Finite Group Databasebeta

← #11662164

Subgroups — #11662164

Order 768.

2750 conjugacy classes of subgroups.

The subgroup lattice has 858 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×#5827C211yesmaximal, characteristic, complemented
4C2×#5822C211yesmaximal, characteristic, complemented
5C2×#5232C211yesmaximal, characteristic, complemented
6#83971C214yesmaximal, complemented
7#83966C214yesmaximal, complemented
8#83936C214yesmaximal, complemented
9#83931C214yesmaximal, complemented
10#83902C214yesmaximal, complemented
11#83901C214yesmaximal, complemented
12C2×#5133C211yesmaximal, characteristic, complemented
13#83750C211yesmaximal, characteristic, complemented
14#60425—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic
17C22×#235C2211yescharacteristic
18C3×#575—28no—
19C2×C3×#137C2212yescomplemented
20C2×C3×#137C2212yescomplemented
21C2×C3×AGL(1,ℤ/8)C2212yescomplemented
22C2×C3×AGL(1,ℤ/8)C2212yescomplemented
23C2×C3×#135C2214yes—
24C22×C3×M16C2211yescharacteristic
25#5833—21no—
26#5833—21no—
27#5832C2214yes—
28#5830C2212yescomplemented
29#5828—22no—
30#5827—22no—
31#5827—22no—
32#5827C2214yescomplemented
33#5827C2214yescomplemented
34#5825C2212yescomplemented
35C2×#951C2212yescomplemented
36#5822—28no—
37C2×#950C2214yes—
38C2×#949C2212yescomplemented
39#5816C2212yescomplemented
40C2×Q8×Dic3C2212yescomplemented
41C2×#942C2212yescomplemented
42#5805C2212yescomplemented
43#5804—22no—
44C2×D4×Dic3—22no—
45C2×D4×Dic3C2212yescomplemented
46C2×#932C2212yescomplemented
47#5791—22no—
48C2×#926—21no—
49C2×#926C2211yescharacteristic
50C22×C4⋊Dic3—21no—
51C22×C4⋊Dic3C2211yescharacteristic
52C22×#208C2211yescharacteristic
53#5232C2214yescomplemented
54#5232C2214yescomplemented
55C2×#835C2212yescomplemented
56C2×#832C2212yescomplemented
57#5185C2218yescomplemented
58#5182C2218yescomplemented
59#5166C2218yescomplemented
60#5165C2218yescomplemented
61#5163C2218yescomplemented
62#5162C2218yescomplemented
63#5153C2218yescomplemented
64#5150C2218yescomplemented
65#5133C2214yescomplemented
66#5133C2214yescomplemented
67#5119C2214yescomplemented
68#5118C2214yescomplemented
69C2×#821C2212yescomplemented
70C2×#816C2212yescomplemented
71#5102C2214yescomplemented
72C2×#575—31no—
73C2×#575D311yescharacteristic, complemented
74#3449—31no—
75C2×#520—31no—
76#3046—34no—
77#3046—34no—
78#3045—34no—
79#3045—34no—
80#3037—34no—
81#3036—34no—
82#2905—31no—
83C2×#417—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×#41D418yescomplemented
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—
108C23×Dic3—22no—
109C2×#235—21no—
110C2×#235—21no—
111C2×#235—24no—
112C2×#235—24no—
113C2×#235C2312yes—
114C2×#235C2312yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×Dic6C2311yescharacteristic
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×M16—24no—
128C2×C3×M16C2312yes—
129C2×C3×M16C2312yes—
130C22×C3×C8C2312yes—
131#953—24no—
132C2×#217—22no—
133C2×#217D412yes—
134#951—28no—
135#950—216no—
136#949—28no—
137#947C2314yes—
138#946—22no—
139#946—22no—
140Q8×Dic3—24no—
141Q8×Dic3C2318yes—
142#944C2314yes—
143C2×#216C2314yes—
144#942—28no—
145C2×#215C2314yes—
146#940C2314yes—
147#939—24no—
148#939—24no—
149#938—22no—
150#938—22no—
151#937—24no—
152#936C2314yes—
153#935—24no—
154D4×Dic3—28no—
155D4×Dic3—28no—
156D4×Dic3—24no—
157D4×Dic3C2318yes—
158C2×#214C2314yes—
159#932—28no—
