Finite Group Databasebeta

← #10822696

Subgroups — #10822696

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×#5828C211yesmaximal, characteristic
2C2×C3×#417C211yesmaximal, characteristic, complemented
3C2×#5232C211yesmaximal, characteristic, complemented
4C2×#5126C211yesmaximal, characteristic, complemented
5C2×#5121C211yesmaximal, characteristic, complemented
6C2×#4987C211yesmaximal, characteristic, complemented
7#71558C211yesmaximal, characteristic, complemented
8#70244C212yesmaximal, complemented
9#70243C212yesmaximal, complemented
10#70176C212yesmaximal, complemented
11#70175C212yesmaximal, complemented
12#23482—31nomaximal, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17#5828—24no—
18#5828—24no—
19C2×#946C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#937—21no—
24C2×#935—21no—
25C2×C4×#67—21no—
26C2×C4×#67—21no—
27C22×(C2×D3)⋊C4—21no—
28C2×#926C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×#208C2211yescharacteristic
31C3×#417—24no—
32C2×C3×#103C2212yescomplemented
33C2×C3×#102C2212yescomplemented
34#5232—24no—
35C2×#835C2212yescomplemented
36C2×#832C2212yescomplemented
37C2×C3⋊#95—21no—
38#5126—24no—
39#5121—24no—
40C2×(C2×D3)⋊C8C2212yes—
41C2×(C2×D3)⋊C8C2212yes—
42C2×#818C2212yescomplemented
43C2×#817C2212yescomplemented
44#4987—21no—
45#4987—21no—
46#4987C2212yes—
47#4987C2212yes—
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C2×#428—31no—
52C2×#417—31no—
53C2×#417D311yescharacteristic, complemented
54C2×#407—31no—
55C2×#380—31no—
56#2036—32no—
57#2035—32no—
58#2034—32no—
59#2033—32no—
60#1736—31no—
61C24×D3D411yescharacteristic
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×D4C2311yescharacteristic
71C23×C3×C4—21no—
72C23×C3×C4—21no—
73C23×C3×C4C2311yescharacteristic
74C22×#67—21no—
75C22×#67—21no—
76C23×Dic3—21no—
77C23×Dic3D411yescharacteristic
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C2×C3×M16—22no—
89C2×C3×M16—22no—
90C2×C3×M16D414yescomplemented
91C22×C3×C8C2312yes—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2312yes—
96C2×#217—21no—
97C2×#217—21no—
98C2×#217—21no—
99#946—22no—
100#946—22no—
101#946—22no—
102#946—22no—
103#938—22no—
104#938—22no—
105#938—22no—
106#938—22no—
107#937—28no—
108#935—28no—
109C4×#67—28no—
110C4×#67—28no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—44no—
116#926—22no—
117#926D414yes—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C2312yes—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×#208—22no—
128C2×#208—22no—
129C2×#208—22no—
130C22×C3⋊C8C2312yes—
131C3×#103—24no—
132C3×#102—24no—
133#835—24no—
134#832—24no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137(C2×D3)⋊C8—24no—
138(C2×D3)⋊C8—24no—
139#818—24no—
140#817—24no—
141C22×#41C2×D311yescharacteristic
142C24×C4—31no—
143C22×M16—31no—
144C22×M16C2×D311yescharacteristic
145#525—64no—
146#525—64no—
147C2×#123—61no—
148C2×C22⋊Q8—31no—
149C2×C22⋊Q8—31no—
150C2×#121—31no—
151C2×#121—31no—
152C2×#120—61no—
153C2×C4×D4—61no—
154C2×C4×D4—61no—
155C2×#117—31no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4C2×D311yescharacteristic
158C22×C22⋊C4—61no—
159#428—64no—
160C2×#107—32no—
161C2×#106—32no—
162#417—24no—
163#417—64no—
164C2×#103—32no—
165C2×#103C2×D312yescomplemented
166C2×#102—32no—
167C2×#102C2×D312yescomplemented
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—21no—
179C24×C3C2×D411yescharacteristic
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—41no—
186C23×D3—41no—
187C23×D3C2×D411yescharacteristic
188C23×D3C2×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—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—42no—
206C2×C3×D4—42no—
207C2×C3×D4C2×D412yes—
208C22×C3×C4—21no—
209C22×C3×C4—24no—
210C22×C3×C4—22no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4#4112yes—
221C22×C3×C4#4112yes—
222C22×C3×C4#4112yes—
223C22×C3×C4C2411yescharacteristic
224C2×#67—24no—
225C2×#67—24no—
226C2×#67—42no—
227C2×#67—42no—
228C2×#67—42no—
