Finite Group Databasebeta

← #11664715

Subgroups — #11664715

Order 768.

3158 conjugacy classes of subgroups.

The subgroup lattice has 840 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×#5825C211yesmaximal, characteristic, complemented
4C22×#951C211yesmaximal, characteristic, complemented
5C2×#5822C211yesmaximal, characteristic, complemented
6C22×#909C211yesmaximal, characteristic, complemented
7#83975C214yesmaximal, complemented
8#83972C214yesmaximal, complemented
9#83939C214yesmaximal, complemented
10#83938C214yesmaximal, complemented
11#83907C214yesmaximal, complemented
12#83905C214yesmaximal, complemented
13#83747C211yesmaximal, characteristic, complemented
14#60645—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic
17C22×#235C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C3×#575—28no—
20C2×C3×#137C2212yescomplemented
21C2×C3×#137C2212yescomplemented
22C2×C3×AGL(1,ℤ/8)C2212yescomplemented
23C2×C3×AGL(1,ℤ/8)C2212yescomplemented
24C2×C3×#135C2214yes—
25C22×C3×M16C2211yescharacteristic
26#5833—22no—
27#5832C2214yes—
28#5830C2212yescomplemented
29#5828—22no—
30#5825—22no—
31#5825—22no—
32#5825C2214yescomplemented
33#5825C2214yescomplemented
34#5825C2212yescomplemented
35C2×#951—28no—
36C2×#951C2214yescomplemented
37C2×#951C2214yescomplemented
38C2×#951C2212yescomplemented
39#5822—28no—
40C2×#950C2214yes—
41C2×#949C2212yescomplemented
42#5816C2212yescomplemented
43C2×#944C2212yescomplemented
44C22×#216C2212yescomplemented
45C2×#942C2212yescomplemented
46#5805C2212yescomplemented
47#5804—22no—
48C2×#936C2212yescomplemented
49C2×#935—22no—
50C22×#214C2212yescomplemented
51C2×#932C2212yescomplemented
52#5791—22no—
53C2×#926C2211yescharacteristic
54C2×#924—22no—
55C22×#208C2211yescharacteristic
56C2×#909—28no—
57C2×#909C2214yescomplemented
58C2×#909C2214yescomplemented
59C22×Dic12C2212yescomplemented
60C22×#204C2212yescomplemented
61#5190C2218yescomplemented
62#5183C2218yescomplemented
63#5175C2218yescomplemented
64#5168C2218yescomplemented
65#5167C2218yescomplemented
66#5167C2218yescomplemented
67#5155C2218yescomplemented
68#5154C2218yescomplemented
69#5122C2214yescomplemented
70Dic3×M16C2214yescomplemented
71#5101C2214yescomplemented
72C2×#575—31no—
73C2×#575D311yescharacteristic, complemented
74C22×#137—31no—
75C22×#137—31no—
76#3449—31no—
77C2×#536—31no—
78#3156—34no—
79#3156—34no—
80#3154—34no—
81#3154—34no—
82#3153—34no—
83#3152—34no—
84#2873—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—21no—
107C23×Dic3—21no—
108C2×#235—21no—
109C2×#235—21no—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235C2312yes—
113C2×#235C2312yes—
114C22×D12C2311yescharacteristic
115C22×C4×D3—21no—
116C22×Dic6—24no—
117C22×Dic6—24no—
118C22×Dic6—21no—
119C22×Dic6—21no—
120C22×Dic6—21no—
121C22×Dic6C2312yes—
122C22×Dic6C2312yes—
123C22×Dic6C2312yes—
124C22×Dic6C2311yescharacteristic
125C3×#137—28no—
126C3×#137—28no—
127C3×AGL(1,ℤ/8)—28no—
128C3×AGL(1,ℤ/8)—28no—
129C3×#135—216no—
130C2×C3×Q16C2314yes—
131C2×C3×SD16C2314yes—
132C2×C3×SD16C2314yes—
133C2×C3×D8C2314yes—
134C2×C3×M16D418yescomplemented
135C2×C3×M16C2312yes—
136C2×C3×M16C2312yes—
137C22×C3×C8C2312yes—
138#953—24no—
139C2×#217—24no—
140C2×#217D412yes—
141#951—28no—
