Finite Group Databasebeta

← #11662472

Subgroups — #11662472

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 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×#5833C211yesmaximal, characteristic, complemented
4C2×#5745C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6C2×#5232C211yesmaximal, characteristic, complemented
7#83986C214yesmaximal, complemented
8#83985C214yesmaximal, complemented
9#83951C214yesmaximal, complemented
10#83950C214yesmaximal, complemented
11#83917C214yesmaximal, complemented
12#83916C214yesmaximal, complemented
13C2×#5121C211yesmaximal, characteristic, complemented
14#60456—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic
17C22×#235C2211yescharacteristic
18C3×#575—28no—
19C2×C3×#137C2212yes—
20C2×C3×#137C2212yescomplemented
21C2×C3×AGL(1,ℤ/8)C2212yes—
22C2×C3×AGL(1,ℤ/8)C2212yescomplemented
23C2×C3×#135C2214yescomplemented
24C22×C3×M16C2211yescharacteristic
25#5833—22no—
26#5833—22no—
27#5833C2214yes—
28#5833C2212yescomplemented
29#5833C2214yescomplemented
30#5833C2212yescomplemented
31#5832—22no—
32#5830—21no—
33#5828C2214yes—
34#5825—21no—
35#5816C2212yescomplemented
36C2×#946C2212yescomplemented
37#5805C2212yescomplemented
38#5804—22no—
39C2×#939—22no—
40C2×#938C2212yescomplemented
41#5791—22no—
42C2×#930—21no—
43C2×#926C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C2×#924—21no—
46C22×#208C2211yescharacteristic
47#5745—28no—
48C2×#907C2214yescomplemented
49C2×D3×M16C2214yescomplemented
50C2×#901C2214yescomplemented
51#5233C2214yescomplemented
52#5232C2214yes—
53#5232C2214yescomplemented
54#5232C2212yescomplemented
55#5232C2212yescomplemented
56#5225C2212yescomplemented
57C2×#835C2212yescomplemented
58#5215C2212yescomplemented
59C2×#832C2212yescomplemented
60#5189C2218yescomplemented
61#5188C2218yescomplemented
62#5174C2218yescomplemented
63#5174C2218yescomplemented
64#5171C2218yescomplemented
65#5171C2218yescomplemented
66#5159C2218yescomplemented
67#5157C2218yescomplemented
68#5121C2214yescomplemented
69#5121C2214yescomplemented
70C2×#818C2212yescomplemented
71C2×#817C2212yescomplemented
72C2×#575D311yescharacteristic, complemented
73C2×#568—31no—
74#3449—31no—
75C2×#537—31no—
76#3063—34no—
77#3062—34no—
78#3061—34no—
79#3060—34no—
80#3056—34no—
81#3055—34no—
82C2×#428—31no—
83#2896—31no—
84C2×#417—31no—
85C2×C3×#41—21no—
86C2×C3×#41—21no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—24no—
90C2×C3×#41—24no—
91C2×C3×#41—24no—
92C2×C3×#41—24no—
93C2×C3×#41C2312yes—
94C2×C3×#41C2312yes—
95C2×C3×#41C2312yes—
96C2×C3×#41C2312yes—
97C22×C3×Q8C2311yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C22×#67—22no—
107C22×#67D412yes—
108C23×Dic3—21no—
109C2×#235—24no—
110C2×#235—24no—
111C2×#235D412yes—
112C2×#235D412yes—
113C2×#235C2312yes—
114C2×#235C2312yes—
115C22×D12D411yescharacteristic
116C22×C4×D3C2312yes—
117C22×Dic6D411yescharacteristic
118C3×#137—28no—
119C3×#137—28no—
120C3×AGL(1,ℤ/8)—28no—
121C3×AGL(1,ℤ/8)—28no—
122C3×#135—216no—
123C2×C3×Q16C2314yes—
124C2×C3×SD16C2314yes—
125C2×C3×SD16C2314yes—
126C2×C3×D8C2314yes—
127C2×C3×M16D418yescomplemented
128C2×C3×M16C2312yes—
129C2×C3×M16C2312yes—
130C22×C3×C8C2312yes—
131#953—24no—
132C2×#217—21no—
133C2×#217—22no—
134#947—22no—
135#946—24no—
136#946C2314yes—
