Finite Group Databasebeta

← #11661581

Subgroups — #11661581

Order 768.

5098 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#41C211yesmaximal, characteristic, complemented
2C2×#5822C212yesmaximal, complemented
3C2×#5791C211yesmaximal, characteristic, complemented
4#84084C214yesmaximal, complemented
5#84082C214yesmaximal, complemented
6#84081C214yesmaximal, complemented
7#84080C218yesmaximal, complemented
8#84072C212yesmaximal, complemented
9#84059C212yesmaximal, complemented
10#84038C212yesmaximal, complemented
11C2×#5207C211yesmaximal, characteristic, complemented
12#60359—31nomaximal, Sylow
13C22×C3×#41—216no—
14C22×C3×#41—22no—
15C22×C3×#41—21no—
16C22×C3×#41—22no—
17C22×C3×#41—21no—
18C22×C3×#41C2214yes—
19C22×C3×#41C2212yes—
20C22×C3×#41C2214yescomplemented
21C22×C3×#41C2212yescomplemented
22C23×C3×Q8C2211yescharacteristic, complemented
23C23×C3×D4—21no—
24C23×C3×D4C2211yescharacteristic, complemented
25C24×C3×C4—21no—
26C24×C3×C4C2211yescharacteristic
27C22×#235C2211yescharacteristic, complemented
28C2×#953—21no—
29C2×#951C2214yescomplemented
30#5822—216no—
31C2×#950C2218yescomplemented
32C2×#949C2214yescomplemented
33C2×#942C2214yescomplemented
34C2×#932C2214yescomplemented
35#5791—22no—
36#5791—21no—
37#5791—21no—
38#5791C2212yes—
39#5791C2214yescomplemented
40#5791C2212yescomplemented
41C2×#930C2212yescomplemented
42C2×#929—21no—
43C2×C4×#67—22no—
44C2×#926C2211yescharacteristic, complemented
45C2×#924C2212yescomplemented
46C22×#208C2212yescomplemented
47#5239C22116yescomplemented
48#5238C22116yescomplemented
49#5233C2218yescomplemented
50#5232C2218yescomplemented
51#5228C2218yescomplemented
52#5227C2218yescomplemented
53#5225C2214yescomplemented
54#5218C2218yescomplemented
55#5217C2218yescomplemented
56#5215C2214yescomplemented
57#5207C2212yescomplemented
58#5207C2214yescomplemented
59#5207C2212yescomplemented
60C2×#830C2214yescomplemented
61C23×#41D311yescharacteristic, complemented
62C2×#575—32no—
63C2×#525—31no—
64#3007—34no—
65#3006—34no—
66#3005—34no—
67#3004—32no—
68#3003—32no—
69#3002—38no—
70#2896—32no—
71C2×#407—31no—
72C25×C3—21no—
73C25×C3D411yescharacteristic
74C2×C3×#41—216no—
75C2×C3×#41—232no—
76C2×C3×#41—232no—
77C2×C3×#41—216no—
78C2×C3×#41—232no—
79C2×C3×#41—232no—
80C2×C3×#41—28no—
81C2×C3×#41—28no—
82C2×C3×#41—28no—
83C2×C3×#41—24no—
84C2×C3×#41—24no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—24no—
88C2×C3×#41—24no—
89C2×C3×#41—24no—
90C2×C3×#41D4116yescomplemented
91C2×C3×#41C2318yes—
92C2×C3×#41C2314yes—
93C2×C3×#41C2314yes—
94C22×C3×Q8—28no—
95C22×C3×Q8—22no—
96C22×C3×Q8—21no—
97C22×C3×Q8C2314yes—
98C22×C3×Q8C2312yes—
99C22×C3×D4—216no—
100C22×C3×D4—24no—
101C22×C3×D4—22no—
102C22×C3×D4—24no—
103C22×C3×D4—22no—
104C22×C3×D4—28no—
105C22×C3×D4—22no—
106C22×C3×D4—21no—
107C22×C3×D4C2314yes—
108C22×C3×D4C2312yes—
109C23×C3×C4—216no—
110C23×C3×C4—21no—
111C23×C3×C4—24no—
112C23×C3×C4—22no—
113C23×C3×C4—24no—
114C23×C3×C4—22no—
115C23×C3×C4—28no—
116C23×C3×C4D411yescharacteristic
