Finite Group Databasebeta

← #10727092

Subgroups — #10727092

Order 768.

3510 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#939C212yesmaximal, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#5220C212yesmaximal, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C22×C3⋊#95C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#71550C212yesmaximal, complemented
11#71547C212yesmaximal, complemented
12#14757—31nomaximal, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C23×#67C2212yes—
18C24×Dic3C2212yes—
19C2×C3×#121—28no—
20C2×C3×#121—24no—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×#217C2211yescharacteristic
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2212yes—
27C2×#939—28no—
28C2×#939—28no—
29C2×#939—28no—
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2212yes—
34#5223—24no—
35#5220—28no—
36#5213—24no—
37C2×C3⋊#95—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2211yescharacteristic
45C22×#121—32no—
46C22×#121D311yescharacteristic, complemented
47C2×#392—31no—
48C2×#386—32no—
49C2×#386—31no—
50C22×#95—31no—
51#1444—31no—
52#1439—31no—
53#1439—32no—
54#1438—31no—
55#1438—32no—
56C25×C3C2312yes—
57C25×C3C2311yescharacteristic
58C24×D3C2311yescharacteristic
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—24no—
65C22×C3×D4—24no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4D418yescomplemented
71C23×C3×C4—24no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—42no—
75C23×C3×C4D414yescomplemented
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2312yes—
78C23×C3×C4C2311yescharacteristic
79C22×#67—22no—
80C22×#67—24no—
81C22×#67—24no—
82C22×#67—24no—
83C22×#67—22no—
84C22×#67—24no—
85C22×#67—24no—
86C22×#67—24no—
87C22×#67—24no—
88C22×#67—42no—
89C22×#67—42no—
90C22×#67D414yescomplemented
91C23×Dic3—24no—
92C23×Dic3—24no—
93C23×Dic3—24no—
94C23×Dic3—24no—
95C23×Dic3—42no—
96C23×Dic3—42no—
97C23×Dic3D418yescomplemented
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2312yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2312yes—
103C3×#121—232no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—24no—
112C2×#217—22no—
113C2×#217—24no—
114C2×#217—24no—
115C2×#217—24no—
116C2×#217—24no—
117C2×#217—24no—
118C2×#217—42no—
119C2×#217—42no—
120#939—264no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—42no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—24no—
136C3⋊#95—24no—
137C3⋊#95—24no—
138C3⋊#95D414yescomplemented
139C23×D4—31no—
140C23×D4—32no—
141C23×D4C2×D312yes—
142C23×D4C2×D311yescharacteristic
143C24×C4—32no—
144C24×C4C2×D311yescharacteristic
145C2×#121—28no—
146C2×#121—24no—
147C2×#121—68no—
148C2×#121—68no—
149C2×#121—68no—
150C22×C4⋊C4—32no—
151C22×C4⋊C4C2×D311yescharacteristic
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4C2×D312yes—
160#392—64no—
161#386—68no—
162#386—64no—
163C2×#95—31no—
164C2×#95—32no—
165C2×#95—31no—
166C2×#95—32no—
167C2×#95—31no—
168C2×#95—32no—
169C2×#95—31no—
170C2×#95—64no—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3C2×D412yes—
192C24×C3C2×D414yes—
193C24×C3C2×D414yes—
194C24×C3C2×D414yes—
195C24×C3C2×D412yes—
196C24×C3#4112yes—
197C24×C3C2411yescharacteristic
198C23×D3—21no—
199C23×D3—22no—
200C23×D3—21no—
201C23×D3—22no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3C2×D412yes—
209C2×C3×D4—28no—
210C2×C3×D4—216no—
211C2×C3×D4—216no—
212C2×C3×D4—216no—
213C2×C3×D4—48no—
214C2×C3×D4—48no—
215C2×C3×D4—44no—
216C2×C3×D4—48no—
217C2×C3×D4—48no—