142#951—216no—
143#951—216no—
144#950—216no—
145#949—28no—
146#947C2314yes—
147#946—24no—
148#944—24no—
149#944C2314yes—
150#944C2318yes—
151C2×#216—28no—
152C2×#216C2314yes—
153C2×#216C2318yes—
154#942—28no—
155C2×#215C2314yes—
156#940C2314yes—
157#939—28no—
158#938—24no—
159#937—24no—
160#936—24no—
161#936C2318yes—
162#936C2314yes—
163#935—28no—
164#935—28no—
165#935—24no—
166C2×#214—28no—
167C2×#214C2318yes—
168C2×#214C2314yes—
169#932—28no—
170C2×#213C2314yes—
171#930—24no—
172#929—24no—
173C4×#67—28no—
174#926D412yes—
175#926D412yes—
176#926C2312yes—
177#926C2312yes—
178C2×C4⋊Dic3D412yes—
179#924—28no—
180#924—28no—
181#924—24no—
182C2×Dic3⋊C4—24no—
183C2×C4×Dic3C2312yes—
184C2×#208D418yescomplemented
185C2×#208C2312yes—
186C2×#208C2312yes—
187C22×C3⋊C8C2312yes—
188#909—216no—
189#909—216no—
190C2×Dic12—28no—
191C2×Dic12C2318yes—
192C2×#204—28no—
193C2×#204C2318yes—
194#815C2318yes—
195C8×Dic3C2318yes—
196C22×#41—31no—
197C22×#41C2×D311yescharacteristic
198C22×#41C2×D311yescharacteristic
199C23×Q8—31no—
200#575—28no—
201#575—68no—
202C2×#137—34no—
203C2×#137—34no—
204C2×#137—32no—
205C2×#137—32no—
206C2×#137—34no—
207C2×#137—34no—
208C2×#137—68no—
209C2×#137—68no—
210C2×#137C2×D312yescomplemented
211C2×#137C2×D312yescomplemented
212C2×AGL(1,ℤ/8)—32no—
213C2×AGL(1,ℤ/8)—32no—
214C2×AGL(1,ℤ/8)C2×D312yescomplemented
215C2×AGL(1,ℤ/8)C2×D312yescomplemented
216C2×#135—34no—
217C2×#135C2×D314yes—
218C22×Q16—32no—
219C22×Q16—32no—
220C22×SD16—32no—
221C22×SD16—32no—
222C22×M16—31no—
223C22×M16C2×D311yescharacteristic
224#537—62no—
225#536—34no—
226#536—34no—
227#536—32no—
228#536—32no—
229#536—62no—
230#536—62no—
231#535—32no—
232#535—32no—
233#534—62no—
234#532—34no—
235C2×C4⋊Q8—32no—
236C2×#124—32no—
237#525—62no—
238#525—62no—
239C2×#123—62no—
240C2×C22⋊Q8—62no—
241C2×#117—31no—
242#497—38no—
243#497—38no—
244#497—38no—
245#496—38no—
246#495—38no—
247#495—38no—
248#494—38no—
249#492—38no—
250#405—34no—
251#405—34no—
252C4×M16—34no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3C2×D411yescharacteristic
256C23×D3—21no—
257C3×#41—24no—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—24no—
265C3×#41—44no—
266C3×#41—44no—
267C3×#41—44no—
268C3×#41—44no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8—22no—
275C2×C3×Q8C2412yes—
276C2×C3×Q8C2412yes—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
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—44no—
288C2×C3×D4—44no—
289C2×C3×D4C2412yes—
290C2×C3×D4C2412yes—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D414yes—
303C22×C3×C4C2×D414yes—
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C2×#67—22no—
308C2×#67—22no—
309C2×#67—28no—
310C2×#67—44no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—21no—
315C22×Dic3—44no—
316C22×Dic3C2×D414yes—
317#235—24no—
318#235—24no—
319#235—24no—
320#235—24no—
321#235—44no—
322#235—44no—
323C2×D12—22no—
324C2×D12—22no—
325C2×D12—21no—
326C2×D12C2412yes—
327C2×C4×D3—22no—
328C2×C4×D3—22no—
329C2×C4×D3—44no—
330C2×Dic6—24no—
331C2×Dic6—22no—
332C2×Dic6—24no—
333C2×Dic6—24no—
334C2×Dic6—24no—
335C2×Dic6—24no—
336C2×Dic6—24no—
337C2×Dic6—22no—
338C2×Dic6—22no—
339C2×Dic6—22no—
340C2×Dic6—21no—
341C2×Dic6—22no—
342C2×Dic6—44no—
343C2×Dic6—44no—