117C23×C3×C4D412yes—
118C23×C3×C4D411yescharacteristic
119C23×C3×C4D412yes—
120C23×C3×C4D411yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2312yes—
123C23×C3×C4C2312yes—
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C22×#67—21no—
127C22×#67—22no—
128C2×#235—21no—
129C2×#235—21no—
130C2×#235—28no—
131C2×#235C2312yes—
132C2×#235C2312yescomplemented
133C22×D12C2311yescharacteristic, complemented
134C22×C4×D3—21no—
135C22×Dic6C2311yescharacteristic, complemented
136#953—22no—
137#953—24no—
138#953—22no—
139C2×#217—22no—
140C2×#217—21no—
141#951—216no—
142#950—232no—
143#949—216no—
144C2×#216C2318yescomplemented
145#942—216no—
146C2×#215C2318yescomplemented
147C2×#214C2318yescomplemented
148#932—216no—
149C2×#213C2318yescomplemented
150#930—22no—
151#930—22no—
152#930C2314yes—
153#930C2314yescomplemented
154#929—22no—
155#929—24no—
156#929—22no—
157C4×#67—24no—
158C4×#67—24no—
159C4×#67—24no—
160C4×#67—24no—
161C2×(C2×D3)⋊C4—22no—
162#926—21no—
163#926—21no—
164#926C2312yes—
165#926C2312yescomplemented
166C2×C4⋊Dic3C2312yescomplemented
167#924—22no—
168#924—22no—
169#924C2314yes—
170#924C2314yescomplemented
171C2×Dic3⋊C4—22no—
172C2×C4×Dic3—21no—
173C2×#208—28no—
174C2×#208C2314yes—
175C2×#208C2314yescomplemented
176C22×C3⋊C8C2314yescomplemented
177#835C23116yescomplemented
178#832C23116yescomplemented
179#830C2318yes—
180#830C2318yescomplemented
181C22×#41—216no—
182C22×#41—22no—
183C22×#41—21no—
184C22×#41—22no—
185C22×#41—21no—
186C22×#41—31no—
187C22×#41C2×D314yes—
188C22×#41C2×D312yes—
189C22×#41C2×D314yescomplemented
190C22×#41C2×D312yescomplemented
191C23×Q8C2×D311yescharacteristic, complemented
192C23×D4—21no—
193C23×D4C2×D311yescharacteristic, complemented
194C24×C4—21no—
195C24×C4C2×D311yescharacteristic
196#575—616no—
197C2×#137—34no—
198C2×#137—34no—
199C2×AGL(1,ℤ/8)—34no—
200C2×AGL(1,ℤ/8)—34no—
201C2×#135—38no—
202C22×M16—32no—
203#525—32no—
204#525—34no—
205#525—32no—
206#525—61no—
207#525—62no—
208#525—61no—
209C2×#123—61no—
210C2×C22⋊Q8—32no—
211C2×#121—32no—
212C2×#120—61no—
213C2×C4×D4—62no—
214C2×#117—31no—
215#452—316no—
216#451—38no—
217#450—38no—
218#449—316no—
219#448—38no—
220#447—38no—
221#419—34no—
222#418—34no—
223#417—38no—
224#416—38no—
225#407—32no—
226#407—32no—
227#407—34no—
228C2×C22⋊C8—34no—
229C24×C3—28no—
230C24×C3—24no—
231C24×C3—24no—
232C24×C3—22no—
233C24×C3—44no—
234C24×C3—48no—
235C24×C3C2×D411yescharacteristic
236C24×C3C2×D412yes—
237C24×C3C2×D412yes—
238C24×C3C2×D411yescharacteristic
239C24×C3C2×D411yescharacteristic
240C23×D3—21no—
241C3×#41—232no—
242C3×#41—232no—
243C3×#41—232no—
244C3×#41—232no—
245C3×#41—232no—
246C3×#41—216no—
247C3×#41—216no—
248C3×#41—216no—
249C3×#41—216no—
250C3×#41—28no—
251C3×#41—28no—
252C3×#41C2×D4116yes—
253C3×#41C2×D4116yescomplemented
254C2×C3×Q8—216no—
255C2×C3×Q8—28no—
256C2×C3×Q8—216no—
257C2×C3×Q8—24no—
258C2×C3×Q8—24no—
259C2×C3×Q8—22no—
260C2×C3×Q8C2×D418yescomplemented
261C2×C3×Q8C2414yes—
262C2×C3×D4—232no—
263C2×C3×D4—232no—