218C2×C3×D4—48no—
219C2×C3×D4—48no—
220C2×C3×D4—44no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—28no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—28no—
235C22×C3×C4—44no—
236C22×C3×C4—48no—
237C22×C3×C4—48no—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D414yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4#4112yes—
243C2×#67—216no—
244C2×#67—216no—
245C2×#67—28no—
246C2×#67—48no—
247C2×#67—48no—
248C2×#67—48no—
249C2×#67—48no—
250C2×#67—48no—
251C2×#67—44no—
252C2×#67—48no—
253C2×#67—44no—
254C2×#67—48no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—216no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—21no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—216no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—48no—
282C22×Dic3—48no—
283C22×Dic3—48no—
284C22×Dic3—48no—
285C22×Dic3—48no—
286C22×Dic3C2×D414yes—
287C22×Dic3C2×D412yes—
288C22×Dic3C2×D414yes—
289C22×Dic3C2×D414yes—
290C22×Dic3#4114yes—
291C3×C4⋊C4—28no—
292C3×C22⋊C4—216no—
293#217—216no—
294#217—48no—
295#217—44no—
296#217—48no—
297(C2×D3)⋊C4—216no—
298(C2×D3)⋊C4—44no—
299(C2×D3)⋊C4—44no—
300Dic3⋊C4—216no—
301C25—31no—
302C25C22×D312yes—
303C25C22×D311yescharacteristic
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—34no—
315C22×D4—42no—
316C22×D4—64no—
317C22×D4—64no—
318C22×D4—64no—
319C22×D4—64no—
320C22×D4—64no—
321C22×D4—62no—
322C22×D4—64no—
323C22×D4—64no—
324C22×D4—62no—
325C22×D4—122no—
326C22×D4—122no—
327C22×D4#6718yescomplemented
328C23×C4—24no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—32no—
332C23×C4—32no—
333C23×C4—31no—
334C23×C4—38no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—42no—
338C23×C4—64no—
339C23×C4—64no—
340C23×C4—64no—
341C23×C4—64no—
342C23×C4—122no—
343C23×C4—122no—
344C23×C4#6714yescomplemented
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D312yes—
347C23×C4C22×D311yescharacteristic
348#121—232no—
349#121—664no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—64no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—122no—
375C2×C22⋊C4—122no—
376C2×C22⋊C4—122no—
377#95—34no—
378#95—64no—
379#95—64no—
380#95—64no—
381#95—62no—
382#95—62no—
383#95—62no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—24no—
392C23×C3—22no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—24no—
401C23×C3—22no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3#12018yes—
438C23×C3#12014yes—
439C23×C3#12114yes—
440C23×C3#12118yes—
441C23×C3#12714yes—
442C23×C3C22×D411yescharacteristic
443C23×C3C22×D412yes—
444C23×C3C22×D411yescharacteristic
445C23×C3C22×D412yes—
446C23×C3C22×D411yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4112yes—
450C23×C3H(5,𝔽2)12yes—
451C23×C3H(5,𝔽2)11yescharacteristic
452C23×C32−1+411yescharacteristic
453C22×D3—24no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—42no—
465C22×D3—41no—
466C22×D3—42no—
467C22×D3—41no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3—41no—
474C22×D3—42no—
475C22×D3—41no—
476C3×D4—416no—
477C3×D4—432no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—24no—
487C2×C3×C4—22no—
488C2×C3×C4—416no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4#12114yescomplemented
496#67—432no—
497#67—416no—
498C2×Dic3—24no—
499C2×Dic3—24no—
500C2×Dic3—24no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—432no—
510C2×Dic3—41no—
511C2×Dic3—42no—
512C2×Dic3—41no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3—42no—
516C2×Dic3—42no—
517C2×Dic3—41no—
