Finite Group Databasebeta

← #10822195

Subgroups — #10822195

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4C2×#5240C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6C2×#5139C211yesmaximal, characteristic, complemented
7#72111C214yesmaximal, complemented
8#72099C214yesmaximal, complemented
9C2×#4559C211yesmaximal, characteristic, complemented
10#23412—31nomaximal, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C22×#235C2211yescharacteristic
14C3×#575—22no—
15C3×#575—22no—
16C3×#575—22no—
17C3×#575—22no—
18C2×C3×#137—21no—
19C2×C3×#137C2212yescomplemented
20C2×C3×AGL(1,ℤ/8)—21no—
21C2×C3×AGL(1,ℤ/8)C2212yescomplemented
22C2×C3×#135—22no—
23C22×C3×M16C2211yescharacteristic
24#5833—22no—
25#5832—22no—
26#5830—21no—
27#5828—22no—
28#5825—21no—
29C2×#951—21no—
30#5822—22no—
31#5822—22no—
32#5822—22no—
33#5822C2214yes—
34C2×#950—22no—
35C2×#949—21no—
36#5816C2212yescomplemented
37C2×#942—21no—
38#5805C2212yescomplemented
39#5804—22no—
40C2×#932—21no—
41#5791—22no—
42C2×#926C2211yescharacteristic
43C2×#926C2211yescharacteristic
44C22×#208C2211yescharacteristic
45#5240—22no—
46#5240C2214yescomplemented
47#5233—22no—
48#5232—22no—
49#5225C2212yescomplemented
50C2×#834—22no—
51#5215C2212yescomplemented
52#5139—22no—
53#5139C2214yescomplemented
54C2×#825—22no—
55#4559C2214yescomplemented
56C2×#575—31no—
57C2×#575D311yescharacteristic, complemented
58#3449—31no—
59C2×#421—31no—
60#2896—31no—
61C2×#410—31no—
62#2009—34no—
63#2008—34no—
64C2×#344—31no—
65C2×C3×#41—21no—
66C2×C3×#41—21no—
67C2×C3×#41—21no—
68C2×C3×#41—21no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×#41—21no—
72C2×C3×#41—21no—
73C2×C3×#41—21no—
74C2×C3×#41—21no—
75C2×C3×#41—21no—
76C2×C3×#41—21no—
77C2×C3×#41—21no—
78C2×C3×#41—21no—
79C2×C3×#41—21no—
80C2×C3×#41—21no—
81C2×C3×#41—21no—
82C2×C3×#41—21no—
83C2×C3×#41—21no—
84C2×C3×#41—21no—
85C2×C3×#41D412yes—
86C2×C3×#41D412yes—
87C2×C3×#41D412yescomplemented
88C2×C3×#41C2312yes—
89C22×C3×Q8D411yescharacteristic, complemented
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4D411yescharacteristic, complemented
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C2×#235—21no—
100C2×#235—21no—
101C2×#235—21no—
102C2×#235—21no—
103C2×#235—21no—
104C2×#235—21no—
105C2×#235—21no—
106C2×#235—21no—
107C2×#235—21no—
108C2×#235—21no—
109C2×#235D412yes—
110C2×#235C2312yes—
111C22×D12D411yescharacteristic
112C22×C4×D3—21no—
113C22×Dic6D411yescharacteristic
114C3×#137—24no—
115C3×#137—24no—
116C3×#137—24no—
117C3×#137—24no—
118C3×AGL(1,ℤ/8)—24no—
119C3×AGL(1,ℤ/8)—24no—
120C3×AGL(1,ℤ/8)—24no—
121C3×AGL(1,ℤ/8)—24no—
122C3×#135—28no—
123C3×#135—28no—
124C2×C3×Q16—22no—
125C2×C3×SD16—22no—
126C2×C3×SD16—22no—
127C2×C3×D8—22no—
128C2×C3×M16—21no—
129C2×C3×M16—21no—
130C2×C3×M16—21no—
131C2×C3×M16D412yescomplemented
132C2×C3×M16D412yescomplemented
133C2×C3×M16C2312yes—
134C22×C3×C8—21no—
135#953—24no—
136C2×#217—21no—
137C2×#217D412yes—
138#951—24no—
139#951—24no—
140#950—28no—
141#950—28no—
142#949—24no—
143#949—24no—
144#947—22no—
145#946—24no—
146#944—22no—