160C2×#213C2314yes—
161#930—22no—
162#930—22no—
163#929—24no—
164C4×#67—24no—
165C4×#67—24no—
166#926—24no—
167#926—24no—
168#926D412yes—
169#926D412yes—
170#926C2312yes—
171#926C2312yes—
172C2×C4⋊Dic3—21no—
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3—21no—
175C2×C4⋊Dic3—22no—
176C2×C4⋊Dic3—24no—
177C2×C4⋊Dic3—24no—
178C2×C4⋊Dic3D411yescharacteristic
179C2×C4⋊Dic3D411yescharacteristic
180C2×C4⋊Dic3C2312yes—
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2312yes—
183#924—22no—
184#924—22no—
185C2×C4×Dic3—22no—
186C2×C4×Dic3C2312yes—
187C2×#208—24no—
188C2×#208C2312yes—
189C2×#208C2312yes—
190C22×C3⋊C8C2312yes—
191#835C2318yes—
192#832C2318yes—
193#821C2318yes—
194#816C2318yes—
195Dic3⋊C8C2318yes—
196Dic3⋊C8C2318yes—
197C22×#41—31no—
198C22×#41C2×D311yescharacteristic
199C22×#41C2×D311yescharacteristic
200#575—28no—
201#575—68no—
202C2×#137—32no—
203C2×#137—32no—
204C2×#137C2×D312yescomplemented
205C2×#137C2×D312yescomplemented
206C2×AGL(1,ℤ/8)—32no—
207C2×AGL(1,ℤ/8)—32no—
208C2×AGL(1,ℤ/8)C2×D312yescomplemented
209C2×AGL(1,ℤ/8)C2×D312yescomplemented
210C2×#135—34no—
211C2×#135C2×D314yes—
212C22×M16—31no—
213C22×M16C2×D311yescharacteristic
214#537—61no—
215#537—61no—
216#536—32no—
217#536—32no—
218#535—32no—
219#535—32no—
220#534—62no—
221#532—34no—
222#525—62no—
223#525—62no—
224#520—34no—
225#520—34no—
226#520—62no—
227#520—62no—
228C2×C4×Q8—32no—
229C2×C4×D4—32no—
230C2×C4×D4—62no—
231C2×#117—31no—
232C2×#117—61no—
233C22×C4⋊C4—31no—
234C22×C4⋊C4—61no—
235#464—38no—
236#464—38no—
237#463—38no—
238#463—38no—
239#462—38no—
240#461—38no—
241#460—38no—
242#459—38no—
243#424—34no—
244#424—34no—
245#423—34no—
246#417—34no—
247#417—34no—
248#417—34no—
249#417—34no—
250C2×#103—32no—
251C2×#103—32no—
252C2×#102—32no—
253C2×#102—32no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3C2×D411yescharacteristic
257C23×D3—21no—
258C3×#41—28no—
259C3×#41—28no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—24no—
265C3×#41—24no—
266C3×#41—44no—
267C3×#41—44no—
268C3×#41C2×D418yes—
269C3×#41C2×D418yes—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8—22no—
275C2×C3×Q8C2×D414yes—
276C2×C3×Q8C2412yes—
277C2×C3×Q8C2412yes—
278C2×C3×D4—28no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—21no—
284C2×C3×D4—22no—
285C2×C3×D4—21no—
286C2×C3×D4—22no—
287C2×C3×D4—22no—
288C2×C3×D4—44no—
289C2×C3×D4C2×D414yes—
290C2×C3×D4C2412yes—
291C2×C3×D4C2412yes—
292C22×C3×C4—21no—
293C22×C3×C4—28no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—21no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—44no—
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D414yes—
304C22×C3×C4#4114yes—
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C2×#67—22no—
309C2×#67—22no—
310C2×#67—24no—
311C2×#67—24no—
312C2×#67—44no—
313C22×Dic3—22no—
314C22×Dic3—21no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—28no—
318C22×Dic3—84no—
319C22×Dic3—82no—
320C22×Dic3C2×D412yes—
321C22×Dic3C2×D412yes—
322#235—24no—
323#235—24no—
324#235—24no—
325#235—24no—
326#235—44no—
327#235—44no—
328C2×D12—22no—
329C2×D12—22no—
330C2×D12—21no—
331C2×D12C2412yes—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C2×C4×D3—44no—
335C2×Dic6—22no—
336C2×Dic6—22no—
337C2×Dic6—21no—
338C2×Dic6C2412yes—
339C3×Q16—28no—
340C3×SD16—28no—
341C3×SD16—28no—
342C3×D8—28no—
343C3×M16—24no—
