Finite Group Databasebeta

← #10822693

Subgroups — #10822693

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C2×#5232C211yesmaximal, characteristic, complemented
3C2×#5232C211yesmaximal, characteristic, complemented
4C2×#5212C211yesmaximal, characteristic, complemented
5C2×#5207C211yesmaximal, characteristic, complemented
6C2×#4995C211yesmaximal, characteristic, complemented
7#71695C212yesmaximal, complemented
8#71694C212yesmaximal, complemented
9#71680C212yesmaximal, complemented
10#71679C212yesmaximal, complemented
11#71581C211yesmaximal, characteristic, complemented
12#23482—31nomaximal, Sylow
13C22×C3×#41C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C3×#525—24no—
16C3×#525—24no—
17C2×C3×#123—21no—
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#120—21no—
23C2×C3×C4×D4—21no—
24C2×C3×C4×D4—21no—
25C2×C3×#117C2211yescharacteristic
26C22×#217—21no—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×#208C2211yescharacteristic
30C22×#208C2211yescharacteristic
31#5232—24no—
32#5232—24no—
33C2×#835C2212yescomplemented
34C2×#835C2212yescomplemented
35C2×#832C2212yescomplemented
36C2×#832C2212yescomplemented
37#5212—21no—
38#5212—21no—
39#5212C2212yes—
40#5212C2212yes—
41C2×C3⋊#95—21no—
42#5207—24no—
43C2×#830C2212yes—
44C2×#830C2212yes—
45#4995—24no—
46C2×#808C2212yescomplemented
47C2×#807C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525D311yescharacteristic
51C2×#428—31no—
52C2×#417—31no—
53C2×#417—31no—
54C2×#407—31no—
55C2×#380—31no—
56#2036—32no—
57#2035—32no—
58#2034—32no—
59#2033—32no—
60#1736—31no—
61C25×C3D411yescharacteristic
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41D414yes—
68C22×C3×Q8C2311yescharacteristic
69C22×C3×D4—21no—
70C22×C3×D4—21no—
71C22×C3×D4—21no—
72C22×C3×D4C2311yescharacteristic
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—21no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4D411yescharacteristic
81C23×C3×C4D411yescharacteristic
82C23×C3×C4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×Dic3—21no—
87C23×Dic3—21no—
88C3×#123—28no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—22no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—22no—
97C3×#120—28no—
98C3×C4×D4—28no—
99C3×C4×D4—28no—
100C3×#117—22no—
101C3×#117D414yes—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42—21no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—44no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C2312yes—
122C2×C4⋊Dic3C2312yes—
123C2×#208—22no—
124C2×#208—22no—
125C2×#208—22no—
126C2×#208—22no—
127C2×#208—22no—
128C2×#208D414yescomplemented
129C22×C3⋊C8C2312yes—
130C22×C3⋊C8C2312yes—
131#835—24no—
132#835—24no—
133#832—24no—
134#832—24no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137#830—24no—
138#830—24no—
139#808—24no—
140#807—24no—
141C22×#41C2×D311yescharacteristic
142C24×C4C2×D311yescharacteristic
143C22×M16—31no—
144C22×M16—31no—
145#525—24no—
146#525—24no—
147C2×#123—21no—
148C2×C22⋊Q8C2×D311yescharacteristic
149C2×C22⋊Q8C2×D311yescharacteristic
150C2×#121C2×D311yescharacteristic
151C2×#121C2×D311yescharacteristic
152C2×#120—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×#117C2×D311yescharacteristic
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C22⋊C4—61no—
159#428—64no—
160C2×#107—32no—
161C2×#106—32no—
162#417—64no—
163#417—64no—
164C2×#103—32no—
165C2×#103—32no—
166C2×#102—32no—
167C2×#102—32no—
168#407—64no—
169C2×C22⋊C8—32no—
170C2×C22⋊C8—32no—
171#380—32no—
172#380—32no—
173#380—61no—
174#380—61no—
175C2×#95—61no—
176#340—32no—
177#340—32no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—21no—
184C24×C3—41no—
185C24×C3—41no—
186C24×C3C2×D411yescharacteristic
187C24×C3C2×D411yescharacteristic
