Finite Group Databasebeta

← #10822699

Subgroups — #10822699

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×#407C211yesmaximal, characteristic, complemented
3C2×#5212C211yesmaximal, characteristic, complemented
4C2×#5133C211yesmaximal, characteristic, complemented
5C2×#5133C211yesmaximal, characteristic, complemented
6C2×#5121C211yesmaximal, characteristic, complemented
7#71985C211yesmaximal, characteristic, complemented
8#69937C212yesmaximal, complemented
9#69936C212yesmaximal, complemented
10#69935C212yesmaximal, complemented
11#69934C212yesmaximal, complemented
12#23482—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×#235C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C22×C3×M16C2211yescharacteristic
17C2×#953—21no—
18C22×#217—21no—
19#5791—24no—
20#5791—24no—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#929—21no—
24C2×C4×#67—21no—
25C2×C4×#67—21no—
26C2×#926C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C2×#924C2211yescharacteristic
30C2×#924C2211yescharacteristic
31C3×#407—24no—
32C2×C3×C22⋊C8C2212yes—
33C2×C3×C22⋊C8C2212yes—
34#5212—21no—
35#5212—21no—
36#5212C2212yes—
37#5212C2212yes—
38C2×C3⋊#95—21no—
39#5133—24no—
40#5133—24no—
41#5121—24no—
42C2×#821C2212yescomplemented
43C2×#821C2212yescomplemented
44C2×#818C2212yescomplemented
45C2×#817C2212yescomplemented
46C2×#816C2212yescomplemented
47C2×#816C2212yescomplemented
48#4551C2212yescomplemented
49#4551C2212yescomplemented
50C2×#525—31no—
51C2×#428—31no—
52C2×#417—31no—
53C2×#417—31no—
54C2×#407D311yescharacteristic, complemented
55C2×#380—31no—
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×C4D411yescharacteristic
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C22×#67—21no—
75C22×#67—21no—
76C22×#67—21no—
77C23×Dic3—21no—
78C23×Dic3—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×M16—22no—
89C2×C3×M16—22no—
90C2×C3×M16—22no—
91C2×C3×M16—22no—
92C2×C3×M16—22no—
93C2×C3×M16D414yescomplemented
94C22×C3×C8C2312yes—
95C22×C3×C8C2312yes—
96#953—28no—
97C2×#217—21no—
98C2×#217—21no—
99C2×#217—21no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—44no—
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⋊Dic3—22no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2312yes—
121C2×C4⋊Dic3C2312yes—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124#924—22no—
125#924—22no—
126#924—22no—
127#924—22no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C3×C22⋊C8—24no—
132C3×C22⋊C8—24no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135#821—24no—
136#821—24no—
137#818—24no—
138#817—24no—
139#816—24no—
140#816—24no—
141C22×#41—31no—
142C24×C4C2×D311yescharacteristic
143C22×M16C2×D311yescharacteristic
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⋊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—24no—
169C2×C22⋊C8C2×D312yes—
170C2×C22⋊C8C2×D312yes—
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—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—44no—
211C22×C3×C4—44no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D412yes—
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—24no—
227C2×#67—42no—
228C2×#67—42no—
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—42no—
232C2×#67—42no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—42no—
239C22×Dic3—42no—
240C22×Dic3—42no—
241C22×Dic3—42no—
242C22×Dic3—42no—
243C22×Dic3—42no—
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×M16—28no—
264C3×M16—44no—
265C2×C3×C8—22no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C2×C3×C8—22no—
269C2×C3×C8—22no—
270C2×C3×C8C2×D414yes—
271#217—24no—
272#217—24no—
273#217—24no—
274#217—44no—
275#217—44no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—22no—
281C4⋊Dic3—22no—
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284C4⋊Dic3—42no—
285C4⋊Dic3—42no—
286C4⋊Dic3C2×D412yes—
287C4⋊Dic3C2×D412yes—
288Dic3⋊C4—24no—
289Dic3⋊C4—24no—
290C4×Dic3—24no—
291C25D1211yescharacteristic
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—61no—
310C23×C4—61no—
311C23×C4—61no—
312C23×C4D1211yescharacteristic
313C23×C4D1211yescharacteristic