229C2×#67—42no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—42no—
237C22×Dic3—42no—
238C22×Dic3—42no—
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—22no—
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—44no—
260C2×C4×D3—44no—
261C2×C4×D3—44no—
262C2×C4×D3—44no—
263C3×M16—28no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8C2×D414yes—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—42no—
270#217—24no—
271#217—24no—
272#217—24no—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—24no—
275(C2×D3)⋊C4—44no—
276(C2×D3)⋊C4—44no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—22no—
280C4⋊Dic3—22no—
281C4⋊Dic3—42no—
282C4⋊Dic3C2×D412yes—
283C4⋊Dic3C2×D412yes—
284Dic3⋊C4—24no—
285Dic3⋊C4—24no—
286C4×Dic3—24no—
287#208—44no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C25—31no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41D1214yes—
298C22×Q8C22×D311yescharacteristic
299C22×D4—21no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4C22×D311yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—62no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—62no—
316C23×C4—61no—
317C23×C4C22×D311yescharacteristic
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—62no—
321C2×M16—62no—
322C2×M16—62no—
323C2×M16#6714yescomplemented
324C22×C8—32no—
325C22×C8C22×D312yes—
326#123—68no—
327C22⋊Q8—62no—
328C22⋊Q8—62no—
329C22⋊Q8—62no—
330C22⋊Q8—62no—
331#121—62no—
332#121—62no—
333#121—62no—
334#121—62no—
335#120—68no—
336C4×D4—68no—
337C4×D4—68no—
338#117—34no—
339#117—62no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—32no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—62no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4C22×D312yes—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—124no—
360C2×C42—61no—
361#107—64no—
362#106—64no—
363#103—24no—
364#103—64no—
365#102—24no—
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—22no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3#12012yes—
383C23×C3#12112yes—
384C23×C3#12312yes—
385C23×C3C22×D411yescharacteristic
386C22×D3—28no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—44no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3AGL(1,ℤ/8)12yes—
406C22×D3#13712yes—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—41no—
410C3×Q8—41no—
411C3×D4—22no—
412C3×D4—22no—
413C3×D4—48no—
414C3×D4—41no—
415C3×D4—41no—
416C2×C3×C4—22no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—48no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—84no—
424C2×C3×C4#12012yes—
425C2×C3×C4#12114yes—
426C2×C3×C4#12112yes—
427C2×C3×C4#12114yes—
428C2×C3×C4#12312yes—
429C2×C3×C4#12314yes—
430C2×C3×C4#12414yes—
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437#67—48no—
438#67—48no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—44no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—84no—
456C4×D3—41no—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C4×D3—41no—
462C4×D3—41no—
463C4×D3—41no—
464C4×D3—44no—
465C4×D3—44no—
466C3×C8—24no—
467C3⋊C8—42no—
468C24—21no—
469C24—31no—
470C24—31no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—121no—
477C24—121no—
478C24D3×D411yescharacteristic
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×D1212yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—64no—
498C2×D4—64no—
499C2×D4—122no—
500C2×D4—122no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4C2×D1212yes—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—124no—
539C22×C4—124no—
540C22×C4—124no—
541C22×C4—124no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4—122no—
545C22×C4C2×D1212yes—
546C22×C4#23512yes—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D412yes—
549C22×C4#23712yes—
550C22×C4#23712yes—
551C22×C4C2×#6712yes—
552C22×C4C23×D311yescharacteristic
553M16—28no—
554M16—124no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—62no—
558C2×C8—62no—
559C2×C8—62no—
560C2×C8C2×#6714yes—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—32no—