264C2×C3×D4—216no—
265C2×C3×D4—28no—
266C2×C3×D4—216no—
267C2×C3×D4—216no—
268C2×C3×D4—28no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—216no—
272C2×C3×D4—24no—
273C2×C3×D4—22no—
274C2×C3×D4—24no—
275C2×C3×D4C2×D418yescomplemented
276C2×C3×D4C2414yes—
277C22×C3×C4—28no—
278C22×C3×C4—232no—
279C22×C3×C4—232no—
280C22×C3×C4—216no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—22no—
284C22×C3×C4—24no—
285C22×C3×C4—216no—
286C22×C3×C4—24no—
287C22×C3×C4—28no—
288C22×C3×C4—28no—
289C22×C3×C4—28no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—24no—
293C22×C3×C4—24no—
294C22×C3×C4—28no—
295C22×C3×C4—28no—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D418yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2411yescharacteristic
313C22×C3×C4C2411yescharacteristic
314C22×C3×C4C2411yescharacteristic
315C2×#67—24no—
316C2×#67—24no—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—48no—
320C2×#67—44no—
321C22×Dic3—22no—
322C22×Dic3—21no—
323#235—28no—
324#235—28no—
325#235—44no—
326#235—44no—
327C2×D12—24no—
328C2×D12—21no—
329C2×D12C2412yes—
330C2×C4×D3—22no—
331C2×C4×D3—22no—
332C2×C4×D3—44no—
333C2×Dic6—24no—
334C2×Dic6—21no—
335C2×Dic6C2412yes—
336#217—24no—
337#217—24no—
338#217—22no—
339#217—22no—
340#216—216no—
341#215—216no—
342#214—216no—
343#213—216no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346C4⋊Dic3—22no—
347C4⋊Dic3C2414yes—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350C4×Dic3—22no—
351C4×Dic3—22no—
352#208—28no—
353#208—28no—
354C2×C3⋊C8—28no—
355C2×C3⋊C8C2418yes—
356C25—21no—
357C25#6711yescharacteristic
358C2×#41—216no—
359C2×#41—232no—
360C2×#41—232no—
361C2×#41—216no—
362C2×#41—232no—
363C2×#41—232no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—24no—
368C2×#41—24no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—24no—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—32no—
375C2×#41—32no—
376C2×#41—61no—
377C2×#41—61no—
378C2×#41—68no—
379C2×#41#67116yescomplemented
380C2×#41C22×D318yes—
381C2×#41C22×D314yes—
382C2×#41C22×D314yes—
383C22×Q8—28no—
384C22×Q8—22no—
385C22×Q8—21no—
386C22×Q8—31no—
387C22×Q8C22×D314yes—
388C22×Q8C22×D312yes—
389C22×D4—216no—
390C22×D4—24no—
391C22×D4—22no—
392C22×D4—24no—
393C22×D4—22no—
394C22×D4—28no—
395C22×D4—22no—
396C22×D4—21no—
397C22×D4—31no—
398C22×D4—62no—
399C22×D4—61no—
400C22×D4C22×D314yes—
401C22×D4C22×D312yes—
402C23×C4—216no—
403C23×C4—21no—
404C23×C4—24no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—28no—
409C23×C4—61no—
410C23×C4#6712yes—
411C23×C4#6711yescharacteristic
412C23×C4#6711yescharacteristic
413C23×C4#6712yes—
414C23×C4#6711yescharacteristic
415C23×C4C22×D312yes—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D312yes—
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420#137—616no—
421#137—616no—
422AGL(1,ℤ/8)—616no—
423AGL(1,ℤ/8)—616no—
424#135—632no—
425C2×Q16—38no—
426C2×SD16—38no—
427C2×SD16—38no—
428C2×D8—38no—
429C2×M16—34no—
430C2×M16—34no—
431C2×M16—68no—
432C22×C8—34no—
