Finite Group Databasebeta

← #10729216

Subgroups — #10729216

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#936C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4990C211yesmaximal, characteristic, complemented
6C2×#4957C212yesmaximal, complemented
7C2×#4673C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#71545C212yesmaximal, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12#14928—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×Dic6C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C2×#936—28no—
23C2×#936—24no—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×Dic3⋊C4C2212yes—
29C22×C4×Dic3C2212yes—
30C22×C4×Dic3C2211yescharacteristic
31C3×#394—24no—
32C2×C3×#95C2211yescharacteristic
33#5223—24no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40#4990—24no—
41#4979—24no—
42#4957—28no—
43#4673—24no—
44C22×#124—31no—
45C2×#395—31no—
46C2×#394D311yescharacteristic, complemented
47C2×#393—31no—
48C2×#392—31no—
49C2×#390—32no—
50C2×#388—31no—
51#1439—32no—
52#1438—32no—
53#1437—32no—
54C4×#95—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×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
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×Dic3C2311yescharacteristic
74C23×Dic3C2312yes—
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2312yes—
78C22×Dic6—22no—
79C22×Dic6—24no—
80C22×Dic6—22no—
81C22×Dic6—22no—
82C22×Dic6—42no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—42no—
91C2×C3×C22⋊C4—42no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217D418yescomplemented
101#936—232no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
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—22no—
112C2×(C2×D3)⋊C4—42no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—42no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—42no—
120C2×C4×Dic3D414yescomplemented
121C3×#95D414yescomplemented
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95D414yes—
128C23×Q8—31no—
129C23×D4—32no—
130C23×D4C2×D311yescharacteristic
131C2×#124—64no—
132C2×#124—68no—
133C22×C4⋊C4—32no—
134C22×C4⋊C4C2×D311yescharacteristic
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4—31no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4C2×D312yes—
143C22×C22⋊C4C2×D312yes—
144C22×C42—31no—
145C22×C42—32no—
146#395—64no—
147#394—24no—
148#393—64no—
149#392—64no—
150#390—68no—
151#388—64no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95C2×D311yescharacteristic
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×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3C2×D414yes—
174C24×C3C2411yescharacteristic
175C23×D3—21no—
176C23×D3—21no—
177C23×D3—22no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3#4112yes—
186C2×C3×D4—28no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D414yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4#4112yes—
215C2×#67—216no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C2×#67—48no—
221C2×#67—48no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
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—21no—
236C22×Dic3—21no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3C2×D412yes—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D414yes—
248C22×Dic3C2×D414yes—
249C22×Dic3#4114yes—
250C22×Dic3#4114yes—
251C2×Dic6—28no—
252C2×Dic6—48no—
253C2×Dic6—48no—
254C2×Dic6—44no—
255C2×Dic6—44no—
256C3×C4⋊C4—44no—
257C3×C22⋊C4—48no—
258C3×C22⋊C4—48no—
259#217—216no—
260#217—216no—
261#217—48no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—44no—
265(C2×D3)⋊C4—44no—
266Dic3⋊C4—48no—
267C4×Dic3—28no—
268C4×Dic3—48no—
269C25—31no—
270C25C22×D312yes—
271C22×Q8—64no—
272C22×Q8—62no—
273C22×Q8—62no—
274C22×Q8—62no—
275C22×Q8—122no—
276C22×D4—24no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—42no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—31no—
289C23×C4—32no—
290C23×C4—32no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4C22×D311yescharacteristic
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D312yes—
296C23×C4C22×D311yescharacteristic
297#124—632no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—122no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—38no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—122no—
330C2×C42—34no—
331C2×C42—64no—
332C2×C42—64no—
333C2×C42—64no—
334C2×C42—122no—
335#95—34no—
336#95—64no—
337#95—62no—
338#95—62no—
339#95—64no—
340#95—64no—
341#95#6714yescomplemented
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
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×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3C22×D411yescharacteristic
378C23×C3C22×D412yes—
379C23×C3C22×D411yescharacteristic
380C23×C3C22×D411yescharacteristic
381C23×C3C2×#4111yescharacteristic
382C23×C3C2×#4111yescharacteristic
383C23×C3C2×#4112yes—
384C23×C3C2×#4112yes—
385C23×C3H(5,𝔽2)12yes—
386C23×C3H(5,𝔽2)11yescharacteristic
387C23×C32−1+411yescharacteristic
388C22×D3—22no—
389C22×D3—24no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—24no—
393C22×D3—41no—
394C22×D3—42no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—41no—
408C22×D3—42no—
409C22×D3—41no—
410C22×D3—42no—
411C3×D4—416no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—22no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4#12714yes—
436#67—432no—
437C2×Dic3—24no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—22no—
448C2×Dic3—24no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—42no—
464C2×Dic3#12014yes—
