Finite Group Databasebeta

← #10801113

Subgroups — #10801113

Order 768.

1422 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85886C211yesmaximal, characteristic
2#79200C211yesmaximal, characteristic, complemented
3C2×#4825C211yesmaximal, characteristic
4#78867C211yesmaximal, characteristic, complemented
5#74321C211yesmaximal, characteristic, complemented
6C3×#1859C211yesmaximal, characteristic, complemented
7#71666C211yesmaximal, characteristic, complemented
8#70674C211yesmaximal, characteristic, complemented
9#70354C211yesmaximal, characteristic, complemented
10#70305C211yesmaximal, characteristic
11#69592C211yesmaximal, characteristic, complemented
12#69004C211yesmaximal, characteristic, complemented
13#68972C211yesmaximal, characteristic, complemented
14#68759C211yesmaximal, characteristic, complemented
15#68729C211yesmaximal, characteristic, complemented
16#21474—31nomaximal, Sylow
17C2×#1009C2211yescharacteristic
18C3×#520C2211yescharacteristic
19Dic3×#41C2211yescharacteristic
20C2×#951C2211yescharacteristic
21C2×#909C2211yescharacteristic
22#5574—21no—
23C4×#239—21no—
24#5545—21no—
25#5545—22no—
26C4×D3×D4—22no—
27C4×D3×D4—21no—
28#5522—21no—
29#5522C2211yescharacteristic
30#5521—21no—
31#5521C2211yescharacteristic
32#5504—21no—
33#5504C2211yescharacteristic
34C2×#893—21no—
35C2×#893C2211yescharacteristic
36C2×#887C2211yescharacteristic, complemented
37C2×#875C2211yescharacteristic
38C3×#428C2211yescharacteristic, complemented
39C2×C3×#104C2211yescharacteristic
40C3×#417C2211yescharacteristic
41C3×#384C2211yescharacteristic, complemented
42C2×#837C2211yescharacteristic
43C2×#825C2211yescharacteristic
44C2×#823C2211yescharacteristic
45C2×#823C2211yescharacteristic
46#5120C2211yescharacteristic, complemented
47Dic3×M16C2211yescharacteristic, complemented
48Dic3×M16C2211yescharacteristic, complemented
49#5004C2211yescharacteristic, complemented
50#4990—22no—
51#4989—22no—
52#4988C2211yescharacteristic
53#4973C2211yescharacteristic, complemented
54#4966C2211yescharacteristic
55#4964C2211yescharacteristic, complemented
56#4932C2211yescharacteristic, complemented
57C2×#805C2211yescharacteristic
58#4889—21no—
59#4873—21no—
60#4853—21no—
61#4852—21no—
62#4825C418yescomplemented
63#4790—21no—
64#4789—21no—
65#4758—21no—
66#4757—21no—
67C3×#343C2211yescharacteristic, complemented
68C3×#339C2211yescharacteristic, complemented
69#4555C2211yescharacteristic, complemented
70#4532C2211yescharacteristic, complemented
71#4530C2211yescharacteristic, complemented
72#4523C2211yescharacteristic, complemented
73C4×H(5,𝔽2)—31no—
74C2×#455—31no—
75C4×#137—31no—
76C4×#137—31no—
77#2326—31no—
78#1885—31no—
79#1882—31no—
80#1882—31no—
81#1859—31no—
82#1859D311yescharacteristic, complemented
83#1856—31no—
84#1792—31no—
85#1759—31no—
86#1759—31no—
87C4×#100—31no—
88C2×C3×#41C2311yescharacteristic
89#1009—22no—
90#1009—22no—
91#1009—22no—
92#1009C2×C414yes—
93C2×#239—21no—
94C2×D3×D4—22no—
95C2×D3×D4—21no—
96C2×#235—21no—
97C2×#235C2311yescharacteristic
98C22×D12—21no—
99C22×D12C2311yescharacteristic
100C22×C4×D3—22no—
101C22×C4×D3D412yes—
102C22×Dic6C2311yescharacteristic
103C2×C3×M16C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C3×C4×Q8—21no—
106C3×C4×D4—21no—
107C3×C4×D4—22no—
108C3×#117—21no—
109C3×#117C2311yescharacteristic
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C42C2311yescharacteristic
115#951—22no—
116#951C2×C414yescomplemented
117Q8×Dic3D411yescharacteristic
118Q8×Dic3D411yescharacteristic
119C2×#216—21no—
120D4×Dic3—21no—
121D4×Dic3—21no—