344C2×Dic6—44no—
345C2×Dic6C2414yes—
346C2×Dic6C2412yes—
347C3×Q16—28no—
348C3×SD16—28no—
349C3×SD16—28no—
350C3×D8—28no—
351C3×M16C2×D418yes—
352C3×M16C2×D418yes—
353C2×C3×C8C2×D418yes—
354C2×C3×C8C2414yes—
355#217—216no—
356#217—28no—
357#217C2×D414yes—
358#217C2×D414yes—
359#216—28no—
360#216—216no—
361#215—28no—
362#214—28no—
363#214—216no—
364#213—28no—
365(C2×D3)⋊C4—28no—
366C4⋊Dic3C2×D414yes—
367C4⋊Dic3C2×D414yes—
368Dic3⋊C4—216no—
369Dic3⋊C4—28no—
370C4×Dic3C2×D414yes—
371C4×Dic3C2414yes—
372#208C2×D418yes—
373#208C2×D418yes—
374C2×C3⋊C8C2×D418yes—
375C2×C3⋊C8C2414yes—
376Dic12—216no—
377#204—216no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—24no—
383C2×#41—24no—
384C2×#41—24no—
385C2×#41—24no—
386C2×#41—32no—
387C2×#41—32no—
388C2×#41—61no—
389C2×#41—61no—
390C2×#41—64no—
391C2×#41—64no—
392C2×#41C22×D312yes—
393C2×#41C22×D312yes—
394C2×#41C22×D312yes—
395C2×#41C22×D312yes—
396C22×Q8—32no—
397C22×Q8—32no—
398C22×Q8—32no—
399C22×Q8—31no—
400C22×Q8—61no—
401C22×Q8—61no—
402C22×Q8—61no—
403C22×Q8—64no—
404C22×Q8—64no—
405C22×Q8C22×D311yescharacteristic
406C22×Q8C22×D311yescharacteristic
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—31no—
410C22×D4—61no—
411C22×D4C22×D311yescharacteristic
412C22×D4C22×D311yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—61no—
416C23×C4—61no—
417C23×C4C22×D311yescharacteristic
418#137—28no—
419#137—28no—
420#137—68no—
421#137—616no—
422#137—616no—
423#137—68no—
424#137—616no—
425#137—616no—
426AGL(1,ℤ/8)—28no—
427AGL(1,ℤ/8)—28no—
428AGL(1,ℤ/8)—68no—
429AGL(1,ℤ/8)—68no—
430#135—216no—
431#135—616no—
432C2×Q16—38no—
433C2×Q16—34no—
434C2×Q16—38no—
435C2×Q16—68no—
436C2×Q16—68no—
437C2×Q16C22×D314yes—
438C2×SD16—34no—
439C2×SD16—38no—
440C2×SD16—34no—
441C2×SD16—38no—
442C2×SD16—68no—
443C2×SD16—68no—
444C2×SD16C22×D314yes—
445C2×SD16C22×D314yes—
446C2×D8—34no—
447C2×D8C22×D314yes—
448C2×M16—38no—
449C2×M16—32no—
450C2×M16—32no—
451C2×M16#6718yescomplemented
452C2×M16C22×D312yes—
453C2×M16C22×D312yes—
454C22×C8—32no—
455C22×C8C22×D312yes—
456C4⋊Q8—38no—
457C4⋊Q8—34no—
458C4⋊Q8—64no—
459#127—34no—
460#124—34no—
461#124—38no—
462#124—34no—
463#124—64no—
464#123—64no—
465#123—68no—
466#123—68no—
467#123—64no—
468C22⋊Q8—68no—
469C22⋊Q8—68no—
470C22⋊Q8—64no—
471C22⋊Q8—64no—
472#121—64no—
473#121—64no—
474#121—68no—
475#120—64no—
476#120—64no—
477C4×D4—68no—
478#117—32no—
479#117—32no—
480#117—32no—
481#117—32no—
482C2×C4⋊C4—32no—
483C2×C4⋊C4—64no—
484C2×C22⋊C4—32no—
485C2×C22⋊C4—64no—
486C2×C42—32no—
487#97—38no—
488C4×C8—38no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—42no—
492C23×C3—44no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—82no—
496C23×C3#12714yes—
497C23×C3C22×D411yescharacteristic
498C23×C3C22×D411yescharacteristic
499C23×C3C22×D411yescharacteristic
500C22×D3—22no—
501C22×D3—42no—
502C22×D3—82no—
503C3×Q8—22no—
504C3×Q8—22no—
505C3×Q8—22no—
506C3×Q8—22no—
507C3×Q8—42no—
508C3×Q8—42no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—44no—
514C3×D4—44no—
515C3×D4—44no—
516C3×D4—44no—
517C3×D4—42no—
518C3×D4—42no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—44no—
524C2×C3×C4—44no—
525C2×C3×C4—44no—
526C2×C3×C4—44no—
527C2×C3×C4#12714yes—
