Finite Group Databasebeta

← #10750394

Subgroups — #10750394

Order 768.

2266 conjugacy classes of subgroups.

The subgroup lattice has 824 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×#4961C212yesmaximal, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6#72134C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#71546C212yesmaximal, complemented
11#71535C211yesmaximal, characteristic, complemented
12#16504—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×#67C2212yes—
16C2×C3×#124—28no—
17C2×C3×#124—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
28C22×C4⋊Dic3C2212yes—
29C22×Dic3⋊C4C2211yescharacteristic
30#5231—24no—
31#5223—24no—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4961—28no—
41#4940—24no—
42C22×#124D311yescharacteristic, complemented
43C2×#394—32no—
44C2×#393—31no—
45C2×#392—31no—
46C2×#388—31no—
47#1446—31no—
48#1439—32no—
49#1439—32no—
50#1438—31no—
51#1438—32no—
52C4⋊#95—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—42no—
73C22×#67—42no—
74C22×#67—42no—
75C22×#67—42no—
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2312yes—
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2312yes—
81C3×#124—232no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4D418yescomplemented
88C2×C3×C42—24no—
89C2×C3×C42D414yescomplemented
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—24no—
93C2×#217—42no—
94C2×#217—42no—
95C2×#217—42no—
96C2×#217—42no—
97C2×#217—42no—
98C2×#217—42no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×(C2×D3)⋊C4D414yes—
109C2×C4⋊Dic3—24no—
110C2×C4⋊Dic3—24no—
111C2×C4⋊Dic3—42no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—42no—
114C3⋊#95—22no—
115C3⋊#95—22no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—42no—
121C3⋊#95—42no—
122C23×Q8C2×D311yescharacteristic
123C23×D4—32no—
124C23×D4C2×D311yescharacteristic
125C2×#124—28no—
126C2×#124—24no—
127C22×C4⋊C4—32no—
128C22×C4⋊C4—31no—
129C22×C22⋊C4—31no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D312yes—
137C22×C22⋊C4C2×D312yes—
138C22×C42C2×D311yescharacteristic
139#394—68no—
140#393—64no—
141#392—64no—
142#388—64no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—31no—
149C2×#95—32no—
150C2×#95—32no—
151C24×C3—22no—
152C24×C3—22no—
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×C3C2×D414yes—
166C24×C3C2411yescharacteristic
167C23×D3—21no—
168C23×D3—22no—
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—21no—
177C23×D3C2×D412yes—
178C2×C3×Q8—28no—
179C2×C3×Q8—48no—
180C2×C3×Q8—48no—
181C2×C3×Q8—44no—
182C2×C3×Q8—44no—
183C2×C3×D4—28no—
184C2×C3×D4—48no—
185C2×C3×D4—48no—
186C2×C3×D4—44no—
187C2×C3×D4—44no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
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—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D414yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D414yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4#4112yes—
210C2×#67—48no—
211C2×#67—48no—
212C2×#67—48no—
213C2×#67—48no—
214C2×#67—48no—
215C2×#67—48no—
216C2×#67—48no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
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—21no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D412yes—
245C22×Dic3#4114yes—
246C3×C22⋊C4—216no—
247C3×C22⋊C4—216no—
248C3×C42—28no—
249#217—48no—
250#217—48no—
251#217—48no—
252(C2×D3)⋊C4—28no—
253(C2×D3)⋊C4—48no—
254(C2×D3)⋊C4—44no—
255(C2×D3)⋊C4—44no—
256C4⋊Dic3—48no—
257Dic3⋊C4—44no—
258C25—31no—
259C25C22×D312yes—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—24no—
263C22×Q8—22no—
264C22×Q8—42no—
265C22×D4—24no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—42no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—122no—
274C22×D4—122no—
275C22×D4—122no—
276C22×D4—122no—
277C23×C4—31no—
278C23×C4—32no—
279C23×C4—32no—
280C23×C4—31no—
281C23×C4—31no—
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286#124—232no—
287C2×C4⋊C4—64no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—122no—
291C2×C4⋊C4—122no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—34no—
298C2×C22⋊C4—62no—
299C2×C22⋊C4—62no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—122no—
309C2×C22⋊C4—122no—
310C2×C22⋊C4—122no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4#6718yescomplemented
317C2×C42—24no—
318C2×C42#6714yescomplemented
319#95—64no—
320#95—62no—
321#95—62no—
322#95—62no—
323#95—62no—
324#95—64no—
325#95—122no—
326#95—122no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
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×C3C22×D411yescharacteristic
363C23×C3C22×D411yescharacteristic
364C23×C3C22×D412yes—
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4112yes—
367C23×C3H(5,𝔽2)12yes—
368C23×C3H(5,𝔽2)11yescharacteristic
369C23×C3H(5,𝔽2)12yes—
370C23×C3H(5,𝔽2)11yescharacteristic
371C23×C32−1+411yescharacteristic
372C23×C32−1+411yescharacteristic
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—42no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3—41no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—41no—
389C22×D3—41no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C3×Q8—416no—
397C3×D4—416no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4#12014yes—
419C2×C3×C4#12114yes—
420#67—432no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—32no—
465C24—61no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24—61no—