122D4×Dic3D411yescharacteristic
123D4×Dic3D411yescharacteristic
124C2×#214—21no—
125C4×#67—22no—
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4D412yes—
132#926—21no—
133#926C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C2×#208C2311yescharacteristic
140C2×#208C2311yescharacteristic
141#909—22no—
142#909C2×C414yescomplemented
143C2×Dic12—21no—
144C2×#204—21no—
145#893—22no—
146#893—22no—
147#893—21no—
148#893—21no—
149#893—21no—
150#893—21no—
151#893—21no—
152#893—21no—
153#893—21no—
154#893D411yescharacteristic
155#893D411yescharacteristic
156#892—22no—
157#892—21no—
158D3×C4⋊C4—22no—
159D3×C4⋊C4—21no—
160#887—21no—
161#887—21no—
162#887—21no—
163#887—21no—
164#887—21no—
165#887D411yescharacteristic
166#887D411yescharacteristic
167#67⋊C4—22no—
168#67⋊C4—22no—
169#67⋊C4—21no—
170#67⋊C4—21no—
171D3×C22⋊C4—22no—
172D3×C22⋊C4—22no—
173D3×C22⋊C4—22no—
174#875—22no—
175#875C2×C414yescomplemented
176C4×D12—22no—
177C4×D12—22no—
178C4×D12—21no—
179C4×D12—21no—
180#872—22no—
181#872—21no—
182C42×D3—22no—
183C42×D3—21no—
184C3×#107—21no—
185C3×#106—21no—
186C3×#104C2×C414yescomplemented
187C3×#103—21no—
188C3×#102—21no—
189#837—22no—
190C3⋊#95—22no—
191C3⋊#95—21no—
192C3⋊#95—21no—
193#825—22no—
194#823—22no—
195#823C2×C414yescomplemented
196#816—21no—
197#816—21no—
198#815—21no—
199#815—21no—
200C8×Dic3—21no—
201C8×Dic3—21no—
202#810—21no—
203#810—21no—
204#810—21no—
205#809—21no—
206#808—21no—
207#807—21no—
208#805C2×C414yescomplemented
209C2×H(5,𝔽2)—31no—
210C2×#137—31no—
211C2×#137—31no—
212C2×#124—31no—
213#520—31no—
214#520—61no—
215#520—61no—
216#520C2×D311yescharacteristic
217#518—31no—
218#518—62no—
219#518—61no—
220#518—61no—
221C4×#41—31no—
222C4×#41—31no—
223C4×#41—61no—
224C4×#41—61no—
225C2×C4×Q8—31no—
226C2×C4×D4—31no—
227C2×C4×D4—61no—
228C2×C4×D4—61no—
229C2×C4×D4—62no—
230#455—38no—
231#441—61no—
232#441—61no—
233#440—61no—
234#440—61no—
235C4×Q16—61no—
236C4×Q16—61no—
237C4×SD16—61no—
238C4×SD16—61no—
239#428—31no—
240#428C2×D311yescharacteristic, complemented
241C2×#104—31no—
242C2×#104—31no—
243C2×#104—31no—
244C2×#104C2×D311yescharacteristic
245#419—31no—
246#419—31no—
247#417—31no—
248#417C2×D311yescharacteristic
249C2×#100—31no—
250C2×#100—31no—
251C4×M16—31no—
252C4×M16—31no—
253#391—31no—
254#390—31no—
255#388—62no—
256#385—62no—
257#384C2×D311yescharacteristic, complemented
258#376—31no—
259#343—31no—
260#343C2×D311yescharacteristic, complemented
261#339—31no—
262#339—31no—
263#339—31no—
264#339C2×D311yescharacteristic, complemented
265C23×D3—22no—
266C23×D3C2×D412yes—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41C22×C412yes—
270C3×#41#4112yes—
271C2×C3×Q8C2×D411yescharacteristic
272C2×C3×D4—21no—
273C2×C3×D4C2×D411yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—22no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2411yescharacteristic
280C2×#67—22no—
281C2×#67—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3C2×D411yescharacteristic
287C22×Dic3C2×D411yescharacteristic
288#239—24no—
289#239—24no—
290D3×D4—28no—
291D3×D4—24no—
292D3×D4—28no—
293D3×D4—24no—
294#235—24no—
295#235—21no—
296#235—21no—
297#235—24no—
298#235C22×C412yes—
299#235#4112yes—
300C2×D12—22no—
301C2×D12—24no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—24no—
307C2×D12C22×C412yes—
308C2×D12C2×D411yescharacteristic
309C2×D12#4112yes—
310C2×C4×D3—22no—
311C2×C4×D3—21no—
312C2×C4×D3—22no—
313C2×C4×D3—21no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—22no—
317C2×C4×D3—21no—
318C2×C4×D3—22no—
319C2×C4×D3—84no—
