Finite Group Databasebeta

← #11633018

Subgroups — #11633018

Order 768.

3272 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5598C212yesmaximal, complemented
2C2×#5606C212yesmaximal, complemented
3C3×#2541C211yesmaximal, characteristic, complemented
4#83190C212yesmaximal, complemented
5#83187C212yesmaximal, complemented
6#83173C212yesmaximal, complemented
7#82703C212yesmaximal, complemented
8#82646C212yesmaximal, complemented
9C4×#937C211yesmaximal, characteristic, complemented
10#82349C211yesmaximal, characteristic, complemented
11#76767C212yesmaximal, complemented
12#76681C212yesmaximal, complemented
13#76677C214yesmaximal, complemented
14#76327C214yesmaximal, complemented
15#73647C212yesmaximal, complemented
16#59001—31nomaximal, Sylow
17C22×#237C2212yes—
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic, complemented
20C2×C3×#127C2212yes—
21C2×C3×#127C2211yescharacteristic, complemented
22C2×C3×#121C2212yes—
23C2×C3×#121C2212yescomplemented
24C2×C3×C4×D4C2211yescharacteristic
25C2×#939C2214yes—
26C2×#938C2212yes—
27C2×#937C2214yes—
28C2×#937C2211yescharacteristic
29C2×#936C2212yescomplemented
30C2×D4×Dic3C2214yes—
31C2×D4×Dic3C2214yescomplemented
32C2×C4×#67C2212yes—
33C2×#924C2212yes—
34#5606—216no—
35#5598—216no—
36C2×#897C2212yes—
37C2×#892C2212yes—
38C2×#887C2212yescomplemented
39C2×#885C2214yes—
40C2×#883C2214yes—
41C2×#67⋊C4C2214yes—
42C2×#878C2214yescomplemented
43C3×#392C2212yes—
44C3×#392C2212yescomplemented
45C3×#390C2212yescomplemented
46C3×C4×C4⋊C4C2211yescharacteristic, complemented
47#5223C2214yes—
48#5223C2214yes—
49#5223C2214yes—
50#5222C2214yes—
51#5221C2214yes—
52#5221C2214yescomplemented
53#5221C2212yescomplemented
54#5220C2212yes—
55#5220C2211yescharacteristic
56#5220C2214yescomplemented
57#5220C2214yescomplemented
58#5212C2211yescharacteristic, complemented
59C4×#217C2211yescharacteristic
60#4989C2212yes—
61#4984C2212yescomplemented
62#4979C2212yescomplemented
63#4961C2214yes—
64#4956C2212yes—
65#4955C2211yescharacteristic
66#4948C2214yescomplemented
67#4947C2212yes—
68#4946C2211yescharacteristic
69#4946C2212yescomplemented
70#4944C2214yescomplemented
71#4944C2214yescomplemented
72#4940C2214yes—
73C4×(C2×D3)⋊C4C2212yes—
74C4×C4⋊Dic3C2214yescomplemented
75#4929C2212yescomplemented
76#4670C2214yes—
77#4653C2214yescomplemented
78C2×#548—32no—
79C2×#525—32no—
80#2670—32no—
81#2669—32no—
82#2541D311yescharacteristic, complemented
83#2463—32no—
84#2461—34no—
85#2456—34no—
86#2431—32no—
87#2426—32no—
88#2414—32no—
89#2409—31no—
90#2366—32no—
91#2362—32no—
92C4×#120—31no—
93C24×D3C2311yescharacteristic
94C22×C3×D4C2312yes—
95C22×C3×D4C2314yes—
96C22×C3×D4C2314yes—
97C22×C3×D4C2312yes—
98C22×C3×D4C2312yes—
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C22×#67C2314yes—
103C22×#67C2312yes—
104C22×#67C2314yes—
105C23×Dic3C2312yes—
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2314yes—
108C2×#237—28no—
109C2×#237—28no—
110C2×#237—44no—
111C22×C4×D3—28no—
112C22×C4×D3—42no—
113C22×C4×D3C2312yes—
114C22×C4×D3C2312yes—
115C22×Dic6—28no—
116C22×Dic6—42no—
117C22×Dic6C2312yes—
118C22×Dic6C2312yes—
119C3×#127—28no—
120C3×#127—42no—
121C3×#121—28no—
122C3×#121—28no—
123C3×C4×D4—42no—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2312yes—