147C2×#216—22no—
148#942—24no—
149#942—24no—
150C2×#215—22no—
151#940—22no—
152#939—28no—
153#938—24no—
154#937—24no—
155#936—22no—
156#935—24no—
157C2×#214—22no—
158#932—24no—
159#932—24no—
160C2×#213—22no—
161#930—24no—
162#929—24no—
163C4×#67—28no—
164#926—21no—
165#926—21no—
166#926—21no—
167#926—21no—
168#926—21no—
169#926D412yes—
170#926C2312yes—
171#926C2312yes—
172C2×C4⋊Dic3—21no—
173C2×C4⋊Dic3—21no—
174#924—24no—
175C2×C4×Dic3—21no—
176C2×C4×Dic3—21no—
177C2×#208—21no—
178C2×#208—21no—
179C2×#208—21no—
180C2×#208—21no—
181C2×#208D412yescomplemented
182C2×#208C2312yes—
183C22×C3⋊C8D412yescomplemented
184#835—24no—
185#834—28no—
186#832—24no—
187#825—28no—
188C22×#41—31no—
189C22×#41C2×D311yescharacteristic
190C22×#41C2×D311yescharacteristic
191#575—22no—
192#575—22no—
193#575—22no—
194#575—22no—
195#575—34no—
196#575—62no—
197#575—62no—
198#575—62no—
199C2×#137—21no—
200C2×#137—61no—
201C2×#137—61no—
202C2×#137C2×D312yescomplemented
203C2×AGL(1,ℤ/8)—21no—
204C2×AGL(1,ℤ/8)—61no—
205C2×AGL(1,ℤ/8)—61no—
206C2×AGL(1,ℤ/8)C2×D312yescomplemented
207C2×#135—22no—
208C2×#135—62no—
209C22×M16—31no—
210C22×M16C2×D311yescharacteristic
211#537—62no—
212#536—32no—
213#536—61no—
214#535—32no—
215#535—61no—
216#534—62no—
217#532—62no—
218#525—62no—
219#525—62no—
220C2×#117—31no—
221C2×#117—31no—
222#421—34no—
223#421—62no—
224C2×#104—62no—
225#419—32no—
226#418—32no—
227#417—62no—
228#416—62no—
229#410—34no—
230#410—62no—
231C2×#99—62no—
232#344—34no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3C2×D411yescharacteristic
236C23×D3—21no—
237C3×#41—22no—
238C3×#41—22no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—22no—
242C3×#41—22no—
243C3×#41—22no—
244C3×#41—22no—
245C3×#41—22no—
246C3×#41—22no—
247C3×#41—22no—
248C3×#41—22no—
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—22no—
253C3×#41—41no—
254C3×#41—41no—
255C3×#41—41no—
256C3×#41—41no—
257C3×#41—41no—
258C3×#41—41no—
259C3×#41—41no—
260C3×#41—41no—
261C3×#41—41no—
262C3×#41—41no—
263C3×#41—41no—
264C3×#41—41no—
265C3×#41—41no—
266C3×#41—41no—
267C3×#41—41no—
268C3×#41—41no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—21no—
279C2×C3×Q8C2×D412yes—
280C2×C3×Q8C2×D412yes—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—22no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—41no—
296C2×C3×D4—41no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—41no—
300C2×C3×D4—41no—
301C2×C3×D4—41no—
302C2×C3×D4—41no—
303C2×C3×D4C2×D412yes—
304C2×C3×D4C2×D412yes—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—41no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—41no—
315C22×C3×C4—41no—
316C22×C3×C4—41no—
317C22×C3×C4—41no—
318C22×C3×C4—41no—
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2×D411yescharacteristic
328C22×C3×C4C2×D411yescharacteristic
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4#4111yescharacteristic
331C22×C3×C4#4111yescharacteristic
332C22×C3×C4C2411yescharacteristic
333C2×#67—22no—
334C2×#67—22no—
335C2×#67—28no—
336C2×#67—41no—
337C2×#67—41no—
338C2×#67—41no—