344C3×M16—24no—
345C2×C3×C8—24no—
346C2×C3×C8C2414yes—
347#217—24no—
348#217—24no—
349#217—28no—
350#217C2×D414yes—
351#217C2×D414yes—
352#216—28no—
353#215—28no—
354#214—28no—
355#213—28no—
356(C2×D3)⋊C4—24no—
357(C2×D3)⋊C4—24no—
358C4⋊Dic3—22no—
359C4⋊Dic3—22no—
360C4⋊Dic3—22no—
361C4⋊Dic3—28no—
362C4⋊Dic3C2×D412yes—
363C4⋊Dic3C2×D412yes—
364C4⋊Dic3C2×D412yes—
365C4⋊Dic3C2×D412yes—
366C4⋊Dic3C2414yes—
367Dic3⋊C4—24no—
368Dic3⋊C4—24no—
369C4×Dic3—28no—
370C4×Dic3C2×D414yes—
371C4×Dic3C2414yes—
372#208—24no—
373#208—24no—
374C2×C3⋊C8—24no—
375C2×C3⋊C8C2414yes—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—24no—
381C2×#41—24no—
382C2×#41—24no—
383C2×#41—32no—
384C2×#41—32no—
385C2×#41—61no—
386C2×#41—61no—
387C2×#41—64no—
388C2×#41—64no—
389C2×#41#6718yescomplemented
390C2×#41C22×D312yes—
391C2×#41C22×D312yes—
392C2×#41C22×D312yes—
393C2×#41C22×D312yes—
394C22×Q8—31no—
395C22×Q8C22×D311yescharacteristic
396C22×Q8C22×D311yescharacteristic
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—31no—
400C22×D4—61no—
401C22×D4C22×D311yescharacteristic
402C22×D4C22×D311yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—62no—
406C23×C4—61no—
407C23×C4—61no—
408C23×C4C22×D311yescharacteristic
409#137—28no—
410#137—28no—
411#137—68no—
412#137—68no—
413AGL(1,ℤ/8)—28no—
414AGL(1,ℤ/8)—28no—
415AGL(1,ℤ/8)—68no—
416AGL(1,ℤ/8)—68no—
417#135—216no—
418#135—616no—
419C2×Q16—34no—
420C2×Q16C22×D314yes—
421C2×SD16—34no—
422C2×SD16—34no—
423C2×SD16C22×D314yes—
424C2×SD16C22×D314yes—
425C2×D8—34no—
426C2×D8C22×D314yes—
427C2×M16—24no—
428C2×M16—32no—
429C2×M16—32no—
430C2×M16—64no—
431C2×M16C22×D312yes—
432C2×M16C22×D312yes—
433C22×C8—32no—
434C22×C8C22×D312yes—
435C4⋊Q8—34no—
436#127—34no—
437#124—34no—
438#124—34no—
439#123—64no—
440#123—64no—
441C22⋊Q8—62no—
442C22⋊Q8—62no—
443C22⋊Q8—62no—
444C22⋊Q8—62no—
445#121—62no—
446#121—62no—
447#121—62no—
448#121—62no—
449#121—64no—
450#121—64no—
451#120—64no—
452#120—64no—
453C4×Q8—38no—
454C4×Q8—64no—
455C4×D4—38no—
456C4×D4—64no—
457C4×D4—64no—
458C4×D4—64no—
459C4×D4—68no—
460C4×D4—68no—
461#117—32no—
462#117—32no—
463#117—32no—
464#117—32no—
465#117—64no—
466#117—64no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—32no—
470C2×C4⋊C4—32no—
471C2×C4⋊C4—32no—
472C2×C4⋊C4—64no—
473C2×C4⋊C4—64no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—61no—
476C2×C4⋊C4—61no—
477C2×C4⋊C4—61no—
478C2×C22⋊C4—32no—
479C2×C22⋊C4—62no—
480C2×C42—32no—
481C2×C42—62no—
482C4⋊C8—38no—
483C4⋊C8—38no—
484#103—38no—
485#103—38no—
486#102—38no—
487#102—38no—
488C23×C3—24no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—81no—
497C23×C3—81no—
498C23×C3#12114yes—
499C23×C3C22×D411yescharacteristic
500C23×C3C22×D411yescharacteristic
501C23×C3C22×D411yescharacteristic
502C22×D3—22no—
503C22×D3—42no—
504C22×D3—81no—
505C22×D3—81no—
506C3×Q8—24no—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—22no—
510C3×Q8—42no—
511C3×Q8C22×D414yes—
512C3×D4—28no—
513C3×D4—28no—
514C3×D4—24no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—22no—
518C3×D4—44no—
519C3×D4—44no—
520C3×D4—42no—
521C3×D4C22×D414yes—
522C2×C3×C4—24no—
523C2×C3×C4—22no—
524C2×C3×C4—28no—
525C2×C3×C4—28no—
526C2×C3×C4—22no—
527C2×C3×C4—42no—
528C2×C3×C4—44no—
529C2×C3×C4—44no—
530C2×C3×C4#12114yes—
531C2×C3×C4#12114yes—
532C2×C3×C4#12114yes—
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C22×D412yes—