137#946C2318yes—
138#946C2314yes—
139#944—22no—
140#940—22no—
141#939—28no—
142#939—28no—
143#939—24no—
144#939—24no—
145#938—24no—
146#938C2314yes—
147#938C2318yes—
148#938C2314yes—
149#937—24no—
150#936—22no—
151#935—24no—
152#930—24no—
153#930—24no—
154#930—22no—
155#930—22no—
156#929—24no—
157C4×#67—24no—
158C4×#67—24no—
159C2×(C2×D3)⋊C4—22no—
160#926—21no—
161#926—21no—
162#926C2312yes—
163#926C2312yes—
164C2×C4⋊Dic3—21no—
165C2×C4⋊Dic3—21no—
166C2×C4⋊Dic3—21no—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2311yescharacteristic
172#924—24no—
173#924—24no—
174#924—22no—
175#924—22no—
176C2×Dic3⋊C4—22no—
177C2×C4×Dic3—21no—
178C2×#208—24no—
179C2×#208C2312yes—
180C2×#208C2312yes—
181C22×C3⋊C8C2312yes—
182#907—216no—
183D3×M16—216no—
184#901—216no—
185C2×ΓL(1,𝔽25)C2318yes—
186C2×D3×C8C2318yes—
187#835C2314yes—
188#835C2318yes—
189#835C2314yes—
190#832C2314yes—
191#832C2318yes—
192#832C2314yes—
193#818C2318yes—
194#817C2318yes—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C22×#41C2×D311yescharacteristic
198#575—28no—
199C2×#137C2×D312yes—
200C2×#137C2×D312yescomplemented
201C2×AGL(1,ℤ/8)C2×D312yes—
202C2×AGL(1,ℤ/8)C2×D312yescomplemented
203C2×#135C2×D314yescomplemented
204#568—68no—
205C2×#131—34no—
206C2×#131—34no—
207C22×M16—31no—
208C22×M16—34no—
209C22×M16C2×D311yescharacteristic
210#537—34no—
211#537—34no—
212#537—32no—
213#537—32no—
214#537—62no—
215#537—62no—
216#536—32no—
217#536—61no—
218#535—32no—
219#535—61no—
220#534—62no—
221#532—62no—
222#525—34no—
223#525—62no—
224C2×C22⋊Q8—32no—
225C2×C22⋊Q8—61no—
226C2×#121—32no—
227C2×#121—61no—
228C2×#121—62no—
229C2×#117—31no—
230C22×C4⋊C4—31no—
231#470—38no—
232#469—38no—
233#468—38no—
234#468—38no—
235#467—38no—
236#466—38no—
237#465—38no—
238#465—38no—
239#428—34no—
240#428—34no—
241C2×#107—32no—
242C2×#106—32no—
243#419—32no—
244#418—32no—
245#417—34no—
246#417—34no—
247#417—32no—
248#417—32no—
249#416—34no—
250C2×#103—32no—
251C2×#102—32no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3C2×D411yescharacteristic
255C23×D3C2×D412yes—
256C3×#41—24no—
257C3×#41—24no—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—44no—
265C3×#41—44no—
266C3×#41—44no—
267C3×#41—44no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—22no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8C2412yes—
275C2×C3×Q8C2412yes—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—22no—
285C2×C3×D4—22no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4C2412yes—
289C2×C3×D4C2412yes—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D414yes—
302C22×C3×C4#4114yes—
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C2×#67—28no—
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—28no—
310C2×#67—84no—
311C2×#67C2×D414yes—
312C2×#67C2×D414yes—
313C22×Dic3—22no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—82no—
319C22×Dic3C2×D412yes—
320#235—28no—
321#235—28no—
322#235—24no—
323#235—24no—
324#235—24no—
325#235—24no—
326C2×D12—24no—
327C2×D12C2×D412yes—
328C2×D12C2×D412yes—
329C2×C4×D3—24no—
330C2×C4×D3—24no—
331C2×C4×D3C2×D414yes—
332C2×C4×D3C2414yes—
333C2×Dic6—24no—
334C2×Dic6C2×D412yes—
335C2×Dic6C2×D412yes—
336C3×Q16—28no—
337C3×SD16—28no—
338C3×SD16—28no—
339C3×D8—28no—
340C3×M16C2×D418yes—
341C3×M16C2×D418yescomplemented
