Finite Group Databasebeta

← #10822700

Subgroups — #10822700

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×#5524C211yesmaximal, characteristic
2C2×C3×#428C211yesmaximal, characteristic, complemented
3C2×#5133C211yesmaximal, characteristic, complemented
4C2×#5126C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4966C211yesmaximal, characteristic, complemented
7#71581C211yesmaximal, characteristic, complemented
8#70635C212yesmaximal, complemented
9#70634C212yesmaximal, complemented
10#70582C212yesmaximal, complemented
11#70581C212yesmaximal, complemented
12#23482—31nomaximal, Sylow
13C22×#235C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C2×C3×#117C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4—21no—
19C22×C4⋊Dic3C2211yescharacteristic
20C22×#208C2211yescharacteristic
21#5524—24no—
22#5524—24no—
23C2×#897C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#886—21no—
28C2×#882—21no—
29C2×C4×D12—21no—
30C2×C4×D12—21no—
31C3×#428—24no—
32C2×C3×#107C2212yescomplemented
33C2×C3×#106C2212yescomplemented
34C2×C3⋊#95—21no—
35#5133—24no—
36#5126—24no—
37C2×#821C2212yescomplemented
38C2×(C2×D3)⋊C8C2212yes—
39C2×(C2×D3)⋊C8C2212yes—
40C2×#816C2212yescomplemented
41#4987—21no—
42#4987—21no—
43#4987C2212yes—
44#4987C2212yes—
45C2×#810C2212yescomplemented
46#4966—24no—
47C2×#809C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C2×#428D311yescharacteristic, complemented
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—
61C24×D3D411yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4C2311yescharacteristic
64C22×#67—21no—
65C23×Dic3—21no—
66C23×Dic3D411yescharacteristic
67C2×#235—22no—
68C2×#235—22no—
69C2×#235—22no—
70C2×#235—22no—
71C2×#235—22no—
72C2×#235D414yes—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12C2311yescharacteristic
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—21no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×M16—22no—
89C2×C3×M16—22no—
90C2×C3×M16D414yescomplemented
91C22×C3×C8C2312yes—
92C3×#117—22no—
93C3×#117D414yes—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2312yes—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—44no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3C2312yes—
115C2×#208—22no—
116C2×#208—22no—
117C2×#208—22no—
118C22×C3⋊C8C2312yes—
119#897—22no—
120#897—22no—
121#897—22no—
122#897—22no—
123#895—22no—
124#895—22no—
125#895—22no—
126#895—22no—
127#886—28no—
128#882—28no—
129C4×D12—28no—
130C4×D12—28no—
131C3×#107—24no—
132C3×#106—24no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135#821—24no—
136(C2×D3)⋊C8—24no—
137(C2×D3)⋊C8—24no—
138#816—24no—
139#810—24no—
140#809—24no—
141C22×#41—31no—
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×#117C2×D311yescharacteristic
156C22×C4⋊C4—31no—
157C22×C4⋊C4C2×D311yescharacteristic
158C22×C22⋊C4—61no—
159#428—24no—
160C2×#107C2×D312yescomplemented
161C2×#106C2×D312yescomplemented
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×C3C2×D411yescharacteristic
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—21no—
185C23×D3—41no—
186C23×D3—41no—
187C23×D3C2×D411yescharacteristic
188C23×D3C2×D411yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D411yescharacteristic
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×C3×C4#4112yes—
202C22×C3×C4C2411yescharacteristic
203C2×#67—24no—
204C2×#67—42no—
205C2×#67—42no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—42no—
212C22×Dic3—42no—
213C22×Dic3—42no—
214C22×Dic3C2×D411yescharacteristic
215C22×Dic3C2×D411yescharacteristic
216#235—28no—
217#235—28no—
218#235—44no—
219#235—44no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—24no—
225C2×D12—24no—
226C2×D12—21no—
227C2×D12—42no—
228C2×D12—42no—
229C2×D12—42no—
230C2×D12—42no—
231C2×D12C2×D412yes—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—24no—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—44no—
252C2×C4×D3—44no—
253C2×C4×D3—42no—
254C2×C4×D3—44no—
255C2×C4×D3—42no—
256C2×C4×D3—44no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6C2×D412yes—
263C3×M16—28no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8C2×D414yes—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4C2×D412yes—
273C3×C4⋊C4C2×D412yes—
274C3×C22⋊C4—24no—
275C3×C42—24no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—44no—
281(C2×D3)⋊C4—44no—
282C4⋊Dic3—24no—
283C4⋊Dic3—24no—
284C4⋊Dic3—22no—
285C4⋊Dic3—22no—
286C4⋊Dic3—42no—
287#208—44no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C25—31no—
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—21no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—61no—
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×M16D1214yescomplemented
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—22no—
339#117#6714yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4C22×D312yes—
350C2×C4⋊C4C22×D311yescharacteristic
351C2×C4⋊C4C22×D311yescharacteristic
352C2×C22⋊C4—21no—
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—21no—
361#107—24no—
362#106—24no—
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#12012yes—
376C23×C3#12112yes—
377C23×C3#12312yes—
378C23×C3C22×D411yescharacteristic
379C22×D3—28no—
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—21no—
383C22×D3—21no—
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—22no—
393C22×D3—44no—
394C22×D3—44no—
395C22×D3—44no—
396C22×D3—44no—
397C22×D3—44no—
398C22×D3—44no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3AGL(1,ℤ/8)12yes—