537C2×C3×C4C22×D412yes—
538C2×C3×C4C22×D412yes—
539C2×C3×C4C2×#4112yes—
540C2×C3×C4C2×#4112yes—
541C2×C3×C4C2×#4112yes—
542C2×C3×C4C2511yescharacteristic
543#67—44no—
544#67—44no—
545#67—84no—
546#67—84no—
547C2×Dic3—24no—
548C2×Dic3—22no—
549C2×Dic3—42no—
550C2×Dic3—42no—
551C2×Dic3—44no—
552C2×Dic3—42no—
553C2×Dic3—88no—
554C2×Dic3—82no—
555C2×Dic3—82no—
556C2×Dic3C22×D414yes—
557C2×Dic3C22×D414yes—
558D12—22no—
559D12—22no—
560D12—42no—
561C4×D3—44no—
562C4×D3—44no—
563Dic6—22no—
564Dic6—22no—
565Dic6—42no—
566C3×C8—24no—
567C3⋊C8—24no—
568C24—21no—
569C24—21no—
570C24—61no—
571C24D3×D411yescharacteristic
572#41—28no—
573#41—28no—
574#41—24no—
575#41—24no—
576#41—24no—
577#41—24no—
578#41—24no—
579#41—24no—
580#41—44no—
581#41—44no—
582#41—64no—
583#41—64no—
584#41—64no—
585#41—64no—
586#41—124no—
587#41—124no—
588#41C2×#6718yes—
589#41C2×#6718yes—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—32no—
596C2×Q8—61no—
597C2×Q8—62no—
598C2×Q8—62no—
599C2×Q8C2×#6714yes—
600C2×Q8C23×D312yes—
601C2×Q8C23×D312yes—
602C2×D4—28no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—32no—
613C2×D4—44no—
614C2×D4—64no—
615C2×D4—64no—
616C2×D4—62no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—62no—
620C2×D4—62no—
621C2×D4—124no—
622C2×D4C2×#6714yes—
623C2×D4C23×D312yes—
624C2×D4C23×D312yes—
625C22×C4—21no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—44no—
635C22×C4—68no—
636C22×C4—62no—
637C22×C4—61no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—124no—
643C22×C4—244no—
644C22×C4—242no—
645C22×C4D3×D411yescharacteristic
646C22×C4D3×D411yescharacteristic
647C22×C4D3×D411yescharacteristic
648C22×C4#23714yes—
649C22×C4C2×#6714yes—
650C22×C4C23×D311yescharacteristic
651C22×C4C23×D311yescharacteristic
652C22×C4C23×D311yescharacteristic
653Q16—28no—
654Q16—68no—
655SD16—28no—
656SD16—28no—
657SD16—68no—
658SD16—68no—
659D8—28no—
660D8—68no—
661M16—24no—
662M16—24no—
663M16—64no—
664M16—64no—
665C2×C8—24no—
666C2×C8—34no—
667C2×C8—64no—
668C2×C8C23×D314yes—
669C4⋊C4—32no—
670C4⋊C4—32no—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—34no—
674C4⋊C4—68no—
675C4⋊C4—64no—
676C4⋊C4—64no—
677C4⋊C4—62no—
678C4⋊C4—62no—
679C4⋊C4—62no—
680C22⋊C4—34no—
681C22⋊C4—34no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—68no—
685C22⋊C4—64no—
686C22⋊C4—64no—
687C42—34no—
688C42—34no—
689C42—68no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—24no—
697C22×C3—44no—
698C22×C3—48no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—84no—
705C22×C3C2×#12112yes—
706C22×C3C2×#12112yes—
707C22×C3C2×#12112yes—
708C22×C3C23×D411yescharacteristic
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—84no—
713C3×C4—24no—
714C3×C4—42no—
715C3×C4C2×#12112yes—
716C3×C4C2×#12112yes—
717C3×C4C2×#12112yes—
718C3×C4C23×D411yescharacteristic
719C3×C4C22×#4111yescharacteristic
720Dic3—24no—
721Dic3—24no—
722Dic3—44no—
723Dic3—42no—
724C23—22no—
725C23—24no—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—62no—
733C23—81no—
734C23—81no—
735C23—122no—
736C23—241no—
737C23—241no—
738C23#93914yes—
739C23C2×D3×D411yescharacteristic
740C23C2×D3×D411yescharacteristic
741C23C2×D3×D411yescharacteristic
742Q8—22no—
743Q8—24no—
744Q8—22no—
745Q8—22no—
746Q8—42no—
747Q8—62no—
748Q8—62no—
749Q8—122no—
750Q8C22×#6714yes—
751D4—28no—
752D4—28no—