433#123—62no—
434#123—62no—
435#123—64no—
436C22⋊Q8—34no—
437C22⋊Q8—34no—
438C22⋊Q8—62no—
439C22⋊Q8—62no—
440#121—34no—
441#121—34no—
442#121—62no—
443#121—62no—
444#120—62no—
445#120—64no—
446#120—62no—
447C4×D4—64no—
448C4×D4—64no—
449C4×D4—64no—
450C4×D4—64no—
451#117—32no—
452#117—32no—
453#117—61no—
454#117—61no—
455C2×C4⋊C4—32no—
456C2×C4⋊C4—62no—
457C2×C22⋊C4—61no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C42—61no—
461#103—316no—
462#102—316no—
463C22⋊C8—38no—
464C22⋊C8—38no—
465C23×C3—22no—
466C23×C3—24no—
467C23×C3—216no—
468C23×C3—24no—
469C23×C3—24no—
470C23×C3—22no—
471C23×C3—28no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—24no—
475C23×C3—42no—
476C23×C3—42no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—416no—
480C23×C3—432no—
481C23×C3—48no—
482C23×C3—48no—
483C23×C3—48no—
484C23×C3#12014yes—
485C23×C3C22×D412yes—
486C23×C3C22×D411yescharacteristic
487C23×C3C22×D411yescharacteristic
488C23×C3C22×D411yescharacteristic
489C23×C3C22×D412yes—
490C22×D3—22no—
491C22×D3—44no—
492C22×D3—42no—
493C3×Q8—216no—
494C3×Q8—28no—
495C3×Q8—24no—
496C3×Q8C22×D418yes—
497C3×D4—232no—
498C3×D4—216no—
499C3×D4—216no—
500C3×D4—216no—
501C3×D4—28no—
502C3×D4—24no—
503C3×D4C22×D418yes—
504C2×C3×C4—216no—
505C2×C3×C4—232no—
506C2×C3×C4—22no—
507C2×C3×C4—28no—
508C2×C3×C4—22no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—216no—
515C2×C3×C4—216no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4#12014yes—
523C2×C3×C4#12014yes—
524C2×C3×C4#12014yes—
525C2×C3×C4C22×D412yes—
526C2×C3×C4C22×D412yes—
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D414yes—
530C2×C3×C4C22×D414yes—
531C2×C3×C4C22×D414yes—
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C2511yescharacteristic
534#67—48no—
535#67—44no—
536#67—44no—
537#67—48no—
538C2×Dic3—24no—
539C2×Dic3—22no—
540C2×Dic3—44no—
541C2×Dic3—42no—
542D12—24no—
543D12—42no—
544C4×D3—44no—
545C4×D3—44no—
546Dic6—24no—
547Dic6—42no—
548C3⋊C8—28no—
549C24—28no—
550C24—24no—
551C24—24no—
552C24—22no—
553C24—44no—
554C24—48no—
555C24—61no—
556C24C2×#6711yescharacteristic
557C24C2×#6712yes—
558C24C2×#6712yes—
559C24C2×#6711yescharacteristic
560C24C2×#6711yescharacteristic
561#41—232no—
562#41—232no—
563#41—232no—
564#41—232no—
565#41—232no—
566#41—216no—
567#41—216no—
568#41—216no—
569#41—216no—
570#41—28no—
571#41—28no—
572#41—68no—
573#41—68no—
574#41—124no—
575#41—124no—
576#41C2×#67116yes—
577#41C2×#67116yescomplemented
578C2×Q8—216no—
579C2×Q8—28no—
580C2×Q8—216no—
581C2×Q8—24no—
582C2×Q8—22no—
583C2×Q8—24no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—64no—
587C2×Q8C2×#6718yescomplemented
588C2×Q8C23×D314yes—
589C2×D4—232no—
590C2×D4—232no—
591C2×D4—216no—
592C2×D4—28no—
593C2×D4—216no—
594C2×D4—216no—
595C2×D4—28no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—216no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—22no—
602C2×D4—32no—
603C2×D4—64no—
604C2×D4—64no—
605C2×D4—62no—
606C2×D4—62no—
607C2×D4—64no—
608C2×D4—61no—
