Finite Group Databasebeta

← #10735668

Subgroups — #10735668

Order 768.

2506 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C2×C3×#390C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#4956C212yesmaximal, complemented
6C2×#4947C212yesmaximal, complemented
7#71569C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#71537C211yesmaximal, characteristic, complemented
11#71536C211yesmaximal, characteristic, complemented
12#15453—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×C4×D3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C42C2211yescharacteristic
21C22×#217C2212yes—
22C22×#217C2212yes—
23C22×#217C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C2×#896—24no—
30C2×#896—24no—
31C2×#896—24no—
32C3×#390—24no—
33#5223—24no—
34#5222—24no—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42#4956—28no—
43#4947—28no—
44C22×C22⋊Q8—31no—
45C2×#394—31no—
46C2×#393—32no—
47C2×#392—31no—
48C2×#390D311yescharacteristic, complemented
49C2×#386—32no—
50#1445—31no—
51#1439—32no—
52#1438—32no—
53#1437—31no—
54#1436—31no—
55C25×C3C2312yes—
56C24×D3C2311yescharacteristic
57C22×C3×D4—24no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—42no—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2312yes—
65C23×C3×C4C2311yescharacteristic
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—42no—
72C22×#67—42no—
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—24no—
82C22×C4×D3—42no—
83C22×Dic6—22no—
84C22×Dic6—22no—
85C22×Dic6—22no—
86C22×Dic6—24no—
87C22×Dic6—42no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4D414yescomplemented
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C42—22no—
98C2×C3×C42—42no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—42no—
107C2×#217—42no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—42no—
116C2×(C2×D3)⋊C4D414yes—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4D414yescomplemented
123#896—232no—
124C3⋊#95—24no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—42no—
130C3⋊#95D418yescomplemented
131C23×Q8—31no—
132C23×D4—32no—
133C23×D4C2×D311yescharacteristic
134C24×C4—31no—
135C2×C22⋊Q8—64no—
136C2×C22⋊Q8—64no—
137C2×C22⋊Q8—64no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4C2×D311yescharacteristic
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4C2×D312yes—
148C22×C22⋊C4C2×D312yes—
149C22×C42C2×D311yescharacteristic
150#394—64no—
151#393—68no—
152#392—64no—
153#390—24no—
154#386—68no—
155C2×#95—32no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—31no—
160C2×#95—32no—
161C2×#95—32no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
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#4114yes—
177C24×C3C2411yescharacteristic
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3C2×D412yes—
186C23×D3#4114yes—
187C2×C3×D4—28no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—44no—
191C2×C3×D4—44no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C2×#67—216no—
215C2×#67—48no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C2×#67—48no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
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×Dic3—22no—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D412yes—
248C22×Dic3C2×D414yes—
249C22×Dic3C2×D412yes—
250C2×C4×D3—28no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C2×C4×D3—44no—
254C2×C4×D3—44no—
255C2×Dic6—28no—
256C2×Dic6—48no—
257C2×Dic6—48no—
258C2×Dic6—44no—
259C2×Dic6—44no—
260C3×C4⋊C4—28no—
261C3×C22⋊C4—48no—
262C3×C22⋊C4—48no—
263C3×C42—44no—
264#217—48no—
265#217—48no—
266#217—48no—
267(C2×D3)⋊C4—28no—
268(C2×D3)⋊C4—28no—
269(C2×D3)⋊C4—48no—
270Dic3⋊C4—28no—
271Dic3⋊C4—28no—
272C25—31no—
273C25C22×D312yes—
274C22×Q8—62no—
275C22×Q8—62no—
276C22×Q8—64no—
277C22×Q8—62no—
278C22×Q8—122no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—42no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C22×D4—64no—
288C22×D4—64no—
289C22×D4—122no—
290C22×D4—122no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—32no—
295C23×C4—32no—
296C23×C4—62no—
297C23×C4—64no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—122no—
301C23×C4C22×D312yes—
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304C23×C4C22×D311yescharacteristic
305C22⋊Q8—632no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—34no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—62no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4#6714yescomplemented
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—34no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—62no—
324C2×C22⋊C4—62no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—64no—
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—64no—
336C2×C22⋊C4—122no—
337C2×C22⋊C4—122no—
338C2×C22⋊C4—122no—
339C2×C42—22no—
340C2×C42—42no—
341#95—38no—
342#95—64no—
343#95—64no—
344#95—62no—
345#95—64no—
346#95—62no—
347#95—122no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
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×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3C22×D411yescharacteristic
384C23×C3C22×D411yescharacteristic
385C23×C3C22×D412yes—
386C23×C3C22×D411yescharacteristic
387C23×C3C2×#4112yes—
388C23×C3C2×#4112yes—