465C2×Dic3#12418yescomplemented
466Dic6—416no—
467C24—22no—
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—32no—
482C24—61no—
483C24—62no—
484C24—61no—
485C24—61no—
486C24—62no—
487C24—61no—
488C24—62no—
489C24—62no—
490C24—61no—
491C24—61no—
492C24D3×D414yes—
493C24C23×D311yescharacteristic
494C2×Q8—68no—
495C2×Q8—128no—
496C2×Q8—128no—
497C2×Q8—124no—
498C2×Q8—124no—
499C2×D4—28no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—616no—
505C2×D4—128no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—128no—
510C2×D4—128no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—34no—
531C22×C4—32no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—34no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—61no—
553C22×C4—62no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4D3×D412yes—
560C22×C4D3×D412yes—
561C22×C4#23712yes—
562C22×C4C2×#6714yes—
563C22×C4C2×#6712yes—
564C4⋊C4—44no—
565C4⋊C4—128no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—68no—
569C22⋊C4—616no—
570C22⋊C4—616no—
571C22⋊C4—128no—
572C22⋊C4—124no—
573C22⋊C4—128no—
574C22⋊C4—124no—
575C42—68no—
576C42—128no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3C2×#12011yescharacteristic
593C22×C3#52512yes—
594C22×C3#52511yescharacteristic
595C22×C3C2×#12412yes—
596C22×C3C2×#12711yescharacteristic
597C22×C3#53211yescharacteristic
598C22×C3#53211yescharacteristic
599C22×C3#53212yes—
600C22×C3#53212yes—
601C22×C3#53511yescharacteristic
602C22×C3#53711yescharacteristic
603C22×C3#53812yes—
604C22×C3#54212yes—
605C22×C3D4212yes—
606C22×C3D4212yes—
607C22×C3#54611yescharacteristic
608C22×C3#54612yes—
609C22×C3#54611yescharacteristic
610C22×C3#54712yes—
611C22×C3#54811yescharacteristic
612C22×C3#54811yescharacteristic
613C22×C3#55112yes—
614C22×C3#55512yes—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—42no—
620C2×D3—81no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—82no—
625C2×D3—82no—
626C3×C4—24no—
627C3×C4—42no—
628C3×C4—44no—
629C3×C4—81no—
630Dic3—24no—
631Dic3—28no—
632Dic3—42no—
633Dic3—44no—
634Dic3—81no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
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—42no—
669C23—42no—
670C23—64no—
671C23—64no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—122no—
676C23—122no—
677C23—121no—
678C23—121no—
679C23—122no—
680C23—122no—
681C23—121no—
682C23—121no—
683C23—122no—
684C23—121no—
685C23—122no—
686C23—121no—
687C23—122no—
688C23—121no—
689C23—121no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23C2×D3×D412yes—
694C23C2×D3×D411yescharacteristic
695C23C2×D3×D411yescharacteristic
696C23C2×#23711yescharacteristic
697C23#100412yes—
698C23#100411yescharacteristic
699C23D3×#4112yes—
700C23D3×#4111yescharacteristic
701C23D3×#4112yes—
702C23#101011yescharacteristic
703C23C22×#6711yescharacteristic
704Q8—1216no—
705D4—416no—
706D4—1232no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—38no—
718C2×C4—34no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—64no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—62no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—122no—
757C2×C4—121no—
758C2×C4—122no—
759C2×C4#94014yes—
760C2×C3—84no—
761C2×C3#238811yescharacteristic
762C2×C3#243011yescharacteristic
763C2×C3#243311yescharacteristic
764C2×C3#246112yes—
765C2×C3#247212yes—
766C2×C3#249112yes—
767C2×C3#254011yescharacteristic
768C2×C3#255512yes—
769C2×C3#261011yescharacteristic
770C2×C3#266211yescharacteristic
771C2×C3#285811yescharacteristic
772D3—82no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—122no—
789C22—124no—
790C22—124no—
791C22—122no—
792C22—122no—
793C22—241no—
794C22—241no—
795C22—242no—
796C22—241no—
797C22—241no—
798C22—242no—
799C22D3×#12011yescharacteristic
800C22#559012yes—
801C22#559211yescharacteristic
802C22#559612yes—
803C22#559811yescharacteristic
804C22#560611yescharacteristic
805C22#560811yescharacteristic
806C22#561012yes—
807C22#561211yescharacteristic
808C22#561312yes—
809C22#561612yes—
810C22#565512yes—
811C22#565612yes—
812C22#565912yes—
813C22#566212yes—
814C22#566811yescharacteristic
815C22#566811yescharacteristic
816C22D3×#12412yes—
817C22D4×#6712yes—
818C22C2×#94011yescharacteristic
819C22#580611yescharacteristic
820C22#583111yescharacteristic
821C22#583212yes—
822C4—24no—
823C4—42no—
824C4—44no—
825C4—64no—
826C4—68no—
827C4—81no—
828C4—122no—
829C4—124no—
830C4—241no—
831C3#1492811yescharacteristic, complemented, Sylow
832C2—84no—
833C2—242no—
834C2#7688911yescharacteristic
835C2#7692612yes—
836C2#7693512yes—
837C2#7696911yescharacteristic
838C2#7699711yescharacteristic
839C2#7711611yescharacteristic
840C2#8258811yescharacteristic
841C2#8266811yescharacteristic
842C2#8267212yes—
843C2#8285212yes—
844C2#8299311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3#14928
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#936C2semidirect
2. C2×C3×#394C2semidirect
4. C2×#4979C2semidirect
5. C2×#4990C2semidirect
6. C2×#4957C2semidirect
7. C2×#4673C2semidirect
8. #71550C2semidirect
9. #71547C2semidirect
10. #71545C2semidirect
11. Dic3×#95C2semidirect
46. C2×#394D3semidirect
100. C2×#217D4semidirect
120. C2×C4×Dic3D4semidirect
121. C3×#95D4semidirect
341. #95#67semidirect
465. C2×Dic3#124semidirect
831. C3#14928semidirect

Maximal subgroups

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

subgroupindex
C22×#9362
C2×C3×#3942
C2×#52232
C2×#49792
C2×#49902
C2×#49572
C2×#46732
#715502
#715472
#715452
Dic3×#952
#149283