342C2×C3×C8C2×D418yescomplemented
343C2×C3×C8C2414yes—
344#217—22no—
345#217—22no—
346#217—28no—
347#217—24no—
348#217—24no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—24no—
352C4⋊Dic3—22no—
353C4⋊Dic3—22no—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—22no—
357C4⋊Dic3C2412yes—
358C4⋊Dic3C2414yes—
359C4⋊Dic3C2412yes—
360Dic3⋊C4—28no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363C4×Dic3—22no—
364C4×Dic3—22no—
365#208—24no—
366#208—24no—
367C2×C3⋊C8—24no—
368C2×C3⋊C8C2414yes—
369ΓL(1,𝔽25)—216no—
370D3×C8—216no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—24no—
378C2×#41—24no—
379C2×#41—32no—
380C2×#41—32no—
381C2×#41—32no—
382C2×#41—32no—
383C2×#41—64no—
384C2×#41—64no—
385C2×#41C22×D312yes—
386C2×#41C22×D312yes—
387C2×#41C22×D312yes—
388C2×#41C22×D312yes—
389C22×Q8—31no—
390C22×Q8C22×D311yescharacteristic
391C22×Q8C22×D311yescharacteristic
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—32no—
395C22×D4—31no—
396C22×D4—62no—
397C22×D4C22×D311yescharacteristic
398C22×D4C22×D311yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—32no—
402C23×C4—61no—
403C23×C4C22×D311yescharacteristic
404#137—28no—
405#137—28no—
406AGL(1,ℤ/8)—28no—
407AGL(1,ℤ/8)—28no—
408#135—216no—
409C2×Q16C22×D314yes—
410C2×SD16C22×D314yes—
411C2×SD16C22×D314yes—
412C2×D8C22×D314yes—
413#131—616no—
414#131—616no—
415C2×M16—32no—
416C2×M16—32no—
417C2×M16—38no—
418C2×M16—64no—
419C2×M16—616no—
420C2×M16#6718yescomplemented
421C2×M16C22×D312yes—
422C2×M16C22×D312yes—
423C22×C8—32no—
424C22×C8—38no—
425C22×C8C22×D312yes—
426C4⋊Q8—62no—
427#127—62no—
428#124—62no—
429#124—62no—
430#123—64no—
431#123—64no—
432C22⋊Q8—38no—
433C22⋊Q8—34no—
434C22⋊Q8—34no—
435C22⋊Q8—64no—
436C22⋊Q8—64no—
437C22⋊Q8—62no—
438C22⋊Q8—62no—
439C22⋊Q8—64no—
440#121—38no—
441#121—34no—
442#121—34no—
443#121—64no—
444#121—64no—
445#121—62no—
446#121—62no—
447#121—64no—
448#121—68no—
449#121—68no—
450#121—64no—
451#121—64no—
452#120—64no—
453#120—64no—
454C4×D4—64no—
455C4×D4—64no—
456#117—32no—
457#117—32no—
458#117—61no—
459#117—61no—
460C2×C4⋊C4—32no—
461C2×C4⋊C4—32no—
462C2×C4⋊C4—32no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—61no—
467C2×C4⋊C4—61no—
468C2×C4⋊C4—61no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—61no—
472C2×C42—61no—
473#107—38no—
474#106—38no—
475#103—38no—
476#103—34no—
477#103—34no—
478#102—38no—
479#102—34no—
480#102—34no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—42no—
488C23×C3—42no—
489C23×C3—81no—
490C23×C3—81no—
491C23×C3#12114yes—
492C23×C3C22×D411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C22×D3—24no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3C22×D414yes—
499C3×Q8—22no—
500C3×Q8—22no—
501C3×Q8—22no—
502C3×Q8—22no—
503C3×Q8—42no—
504C3×Q8—42no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—44no—
510C3×D4—44no—
511C3×D4—44no—
512C3×D4—44no—
513C3×D4—42no—
514C3×D4—42no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—44no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—44no—
523C2×C3×C4#12114yes—
524C2×C3×C4#12114yes—
525C2×C3×C4#12114yes—
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D412yes—
530C2×C3×C4C22×D412yes—
531C2×C3×C4C22×D412yes—
532C2×C3×C4C2×#4112yes—
533C2×C3×C4C2×#4112yes—
534C2×C3×C4C2×#4112yes—