564C4⋊C4—32no—
565C4⋊C4—42no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—122no—
573C22⋊C4—64no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C42—64no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3#39414yes—
595C22×C3C2×#12011yescharacteristic
596C22×C3C2×#12111yescharacteristic
597C22×C3C2×#12311yescharacteristic
598C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
599C22×C3C2×#13711yescharacteristic
600C22×C3#57511yescharacteristic
601C22×C3#57511yescharacteristic
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—416no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C3×C4—42no—
618C3×C4—82no—
619C3×C4#39414yes—
620C3×C4C2×#12111yescharacteristic
621C3×C4C2×#12111yescharacteristic
622C3×C4C2×#12311yescharacteristic
623C3×C4C2×#12411yescharacteristic
624Dic3—41no—
625Dic3—41no—
626Dic3—42no—
627Dic3—42no—
628Dic3—82no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—32no—
635C23—32no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—68no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—124no—
656C23—124no—
657C23—124no—
658C23—124no—
659C23—124no—
660C23—124no—
661C23#88212yes—
662C23#88312yes—
663C23#93812yes—
664C23C2×D3×D411yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—41no—
668Q8—41no—
669D4—22no—
670D4—22no—
671D4—48no—
672D4—41no—
673D4—41no—
674D4—128no—
675D4—128no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—84no—
692C2×C4—124no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—124no—
698C2×C4—124no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—244no—
711C2×C4#88212yes—
712C2×C4#88312yes—
713C2×C4#88514yes—
714C2×C4#88614yes—
715C2×C4#93014yes—
716C2×C4#93812yes—
717C2×C4#93914yes—
718C2×C4C22×D1211yescharacteristic
719C2×C4C2×#23511yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4C2×#23711yescharacteristic
723C2×C4C22×#6711yescharacteristic
724C8—24no—
725C8—122no—
726C2×C3—24no—
727C2×C3—82no—
728C2×C3C2×#39411yescharacteristic
729C2×C3#300611yescharacteristic
730C2×C3#300711yescharacteristic
731C2×C3#305511yescharacteristic
732C2×C3#305611yescharacteristic
733C2×C3#309211yescharacteristic
734C2×C3#309311yescharacteristic
735D3—42no—
736D3—42no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—1216no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22#496114yes—
766C22C2×#88211yescharacteristic
767C22C2×#88311yescharacteristic
768C22D3×AGL(1,ℤ/8)11yescharacteristic
769C22#577311yescharacteristic
770C22D3×#13711yescharacteristic
771C22#577711yescharacteristic
772C22C2×#93811yescharacteristic
773C4—42no—
774C4—82no—
775C4—122no—
776C4—122no—
777C4—121no—
778C4—121no—
779C4—242no—
780C4#496114yes—
781C4C2×#88511yescharacteristic
782C4C2×#88611yescharacteristic
783C4C2×#93011yescharacteristic
784C4C2×#93911yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—82no—
788C2—122no—
789C2—122no—
790C2#7888411yescharacteristic
791C2#7888511yescharacteristic
792C2#7889211yescharacteristic
793C2#7889311yescharacteristic
794C2C2×#496111yescharacteristic
795C2#8395011yescharacteristic
796C2#8398511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#417C2
socleC23×C3C22×D4
prime radicalC2×#5828C2
hypercenterC2×#417D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#417C2semidirect
3. C2×#5232C2semidirect
4. C2×#5126C2semidirect
5. C2×#5121C2semidirect
6. C2×#4987C2semidirect
7. #71558C2semidirect
8. #70244C2semidirect
9. #70243C2semidirect
10. #70176C2semidirect
11. #70175C2semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#102C22semidirect
35. C2×#835C22semidirect
36. C2×#832C22semidirect
42. C2×#818C22semidirect
43. C2×#817C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
53. C2×#417D3semidirect
90. C2×C3×M16D4semidirect
165. C2×#103C2×D3semidirect
167. C2×#102C2×D3semidirect
323. C2×M16#67semidirect
785. C3#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×C3×#4172
C2×#52322
C2×#51262
C2×#51212
C2×#49872
#715582
#702442
#702432
#701762
#701752
#234823