Finite Group Databasebeta

← #10742719

Subgroups — #10742719

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×#123C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic
3C2×#5213C211yesmaximal, characteristic, complemented
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4989C212yesmaximal, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71565C212yesmaximal, complemented
8#71550C212yesmaximal, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71549C211yesmaximal, characteristic, complemented
11#71547C212yesmaximal, complemented
12#15950—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C2×C3×#123—24no—
19C2×C3×#123—28no—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2212yes—
28C2×#938—24no—
29C2×#938—24no—
30C2×#938—24no—
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2212yes—
35#5213—24no—
36#5210—24no—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4989—28no—
44C22×#123D311yescharacteristic, complemented
45C22×#121—31no—
46C2×#386—31no—
47C2×#385—31no—
48C2×#385—32no—
49#1441—32no—
50#1440—31no—
51#1439—32no—
52#1438—31no—
53#1438—31no—
54#1438—32no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—24no—
61C22×C3×D4—42no—
62C22×C3×D4D414yes—
63C23×C3×C4—22no—
64C23×C3×C4—24no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—42no—
68C23×C3×C4C2312yes—
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C22×#67—22no—
72C22×#67—22no—
73C22×#67—22no—
74C22×#67—22no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—22no—
78C22×#67—42no—
79C22×#67—42no—
80C22×#67D414yes—
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2312yes—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—24no—
90C22×C4×D3—42no—
91C3×#123—232no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C4⋊C4D418yescomplemented
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—24no—
107C2×#217—22no—
108C2×#217—24no—
109C2×#217—42no—
110C2×#217—42no—
111C2×#217—42no—
112C2×#217D414yes—
113#938—232no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—42no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×Dic3⋊C4—24no—
124C2×Dic3⋊C4—24no—
125C2×Dic3⋊C4—42no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—42no—
131C3⋊#95—42no—
132C23×D4—31no—
133C23×D4—31no—
134C23×D4C2×D311yescharacteristic
135C24×C4—31no—
136C24×C4C2×D311yescharacteristic
137C2×#123—24no—
138C2×#123—28no—
139C2×#121—64no—
140C2×#121—64no—
141C2×#121—64no—
142C22×C4⋊C4—31no—
143C22×C4⋊C4—32no—
144C22×C4⋊C4C2×D312yes—
145C22×C22⋊C4—31no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—31no—
152C22×C22⋊C4C2×D312yes—
153C22×C22⋊C4C2×D311yescharacteristic
154#386—64no—
155#385—64no—
156#385—68no—
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—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3C2×D412yes—
178C24×C3C2×D412yes—
179C24×C3C2×D412yes—
180C24×C3C2×D412yes—
181C24×C3C2411yescharacteristic
182C23×D3—22no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3C2×D412yes—
190C23×D3#4114yes—
191C2×C3×D4—28no—
192C2×C3×D4—28no—
193C2×C3×D4—44no—
194C2×C3×D4—48no—
195C2×C3×D4—48no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—28no—
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×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4—44no—
215C22×C3×C4—44no—
216C22×C3×C4C2×D414yes—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D414yes—
219C22×C3×C4C2×D412yes—
220C2×#67—28no—
221C2×#67—28no—
222C2×#67—28no—
223C2×#67—44no—
224C2×#67—48no—
225C2×#67—48no—
226C2×#67—48no—
227C2×#67—48no—
228C2×#67—44no—
229C2×#67—44no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
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×Dic3C2×D412yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D412yes—
258C22×Dic3#4114yes—
259C2×C4×D3—28no—
260C2×C4×D3—48no—
261C2×C4×D3—48no—
262C2×C4×D3—44no—
263C2×C4×D3—44no—
264C3×C4⋊C4—216no—
265C3×C22⋊C4—28no—
266C3×C22⋊C4—216no—
267#217—28no—
268#217—28no—
269#217—28no—
270#217—48no—
271#217—44no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4—48no—
274C4⋊Dic3—28no—
275Dic3⋊C4—48no—
276C25—31no—
277C25C22×D311yescharacteristic
278C25C22×D311yescharacteristic
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—24no—
282C22×D4—34no—
283C22×D4—42no—
284C22×D4—62no—
285C22×D4—62no—
286C22×D4—64no—
287C22×D4—62no—
288C22×D4—62no—
289C22×D4—62no—
290C22×D4—64no—
291C22×D4—122no—
292C22×D4—122no—
293C22×D4#6714yes—
294C23×C4—22no—
295C23×C4—24no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—32no—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—32no—
303C23×C4—42no—
304C23×C4—62no—
305C23×C4—62no—
306C23×C4—62no—
307C23×C4—64no—
308C23×C4—122no—
309C23×C4C22×D312yes—
310C23×C4C22×D312yes—
311C23×C4C22×D311yescharacteristic
312#123—232no—
313#121—632no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—62no—
318C2×C4⋊C4—62no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C4⋊C4—122no—
322C2×C4⋊C4#6718yescomplemented
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—34no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4—62no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—62no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—62no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—122no—
344C2×C22⋊C4—122no—
345C2×C22⋊C4—122no—
346C2×C22⋊C4—122no—
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—22no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—24no—
369C23×C3—24no—
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—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
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#12014yes—
395C23×C3C22×D411yescharacteristic