320C2×C4×D3—82no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6—21no—
326C2×Dic6C22×C412yescomplemented
327C2×Dic6C2×D411yescharacteristic
328C3×M16—21no—
329C3×M16—21no—
330C3×M16—21no—
331C3×M16C22×C412yescomplemented
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—82no—
340C3×C4⋊C4C2×D411yescharacteristic
341C3×C4⋊C4C2×D411yescharacteristic
342C3×C22⋊C4—22no—
343C3×C22⋊C4—21no—
344C3×C42—22no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42C22×C412yescomplemented
348#217—21no—
349#217—21no—
350#217—21no—
351#216—24no—
352#214—24no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—22no—
355(C2×D3)⋊C4—22no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—82no—
362C4⋊Dic3—21no—
363C4⋊Dic3—21no—
364C4⋊Dic3C2×D411yescharacteristic
365C4⋊Dic3C2×D411yescharacteristic
366Dic3⋊C4—22no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—41no—
370Dic3⋊C4—41no—
371C4×Dic3—22no—
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—41no—
380C4×Dic3—41no—
381C4×Dic3C2×D411yescharacteristic
382C4×Dic3C2×D411yescharacteristic
383C4×Dic3C2×D411yescharacteristic
384C4×Dic3C2×D411yescharacteristic
385#208—21no—
386#208—21no—
387#208—21no—
388#208C22×C412yescomplemented
389C2×C3⋊C8—21no—
390C2×C3⋊C8—21no—
391Dic12—24no—
392#204—24no—
393H(5,𝔽2)—34no—
394H(5,𝔽2)—62no—
395H(5,𝔽2)—62no—
396H(5,𝔽2)—62no—
397C2×#41—31no—
398C2×#41—61no—
399C2×#41—61no—
400C2×#41C22×D311yescharacteristic
401C22×Q8—31no—
402C22×D4—31no—
403C22×D4—61no—
404C22×D4—62no—
405C22×D4—61no—
406C23×C4—32no—
407C23×C4—62no—
408#137—34no—
409#137—34no—
410#137—62no—
411#137—62no—
412C2×Q16—61no—
413C2×Q16—61no—
414C2×SD16—61no—
415C2×SD16—61no—
416C2×M16—31no—
417C2×M16—31no—
418C2×M16C22×D311yescharacteristic
419C2×M16C22×D311yescharacteristic
420#124—34no—
421#124—62no—
422C4×Q8—21no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—61no—
428C4×Q8—61no—
429C4×Q8—61no—
430C4×Q8—61no—
431C4×Q8—61no—
432C4×D4—21no—
433C4×D4—22no—
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—62no—
441C4×D4—62no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4—62no—
449C4×D4—62no—
450C4×D4—61no—
451C4×D4—62no—
452C4×D4—62no—
453C4×D4—62no—
454C4×D4—62no—
455C4×D4—61no—
456C4×D4—61no—
457C4×D4—62no—
458C4×D4—61no—
459C4×D4—61no—
460#117—21no—
461#117—31no—
462#117—61no—
463#117—62no—
464#117—61no—
465#117—61no—
466#117—62no—
467#117C22×D311yescharacteristic
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—61no—
471C2×C4⋊C4—62no—
472C2×C4⋊C4—61no—
473C2×C4⋊C4C22×D311yescharacteristic
474C2×C4⋊C4C22×D311yescharacteristic
475C2×C22⋊C4—32no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C42—31no—
483C2×C42—31no—
484C2×C42—61no—
485C2×C42—62no—
486C2×C42—61no—
487C2×C42—61no—
488C2×C42C22×D311yescharacteristic
489#107—21no—
490#107—61no—
491#106—21no—
492#106—61no—
493#104—34no—
494#104—62no—
495#104—62no—
496#104C4×D314yescomplemented
497#103—21no—
498#103—61no—
499#103—61no—
500#103—61no—
501#103—61no—
502#103—61no—
503#102—21no—
504#102—61no—
505#100—34no—
506#100—62no—
507#97—61no—
508#97—61no—
509C4×C8—61no—
510C4×C8—61no—
511#95—61no—
512#95—61no—
513#95—62no—
514C23×C3—21no—
515C23×C3C22×D411yescharacteristic
516C22×D3—22no—
517C22×D3—21no—
518C22×D3—28no—
519C22×D3—22no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—82no—
523C22×D3—82no—
524C22×D3C4×D414yes—
525C3×Q8—21no—
526C3×Q8C4×D412yes—
527C3×D4—22no—
528C3×D4—22no—
529C3×D4—21no—
530C3×D4C4×D412yes—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—42no—
542C2×C3×C4—41no—
543C2×C3×C4—82no—