188C24×C3C2×D411yescharacteristic
189C3×#41—28no—
190C3×#41—28no—
191C3×#41—44no—
192C3×#41—44no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8C2×D412yes—
199C2×C3×D4—24no—
200C2×C3×D4—24no—
201C2×C3×D4—24no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—42no—
210C2×C3×D4—42no—
211C2×C3×D4—42no—
212C2×C3×D4—42no—
213C2×C3×D4C2×D412yes—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—24no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—44no—
240C22×C3×C4—44no—
241C22×C3×C4—42no—
242C22×C3×C4—44no—
243C22×C3×C4—42no—
244C22×C3×C4—44no—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4#4112yes—
252C22×C3×C4#4112yes—
253C22×C3×C4#4112yes—
254C22×C3×C4C2411yescharacteristic
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—42no—
258C22×Dic3—42no—
259C22×Dic3—42no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4C2×D412yes—
268C3×C4⋊C4C2×D412yes—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C42—24no—
275#217—44no—
276#217—44no—
277C4⋊Dic3—22no—
278C4⋊Dic3—22no—
279C4⋊Dic3—22no—
280C4⋊Dic3—22no—
281C4⋊Dic3—42no—
282C4⋊Dic3—42no—
283#208—28no—
284#208—44no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8C2×D414yes—
291C25#6711yescharacteristic
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41#6714yes—
298C22×Q8C22×D311yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4C22×D311yescharacteristic
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—61no—
311C23×C4—61no—
312C23×C4#6711yescharacteristic
313C23×C4#6711yescharacteristic
314C23×C4#6711yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C2×M16—34no—
319C2×M16—62no—
320C2×M16—62no—
321C2×M16—62no—
322C2×M16—62no—
323C2×M16—62no—
324C22×C8—32no—
325C22×C8—32no—
326#123—28no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331#121—22no—
332#121—22no—
333#121—22no—
334#121—22no—
335#120—28no—
336C4×D4—28no—
337C4×D4—28no—
338#117—22no—
339#117#6714yes—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4C22×D311yescharacteristic
351C2×C4⋊C4C22×D311yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—124no—
360C2×C42—21no—
361#107—64no—
362#106—64no—
363#103—64no—
364#103—64no—
365#102—64no—
366#102—64no—
367C22⋊C8—64no—
368C22⋊C8—64no—
369#95—62no—
370#95—62no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—28no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—44no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3#12012yes—
402C23×C3#12112yes—
403C23×C3#12312yes—
404C23×C3AGL(1,ℤ/8)12yes—
405C23×C3#13712yes—
406C23×C3C22×D411yescharacteristic
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—41no—
410C3×Q8—41no—
411C3×D4—22no—
412C3×D4—22no—
413C3×D4—48no—
414C3×D4—48no—
415C3×D4—48no—
416C3×D4—41no—
417C3×D4—41no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—44no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4—48no—
445C2×C3×C4#12012yes—
446C2×C3×C4#12114yes—
447C2×C3×C4#12114yes—
448C2×C3×C4#12112yes—
449C2×C3×C4#12314yes—
450C2×C3×C4#12312yes—
451C2×C3×C4#12414yes—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—84no—
465C2×Dic3—84no—
466C3⋊C8—24no—
467C3⋊C8—42no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—41no—
475C24—41no—
476C24C2×#6711yescharacteristic
477C24C2×#6711yescharacteristic
478C24C2×#6711yescharacteristic
479#41—28no—
480#41—28no—
481#41—44no—
482#41—44no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C2×#6712yes—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4C2×#6712yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—44no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—42no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4D3×D412yes—
544C22×C4#23712yes—
545C22×C4#23712yes—
546C22×C4#23712yes—
547C22×C4C2×#6711yescharacteristic
548C22×C4C2×#6711yescharacteristic