339C2×#67—41no—
340C22×Dic3—21no—
341C22×Dic3—22no—
342C22×Dic3—41no—
343#235—22no—
344#235—22no—
345#235—22no—
346#235—22no—
347#235—22no—
348#235—22no—
349#235—22no—
350#235—22no—
351#235—41no—
352#235—41no—
353#235—41no—
354#235—41no—
355#235—41no—
356#235—41no—
357#235—41no—
358#235—41no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12C2×D412yes—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—41no—
368C2×C4×D3—41no—
369C2×C4×D3—41no—
370C2×C4×D3—41no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6C2×D412yes—
377C3×Q16—28no—
378C3×SD16—28no—
379C3×SD16—28no—
380C3×D8—28no—
381C3×M16—22no—
382C3×M16—22no—
383C3×M16—22no—
384C3×M16C2×D414yes—
385C2×C3×C8—22no—
386C2×C3×C8—22no—
387C2×C3×C8—22no—
388#217—28no—
389#217—22no—
390#217—22no—
391#217—41no—
392#217C2×D414yes—
393#216—28no—
394#215—28no—
395#214—28no—
396#213—28no—
397(C2×D3)⋊C4—28no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—41no—
402Dic3⋊C4—28no—
403C4×Dic3—22no—
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—41no—
407#208—22no—
408#208—22no—
409#208—22no—
410#208—22no—
411C2×C3⋊C8—22no—
412C2×C3⋊C8—22no—
413C2×C3⋊C8C2×D414yes—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—32no—
435C2×#41—32no—
436C2×#41—61no—
437C2×#41—61no—
438C2×#41—61no—
439C2×#41—61no—
440C2×#41—61no—
441C2×#41—61no—
442C2×#41—61no—
443C2×#41—61no—
444C2×#41—61no—
445C2×#41—61no—
446C2×#41#6712yes—
447C2×#41#6712yes—
448C2×#41#6712yescomplemented
449C2×#41C22×D312yes—
450C22×Q8—31no—
451C22×Q8#6711yescharacteristic, complemented
452C22×Q8C22×D311yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—31no—
456C22×D4—61no—
457C22×D4#6711yescharacteristic, complemented
458C22×D4C22×D311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—61no—
462C23×C4C22×D311yescharacteristic
463#137—24no—
464#137—24no—
465#137—24no—
466#137—24no—
467#137—64no—
468#137—64no—
469#137—64no—
470#137—64no—
471AGL(1,ℤ/8)—24no—
472AGL(1,ℤ/8)—24no—
473AGL(1,ℤ/8)—24no—
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—64no—
476AGL(1,ℤ/8)—64no—
477AGL(1,ℤ/8)—64no—
478AGL(1,ℤ/8)—64no—
479#135—28no—
480#135—28no—
481#135—68no—
482#135—68no—
483C2×Q16—22no—
484C2×Q16—62no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—62no—
488C2×SD16—62no—
489C2×D8—22no—
490C2×D8—62no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—32no—
495C2×M16—32no—
496C2×M16—61no—
497C2×M16—61no—
498C2×M16—61no—
499C2×M16—61no—
500C2×M16#6712yescomplemented
501C2×M16#6712yescomplemented
502C2×M16C22×D312yes—
503C22×C8—21no—
504C22×C8—32no—
505C4⋊Q8—62no—
506#127—62no—
507#124—62no—
508#124—62no—
509#123—64no—
510#123—64no—
511C22⋊Q8—64no—
512C22⋊Q8—64no—
513#121—64no—
514#121—68no—
515#121—64no—
516#120—64no—
517#120—64no—
518C4×D4—68no—
519#117—32no—
520#117—32no—
521#117—32no—
522#117—61no—
523#117—61no—
524#117—61no—
525#117—61no—
526#117—61no—
527C2×C4⋊C4—61no—
528C2×C4⋊C4—61no—
529C2×C22⋊C4—32no—
530C2×C22⋊C4—61no—
531C2×C42—61no—
532C2×C42—61no—
533#104—68no—
534#103—64no—
535#102—64no—
536#99—68no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—81no—