544C2×C3×C4C23×C411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C2×#4111yescharacteristic
548C2×C3×C4C2×#4111yescharacteristic
549C2×C3×C4C2×#4111yescharacteristic
550#67—28no—
551#67—22no—
552#67—22no—
553C2×Dic3—21no—
554C2×Dic3—22no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—42no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—81no—
566C2×Dic3#12011yescharacteristic
567C2×Dic3#12011yescharacteristic
568C2×Dic3#12011yescharacteristic
569C2×Dic3#12011yescharacteristic
570D12—28no—
571D12—22no—
572D12—22no—
573D12—21no—
574D12—22no—
575D12—22no—
576D12C4×D412yes—
577C4×D3—28no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—44no—
581C4×D3—42no—
582C4×D3—81no—
583C4×D3—82no—
584C4×D3—82no—
585C4×D3—82no—
586C4×D3—82no—
587Dic6—21no—
588Dic6—22no—
589Dic6—22no—
590Dic6—41no—
591Dic6—41no—
592Dic6C4×D412yes—
593C3×C8—22no—
594C3×C8—41no—
595C3⋊C8—22no—
596C3⋊C8—41no—
597C24—32no—
598C24—62no—
599#41—21no—
600#41—21no—
601#41—32no—
602#41—32no—
603#41—64no—
604#41—64no—
605#41—64no—
606#41—64no—
607#41—61no—
608#41—61no—
609#41C2×C4×D312yes—
610#41#23912yes—
611C2×Q8—32no—
612C2×Q8—31no—
613C2×Q8—61no—
614C2×Q8—61no—
615C2×Q8—61no—
616C2×Q8—61no—
617C2×Q8—61no—
618C2×Q8D3×D411yescharacteristic
619C2×D4—21no—
620C2×D4—32no—
621C2×D4—31no—
622C2×D4—32no—
623C2×D4—64no—
624C2×D4—62no—
625C2×D4—64no—
626C2×D4—68no—
627C2×D4—68no—
628C2×D4—64no—
629C2×D4—62no—
630C2×D4—61no—
631C2×D4—64no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4D3×D411yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—242no—
657C22×C4—244no—
658C22×C4D3×D412yes—
659C22×C4C23×D311yescharacteristic
660Q16—64no—
661Q16—64no—
662SD16—64no—
663SD16—64no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—32no—
668M16—61no—
669M16—61no—
670M16—61no—
671M16C2×C4×D312yescomplemented
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—61no—
675C2×C8—61no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—31no—
682C4⋊C4—31no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—62no—
688C4⋊C4—82no—
689C4⋊C4—121no—
690C4⋊C4—121no—
691C4⋊C4D3×D411yescharacteristic
692C4⋊C4D3×D411yescharacteristic
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—62no—
696C22⋊C4—62no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—68no—
700C22⋊C4—62no—
701C22⋊C4—62no—
702C22⋊C4—62no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—242no—
707C42—22no—
708C42—21no—
709C42—21no—
710C42—31no—
711C42—31no—
712C42—31no—
713C42—31no—
714C42—61no—
715C42—61no—
716C42—61no—
717C42—61no—
718C42—62no—
719C42—61no—
720C42—61no—
721C42—61no—
722C42—121no—
723C42—121no—
724C42C2×C4×D312yescomplemented
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—22no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3C2×C4×D411yescharacteristic
731C22×C3C2×#12011yescharacteristic
732C22×C3#52511yescharacteristic
733C2×D3—24no—
734C2×D3—22no—
735C2×D3—42no—
736C2×D3—41no—
737C2×D3—42no—
738C2×D3—41no—
739C2×D3—44no—
740C2×D3—82no—
741C2×D3—88no—
742C3×C4—22no—
743C3×C4—42no—
744C3×C4—42no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—81no—
748C3×C4C2×C4×D411yescharacteristic
749C3×C4C2×C4×D411yescharacteristic
750C3×C4#52511yescharacteristic
751C3×C4#52511yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—21no—
755Dic3—21no—
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—42no—
760Dic3—81no—
761C23—21no—
762C23—34no—
763C23—68no—
764C23—61no—
765C23—62no—
766C23—62no—
767C23—122no—
768C23—122no—
769C23—242no—
770C23—242no—
771C23C2×D3×D411yescharacteristic
772Q8—21no—
773Q8—32no—