406C22×D3#13712yes—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—84no—
417C2×C3×C4#12012yes—
418C2×C3×C4#12114yes—
419C2×C3×C4#12112yes—
420C2×C3×C4#12114yes—
421C2×C3×C4#12314yes—
422C2×C3×C4#12312yes—
423C2×C3×C4#12414yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430#67—48no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—44no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—84no—
445D12—22no—
446D12—22no—
447D12—48no—
448D12—48no—
449D12—41no—
450D12—41no—
451C4×D3—41no—
452C4×D3—41no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—41no—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—44no—
460C4×D3—44no—
461C4×D3—48no—
462Dic6—22no—
463Dic6—22no—
464Dic6—41no—
465Dic6—41no—
466C3×C8—24no—
467C3⋊C8—42no—
468C24—31no—
469C24—31no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—61no—
476C24—121no—
477C24—121no—
478C24D3×D411yescharacteristic
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—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—64no—
523C22×C4—61no—
524C22×C4—61no—
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—62no—
536C22×C4—124no—
537C22×C4—122no—
538C22×C4—124no—
539C22×C4—122no—
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#23912yes—
550C22×C4#23912yes—
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×D1214yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—42no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—122no—
571C4⋊C4C2×#6712yes—
572C4⋊C4C2×#6712yes—
573C22⋊C4—24no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—64no—
577C22⋊C4—64no—
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#39414yes—
588C22×C3C2×#12011yescharacteristic
589C22×C3C2×#12111yescharacteristic
590C22×C3C2×#12311yescharacteristic
591C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
592C22×C3C2×#13711yescharacteristic
593C22×C3#57511yescharacteristic
594C22×C3#57511yescharacteristic
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—416no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—82no—
620C3×C4#39414yes—
621C3×C4C2×#12111yescharacteristic
622C3×C4C2×#12111yescharacteristic
623C3×C4C2×#12311yescharacteristic
624C3×C4C2×#12411yescharacteristic
625Dic3—42no—
626Dic3—41no—
627Dic3—41no—
628Dic3—82no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—32no—
634C23—32no—
635C23—68no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—62no—
649C23—124no—
650C23—124no—
651C23—124no—
652C23—124no—
653C23—124no—
654C23—124no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23#89412yes—
662C23#89512yes—
663C23#93712yes—
664C23C2×D3×D411yescharacteristic
665Q8—62no—
666Q8—62no—
667Q8—121no—
668Q8—121no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—128no—
673D4—128no—
674D4—121no—
675D4—121no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—84no—
693C2×C4—124no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—124no—
697C2×C4—124no—
698C2×C4—128no—
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#89412yes—
712C2×C4#89414yes—
713C2×C4#89512yes—
714C2×C4#89514yes—
715C2×C4#93014yes—
716C2×C4#93712yes—
717C2×C4#94714yes—
718C2×C4C22×D1211yescharacteristic
719C2×C4C2×#23511yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23911yescharacteristic
722C2×C4C2×#23911yescharacteristic
723C2×C4C22×#6711yescharacteristic
724C8—24no—
725C8—122no—
726C2×C3—24no—
727C2×C3C2×#39411yescharacteristic
728C2×C3#300611yescharacteristic
729C2×C3#300711yescharacteristic
730C2×C3#305511yescharacteristic
731C2×C3#305611yescharacteristic
732C2×C3#309211yescharacteristic
733C2×C3#309311yescharacteristic
734D3—42no—
735D3—42no—
736D3—82no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—62no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—1216no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22#499114yes—
766C22C2×#89411yescharacteristic
767C22C2×#89511yescharacteristic
768C22D3×AGL(1,ℤ/8)11yescharacteristic
769C22#577311yescharacteristic
770C22D3×#13711yescharacteristic
771C22#577711yescharacteristic
772C22C2×#93711yescharacteristic
773C4—42no—
774C4—42no—
775C4—82no—
776C4—121no—
777C4—121no—
778C4—122no—
779C4—242no—
780C4#499114yes—
781C4C2×#89411yescharacteristic
782C4C2×#89511yescharacteristic
783C4C2×#93011yescharacteristic
784C4C2×#94711yescharacteristic
785C3#2348211yescharacteristic, complemented, Sylow
786C2—24no—
787C2—122no—
788C2—122no—
789C2—242no—
790C2#7921111yescharacteristic
791C2#7921211yescharacteristic
792C2#7921511yescharacteristic
793C2#7921611yescharacteristic
794C2C2×#499111yescharacteristic
795C2#8394611yescharacteristic
796C2#8398111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#428C2
socleC23×C3C22×D4
prime radicalC2×#5524C2
hypercenterC2×#428D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×C3×#428C2semidirect
3. C2×#5133C2semidirect
4. C2×#5126C2semidirect
5. C2×#4987C2semidirect
6. C2×#4966C2semidirect
7. #71581C2semidirect
8. #70635C2semidirect
9. #70634C2semidirect
10. #70582C2semidirect
11. #70581C2semidirect
32. C2×C3×#107C22semidirect
33. C2×C3×#106C22semidirect
37. C2×#821C22semidirect
40. C2×#816C22semidirect
45. C2×#810C22semidirect
47. C2×#809C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
51. C2×#428D3semidirect
90. C2×C3×M16D4semidirect
160. C2×#107C2×D3semidirect
161. C2×#106C2×D3semidirect
323. C2×M16D12semidirect
785. C3#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#55242
C2×C3×#4282
C2×#51332
C2×#51262
C2×#49872
C2×#49662
#715812
#706352
#706342
#705822
#705812
#234823