544C23×C3—82no—
545C23×C3—82no—
546C23×C3#12011yescharacteristic
547C23×C3#12011yescharacteristic
548C23×C3#12111yescharacteristic
549C23×C3#12111yescharacteristic
550C23×C3#12711yescharacteristic
551C23×C3#12711yescharacteristic
552C23×C3C22×D411yescharacteristic
553C22×D3—22no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—82no—
557C3×Q8—22no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—22no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×Q8—41no—
565C3×D4—22no—
566C3×D4—22no—
567C3×D4—22no—
568C3×D4—22no—
569C3×D4—42no—
570C3×D4—42no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—42no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—42no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—41no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4#12011yescharacteristic
596C2×C3×C4#12011yescharacteristic
597C2×C3×C4#12011yescharacteristic
598C2×C3×C4#12011yescharacteristic
599C2×C3×C4#12011yescharacteristic
600C2×C3×C4#12011yescharacteristic
601C2×C3×C4#12011yescharacteristic
602C2×C3×C4#12011yescharacteristic
603C2×C3×C4#12011yescharacteristic
604C2×C3×C4#12011yescharacteristic
605C2×C3×C4#12111yescharacteristic
606C2×C3×C4#12111yescharacteristic
607C2×C3×C4#12111yescharacteristic
608C2×C3×C4#12111yescharacteristic
609C2×C3×C4#12111yescharacteristic
610C2×C3×C4#12111yescharacteristic
611C2×C3×C4#12111yescharacteristic
612C2×C3×C4#12111yescharacteristic
613C2×C3×C4#12111yescharacteristic
614C2×C3×C4#12111yescharacteristic
615C2×C3×C4#12711yescharacteristic
616C2×C3×C4#12711yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C2×#4111yescharacteristic
623#67—42no—
624#67—42no—
625#67—42no—
626#67—42no—
627#67—88no—
628C2×Dic3—24no—
629C2×Dic3—22no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—42no—
633C2×Dic3—82no—
634C2×Dic3—82no—
635D12—22no—
636D12—22no—
637D12—41no—
638D12—41no—
639C4×D3—42no—
640C4×D3—42no—
641C4×D3—42no—
642C4×D3—42no—
643Dic6—22no—
644Dic6—22no—
645Dic6—41no—
646Dic6—41no—
647C3×C8—24no—
648C3⋊C8—24no—
649C24—21no—
650C24—21no—
651C24—61no—
652C24D3×D411yescharacteristic
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—22no—
667#41—22no—
668#41—22no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682#41—41no—
683#41—41no—
684#41—41no—
685#41—62no—
686#41—62no—
687#41—62no—
688#41—62no—
689#41—62no—
690#41—62no—
691#41—62no—
692#41—62no—
693#41—121no—
694#41—121no—
695#41—121no—
696#41—121no—
697#41—121no—
698#41—121no—
699#41—121no—
700#41—121no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—32no—
712C2×Q8—61no—
713C2×Q8—61no—
714C2×Q8—61no—
715C2×Q8—61no—
716C2×Q8—61no—
717C2×Q8C2×#6712yes—
718C2×Q8C2×#6712yes—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—32no—
734C2×D4—41no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—62no—
743C2×D4—62no—
744C2×D4—68no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—121no—
751C2×D4—121no—
752C2×D4—121no—
753C2×D4—121no—
754C2×D4C2×#6712yes—
755C2×D4C2×#6712yes—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—61no—