774Q8—61no—
775Q8—62no—
776Q8—62no—
777Q8—121no—
778Q8—121no—
779Q8#89312yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—32no—
784D4—68no—
785D4—68no—
786D4—62no—
787D4—62no—
788D4—62no—
789D4—62no—
790D4—62no—
791D4—61no—
792D4—62no—
793D4#89312yes—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—68no—
811C2×C4—61no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—82no—
818C2×C4—124no—
819C2×C4—122no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—122no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—242no—
829C2×C4—241no—
830C2×C4—242no—
831C2×C4—242no—
832C2×C4—242no—
833C2×C4—241no—
834C2×C4C22×C4×D311yescharacteristic
835C2×C4C2×D3×D411yescharacteristic
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×#23911yescharacteristic
838C2×C4D3×#4111yescharacteristic
839C2×C4D3×#4111yescharacteristic
840C8—22no—
841C8—41no—
842C8—62no—
843C8—121no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—42no—
847C2×C3C4×#12011yescharacteristic
848C2×C3#301911yescharacteristic
849C2×C3#302211yescharacteristic
850D3—44no—
851D3—42no—
852C22—21no—
853C22—21no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—62no—
858C22—64no—
859C22—124no—
860C22—122no—
861C22—121no—
862C22—122no—
863C22—121no—
864C22—242no—
865C22—248no—
866C22C4×D3×D411yescharacteristic
867C22D3×#12011yescharacteristic
868C22#562711yescharacteristic
869C4—22no—
870C4—42no—
871C4—42no—
872C4—41no—
873C4—41no—
874C4—62no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—61no—
879C4—81no—
880C4—122no—
881C4—121no—
882C4—121no—
883C4—241no—
884C4C2×#89311yescharacteristic
885C4C4×D3×D411yescharacteristic
886C4#562711yescharacteristic
887C4#565611yescharacteristic
888C3#2147411yescharacteristic, complemented, Sylow
889C2—21no—
890C2—21no—
891C2—42no—
892C2—124no—
893C2—122no—
894C2#7437911yescharacteristic
895C2#8027811yescharacteristic
896C2#8030011yescharacteristic
subgroupG/H
centerC22D3×#120
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1859C2
socleC22×C3C2×#120
prime radicalC2×#1009C22
cosocleC22×C3×C4C24
hypercenter#1859D3
hypocenterC3#21474
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
2. #79200C2semidirect
4. #78867C2semidirect
5. #74321C2semidirect
6. C3×#1859C2semidirect
7. #71666C2semidirect
8. #70674C2semidirect
9. #70354C2semidirect
11. #69592C2semidirect
12. #69004C2semidirect
13. #68972C2semidirect
14. #68759C2semidirect
15. #68729C2semidirect
36. C2×#887C22semidirect
38. C3×#428C22semidirect
41. C3×#384C22semidirect
46. #5120C22semidirect
47. Dic3×M16C22semidirect
48. Dic3×M16C22semidirect
49. #5004C22semidirect
53. #4973C22semidirect
55. #4964C22semidirect
56. #4932C22semidirect
62. #4825C4semidirect
67. C3×#343C22semidirect
68. C3×#339C22semidirect
69. #4555C22semidirect
70. #4532C22semidirect
71. #4530C22semidirect
72. #4523C22semidirect
82. #1859D3semidirect
116. #951C2×C4semidirect
142. #909C2×C4semidirect
175. #875C2×C4semidirect
186. C3×#104C2×C4semidirect
195. #823C2×C4semidirect
208. #805C2×C4semidirect
240. #428C2×D3semidirect
257. #384C2×D3semidirect
260. #343C2×D3semidirect
264. #339C2×D3semidirect
326. C2×Dic6C22×C4semidirect
331. C3×M16C22×C4semidirect
347. C3×C42C22×C4semidirect
388. #208C22×C4semidirect
496. #104C4×D3semidirect
671. M16C2×C4×D3semidirect
724. C42C2×C4×D3semidirect
888. C3#21474semidirect

Maximal subgroups

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

subgroupindex
#858862
#792002
C2×#48252
#788672
#743212
C3×#18592
#716662
#706742
#703542
#703052
#695922
#690042
#689722
#687592
#687292
#214743