609C2×D4—128no—
610C2×D4—124no—
611C2×D4C2×#6718yescomplemented
612C2×D4C23×D314yes—
613C22×C4—28no—
614C22×C4—232no—
615C22×C4—232no—
616C22×C4—216no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—216no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—24no—
632C22×C4—62no—
633C22×C4—61no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—124no—
637C22×C4C2×#6712yes—
638C22×C4C2×#6712yes—
639C22×C4C2×#6712yes—
640C22×C4C2×#6712yes—
641C22×C4C2×#6712yes—
642C22×C4C2×#6711yescharacteristic
643C22×C4C2×#6711yescharacteristic
644C22×C4C2×#6712yes—
645C22×C4C2×#6712yes—
646C22×C4C2×#6712yes—
647C22×C4C2×#6711yescharacteristic
648C22×C4C2×#6711yescharacteristic
649C22×C4C2×#6711yescharacteristic
650C22×C4C2×#6718yes—
651C22×C4C23×D312yes—
652C22×C4C23×D312yes—
653C22×C4C23×D311yescharacteristic
654C22×C4C23×D311yescharacteristic
655C22×C4C23×D311yescharacteristic
656Q16—616no—
657SD16—616no—
658SD16—616no—
659D8—616no—
660M16—68no—
661M16—68no—
662C2×C8—38no—
663C2×C8—68no—
664C4⋊C4—34no—
665C4⋊C4—62no—
666C4⋊C4—64no—
667C4⋊C4—64no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—64no—
671C22⋊C4—64no—
672C22⋊C4—64no—
673C22⋊C4—64no—
674C42—62no—
675C42—62no—
676C22×C3—28no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—28no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—44no—
687C22×C3—48no—
688C22×C3—48no—
689C22×C3—44no—
690C22×C3—416no—
691C22×C3—432no—
692C22×C3—48no—
693C22×C3C2×#12012yes—
694C22×C3C2×#12012yes—
695C22×C3C2×#12012yes—
696C22×C3#57514yescomplemented
697C22×C3C23×D411yescharacteristic
698C2×D3—42no—
699C2×D3—44no—
700C2×D3—84no—
701C3×C4—22no—
702C3×C4—28no—
703C3×C4—22no—
704C3×C4C2×#12012yes—
705C3×C4C2×#12012yes—
706C3×C4C2×#12012yes—
707C3×C4C23×D412yes—
708Dic3—42no—
709Dic3—44no—
710C23—24no—
711C23—22no—
712C23—216no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—22no—
719C23—28no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—416no—
725C23—432no—
726C23—48no—
727C23—48no—
728C23—48no—
729C23—62no—
730C23—124no—
731C23—122no—
732C23#95314yes—
733C23C22×#6712yes—
734C23C22×#6712yes—
735C23C22×#6711yescharacteristic
736C23C22×#6711yescharacteristic
737C23C22×#6711yescharacteristic
738Q8—216no—
739Q8—24no—
740Q8—28no—
741Q8—64no—
742Q8—122no—
743Q8C22×#6718yes—
744D4—232no—
745D4—216no—
746D4—216no—
747D4—216no—
748D4—24no—
749D4—28no—
750D4—64no—
751D4—128no—
752D4—128no—
753D4—124no—
754D4—124no—
755D4—122no—
756D4C22×#6718yes—
757C2×C4—216no—
758C2×C4—232no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—216no—
770C2×C4—216no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—64no—
776C2×C4—62no—
777C2×C4—124no—
778C2×C4—122no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4#95314yes—
782C2×C4#95314yes—
783C2×C4#95314yes—
784C2×C4C22×#6712yes—
785C2×C4C22×#6712yes—
786C2×C4C22×#6714yes—
787C2×C4C22×#6714yes—
788C2×C4C22×#6714yes—
789C2×C4C22×#6711yescharacteristic
790C2×C4C22×#6711yescharacteristic
791C2×C4C22×#6711yescharacteristic
792C2×C4C24×D311yescharacteristic