535C2×C3×C4C2511yescharacteristic
536#67—28no—
537#67—28no—
538#67—84no—
539#67—84no—
540#67—88no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—24no—
545C2×Dic3—44no—
546C2×Dic3—81no—
547C2×Dic3—81no—
548C2×Dic3—82no—
549C2×Dic3—82no—
550C2×Dic3C22×D414yes—
551D12—24no—
552D12—24no—
553C4×D3—28no—
554C4×D3—24no—
555C4×D3—24no—
556Dic6—24no—
557Dic6—24no—
558C3×C8C22×D418yes—
559C3⋊C8—24no—
560C24—21no—
561C24—21no—
562C24—32no—
563C24D3×D411yescharacteristic
564#41—24no—
565#41—24no—
566#41—24no—
567#41—24no—
568#41—24no—
569#41—24no—
570#41—24no—
571#41—24no—
572#41—44no—
573#41—44no—
574#41—44no—
575#41—44no—
576#41—68no—
577#41—68no—
578#41—64no—
579#41—64no—
580#41—64no—
581#41—64no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—32no—
589C2×Q8—32no—
590C2×Q8—64no—
591C2×Q8C23×D312yes—
592C2×Q8C23×D312yes—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—34no—
604C2×D4—34no—
605C2×D4—32no—
606C2×D4—32no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—68no—
610C2×D4—64no—
611C2×D4—64no—
612C2×D4—68no—
613C2×D4—64no—
614C2×D4—244no—
615C2×D4C23×D312yes—
616C2×D4C23×D312yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—32no—
624C22×C4—34no—
625C22×C4—34no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—64no—
629C22×C4—64no—
630C22×C4—62no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—242no—
636C22×C4D3×D411yescharacteristic
637C22×C4D3×D411yescharacteristic
638C22×C4D3×D411yescharacteristic
639C22×C4#23714yes—
640C22×C4C2×#6714yes—
641C22×C4C23×D311yescharacteristic
642C22×C4C23×D311yescharacteristic
643C22×C4C23×D311yescharacteristic
644Q16—28no—
645SD16—28no—
646SD16—28no—
647D8—28no—
648M16—64no—
649M16—64no—
650M16—616no—
651M16C2×#6718yes—
652M16C2×#6718yescomplemented
653C2×C8—34no—
654C2×C8—64no—
655C2×C8—616no—
656C2×C8C2×#6718yescomplemented
657C2×C8C23×D314yes—
658C4⋊C4—32no—
659C4⋊C4—34no—
660C4⋊C4—32no—
661C4⋊C4—68no—
662C4⋊C4—64no—
663C4⋊C4—64no—
664C4⋊C4—62no—
665C4⋊C4—62no—
666C4⋊C4—62no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C22⋊C4—68no—
670C22⋊C4—64no—
671C22⋊C4—64no—
672C22⋊C4—68no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—62no—
676C22⋊C4—62no—
677C42—62no—
678C42—62no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—44no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—84no—
693C22×C3—84no—
694C22×C3C2×#12112yes—
695C22×C3C2×#12112yes—
696C22×C3C2×#12112yes—
697C22×C3C23×D411yescharacteristic
698C2×D3—24no—
699C2×D3—24no—
700C2×D3—24no—
701C2×D3—84no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4C2×#12112yes—
705C3×C4C2×#12112yes—
706C3×C4C2×#12112yes—
707C3×C4C23×D411yescharacteristic
708C3×C4C22×#4111yescharacteristic
709Dic3—24no—
710Dic3—44no—
711Dic3—42no—
712Dic3—42no—
713C23—22no—
714C23—22no—
715C23—34no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—64no—
723C23—81no—
724C23—81no—
725C23—122no—
726C23—122no—
727C23#93814yes—
728C23C2×D3×D411yescharacteristic
729C23C2×D3×D411yescharacteristic
730C23C2×D3×D411yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—42no—
737Q8—64no—
738Q8—64no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—44no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—42no—
748D4—42no—
749D4—68no—
750D4—68no—
751D4—64no—
752D4—64no—