753D4—22no—
754D4—22no—
755D4—22no—
756D4—24no—
757D4—44no—
758D4—44no—
759D4—42no—
760D4—62no—
761D4—62no—
762D4—124no—
763D4—124no—
764D4—122no—
765D4—244no—
766D4—244no—
767D4C22×#6714yes—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—34no—
774C2×C4—34no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—64no—
779C2×C4—62no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—124no—
783C2×C4—122no—
784C2×C4—124no—
785C2×C4—124no—
786C2×C4—248no—
787C2×C4—242no—
788C2×C4—242no—
789C2×C4#93914yes—
790C2×C4#93914yes—
791C2×C4#93914yes—
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4C2×#23712yes—
796C2×C4C2×#23712yes—
797C2×C4C2×#23712yes—
798C2×C4C22×#6712yes—
799C2×C4C22×#6712yes—
800C2×C4C22×#6712yes—
801C2×C4C24×D311yescharacteristic
802C8—24no—
803C8—64no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—22no—
807C2×C3—44no—
808C2×C3—82no—
809C2×C3C22×#12111yescharacteristic
810C2×C3#358511yescharacteristic
811C2×C3#358611yescharacteristic
812D3—82no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—24no—
820C22—44no—
821C22—48no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—84no—
828C22—122no—
829C22—122no—
830C22—122no—
831C22—244no—
832C22C2×#93912yes—
833C22C2×#93912yes—
834C22C2×#93912yes—
835C22C22×D3×D411yescharacteristic
836C4—24no—
837C4—42no—
838C4—64no—
839C4—64no—
840C4—124no—
841C4—122no—
842C4C2×#93912yes—
843C4C2×#93912yes—
844C4C2×#93912yes—
845C4C22×#23711yescharacteristic
846C4C23×#6711yescharacteristic
847C3#6042511yescharacteristic, complemented, Sylow
848C2—22no—
849C2—22no—
850C2—22no—
851C2—44no—
852C2—82no—
853C2—242no—
854C2#8720011yescharacteristic
855C2#8720111yescharacteristic
856C2C22×#93911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C23×D4
hypercenterC2×#575D3
hypocenterC3#60425
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×#5827C2semidirect
4. C2×#5822C2semidirect
5. C2×#5232C2semidirect
6. #83971C2semidirect
7. #83966C2semidirect
8. #83936C2semidirect
9. #83931C2semidirect
10. #83902C2semidirect
11. #83901C2semidirect
12. C2×#5133C2semidirect
13. #83750C2semidirect
19. C2×C3×#137C22semidirect
20. C2×C3×#137C22semidirect
21. C2×C3×AGL(1,ℤ/8)C22semidirect
22. C2×C3×AGL(1,ℤ/8)C22semidirect
28. #5830C22semidirect
32. #5827C22semidirect
33. #5827C22semidirect
34. #5825C22semidirect
35. C2×#951C22semidirect
38. C2×#949C22semidirect
39. #5816C22semidirect
40. C2×Q8×Dic3C22semidirect
41. C2×#942C22semidirect
42. #5805C22semidirect
45. C2×D4×Dic3C22semidirect
46. C2×#932C22semidirect
53. #5232C22semidirect
54. #5232C22semidirect
55. C2×#835C22semidirect
56. C2×#832C22semidirect
57. #5185C22semidirect
58. #5182C22semidirect
59. #5166C22semidirect
60. #5165C22semidirect
61. #5163C22semidirect
62. #5162C22semidirect
63. #5153C22semidirect
64. #5150C22semidirect
65. #5133C22semidirect
66. #5133C22semidirect
67. #5119C22semidirect
68. #5118C22semidirect
69. C2×#821C22semidirect
70. C2×#816C22semidirect
71. #5102C22semidirect
73. C2×#575D3semidirect
92. C2×C3×#41D4semidirect
204. C2×#137C2×D3semidirect
205. C2×#137C2×D3semidirect
208. C2×AGL(1,ℤ/8)C2×D3semidirect
209. C2×AGL(1,ℤ/8)C2×D3semidirect
389. C2×#41#67semidirect
847. C3#60425semidirect

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×#58272
C2×#58222
C2×#52322
#839712
#839662
#839362
#839312
#839022
#839012
C2×#51332
#837502
#604253