Finite Group Databasebeta

← #10828048

Subgroups — #10828048

Order 768.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3488C211yesmaximal, characteristic
2C2×#5232C211yesmaximal, characteristic, complemented
3#82914C211yesmaximal, characteristic, complemented
4#82664C211yesmaximal, characteristic, complemented
5#72140C212yesmaximal, complemented
6#72138C211yesmaximal, characteristic, complemented
7#71876C212yesmaximal, complemented
8#71852C212yesmaximal, complemented
9#71713C211yesmaximal, characteristic, complemented
10#71683C211yesmaximal, characteristic, complemented
11#71664C212yesmaximal, complemented
12#24026—31nomaximal, Sylow
13C2×C3×H(5,𝔽2)C2211yescharacteristic
14C22×C3×#41C2211yescharacteristic
15C3×#550—21no—
16C3×#548—21no—
17C3×#546—21no—
18C3×#546—22no—
19C3×D42—22no—
20C3×D42—21no—
21C3×#537—21no—
22C3×#537C2211yescharacteristic
23C3×#535—21no—
24C3×#535C2211yescharacteristic
25C3×#525—21no—
26C3×#525C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C3×#520C2211yescharacteristic
30C2×#935—22no—
31C22×C4⋊Dic3C2211yescharacteristic, complemented
32C22×#208C2211yescharacteristic, complemented
33C2×#837C2212yes—
34C2×#837C2212yescomplemented
35C2×#837C2212yescomplemented
36#5232—21no—
37#5232—21no—
38#5232C2212yes—
39#5232C2212yescomplemented
40#5232C2212yescomplemented
41C2×#835—21no—
42#5221C2212yescomplemented
43C2×#833C2212yescomplemented
44C2×#832—21no—
45C4×#217C2211yescharacteristic, complemented
46#5207C2211yescharacteristic, complemented
47#5044—21no—
48#5043—21no—
49#5034—21no—
50#5033—21no—
51#4995C2212yescomplemented
52#4975C2212yescomplemented
53#4949—22no—
54#4532C2212yescomplemented
55#4530C2212yescomplemented
56#3488D311yescharacteristic
57#3092—31no—
58C2×#417—31no—
59#2501—31no—
60#2039—32no—
61#2037—32no—
62#1900—31no—
63#1871—31no—
64#1859—32no—
65#1792—32no—
66#1789—31no—
67C3×H(5,𝔽2)—24no—
68C3×H(5,𝔽2)—42no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×#41—21no—
72C2×C3×#41—21no—
73C2×C3×#41—24no—
74C2×C3×#41—42no—
75C2×C3×#41D411yescharacteristic
76C2×C3×#41D411yescharacteristic
77C2×C3×#41C2311yescharacteristic
78C2×C3×#41C2311yescharacteristic
79C2×C3×#41C2311yescharacteristic
80C22×C3×Q8D411yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4D411yescharacteristic
87C22×C3×D4D412yes—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C23×Dic3—21no—
92C3×#127—22no—
93C3×#127—21no—
94C3×#124—22no—
95C3×#124—21no—
96C3×#123—22no—
97C3×#123—21no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—21no—
100C3×C22⋊Q8—21no—
101C3×C22⋊Q8D411yescharacteristic
102C3×C22⋊Q8D411yescharacteristic
103C3×#121—22no—
104C3×#121—22no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—21no—
109C3×#121—21no—
110C3×#121—21no—
111C3×#121—21no—
112C3×#121—21no—
113C3×#121—21no—
114C3×#121—22no—
115C3×#121—21no—
116C3×#121—21no—
117C3×#121D411yescharacteristic
118C3×#121D411yescharacteristic
119C3×#120—22no—
120C3×#120—22no—
121C3×#120—22no—
122C3×#120—21no—
123C3×#120—22no—
124C3×C4×Q8—21no—
125C3×C4×D4—22no—
126C3×C4×D4—22no—
127C3×C4×D4—21no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×#117—21no—
132C3×#117C2311yescharacteristic
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4D412yes—
137C2×#217—21no—
138C2×#217—24no—
139#935—48no—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2312yes—
146C2×Dic3⋊C4—24no—
147C2×C4×Dic3C2312yes—
148C2×#208—21no—
149C2×#208—42no—
150C2×#208C2312yes—
151C2×#208C2312yes—
152C22×C3⋊C8—21no—
153#837—24no—
154#837—42no—
155#837—42no—
156#835—22no—
157#835—22no—
158#835—22no—
159#833—42no—
160#832—22no—
161#832—22no—
162#832—22no—
163C3⋊#95—21no—
164#830—21no—
165#830—21no—
166#808—22no—
167#807—22no—
168C2×H(5,𝔽2)C2×D311yescharacteristic
169C22×#41C2×D311yescharacteristic
170C22×M16—31no—
171#550—21no—
172#548—21no—
173#546—21no—
174#546—22no—
175D42—22no—
176D42—21no—
177#537—21no—
178#537C2×D311yescharacteristic
179#535—21no—
180#535C2×D311yescharacteristic
181#525—21no—
182#525C2×D311yescharacteristic
183C2×#123—62no—
184C2×#121—21no—
185C2×#121C2×D311yescharacteristic
186#520C2×D311yescharacteristic
187C22×C4⋊C4—31no—
188#484—61no—
189#483—61no—
190#481—61no—
191#480—61no—
192#428—32no—
193C2×#104—32no—
194C2×#104—32no—
195C2×#104—32no—
196#417—32no—
197#417—32no—
198#417—32no—
199#417—61no—
200#417—61no—
201C2×#103—61no—
202C2×#102—61no—
203C2×#100—32no—
204#407—31no—
205#399—62no—
206#390—32no—
207#384—32no—
208C4×C22⋊C4—31no—
209#343—32no—
210#339—32no—
