
753C2×C3#240811yescharacteristic
754C2×C3#245912yes—
755C2×C3#247212yes—
756C2×C3#254411yescharacteristic
757C2×C3#255512yes—
758C2×C3#255712yes—
759C2×C3#261011yescharacteristic
760C2×C3#263111yescharacteristic
761C2×C3#285011yescharacteristic
762D3—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—68no—
771C22—64no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—122no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22#566811yescharacteristic
790C22#567012yes—
791C22D3×#12411yescharacteristic
792C22#567612yes—
793C22#567812yes—
794C22#567812yes—
795C22#567912yes—
796C22#568011yescharacteristic
797C22#568011yescharacteristic
798C22#568112yes—
799C22C2×#93811yescharacteristic
800C22D4×#6712yes—
801C22#580511yescharacteristic
802C22#580612yes—
803C22#582812yes—
804C22#582811yescharacteristic
805C22#582811yescharacteristic
806C22#582912yes—
807C22#582912yes—
808C22#583011yescharacteristic
809C22#583211yescharacteristic
810C22#583212yes—
811C22C2×#95311yescharacteristic
812C4—24no—
813C4—24no—
814C4—44no—
815C4—42no—
816C4—124no—
817C4—122no—
818C4—122no—
819C4—122no—
820C4—242no—
821C3#1491511yescharacteristic, complemented, Sylow
822C2—84no—
823C2—124no—
824C2#8296512yes—
825C2#8296911yescharacteristic
826C2#8297512yes—
827C2#8299712yes—
828C2#8299912yes—
829C2#8300011yescharacteristic
830C2#8300211yescharacteristic
831C2#8300811yescharacteristic
832C2#8405311yescharacteristic
833C2#8409511yescharacteristic
834C2#8409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#124C2
prime radicalC2×#5223C2
hypercenterC22×#124D3
hypocenterC3#14915
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×C3×#124C2semidirect
2. C2×#5231C2semidirect
4. C2×#4956C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
6. #72134C2semidirect
7. #72131C2semidirect
8. #71550C2semidirect
9. #71549C2semidirect
10. #71545C2semidirect
11. #71534C2semidirect
42. C22×#124D3semidirect
92. C2×C3×C22⋊C4D4semidirect
94. C2×C3×C42D4semidirect
320. C2×C22⋊C4#67semidirect
324. C2×C42#67semidirect
402. C22×D3#124semidirect
821. C3#14915semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C2×#52312
C2×#52232
C2×#49562
C2×C4×(C2×D3)⋊C42
#721342
#721312
#715502
#715492
#715452
#715342
#149153