314C23×C4D1211yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16#6714yescomplemented
324C22×C8C22×D312yes—
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—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—62no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4—61no—
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—64no—
364#103—64no—
365#102—64no—
366#102—64no—
367C22⋊C8—24no—
368C22⋊C8—24no—
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—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#12012yes—
425C2×C3×C4#12112yes—
426C2×C3×C4#12114yes—
427C2×C3×C4#12114yes—
428C2×C3×C4#12314yes—
429C2×C3×C4#12312yes—
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—
439#67—48no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—84no—
456C2×Dic3—84no—
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×D1211yescharacteristic
477C24C2×D1211yescharacteristic
478C24C2×D1211yescharacteristic
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—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—64no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4C2×D1211yescharacteristic
544C22×C4C2×D1211yescharacteristic
545C22×C4C2×D1211yescharacteristic
546C22×C4#23512yes—
547C22×C4D3×D412yes—
548C22×C4D3×D412yes—
549C22×C4#23712yes—
550C22×C4#23712yes—
551C22×C4C2×#6712yes—
552C22×C4C23×D311yescharacteristic
553M16—28no—
554M16—44no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8C2×#6714yes—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—122no—
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—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#39414yes—
620C3×C4C2×#12111yescharacteristic
621C3×C4C2×#12111yescharacteristic
622C3×C4C2×#12311yescharacteristic
623C3×C4C2×#12411yescharacteristic
624Dic3—42no—
625Dic3—42no—
626Dic3—42no—
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—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#88212yes—
660C23#88612yes—
661C23#90812yes—
662C23#90912yes—
663C23#93012yes—
664C23C22×D1211yescharacteristic
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—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—128no—
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#88212yes—
712C2×C4#88314yes—
713C2×C4#88514yes—
714C2×C4#88612yes—
715C2×C4#93012yes—
716C2×C4#93814yes—
717C2×C4#93914yes—
718C2×C4C2×#23511yescharacteristic
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4C2×#23711yescharacteristic
723C2×C4C22×#6711yescharacteristic
724C8—24no—
725C8—42no—
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#496114yes—
766C22C2×#88211yescharacteristic
767C22C2×#88611yescharacteristic
768C22C2×#90811yescharacteristic
769C22C2×#90911yescharacteristic
770C22#574811yescharacteristic
771C22#574811yescharacteristic
772C22C2×#93011yescharacteristic
773C4—41no—
774C4—41no—
775C4—122no—
776C4—122no—
777C4—122no—
778C4—242no—
779C4—242no—
780C4#496114yes—
781C4C2×#88311yescharacteristic
782C4C2×#88511yescharacteristic
783C4C2×#93811yescharacteristic
784C4C2×#93911yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—42no—
788C2—42no—
789C2—242no—
790C2#7862211yescharacteristic
791C2#7862311yescharacteristic
792C2#7863911yescharacteristic
793C2#7864011yescharacteristic
794C2C2×#496111yescharacteristic
795C2#8377211yescharacteristic
796C2#8377611yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#407C2
socleC23×C3C22×D4
prime radicalC2×#5791C2
hypercenterC2×#407D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C3×#407C2semidirect
3. C2×#5212C2semidirect
4. C2×#5133C2semidirect
5. C2×#5133C2semidirect
6. C2×#5121C2semidirect
7. #71985C2semidirect
8. #69937C2semidirect
9. #69936C2semidirect
10. #69935C2semidirect
11. #69934C2semidirect
42. C2×#821C22semidirect
43. C2×#821C22semidirect
44. C2×#818C22semidirect
45. C2×#817C22semidirect
46. C2×#816C22semidirect
47. C2×#816C22semidirect
48. #4551C22semidirect
49. #4551C22semidirect
54. C2×#407D3semidirect
93. C2×C3×M16D4semidirect
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×#57912
C2×C3×#4072
C2×#52122
C2×#51332
C2×#51212
#719852
#699372
#699362
#699352
#699342
#234823