211C24×C3—22no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D412yes—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—44no—
223C3×#41—41no—
224C3×#41—41no—
225C3×#41—44no—
226C3×#41—44no—
227C3×#41—42no—
228C3×#41—42no—
229C3×#41#4114yes—
230C2×C3×Q8—21no—
231C2×C3×Q8—22no—
232C2×C3×Q8—41no—
233C2×C3×Q8C2×D411yescharacteristic
234C2×C3×Q8C2×D411yescharacteristic
235C2×C3×Q8C2×D411yescharacteristic
236C2×C3×D4—21no—
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—22no—
247C2×C3×D4—22no—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4—22no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—41no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—48no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—44no—
263C2×C3×D4—84no—
264C2×C3×D4C2×D411yescharacteristic
265C2×C3×D4C2×D411yescharacteristic
266C2×C3×D4C2×D411yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—21no—
272C22×C3×C4—22no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—44no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2411yescharacteristic
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—44no—
288C22×Dic3—41no—
289C22×Dic3—41no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4C2×D411yescharacteristic
297C3×C4⋊C4C2×D411yescharacteristic
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—21no—
310C3×C42—22no—
311C3×C42—21no—
312#217—24no—
313#217—48no—
314C4⋊Dic3—22no—
315C4⋊Dic3—22no—
316C4⋊Dic3—41no—
317C4⋊Dic3—41no—
318Dic3⋊C4—48no—
319C4×Dic3—22no—
320C4×Dic3—22no—
321#208—22no—
322#208—22no—
323#208—22no—
324#208—22no—
325#208—42no—
326C2×C3⋊C8—22no—
327C2×C3⋊C8—22no—
328C2×C3⋊C8—42no—
329H(5,𝔽2)—24no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—24no—
336C2×#41—42no—
337C2×#41#6711yescharacteristic
338C2×#41#6711yescharacteristic
339C2×#41C22×D311yescharacteristic
340C2×#41C22×D311yescharacteristic
341C2×#41C22×D311yescharacteristic
342C22×Q8#6711yescharacteristic
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4#6711yescharacteristic
349C22×D4#6712yes—
350C22×D4C22×D311yescharacteristic
351C23×C4—21no—
352C23×C4—61no—
353C23×C4C22×D311yescharacteristic
354C2×M16—32no—
355C2×M16—32no—
356C2×M16—61no—
357C2×M16—122no—
358C22×C8—61no—
359#127—22no—
360#127—21no—
361#124—22no—
362#124—21no—
363#123—22no—
364#123—21no—
365#123—128no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8#6711yescharacteristic
370C22⋊Q8#6711yescharacteristic
371#121—22no—
372#121—22no—
373#121—22no—
374#121—22no—
375#121—22no—
376#121—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121—22no—
383#121—21no—
384#121—21no—
385#121#6711yescharacteristic
386#121#6711yescharacteristic
387#120—22no—
388#120—22no—
389#120—22no—
390#120—21no—
391#120—22no—
392C4×Q8—21no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399#117—21no—
400#117C22×D311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—22no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4#6712yes—
414C2×C42—32no—
415#107—62no—
416#106—62no—
417#104—64no—
418#104—122no—
419#104—122no—
420#103—62no—
421#103—62no—
422#103—62no—
423#102—62no—
424#102—62no—
425#102—62no—
426#100—122no—
427C22⋊C8—61no—
428C22⋊C8—61no—
429#95—61no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—24no—
437C23×C3—41no—
438C23×C3—42no—
439C23×C3—44no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—81no—
444C23×C3—82no—
445C23×C3—82no—
446C23×C3#12011yescharacteristic
447C23×C3#12011yescharacteristic
448C23×C3C22×D411yescharacteristic
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—22no—
453C3×Q8—42no—
454C3×Q8#12312yescomplemented
455C3×D4—24no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—22no—
460C3×D4—42no—
461C3×D4—42no—
462C3×D4—44no—
463C3×D4—42no—
464C3×D4—44no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—44no—
468C3×D4—42no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4—42no—
472C3×D4—81no—
473C3×D4—82no—
474C3×D4—82no—
475C3×D4—82no—
476C3×D4—82no—
477C3×D4#12312yescomplemented
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—24no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—44no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—82no—
501C2×C3×C4#12011yescharacteristic
502C2×C3×C4#12011yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C2×#4112yes—
506C2×C3×C4H(5,𝔽2)12yes—
507C2×Dic3—24no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—44no—
511C2×Dic3—42no—
512C2×Dic3—82no—
513C2×Dic3—82no—
514C3⋊C8—42no—
515C3⋊C8—42no—
516C24—22no—
517C24—21no—
518C24C2×#6711yescharacteristic
519C24C2×#6712yes—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—44no—