396C23×C3C22×D411yescharacteristic
397C23×C3C22×D411yescharacteristic
398C23×C3C22×D412yes—
399C23×C3C2×#4112yes—
400C23×C3C2×#4112yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C3H(5,𝔽2)12yes—
403C23×C32−1+412yes—
404C22×D3—22no—
405C22×D3—24no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—42no—
423C22×D3—42no—
424C22×D3#12314yescomplemented
425C3×D4—416no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—416no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4#12014yes—
446#67—416no—
447#67—416no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—22no—
455C2×Dic3—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
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—
477C4×D3—416no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—32no—
493C24—34no—
494C24—61no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24—61no—
501C24D3×D412yes—
502C24D3×D412yes—
503C24C2×#6712yes—
504C24C2×#6712yes—
505C24C23×D311yescharacteristic
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—68no—
512C2×D4—68no—
513C2×D4—68no—
514C2×D4—124no—
515C2×D4—128no—
516C2×D4—128no—
517C2×D4—128no—
518C2×D4—128no—
519C2×D4—124no—
520C2×D4—124no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—34no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—68no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
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—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—128no—
572C22×C4—128no—
573C22×C4—124no—
574C22×C4—124no—
575C22×C4C2×#6714yes—
576C22×C4C2×#6714yes—
577C22×C4C2×#6714yes—
578C22×C4C2×#6712yes—
579C4⋊C4—216no—
580C4⋊C4—68no—
581C4⋊C4—128no—
582C22⋊C4—28no—
583C22⋊C4—216no—
584C22⋊C4—616no—
585C22⋊C4—68no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—128no—
589C22⋊C4—128no—
590C22⋊C4—124no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3—82no—
608C22×C3—82no—
609C22×C3C2×#12011yescharacteristic
610C22×C3C2×#12011yescharacteristic
611C22×C3C2×#12311yescharacteristic
612C22×C3#52511yescharacteristic
613C22×C3#52512yes—
614C22×C3#53411yescharacteristic
615C22×C3#53411yescharacteristic
616C22×C3#53611yescharacteristic
617C22×C3#53712yes—
618C22×C3#53812yes—
619C22×C3#53912yes—
620C22×C3D4212yes—
621C22×C3D4212yes—
622C22×C3#54612yes—
623C22×C3#54612yes—
624C22×C3#54712yes—
625C22×C3#54712yes—
626C22×C3#54812yes—
627C22×C3#55012yes—
628C22×C3#55312yes—
629C22×C3#56212yes—
630C2×D3—24no—
631C2×D3—28no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—44no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—44no—
638C2×D3—44no—
639C3×C4—24no—
640C3×C4—44no—
641C3×C4—44no—
642Dic3—42no—
643Dic3—42no—
644Dic3—42no—
645Dic3—44no—
646Dic3—82no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—34no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—62no—
690C23—64no—
691C23—64no—
692C23—64no—
693C23—64no—
694C23—62no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23—64no—
699C23—121no—
700C23—121no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—121no—
705C23—122no—
706C23—122no—
707C23—122no—
708C23—121no—
709C23#93714yes—
710C23C2×D3×D411yescharacteristic
711C23C2×D3×D411yescharacteristic
712C23#100412yes—
713C23D3×#4112yes—
714C23D3×#4112yes—
715C23#100912yes—
716C23#101012yes—
717C23C22×#6711yescharacteristic
718C23C22×#6712yes—
719D4—416no—
720D4—1216no—
721D4—1216no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—64no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—1216no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—121no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—121no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4#95314yes—
772C2×C3—44no—
773C2×C3—82no—
774C2×C3#240311yescharacteristic
775C2×C3#240511yescharacteristic
776C2×C3#240611yescharacteristic
777C2×C3#240712yes—
778C2×C3#244312yes—
779C2×C3#245612yes—
780C2×C3#268112yes—
781C2×C3#268212yes—
782C2×C3#270812yes—
783D3—44no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—64no—
799C22—68no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—122no—
805C22—124no—
806C22—122no—
807C22—124no—
808C22—124no—
809C22—124no—
810C22—124no—
811C22#564811yescharacteristic
812C22D3×#12311yescharacteristic
813C22#565311yescharacteristic
814C22#565412yes—
815C22#565512yes—
816C22#565611yescharacteristic
817C22#565712yes—
818C22#566012yes—
819C22#566112yes—
820C22#566712yes—
821C22C2×#93711yescharacteristic
822C22D4×#6712yes—
823C22D4×#6712yes—
824C22#580411yescharacteristic
825C22#582412yes—
826C22#582812yes—
827C22#582912yes—
828C22#583112yes—
829C22#583312yes—
830C22#583412yes—
831C22C2×#95311yescharacteristic
832C4—24no—
833C4—44no—
834C4—44no—
835C4—122no—
836C4—122no—
837C4—122no—
838C4—124no—
839C4—242no—
840C3#1595011yescharacteristic, complemented, Sylow
841C2—44no—
842C2—82no—
843C2—124no—
844C2#8284111yescharacteristic
845C2#8287212yes—
846C2#8287312yes—
847C2#8289311yescharacteristic
848C2#8289712yes—
849C2#8289912yes—
850C2#8291012yes—
851C2#8405211yescharacteristic
852C2#8409712yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
prime radicalC22×#938C2
hypercenterC22×#123D3
hypocenterC3#15950
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C2×#5213C2semidirect
4. C2×#5210C2semidirect
5. C2×#4989C2semidirect
6. #72131C2semidirect
7. #71565C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71549C2semidirect
11. #71547C2semidirect
44. C22×#123D3semidirect
94. C2×C3×C4⋊C4D4semidirect
322. C2×C4⋊C4#67semidirect
424. C22×D3#123semidirect
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×#1232
C22×#9382
C2×#52132
C2×#52102
C2×#49892
#721312
#715652
#715502
#715492
#715472
#159503