528C2×C3×C4#12714yes—
529C2×C3×C4#12714yes—
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D412yes—
534C2×C3×C4C22×D412yes—
535C2×C3×C4C22×D412yes—
536C2×C3×C4C22×D412yes—
537C2×C3×C4C22×D412yes—
538C2×C3×C4C22×D412yes—
539C2×C3×C4C2511yescharacteristic
540#67—44no—
541#67—44no—
542#67—88no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3—44no—
546C2×Dic3—44no—
547C2×Dic3—44no—
548C2×Dic3—44no—
549C2×Dic3—42no—
550C2×Dic3C22×D418yes—
551D12—22no—
552D12—22no—
553D12—42no—
554C4×D3—44no—
555C4×D3—44no—
556Dic6—24no—
557Dic6—22no—
558Dic6—24no—
559Dic6—22no—
560Dic6—44no—
561Dic6—44no—
562Dic6—44no—
563Dic6—42no—
564C3×C8C22×D418yes—
565C3⋊C8C22×D418yes—
566C24—21no—
567C24—21no—
568C24—61no—
569C24D3×D411yescharacteristic
570#41—24no—
571#41—24no—
572#41—24no—
573#41—24no—
574#41—24no—
575#41—24no—
576#41—24no—
577#41—24no—
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582#41—64no—
583#41—64no—
584#41—64no—
585#41—64no—
586#41—124no—
587#41—124no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—34no—
595C2×Q8—32no—
596C2×Q8—62no—
597C2×Q8—62no—
598C2×Q8—61no—
599C2×Q8—62no—
600C2×Q8—64no—
601C2×Q8—64no—
602C2×Q8—64no—
603C2×Q8—62no—
604C2×Q8—64no—
605C2×Q8—62no—
606C2×Q8—64no—
607C2×Q8—64no—
608C2×Q8—124no—
609C2×Q8—124no—
610C2×Q8—124no—
611C2×Q8C23×D312yes—
612C2×Q8C23×D312yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—32no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—68no—
627C2×D4—62no—
628C2×D4—62no—
629C2×D4—62no—
630C2×D4—61no—
631C2×D4—62no—
632C2×D4—124no—
633C2×D4C23×D312yes—
634C2×D4C23×D312yes—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—34no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—124no—
651C22×C4—124no—
652C22×C4D3×D411yescharacteristic
653C22×C4D3×D411yescharacteristic
654C22×C4D3×D411yescharacteristic
655C22×C4D3×D414yes—
656C22×C4C2×#6714yes—
657C22×C4C23×D311yescharacteristic
658C22×C4C23×D311yescharacteristic
659C22×C4C23×D311yescharacteristic
660Q16—28no—
661Q16—616no—
662Q16—68no—
663Q16—616no—
664SD16—28no—
665SD16—28no—
666SD16—616no—
667SD16—68no—
668SD16—68no—
669SD16—616no—
670D8—28no—
671D8—68no—
672M16—38no—
673M16—38no—
674M16C2×#6718yes—
675M16C2×#6718yes—
676C2×C8—38no—
677C2×C8—34no—
678C2×C8C2×#6718yes—
679C2×C8C23×D314yes—
680C4⋊C4—34no—
681C4⋊C4—34no—
682C4⋊C4—616no—
683C4⋊C4—68no—
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—68no—
687C22⋊C4—616no—
688C22⋊C4—68no—
689C42—34no—
690C42—34no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—84no—
700C22×C3—84no—
701C22×C3C2×#12712yes—
702C22×C3C2×#12712yes—
703C22×C3C2×#12712yes—
704C22×C3C23×D411yescharacteristic
705C2×D3—44no—
706C2×D3—42no—
707C2×D3—84no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4C2×#12712yes—
711C3×C4C2×#12712yes—
712C3×C4C2×#12712yes—
713C3×C4C23×D411yescharacteristic
714C3×C4C23×D411yescharacteristic
715Dic3—28no—
716Dic3—44no—
717Dic3—42no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—62no—
725C23—82no—
726C23—122no—
727C23—242no—
728C23#94014yes—
729C23C2×D3×D411yescharacteristic
730C23C2×D3×D411yescharacteristic
731C23C2×D3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—42no—
737Q8—42no—
738Q8—64no—
739Q8—62no—
740Q8—64no—
741Q8—62no—
742Q8—124no—