389C23×C3H(5,𝔽2)12yes—
390C23×C3H(5,𝔽2)12yes—
391C23×C32−1+412yes—
392C22×D3—22no—
393C22×D3—24no—
394C22×D3—22no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3#12414yes—
413C3×D4—416no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4#12014yes—
436#67—432no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3#12714yes—
466C4×D3—416no—
467Dic6—416no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—32no—
483C24—34no—
484C24—62no—
485C24—61no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—61no—
491C24#23514yes—
492C24C23×D311yescharacteristic
493C2×Q8—68no—
494C2×Q8—128no—
495C2×Q8—124no—
496C2×Q8—128no—
497C2×Q8—124no—
498C2×D4—28no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—616no—
504C2×D4—128no—
505C2×D4—128no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—128no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—34no—
527C22×C4—32no—
528C22×C4—34no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—68no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—128no—
557C22×C4—124no—
558C22×C4—128no—
559C22×C4—124no—
560C22×C4D3×D414yes—
561C22×C4D3×D412yes—
562C22×C4D3×D412yes—
563C22×C4C2×#6712yes—
564C22×C4C2×#6712yes—
565C22×C4C2×#6712yes—
566C4⋊C4—28no—
567C4⋊C4—68no—
568C4⋊C4—68no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—128no—
574C22⋊C4—128no—
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3C2×#12011yescharacteristic
594C22×C3#52511yescharacteristic
595C22×C3#52512yes—
596C22×C3C2×#12411yescharacteristic
597C22×C3C2×#12711yescharacteristic
598C22×C3#53511yescharacteristic
599C22×C3#53511yescharacteristic
600C22×C3#53611yescharacteristic
601C22×C3#53712yes—
602C22×C3#53812yes—
603C22×C3#53912yes—
604C22×C3D4212yes—
605C22×C3D4212yes—
606C22×C3#54612yes—
607C22×C3#54612yes—
608C22×C3#54612yes—
609C22×C3#54812yes—
610C22×C3#54812yes—
611C22×C3#54812yes—
612C22×C3#55112yes—
613C22×C3#56212yes—
614C2×D3—24no—
615C2×D3—28no—
616C2×D3—42no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—42no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—44no—
623C3×C4—24no—
624C3×C4—44no—
625C3×C4—42no—
626C3×C4—42no—
627Dic3—24no—
628Dic3—42no—
629Dic3—42no—
630Dic3—44no—
631Dic3—82no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—34no—
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—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—62no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—62no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—121no—
679C23—121no—
680C23—122no—
681C23—121no—
682C23—122no—
683C23—121no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23C2×#23512yes—
689C23C2×D3×D411yescharacteristic
690C23C2×D3×D411yescharacteristic
691C23C2×D3×D412yes—
692C23#100412yes—
693C23#100412yes—
694C23D3×#4112yes—
695C23#101012yes—
696C23C22×#6711yescharacteristic
697Q8—1216no—
698D4—416no—
699D4—1232no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—34no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—62no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—1216no—
734C2×C4—122no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—121no—
740C2×C4—122no—
741C2×C4—121no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4#93714yes—
752C2×C3—84no—
753C2×C3#240411yescharacteristic
754C2×C3#243311yescharacteristic
755C2×C3#243611yescharacteristic
756C2×C3#246312yes—
757C2×C3#247212yes—
758C2×C3#254012yes—
759C2×C3#267612yes—
760C2×C3#268112yes—
761C2×C3#269612yes—
762D3—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—64no—
771C22—68no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—124no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—122no—
786C22—122no—
787C22#549012yes—
788C22#549012yes—
789C22#554712yes—
790C22#555212yes—
791C22#555612yes—
792C22#556412yes—
793C22#559712yes—
794C22#561012yes—
795C22#561312yes—
796C22#562112yes—
797C22D3×#12411yescharacteristic
798C22#567511yescharacteristic
799C22#567712yes—
800C22D3×#12711yescharacteristic
801C22#571511yescharacteristic
802C22#571712yes—
803C22#579111yescharacteristic
804C22C2×#93711yescharacteristic
805C22D4×#6712yes—
806C22#580511yescharacteristic
807C22#583112yes—
808C4—24no—
809C4—44no—
810C4—42no—
811C4—42no—
812C4—64no—
813C4—124no—
814C4—122no—
815C4—122no—
816C4—242no—
817C3#1545311yescharacteristic, complemented, Sylow
818C2—84no—
819C2—124no—
820C2#7633012yes—
821C2#7634712yes—
822C2#7638412yes—
823C2#7646512yes—
824C2#8212511yescharacteristic
825C2#8236812yes—
826C2#8271912yes—
827C2#8296111yescharacteristic
828C2#8317511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC2×#5223C2
hypercenterC2×#390D3
hypocenterC3#15453
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
2. C2×C3×#390C2semidirect
4. C2×#5222C2semidirect
5. C2×#4956C2semidirect
6. C2×#4947C2semidirect
7. #71569C2semidirect
8. #71550C2semidirect
9. #71547C2semidirect
10. #71537C2semidirect
11. #71536C2semidirect
48. C2×#390D3semidirect
90. C2×C3×C4⋊C4D4semidirect
122. C2×Dic3⋊C4D4semidirect
130. C3⋊#95D4semidirect
314. C2×C4⋊C4#67semidirect
817. C3#15453semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×C3×#3902
C2×#52232
C2×#52222
C2×#49562
C2×#49472
#715692
#715502
#715472
#715372
#715362
#154533