518C2×Dic3—42no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—42no—
523C2×Dic3—41no—
524C2×Dic3—42no—
525C2×Dic3—41no—
526C2×Dic3—42no—
527C2×Dic3#12118yescomplemented
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—32no—
549C24—62no—
550C24—61no—
551C24—61no—
552C24—61no—
553C24—62no—
554C24—62no—
555C24—61no—
556C24—61no—
557C24—61no—
558C24—62no—
559C24D3×D412yes—
560C24D3×D414yes—
561C24#23712yes—
562C24C2×#6714yes—
563C24C2×#6714yes—
564C24C2×#6712yes—
565C24C23×D311yescharacteristic
566C2×D4—28no—
567C2×D4—216no—
568C2×D4—216no—
569C2×D4—216no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—44no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—48no—
577C2×D4—44no—
578C2×D4—616no—
579C2×D4—616no—
580C2×D4—68no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—128no—
586C2×D4—128no—
587C2×D4—128no—
588C2×D4—124no—
589C2×D4—124no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—28no—
604C22×C4—34no—
605C22×C4—34no—
606C22×C4—34no—
607C22×C4—34no—
608C22×C4—32no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—616no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—616no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—61no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—61no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—128no—
639C22×C4—128no—
640C22×C4—128no—
641C22×C4—128no—
642C22×C4—128no—
643C22×C4D3×D412yes—
644C22×C4#23712yes—
645C22×C4C2×#6712yes—
646C22×C4C2×#6714yes—
647C22×C4C2×#6712yes—
648C4⋊C4—28no—
649C4⋊C4—616no—
650C22⋊C4—216no—
651C22⋊C4—616no—
652C22⋊C4—616no—
653C22⋊C4—124no—
654C22⋊C4—128no—
655C22⋊C4—128no—
656C22⋊C4—124no—
657C22⋊C4—124no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3—28no—
661C22×C3—24no—
662C22×C3—24no—
663C22×C3—28no—
664C22×C3—24no—
665C22×C3—28no—
666C22×C3—28no—
667C22×C3—24no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3—44no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—82no—
676C22×C3—82no—
677C22×C3—82no—
678C22×C3—82no—
679C22×C3—82no—
680C22×C3—82no—
681C22×C3—82no—
682C22×C3—82no—
683C22×C3#39218yescomplemented
684C22×C3C2×#12012yes—
685C22×C3C2×#12011yescharacteristic
686C22×C3C2×#12111yescharacteristic
687C22×C3C2×#12111yescharacteristic
688C22×C3C2×#12112yes—
689C22×C3C2×#12112yes—
690C22×C3C2×#12711yescharacteristic
691C22×C3#53211yescharacteristic
692C22×C3#53212yes—
693C22×C3#53411yescharacteristic
694C22×C3#53412yes—
695C22×C3#53711yescharacteristic
696C22×C3#53712yes—
697C22×C3D4212yes—
698C22×C3D4211yescharacteristic
699C22×C3#54612yes—
700C22×C3#54612yes—
701C22×C3#54612yes—
702C22×C3#54712yes—
703C22×C3#54711yescharacteristic
704C22×C3#54811yescharacteristic
705C22×C3#55312yes—
706C22×C3#55311yescharacteristic
707C2×D3—42no—
708C2×D3—44no—
709C2×D3—42no—
710C2×D3—44no—
711C2×D3—42no—
712C2×D3—81no—
713C2×D3—81no—
714C2×D3—81no—
715C2×D3—82no—
716C2×D3—81no—
717C2×D3—82no—
718C3×C4—24no—
719C3×C4—44no—
720C3×C4—42no—
721Dic3—28no—
722Dic3—42no—
723Dic3—44no—
724Dic3—81no—
725Dic3—81no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—22no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—64no—
780C23—62no—
781C23—62no—
782C23—64no—
783C23—62no—
784C23—122no—
785C23—121no—
786C23—122no—
787C23—121no—
788C23—121no—
789C23—122no—
790C23—122no—
791C23—122no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—122no—
796C23—122no—
797C23—121no—
798C23—122no—
799C23—122no—
800C23—122no—
801C23—121no—
802C23#93718yes—
803C23#93814yes—
804C23#93918yes—
805C23#94014yes—