549C22×C4C2×#6711yescharacteristic
550C22×C4C2×#6712yes—
551C22×C4C2×#6712yes—
552C22×C4C23×D311yescharacteristic
553M16—68no—
554M16—124no—
555C2×C8—34no—
556C2×C8—62no—
557C2×C8—62no—
558C2×C8—62no—
559C2×C8—62no—
560C2×C8—62no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4C2×#6712yes—
572C4⋊C4C2×#6712yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C42—24no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—416no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3#39414yes—
610C22×C3C2×#12011yescharacteristic
611C22×C3C2×#12111yescharacteristic
612C22×C3C2×#12311yescharacteristic
613C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
614C22×C3C2×#13711yescharacteristic
615C22×C3#57511yescharacteristic
616C22×C3#57511yescharacteristic
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4#39414yes—
623C3×C4C2×#12111yescharacteristic
624C3×C4C2×#12111yescharacteristic
625C3×C4C2×#12311yescharacteristic
626C3×C4C2×#12411yescharacteristic
627Dic3—82no—
628Dic3—82no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—28no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23#93512yes—
660C23#93912yes—
661C23#94912yes—
662C23#95112yes—
663C23#95312yes—
664C23C22×#6711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—41no—
668Q8—41no—
669D4—22no—
670D4—22no—
671D4—48no—
672D4—48no—
673D4—48no—
674D4—41no—
675D4—41no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—244no—
710C2×C4—244no—
711C2×C4#93512yes—
712C2×C4#93514yes—
713C2×C4#93614yes—
714C2×C4#93814yes—
715C2×C4#93912yes—
716C2×C4#93914yes—
717C2×C4#95312yes—
718C2×C4C2×D3×D411yescharacteristic
719C2×C4C2×#23711yescharacteristic
720C2×C4C2×#23711yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4C22×#6711yescharacteristic
723C2×C4C22×#6711yescharacteristic
724C8—64no—
725C8—122no—
726C2×C3—24no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—82no—
730C2×C3C2×#39411yescharacteristic
731C2×C3#300611yescharacteristic
732C2×C3#300711yescharacteristic
733C2×C3#305511yescharacteristic
734C2×C3#305611yescharacteristic
735C2×C3#309211yescharacteristic
736C2×C3#309311yescharacteristic
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—416no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22#522214yes—
766C22C2×#93511yescharacteristic
767C22C2×#93911yescharacteristic
768C22C2×#94911yescharacteristic
769C22#582211yescharacteristic
770C22#582211yescharacteristic
771C22C2×#95111yescharacteristic
772C22C2×#95311yescharacteristic
773C4—41no—
774C4—41no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—242no—
779C4—242no—
780C4#522214yes—
781C4C2×#93511yescharacteristic
782C4C2×#93611yescharacteristic
783C4C2×#93811yescharacteristic
784C4C2×#93911yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2#8291411yescharacteristic
791C2#8291511yescharacteristic
792C2#8292411yescharacteristic
793C2#8292511yescharacteristic
794C2C2×#522211yescharacteristic
795C2#8408211yescharacteristic
796C2#8408411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#525C2
socleC23×C3C22×D4
hypercenterC2×#525D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C2×#5232C2semidirect
3. C2×#5232C2semidirect
4. C2×#5212C2semidirect
5. C2×#5207C2semidirect
6. C2×#4995C2semidirect
7. #71695C2semidirect
8. #71694C2semidirect
9. #71680C2semidirect
10. #71679C2semidirect
11. #71581C2semidirect
33. C2×#835C22semidirect
34. C2×#835C22semidirect
35. C2×#832C22semidirect
36. C2×#832C22semidirect
46. C2×#808C22semidirect
47. C2×#807C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
128. C2×#208D4semidirect
785. C3#23482semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×#52322
C2×#52122
C2×#52072
C2×#49952
#716952
#716942
#716802
#716792
#715812
#234823