771C22×C4—62no—
772C22×C4—62no—
773C22×C4—62no—
774C22×C4—121no—
775C22×C4—121no—
776C22×C4—121no—
777C22×C4—121no—
778C22×C4—121no—
779C22×C4D3×D411yescharacteristic
780C22×C4D3×D411yescharacteristic
781C22×C4D3×D411yescharacteristic
782C22×C4D3×D411yescharacteristic
783C22×C4D3×D411yescharacteristic
784C22×C4#23711yescharacteristic
785C22×C4#23711yescharacteristic
786C22×C4C2×#6711yescharacteristic
787C22×C4C2×#6711yescharacteristic
788C22×C4C2×#6711yescharacteristic
789C22×C4C2×#6711yescharacteristic
790C22×C4C2×#6711yescharacteristic
791C22×C4C2×#6711yescharacteristic
792C22×C4C23×D311yescharacteristic
793Q16—28no—
794Q16—68no—
795SD16—28no—
796SD16—28no—
797SD16—68no—
798SD16—68no—
799D8—28no—
800D8—68no—
801M16—22no—
802M16—22no—
803M16—22no—
804M16—62no—
805M16—62no—
806M16—62no—
807M16—62no—
808M16C2×#6714yes—
809C2×C8—22no—
810C2×C8—22no—
811C2×C8—22no—
812C2×C8—34no—
813C2×C8—62no—
814C2×C8—62no—
815C4⋊C4—68no—
816C4⋊C4—62no—
817C4⋊C4—62no—
818C4⋊C4—62no—
819C4⋊C4—121no—
820C22⋊C4—34no—
821C22⋊C4—68no—
822C22⋊C4—68no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—121no—
826C42—62no—
827C42—62no—
828C42—62no—
829C42—121no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—44no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—82no—
841C22×C3—82no—
842C22×C3—82no—
843C22×C3—82no—
844C22×C3—82no—
845C22×C3#39211yescharacteristic
846C22×C3#39211yescharacteristic
847C22×C3#39211yescharacteristic
848C22×C3#39211yescharacteristic
849C22×C3C2×#12011yescharacteristic
850C22×C3C2×#12111yescharacteristic
851C22×C3C2×#12711yescharacteristic
852C2×D3—44no—
853C2×D3—42no—
854C2×D3—82no—
855C2×D3—82no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4#39211yescharacteristic
859C3×C4#39211yescharacteristic
860C3×C4#39211yescharacteristic
861C3×C4#39211yescharacteristic
862C3×C4C2×#12011yescharacteristic
863C3×C4C2×#12011yescharacteristic
864C3×C4C2×#12111yescharacteristic
865C3×C4C2×#12111yescharacteristic
866Dic3—44no—
867Dic3—42no—
868Dic3—82no—
869C23—22no—
870C23—22no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—62no—
876C23—81no—
877C23—82no—
878C23—82no—
879C23—121no—
880C23—121no—
881C23—242no—
882C23#93711yescharacteristic
883C23#93711yescharacteristic
884C23#93911yescharacteristic
885C23#93911yescharacteristic
886C23#94011yescharacteristic
887C23#94011yescharacteristic
888C23C2×D3×D411yescharacteristic
889Q8—22no—
890Q8—22no—
891Q8—22no—
892Q8—22no—
893Q8—41no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—62no—
898Q8—62no—
899Q8—121no—
900Q8—121no—
901D4—22no—
902D4—22no—
903D4—22no—
904D4—22no—
905D4—42no—
906D4—42no—
907D4—42no—
908D4—42no—
909D4—42no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—41no—
917D4—62no—
918D4—62no—
919D4—122no—
920D4—122no—
921D4—122no—
922D4—122no—
923D4—121no—
924D4—121no—
925D4—248no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—64no—
941C2×C4—62no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—122no—
945C2×C4—122no—
946C2×C4—122no—
947C2×C4—122no—
948C2×C4—122no—
949C2×C4—242no—