806C23#95314yes—
807C23C2×D3×D411yescharacteristic
808C23C2×D3×D412yes—
809C23C2×D3×D411yescharacteristic
810C23C2×#23711yescharacteristic
811C23C2×#23711yescharacteristic
812C23#100412yes—
813C23D3×#4112yes—
814C23#100911yescharacteristic
815C23#101011yescharacteristic
816C23C22×#6712yes—
817C23C22×#6711yescharacteristic
818D4—416no—
819D4—432no—
820D4—1232no—
821D4—1216no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—38no—
833C2×C4—416no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—64no—
841C2×C4—64no—
842C2×C4—64no—
843C2×C4—64no—
844C2×C4—64no—
845C2×C4—64no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—62no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—1232no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—121no—
855C2×C4—122no—
856C2×C4—121no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4#93914yescomplemented
870C2×C3—28no—
871C2×C3—84no—
872C2×C3C2×#39211yescharacteristic
873C2×C3#241012yes—
874C2×C3#241011yescharacteristic
875C2×C3#241611yescharacteristic
876C2×C3#241612yes—
877C2×C3#243011yescharacteristic
878C2×C3#243012yes—
879C2×C3#254312yes—
880C2×C3#254311yescharacteristic
881C2×C3#265611yescharacteristic
882C2×C3#285611yescharacteristic
883D3—82no—
884C22—24no—
885C22—28no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—28no—
890C22—28no—
891C22—28no—
892C22—24no—
893C22—24no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—124no—
910C22—122no—
911C22—122no—
912C22—124no—
913C22—122no—
914C22—241no—
915C22—241no—
916C22—241no—
917C22—242no—
918C22—242no—
919C22—241no—
920C22#522318yescomplemented
921C22#559612yes—
922C22#559712yes—
923C22#559811yescharacteristic
924C22#560112yes—
925C22D3×#12112yes—
926C22#560512yes—
927C22#560911yescharacteristic
928C22#561012yes—
929C22#561111yescharacteristic
930C22#561811yescharacteristic
931C22C2×#93712yes—
932C22C2×#93811yescharacteristic
933C22D4×#6712yes—
934C22C2×#93911yescharacteristic
935C22C2×#93912yes—
936C22C2×#94011yescharacteristic
937C22#580411yescharacteristic
938C22#580612yes—
939C22#582412yes—
940C22#582912yes—
941C22#583211yescharacteristic
942C22#583311yescharacteristic
943C22C2×#95311yescharacteristic
944C4—24no—
945C4—42no—
946C4—44no—
947C4—68no—
948C4—124no—
949C4—122no—
950C4—241no—
951C4—241no—
952C3#1475711yescharacteristic, complemented, Sylow
953C2—28no—
954C2—84no—
955C2—242no—
956C2#8264212yes—
957C2#8265112yes—
958C2#8267012yes—
959C2#8267111yescharacteristic
960C2#8268011yescharacteristic
961C2#8270011yescharacteristic
962C2#8270212yes—
963C2#8270511yescharacteristic
964C2#8404811yescharacteristic
965C2C2×#522311yescharacteristic
966C2#8409111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#14757
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#939C2semidirect
3. C2×#5223C2semidirect
4. C2×#5220C2semidirect
5. C2×#5213C2semidirect
6. C22×C3⋊#95C2semidirect
7. #72131C2semidirect
8. #71570C2semidirect
9. #71568C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
46. C22×#121D3semidirect
70. C22×C3×D4D4semidirect
75. C23×C3×C4D4semidirect
90. C22×#67D4semidirect
97. C23×Dic3D4semidirect
138. C3⋊#95D4semidirect
327. C22×D4#67semidirect
344. C23×C4#67semidirect
495. C2×C3×C4#121semidirect
527. C2×Dic3#121semidirect
683. C22×C3#392semidirect
869. C2×C4#939semidirect
920. C22#5223semidirect
952. C3#14757semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9392
C2×#52232
C2×#52202
C2×#52132
C22×C3⋊#952
#721312
#715702
#715682
#715502
#715472
#147573