Finite Group Databasebeta

← #10822697

Subgroups — #10822697

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×#5791C211yesmaximal, characteristic
2C2×C3×#380C211yesmaximal, characteristic, complemented
3C2×#5207C211yesmaximal, characteristic, complemented
4C2×#4966C211yesmaximal, characteristic, complemented
5C2×#4966C211yesmaximal, characteristic, complemented
6C2×#4964C211yesmaximal, characteristic, complemented
7#71558C211yesmaximal, characteristic, complemented
8#69527C212yesmaximal, complemented
9#69526C212yesmaximal, complemented
10#69524C212yesmaximal, complemented
11#69523C212yesmaximal, complemented
12#23482—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×#235C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4—21no—
18C2×#953—21no—
19#5791—24no—
20#5791—24no—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#929—21no—
24C2×C4×#67—21no—
25C2×C4×#67—21no—
26C2×#926C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×#208C2211yescharacteristic
30C22×#208C2211yescharacteristic
31C3×#380—21no—
32C3×#380—21no—
33C3×#380C2212yes—
34C3×#380C2212yes—
35C2×C3×#95—21no—
36#5207—24no—
37C2×#830C2212yes—
38C2×#830C2212yes—
39C2×#810C2212yescomplemented
40C2×#810C2212yescomplemented
41#4966—24no—
42#4966—24no—
43C2×#809C2212yescomplemented
44C2×#809C2212yescomplemented
45#4964—24no—
46C2×#808C2212yescomplemented
47C2×#807C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C2×#428—31no—
52C2×#417—31no—
53C2×#417—31no—
54C2×#407—31no—
55C2×#380D311yescharacteristic, complemented
56#2036—32no—
57#2035—32no—
58#2034—32no—
59#2033—32no—
60#1736—31no—
61C25×C3D411yescharacteristic
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—21no—
69C23×C3×C4—21no—
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C22×#67—21no—
77C22×#67—21no—
78C22×#67—21no—
79C2×#235—22no—
80C2×#235—22no—
81C2×#235—22no—
82C2×#235—22no—
83C2×#235—22no—
84C2×#235D414yes—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6C2311yescharacteristic
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2312yes—
95C2×C3×C4⋊C4C2312yes—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—44no—
99#953—28no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103#930—22no—
104#930—22no—
105#930—22no—
106#930—22no—
107#929—28no—
108C4×#67—28no—
109C4×#67—28no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112#926—22no—
113#926D414yes—
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116#924—22no—
117#924—22no—
118#924—22no—
119#924—22no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×C4×Dic3—21no—
123C2×#208—22no—
124C2×#208—22no—
125C2×#208—22no—
126C2×#208—22no—
127C2×#208—22no—
128C2×#208D414yescomplemented
129C22×C3⋊C8C2312yes—
130C22×C3⋊C8C2312yes—
131C3×#95—22no—
132C3×#95—22no—
133#830—24no—
134#830—24no—
135#810—24no—
136#810—24no—
137#809—24no—
138#809—24no—
139#808—24no—
140#807—24no—
141C22×#41—31no—
142C24×C4C2×D311yescharacteristic
143C22×M16—31no—
144C22×M16—31no—
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⋊C4C2×D311yescharacteristic
157C22×C4⋊C4C2×D311yescharacteristic
158C22×C22⋊C4—21no—
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—21no—
172#380—21no—
173#380C2×D312yes—
174#380C2×D312yes—
175C2×#95—21no—
176#340—32no—
177#340—32no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—41no—
184C24×C3—41no—
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2×D411yescharacteristic
188C23×D3—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4—44no—
215C22×C3×C4—44no—
216C22×C3×C4—42no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4#4112yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4112yes—
231C22×C3×C4C2411yescharacteristic
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244#235—28no—
245#235—28no—
246#235—44no—
247#235—44no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12C2×D412yes—
254C2×C4×D3—24no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6C2×D412yes—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C22⋊C4—44no—
270C3×C22⋊C4—44no—
271#217—24no—
272#217—24no—
273#217—24no—
274(C2×D3)⋊C4—24no—
275(C2×D3)⋊C4—24no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3C2×D412yes—
279C4⋊Dic3C2×D412yes—
280Dic3⋊C4—24no—
281Dic3⋊C4—24no—
282C4×Dic3—24no—
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—34no—
293C2×#41—62no—
294C2×#41—62no—
295C2×#41—62no—
296C2×#41—62no—
297C2×#41—62no—
298C22×Q8—31no—
299C22×D4—31no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4—61no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—21no—
310C23×C4—21no—
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—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—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4C22×D312yes—
351C2×C4⋊C4C22×D312yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C42—61no—
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—22no—
370#95—22no—
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—44no—
389C23×C3—44no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3#12012yes—
395C23×C3#12112yes—
396C23×C3#12312yes—
397C23×C3AGL(1,ℤ/8)12yes—
398C23×C3#13712yes—
399C23×C3C22×D411yescharacteristic
400C22×D3—22no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—44no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—44no—