753D4—248no—
754D4—244no—
755D4—244no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—34no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—64no—
768C2×C4—68no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—64no—
772C2×C4—124no—
773C2×C4—242no—
774C2×C4—242no—
775C2×C4—241no—
776C2×C4—241no—
777C2×C4#93814yes—
778C2×C4#93814yes—
779C2×C4#93814yes—
780C2×C4C2×D3×D411yescharacteristic
781C2×C4C2×D3×D411yescharacteristic
782C2×C4C2×D3×D411yescharacteristic
783C2×C4C2×#23712yes—
784C2×C4C2×#23712yes—
785C2×C4C2×#23712yes—
786C2×C4C22×#6712yes—
787C2×C4C22×#6712yes—
788C2×C4C22×#6712yes—
789C2×C4C24×D311yescharacteristic
790C8—64no—
791C8C22×#6718yes—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—82no—
796C2×C3—82no—
797C2×C3C22×#12111yescharacteristic
798C2×C3#358511yescharacteristic
799C2×C3#358611yescharacteristic
800D3—44no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—44no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—64no—
815C22—64no—
816C22—64no—
817C22—84no—
818C22—84no—
819C22—244no—
820C22C2×#93812yes—
821C22C2×#93812yes—
822C22C2×#93812yes—
823C22C22×D3×D411yescharacteristic
824C4—42no—
825C4—42no—
826C4—64no—
827C4—124no—
828C4—122no—
829C4—122no—
830C4C2×#93812yes—
831C4C2×#93812yes—
832C4C2×#93812yes—
833C4C22×#23711yescharacteristic
834C4C23×#6711yescharacteristic
835C3#6045611yescharacteristic, complemented, Sylow
836C2—22no—
837C2—22no—
838C2—22no—
839C2—82no—
840C2—82no—
841C2—124no—
842C2#8720011yescharacteristic
843C2#8720111yescharacteristic
844C2C22×#93811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C23×D4
hypercenterC2×#575D3
hypocenterC3#60456
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ 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×#5833C2semidirect
4. C2×#5745C2semidirect
5. #84072C2semidirect
6. C2×#5232C2semidirect
7. #83986C2semidirect
8. #83985C2semidirect
9. #83951C2semidirect
10. #83950C2semidirect
11. #83917C2semidirect
12. #83916C2semidirect
13. C2×#5121C2semidirect
20. C2×C3×#137C22semidirect
22. C2×C3×AGL(1,ℤ/8)C22semidirect
23. C2×C3×#135C22semidirect
28. #5833C22semidirect
29. #5833C22semidirect
30. #5833C22semidirect
35. #5816C22semidirect
36. C2×#946C22semidirect
37. #5805C22semidirect
40. C2×#938C22semidirect
48. C2×#907C22semidirect
49. C2×D3×M16C22semidirect
50. C2×#901C22semidirect
51. #5233C22semidirect
53. #5232C22semidirect
54. #5232C22semidirect
55. #5232C22semidirect
56. #5225C22semidirect
57. C2×#835C22semidirect
58. #5215C22semidirect
59. C2×#832C22semidirect
60. #5189C22semidirect
61. #5188C22semidirect
62. #5174C22semidirect
63. #5174C22semidirect
64. #5171C22semidirect
65. #5171C22semidirect
66. #5159C22semidirect
67. #5157C22semidirect
68. #5121C22semidirect
69. #5121C22semidirect
70. C2×#818C22semidirect
71. C2×#817C22semidirect
72. C2×#575D3semidirect
127. C2×C3×M16D4semidirect
200. C2×#137C2×D3semidirect
202. C2×AGL(1,ℤ/8)C2×D3semidirect
203. C2×#135C2×D3semidirect
341. C3×M16C2×D4semidirect
342. C2×C3×C8C2×D4semidirect
420. C2×M16#67semidirect
652. M16C2×#67semidirect
656. C2×C8C2×#67semidirect
835. C3#60456semidirect

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×#58332
C2×#57452
#840722
C2×#52322
#839862
#839852
#839512
#839502
#839172
#839162
C2×#51212
#604563