793C8—68no—
794C2×C3—22no—
795C2×C3—22no—
796C2×C3—24no—
797C2×C3—22no—
798C2×C3—42no—
799C2×C3—48no—
800C2×C3C22×#12011yescharacteristic
801C2×C3C2×#57512yes—
802D3—82no—
803C22—28no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—44no—
814C22—48no—
815C22—48no—
816C22—432no—
817C22—44no—
818C22—416no—
819C22—48no—
820C22—122no—
821C22—124no—
822C22—244no—
823C22#582214yescomplemented
824C22C2×#95312yes—
825C22C2×#95312yes—
826C22C2×#95312yes—
827C22C23×#6711yescharacteristic
828C4—22no—
829C4—28no—
830C4—22no—
831C4—122no—
832C4—124no—
833C4C2×#95312yes—
834C4C2×#95312yes—
835C4C2×#95312yes—
836C4C23×#6712yes—
837C3#6035911yescharacteristic, complemented, Sylow
838C2—24no—
839C2—22no—
840C2—22no—
841C2—22no—
842C2—42no—
843C2—48no—
844C2—242no—
845C2C2×#582212yes—
846C2C22×#95311yescharacteristic
subgroupG/H
centerC2×C4C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC23×C3×#41C2
socleC22×C3C23×D4
hypercenterC23×#41D3
hypocenterC3#60359
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C23×C3×#41C2semidirect
2. C2×#5822C2semidirect
3. C2×#5791C2semidirect
4. #84084C2semidirect
5. #84082C2semidirect
6. #84081C2semidirect
7. #84080C2semidirect
8. #84072C2semidirect
9. #84059C2semidirect
10. #84038C2semidirect
11. C2×#5207C2semidirect
20. C22×C3×#41C22semidirect
21. C22×C3×#41C22semidirect
22. C23×C3×Q8C22semidirect
24. C23×C3×D4C22semidirect
27. C22×#235C22semidirect
29. C2×#951C22semidirect
31. C2×#950C22semidirect
32. C2×#949C22semidirect
33. C2×#942C22semidirect
34. C2×#932C22semidirect
39. #5791C22semidirect
40. #5791C22semidirect
41. C2×#930C22semidirect
44. C2×#926C22semidirect
45. C2×#924C22semidirect
46. C22×#208C22semidirect
47. #5239C22semidirect
48. #5238C22semidirect
49. #5233C22semidirect
50. #5232C22semidirect
51. #5228C22semidirect
52. #5227C22semidirect
53. #5225C22semidirect
54. #5218C22semidirect
55. #5217C22semidirect
56. #5215C22semidirect
57. #5207C22semidirect
58. #5207C22semidirect
59. #5207C22semidirect
60. C2×#830C22semidirect
61. C23×#41D3semidirect
90. C2×C3×#41D4semidirect
132. C2×#235C23semidirect
133. C22×D12C23semidirect
135. C22×Dic6C23semidirect
144. C2×#216C23semidirect
146. C2×#215C23semidirect
147. C2×#214C23semidirect
149. C2×#213C23semidirect
153. #930C23semidirect
165. #926C23semidirect
166. C2×C4⋊Dic3C23semidirect
170. #924C23semidirect
175. C2×#208C23semidirect
176. C22×C3⋊C8C23semidirect
177. #835C23semidirect
178. #832C23semidirect
180. #830C23semidirect
189. C22×#41C2×D3semidirect
190. C22×#41C2×D3semidirect
191. C23×Q8C2×D3semidirect
193. C23×D4C2×D3semidirect
253. C3×#41C2×D4semidirect
260. C2×C3×Q8C2×D4semidirect
275. C2×C3×D4C2×D4semidirect
379. C2×#41#67semidirect
577. #41C2×#67semidirect
587. C2×Q8C2×#67semidirect
611. C2×D4C2×#67semidirect
696. C22×C3#575semidirect
823. C22#5822semidirect
837. C3#60359semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#412
C2×#58222
C2×#57912
#840842
#840822
#840812
#840802
#840722
#840592
#840382
C2×#52072
#603593