423C2×C3×C4—44no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—84no—
431C2×C3×C4—84no—
432C2×C3×C4#12012yes—
433C2×C3×C4#12114yes—
434C2×C3×C4#12114yes—
435C2×C3×C4#12112yes—
436C2×C3×C4#12314yes—
437C2×C3×C4#12312yes—
438C2×C3×C4#12414yes—
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445#67—48no—
446#67—48no—
447#67—48no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457D12—22no—
458D12—22no—
459D12—41no—
460D12—41no—
461C4×D3—48no—
462Dic6—22no—
463Dic6—22no—
464Dic6—41no—
465Dic6—41no—
466C3⋊C8—24no—
467C3⋊C8—42no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—41no—
474C24—41no—
475C24—61no—
476C24C2×#6711yescharacteristic
477C24C2×#6711yescharacteristic
478C24C2×#6711yescharacteristic
479#41—68no—
480#41—68no—
481#41—124no—
482#41—124no—
483C2×Q8—32no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×D4—32no—
490C2×D4—64no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—122no—
499C2×D4—122no—
500C2×D4—122no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4—122no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
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—22no—
526C22×C4—22no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—64no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4#23512yes—
544C22×C4#23512yes—
545C22×C4D3×D412yes—
546C22×C4D3×D412yes—
547C22×C4D3×D412yes—
548C22×C4#23712yes—
549C22×C4C2×#6711yescharacteristic
550C22×C4C2×#6711yescharacteristic
551C22×C4C2×#6711yescharacteristic
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—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—32no—
566C4⋊C4—32no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C22⋊C4—44no—
574C22⋊C4—44no—
575C22⋊C4—64no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C42—64no—
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#39414yes—
603C22×C3C2×#12011yescharacteristic
604C22×C3C2×#12111yescharacteristic
605C22×C3C2×#12311yescharacteristic
606C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3#57511yescharacteristic
609C22×C3#57511yescharacteristic
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—82no—
620C3×C4—82no—
621C3×C4#39414yes—
622C3×C4C2×#12111yescharacteristic
623C3×C4C2×#12111yescharacteristic
624C3×C4C2×#12311yescharacteristic
625C3×C4C2×#12411yescharacteristic
626Dic3—42no—
627Dic3—42no—
628Dic3—42no—
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—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—62no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23#92912yes—
660C23#93212yes—
661C23#93712yes—
662C23#93912yes—
663C23#94212yes—
664C23C22×#6711yescharacteristic
665Q8—62no—
666Q8—62no—
667Q8—121no—
668Q8—121no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—128no—
673D4—128no—
674D4—121no—
675D4—121no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—128no—
711C2×C4#88314yes—
712C2×C4#88414yes—
713C2×C4#88414yes—
714C2×C4#88514yes—
715C2×C4#92912yes—
716C2×C4#93712yes—
717C2×C4#93912yes—
718C2×C4C2×#23511yescharacteristic
719C2×C4C2×#23511yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×D3×D411yescharacteristic
722C2×C4C2×D3×D411yescharacteristic
723C2×C4C2×#23711yescharacteristic
724C8—64no—
725C8—122no—
726C2×C3—24no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3C2×#39411yescharacteristic
730C2×C3#300611yescharacteristic
731C2×C3#300711yescharacteristic
732C2×C3#305511yescharacteristic
733C2×C3#305611yescharacteristic
734C2×C3#309211yescharacteristic
735C2×C3#309311yescharacteristic
736D3—82no—
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—122no—
759C22—122no—
760C22—122no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22#495914yes—
766C22C2×#92911yescharacteristic
767C22C2×#93211yescharacteristic
768C22C2×#93711yescharacteristic
769C22C2×#93911yescharacteristic
770C22C2×#94211yescharacteristic
771C22#582211yescharacteristic
772C22#582211yescharacteristic
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C4—122no—
778C4—122no—
779C4—122no—
780C4#495914yes—
781C4C2×#88311yescharacteristic
782C4C2×#88411yescharacteristic
783C4C2×#88411yescharacteristic
784C4C2×#88511yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—42no—
788C2—42no—
789C2—242no—
790C2C2×#495911yescharacteristic
791C2#8213911yescharacteristic
792C2#8221611yescharacteristic
793C2#8262111yescharacteristic
794C2#8262411yescharacteristic
795C2#8273211yescharacteristic
796C2#8273511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#380C2
socleC23×C3C22×D4
prime radicalC2×#5791C2
hypercenterC2×#380D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#380C2semidirect
3. C2×#5207C2semidirect
4. C2×#4966C2semidirect
5. C2×#4966C2semidirect
6. C2×#4964C2semidirect
7. #71558C2semidirect
8. #69527C2semidirect
9. #69526C2semidirect
10. #69524C2semidirect
11. #69523C2semidirect
39. C2×#810C22semidirect
40. C2×#810C22semidirect
43. C2×#809C22semidirect
44. C2×#809C22semidirect
46. C2×#808C22semidirect
47. C2×#807C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
55. C2×#380D3semidirect
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×#57912
C2×C3×#3802
C2×#52072
C2×#49662
C2×#49642
#715582
#695272
#695262
#695242
#695232
#234823