950C2×C4—242no—
951C2×C4#93711yescharacteristic
952C2×C4#93711yescharacteristic
953C2×C4#93711yescharacteristic
954C2×C4#93711yescharacteristic
955C2×C4#93711yescharacteristic
956C2×C4#93711yescharacteristic
957C2×C4#93811yescharacteristic
958C2×C4#93811yescharacteristic
959C2×C4#93811yescharacteristic
960C2×C4#93811yescharacteristic
961C2×C4#93911yescharacteristic
962C2×C4#93911yescharacteristic
963C2×C4#93911yescharacteristic
964C2×C4#93911yescharacteristic
965C2×C4#93911yescharacteristic
966C2×C4#93911yescharacteristic
967C2×C4#94011yescharacteristic
968C2×C4#94011yescharacteristic
969C2×C4#95311yescharacteristic
970C2×C4#95311yescharacteristic
971C2×C4#95311yescharacteristic
972C2×C4#95311yescharacteristic
973C2×C4C2×D3×D411yescharacteristic
974C2×C4C2×D3×D411yescharacteristic
975C2×C4C2×#23711yescharacteristic
976C2×C4C22×#6711yescharacteristic
977C2×C4C22×#6711yescharacteristic
978C2×C4C22×#6711yescharacteristic
979C8—24no—
980C8—64no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—82no—
989C2×C3—82no—
990C2×C3C2×#39211yescharacteristic
991D3—82no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—124no—
1008C22—122no—
1009C22—242no—
1010C22—242no—
1011C22#522311yescharacteristic
1012C22#522311yescharacteristic
1013C22#522311yescharacteristic
1014C22#522311yescharacteristic
1015C22C2×#93711yescharacteristic
1016C22C2×#93911yescharacteristic
1017C22C2×#94011yescharacteristic
1018C4—42no—
1019C4—42no—
1020C4—124no—
1021C4—122no—
1022C4—242no—
1023C4#522311yescharacteristic
1024C4#522311yescharacteristic
1025C4#522311yescharacteristic
1026C4#522311yescharacteristic
1027C4C2×#93711yescharacteristic
1028C4C2×#93811yescharacteristic
1029C4C2×#93911yescharacteristic
1030C4C2×#95311yescharacteristic
1031C3#2341211yescharacteristic, complemented, Sylow
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—242no—
1042C2C2×#522311yescharacteristic
subgroupG/H
centerC4#5223
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#575C2
socleC2×C3C2×#392
hypercenterC2×#575D3
hypocenterC3#23412
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. #87268C2semidirect
3. C2×#5822C2semidirect
4. C2×#5240C2semidirect
5. #84072C2semidirect
6. C2×#5139C2semidirect
7. #72111C2semidirect
8. #72099C2semidirect
9. C2×#4559C2semidirect
19. C2×C3×#137C22semidirect
21. C2×C3×AGL(1,ℤ/8)C22semidirect
36. #5816C22semidirect
38. #5805C22semidirect
46. #5240C22semidirect
49. #5225C22semidirect
51. #5215C22semidirect
53. #5139C22semidirect
55. #4559C22semidirect
57. C2×#575D3semidirect
87. C2×C3×#41D4semidirect
89. C22×C3×Q8D4semidirect
93. C22×C3×D4D4semidirect
131. C2×C3×M16D4semidirect
132. C2×C3×M16D4semidirect
181. C2×#208D4semidirect
183. C22×C3⋊C8D4semidirect
202. C2×#137C2×D3semidirect
206. C2×AGL(1,ℤ/8)C2×D3semidirect
448. C2×#41#67semidirect
451. C22×Q8#67semidirect
457. C22×D4#67semidirect
500. C2×M16#67semidirect
501. C2×M16#67semidirect
1031. C3#23412semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
#872682
C2×#58222
C2×#52402
#840722
C2×#51392
#721112
#720992
C2×#45592
#234123