743Q8—124no—
744Q8—124no—
745Q8—122no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—44no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—42no—
755D4—42no—
756D4—62no—
757D4—62no—
758D4—124no—
759D4—124no—
760D4—122no—
761D4—248no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—38no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—62no—
772C2×C4—64no—
773C2×C4—124no—
774C2×C4—122no—
775C2×C4—124no—
776C2×C4—124no—
777C2×C4—124no—
778C2×C4—124no—
779C2×C4—124no—
780C2×C4#94014yes—
781C2×C4#94014yes—
782C2×C4#94014yes—
783C2×C4C2×D3×D412yes—
784C2×C4C2×D3×D412yes—
785C2×C4C2×D3×D412yes—
786C2×C4C2×D3×D411yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C22×#6712yes—
790C2×C4C22×#6712yes—
791C2×C4C22×#6712yes—
792C2×C4C24×D311yescharacteristic
793C8—38no—
794C8C22×#6718yes—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—82no—
799C2×C3—82no—
800C2×C3C22×#12711yescharacteristic
801C2×C3#358612yes—
802D3—82no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—42no—
810C22—42no—
811C22—84no—
812C22—84no—
813C22—124no—
814C22—122no—
815C22—244no—
816C22C2×#94012yes—
817C22C2×#94012yes—
818C22C2×#94012yes—
819C22C22×D3×D411yescharacteristic
820C4—42no—
821C4—42no—
822C4—68no—
823C4—122no—
824C4—124no—
825C4C2×#94012yes—
826C4C2×#94012yes—
827C4C2×#94012yes—
828C4C22×D3×D411yescharacteristic
829C4C23×#6711yescharacteristic
830C3#6064511yescharacteristic, complemented, Sylow
831C2—22no—
832C2—22no—
833C2—22no—
834C2—82no—
835C2—82no—
836C2—242no—
837C2#8720112yes—
838C2C22×#94011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C23×D4
hypercenterC2×#575D3
hypocenterC3#60645
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×#5825C2semidirect
4. C22×#951C2semidirect
5. C2×#5822C2semidirect
6. C22×#909C2semidirect
7. #83975C2semidirect
8. #83972C2semidirect
9. #83939C2semidirect
10. #83938C2semidirect
11. #83907C2semidirect
12. #83905C2semidirect
13. #83747C2semidirect
20. C2×C3×#137C22semidirect
21. C2×C3×#137C22semidirect
22. C2×C3×AGL(1,ℤ/8)C22semidirect
23. C2×C3×AGL(1,ℤ/8)C22semidirect
28. #5830C22semidirect
32. #5825C22semidirect
33. #5825C22semidirect
34. #5825C22semidirect
36. C2×#951C22semidirect
37. C2×#951C22semidirect
38. C2×#951C22semidirect
41. C2×#949C22semidirect
42. #5816C22semidirect
43. C2×#944C22semidirect
44. C22×#216C22semidirect
45. C2×#942C22semidirect
46. #5805C22semidirect
48. C2×#936C22semidirect
50. C22×#214C22semidirect
51. C2×#932C22semidirect
57. C2×#909C22semidirect
58. C2×#909C22semidirect
59. C22×Dic12C22semidirect
60. C22×#204C22semidirect
61. #5190C22semidirect
62. #5183C22semidirect
63. #5175C22semidirect
64. #5168C22semidirect
65. #5167C22semidirect
66. #5167C22semidirect
67. #5155C22semidirect
68. #5154C22semidirect
69. #5122C22semidirect
70. Dic3×M16C22semidirect
71. #5101C22semidirect
73. C2×#575D3semidirect
134. C2×C3×M16D4semidirect
184. C2×#208D4semidirect
210. C2×#137C2×D3semidirect
211. C2×#137C2×D3semidirect
214. C2×AGL(1,ℤ/8)C2×D3semidirect
215. C2×AGL(1,ℤ/8)C2×D3semidirect
451. C2×M16#67semidirect
830. C3#60645semidirect

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×#58252
C22×#9512
C2×#58222
C22×#9092
#839752
#839722
#839392
#839382
#839072
#839052
#837472
#606453