470C24—61no—
471C24—61no—
472C24—61no—
473C24—61no—
474C24—62no—
475C24C2×#6714yes—
476C24C23×D311yescharacteristic
477C2×Q8—28no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×D4—28no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—128no—
488C2×D4—128no—
489C2×D4—128no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—128no—
493C2×D4—128no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—32no—
510C22×C4—34no—
511C22×C4—62no—
512C22×C4—61no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4D3×D412yes—
539C22×C4#23712yes—
540C22×C4C2×#6714yes—
541C22×C4C2×#6712yes—
542C22×C4C2×#6712yes—
543C22×C4C2×#6712yes—
544C22×C4C2×#6714yes—
545C4⋊C4—128no—
546C4⋊C4—124no—
547C22⋊C4—216no—
548C22⋊C4—216no—
549C22⋊C4—68no—
550C22⋊C4—128no—
551C22⋊C4—124no—
552C22⋊C4—128no—
553C22⋊C4—128no—
554C22⋊C4—128no—
555C22⋊C4—124no—
556C42—28no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—82no—
565C22×C3—82no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—82no—
571C22×C3—82no—
572C22×C3C2×#12011yescharacteristic
573C22×C3C2×#12111yescharacteristic
574C22×C3#53211yescharacteristic
575C22×C3#53511yescharacteristic
576C22×C3#53511yescharacteristic
577C22×C3#53511yescharacteristic
578C22×C3#53512yes—
579C22×C3#53611yescharacteristic
580C22×C3#53711yescharacteristic
581C22×C3#53711yescharacteristic
582C22×C3#53712yes—
583C22×C3#53812yes—
584C22×C3#54212yes—
585C22×C3#54211yescharacteristic
586C22×C3#54211yescharacteristic
587C22×C3D4212yes—
588C22×C3#54612yes—
589C22×C3#54612yes—
590C22×C3#54612yes—
591C22×C3#54712yes—
592C22×C3#55912yes—
593C22×C3H(3,𝔽4)12yes—
594C22×C3#56212yes—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—44no—
598C2×D3—44no—
599C2×D3—42no—
600C2×D3—81no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C2×D3—82no—
605C2×D3—82no—
606C3×C4—24no—
607C3×C4—24no—
608C3×C4—42no—
609C3×C4—44no—
610Dic3—44no—
611Dic3—42no—
612Dic3—81no—
613Dic3—81no—
614Dic3—82no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
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—62no—
651C23—62no—
652C23—64no—
653C23—62no—
654C23—64no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—121no—
659C23—121no—
660C23—122no—
661C23—122no—
662C23—121no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—121no—
667C23—122no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—122no—
672C23—121no—
673C23C2×D3×D411yescharacteristic
674C23C2×#23711yescharacteristic
675C23#100412yes—
676C23D3×#4112yes—
677C23#100911yescharacteristic
678C23#100911yescharacteristic
679C23#100912yes—
680C23#101011yescharacteristic
681C23#101011yescharacteristic
682C23C22×#6711yescharacteristic
683C23C22×#6712yes—
684Q8—416no—
685D4—416no—
686D4—1232no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—62no—
711C2×C4—64no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—121no—
717C2×C4—122no—
718C2×C4—121no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—121no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—121no—
730C2×C4—122no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—121no—
736C2×C4#93814yes—
737C2×C4#95314yes—
738C2×C3—84no—
739C2×C3#240811yescharacteristic
740C2×C3#243011yescharacteristic
741C2×C3#254411yescharacteristic
742C2×C3#261511yescharacteristic
743C2×C3#262011yescharacteristic
744C2×C3#266211yescharacteristic
745C2×C3#267012yes—
746C2×C3#267212yes—
747C2×C3#271012yes—
748C2×C3#271212yes—
749C2×C3#281911yescharacteristic
750D3—82no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—122no—
767C22—122no—
768C22—124no—
769C22—124no—
770C22—122no—
771C22—241no—
772C22—242no—
773C22—242no—
774C22—241no—
775C22—241no—
776C22—241no—
777C22#566912yes—
778C22#567411yescharacteristic
779C22#567511yescharacteristic
780C22#567612yes—
781C22#567812yes—
782C22#568112yes—
783C22#568211yescharacteristic
784C22#568211yescharacteristic
785C22#568312yes—
786C22#568412yes—
787C22C2×#93811yescharacteristic
788C22D4×#6712yes—
789C22#580511yescharacteristic
790C22#580612yes—
791C22#582412yes—
792C22#582912yes—
793C22#583011yescharacteristic
794C22#583012yes—
795C22#583211yescharacteristic
796C22#583311yescharacteristic
797C22#583312yes—
798C22#583311yescharacteristic
799C22C2×#95311yescharacteristic
800C4—24no—
801C4—24no—
802C4—44no—
803C4—42no—
804C4—122no—
805C4—124no—
806C4—242no—
807C4—241no—
808C4—241no—
809C3#1650411yescharacteristic, complemented, Sylow
810C2—84no—
811C2—242no—
812C2#8296911yescharacteristic
813C2#8298111yescharacteristic
814C2#8298612yes—
815C2#8298712yes—
816C2#8300111yescharacteristic
817C2#8300312yes—
818C2#8300412yes—
819C2#8300711yescharacteristic
820C2#8405311yescharacteristic
821C2#8409111yescharacteristic
822C2#8409811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#124C2
prime radicalC2×#5223C2
hypercenterC22×#124D3
hypocenterC3#16504
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×#4961C2semidirect
5. C2×#4940C2semidirect
6. #72134C2semidirect
7. #72131C2semidirect
8. #71550C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71535C2semidirect
42. C22×#124D3semidirect
87. C2×C3×C22⋊C4D4semidirect
89. C2×C3×C42D4semidirect
316. C2×C22⋊C4#67semidirect
318. C2×C42#67semidirect
809. C3#16504semidirect

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×#49612
C2×#49402
#721342
#721312
#715502
#715472
#715462
#715352
#165043