528#41—41no—
529#41—41no—
530#41—44no—
531#41—44no—
532#41—42no—
533#41—42no—
534#41#23714yes—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—41no—
538C2×Q8C2×#6711yescharacteristic
539C2×Q8C2×#6711yescharacteristic
540C2×Q8C2×#6711yescharacteristic
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—48no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—84no—
569C2×D4C2×#6711yescharacteristic
570C2×D4C2×#6711yescharacteristic
571C2×D4C2×#6711yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—124no—
586C22×C4—121no—
587C22×C4—121no—
588C22×C4C2×#6711yescharacteristic
589C22×C4C2×#6711yescharacteristic
590C22×C4C2×#6711yescharacteristic
591C22×C4C2×#6711yescharacteristic
592C22×C4C2×#6711yescharacteristic
593C22×C4C2×#6712yes—
594C22×C4C23×D311yescharacteristic
595M16—62no—
596M16—62no—
597M16—62no—
598M16—62no—
599M16—122no—
600C2×C8—62no—
601C2×C8—62no—
602C2×C8—122no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—128no—
612C4⋊C4—121no—
613C4⋊C4—121no—
614C4⋊C4C2×#6711yescharacteristic
615C4⋊C4C2×#6711yescharacteristic
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—64no—
629C22⋊C4—128no—
630C42—22no—
631C42—21no—
632C42—62no—
633C42—62no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—44no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—84no—
655C22×C3—84no—
656C22×C3—164no—
657C22×C3#45312yes—
658C22×C3C2×#12011yescharacteristic
659C22×C3#54612yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—22no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4C2×#12311yescharacteristic
669C3×C4#53411yescharacteristic
670C3×C4#54612yes—
671Dic3—44no—
672Dic3—82no—
673C23—22no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—24no—
680C23—41no—
681C23—42no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—81no—
687C23—82no—
688C23—82no—
689C23#95311yescharacteristic
690C23#95311yescharacteristic
691C23C22×#6711yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—22no—
696Q8—42no—
697Q8#93512yescomplemented
698D4—24no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—44no—
706D4—42no—
707D4—44no—
708D4—44no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—41no—
713D4—41no—
714D4—42no—
715D4—82no—
716D4—81no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4#93512yescomplemented
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—64no—
744C2×C4—82no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—124no—
748C2×C4—122no—
749C2×C4—242no—
750C2×C4—242no—
751C2×C4#95311yescharacteristic
752C2×C4#95311yescharacteristic
753C2×C4C2×#23712yes—
754C2×C4#100412yes—
755C2×C4C22×#6711yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—122no—
758C8—122no—
759C2×C3—22no—
760C2×C3—22no—
761C2×C3—41no—
762C2×C3—42no—
763C2×C3—81no—
764C2×C3—82no—
765C2×C3—81no—
766C2×C3#240511yescharacteristic
767C2×C3C2×#45311yescharacteristic
768C2×C3#302211yescharacteristic
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—22no—
775C22—21no—
776C22—21no—
777C22—44no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—84no—
790C22—84no—
791C22—164no—
792C22#524112yes—
793C22#580612yes—
794C22C2×#95311yescharacteristic
795C4—21no—
796C4—21no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—124no—
804C4—242no—
805C4C2×#93511yescharacteristic
806C4#580411yescharacteristic
807C4#580612yes—
808C3#2402611yescharacteristic, complemented, Sylow
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2#8404711yescharacteristic
817C2C2×#524111yescharacteristic
818C2#8412311yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3488C2
socleC22×C3C2×#120
hypercenter#3488D3
hypocenterC3#24026
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
2. C2×#5232C2semidirect
3. #82914C2semidirect
4. #82664C2semidirect
5. #72140C2semidirect
6. #72138C2semidirect
7. #71876C2semidirect
8. #71852C2semidirect
9. #71713C2semidirect
10. #71683C2semidirect
11. #71664C2semidirect
31. C22×C4⋊Dic3C22semidirect
32. C22×#208C22semidirect
34. C2×#837C22semidirect
35. C2×#837C22semidirect
39. #5232C22semidirect
40. #5232C22semidirect
42. #5221C22semidirect
43. C2×#833C22semidirect
45. C4×#217C22semidirect
46. #5207C22semidirect
51. #4995C22semidirect
52. #4975C22semidirect
54. #4532C22semidirect
55. #4530C22semidirect
454. C3×Q8#123semidirect
477. C3×D4#123semidirect
697. Q8#935semidirect
720. D4#935semidirect
808. C3#24026semidirect

Maximal subgroups

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

subgroupindex
C3×#34882
C2×#52322
#829142
#826642
#721402
#721382
#718762
#718522
#717132
#716832
#716642
#240263