132C2×#217C2314yes—
133C2×#217C2314yes—
134C2×#217C2311yescharacteristic
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2312yes—
141C2×#217C2311yescharacteristic
142#939—216no—
143#938—28no—
144#937—24no—
145#937—216no—
146#936—28no—
147D4×Dic3—216no—
148D4×Dic3—216no—
149C4×#67—28no—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2314yes—
158#924—28no—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2312yes—
165#897D4116yescomplemented
166#892—28no—
167#887—28no—
168#885—216no—
169#883—216no—
170#67⋊C4—216no—
171#878—216no—
172C3×#95C2312yes—
173C3⋊#95C2312yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2312yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C22×#41—32no—
181C23×Q8—31no—
182C24×C4—31no—
183#548—616no—
184C2×#127C2×D312yes—
185C2×#127C2×D311yescharacteristic, complemented
186C2×#124—32no—
187C2×#124—34no—
188#525—616no—
189C2×#123—34no—
190C2×C22⋊Q8—32no—
191C2×C22⋊Q8—32no—
192C2×C22⋊Q8—34no—
193C2×#121—32no—
194C2×#121—34no—
195C2×#121C2×D312yes—
196C2×#121C2×D312yescomplemented
197C2×#120—34no—
198C2×#120—31no—
199C2×C4×Q8—32no—
200C2×C4×D4—34no—
201C2×C4×D4—34no—
202C2×C4×D4—32no—
203C2×C4×D4—34no—
204C2×C4×D4C2×D311yescharacteristic
205C2×#117—32no—
206#396—34no—
207#395—32no—
208#394—34no—
209#394—34no—
210#393—32no—
211#392—34no—
212#392—34no—
213#392—34no—
214#392C2×D312yes—
215#392C2×D312yescomplemented
216#391—32no—
217#390—34no—
218#390—34no—
219#390—32no—
220#390C2×D312yescomplemented
221#389—32no—
222#388—34no—
223#388—34no—
224#388—34no—
225#388—34no—
226#387—34no—
227#386—31no—
228#386—32no—
229#386—34no—
230#386—34no—
231#386—32no—
232#385—32no—
233#385—31no—
234#385—32no—
235#380—31no—
236#379—31no—
237C4×C4⋊C4—34no—
238C4×C4⋊C4C2×D311yescharacteristic, complemented
239C4×C22⋊C4—31no—
240C4×C22⋊C4—32no—
241C24×C3C2414yes—
242C24×C3C2411yescharacteristic
243C24×C3C2411yescharacteristic
244C23×D3—22no—
245C23×D3—24no—
246C23×D3—41no—
247C23×D3—42no—
248C23×D3—41no—
249C23×D3C2412yes—
250C2×C3×D4—28no—
251C2×C3×D4—28no—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—41no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C2×C3×D4—41no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—44no—
266C2×C3×D4#4114yescomplemented
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2414yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—28no—
279C2×#67—28no—
280C2×#67—24no—
281C2×#67—28no—
282C2×#67—44no—
283C2×#67—44no—
284C2×#67—42no—
285C2×#67—44no—
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—24no—
289C22×Dic3—28no—
290C22×Dic3—42no—
291C22×Dic3—41no—
292C22×Dic3—44no—
293C22×Dic3C2412yes—
294C22×Dic3C2414yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2414yes—
298#237—432no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—416no—
304C2×C4×D3—42no—
305C2×C4×D3C2×D418yes—
306C2×Dic6—24no—
307C2×Dic6—24no—
308C2×Dic6—28no—
309C2×Dic6—416no—
310C2×Dic6—42no—
311C2×Dic6C2×D418yes—
312C3×C4⋊C4—41no—
313C3×C4⋊C4C2×D418yes—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—41no—
317C3×C22⋊C4—41no—
318C3×C42—24no—
319C3×C42—22no—
320#217—22no—
321#217—28no—
322#217—28no—
323#217—28no—
324#217—28no—
325#217—24no—
326#217—44no—
327#217—41no—
328#217—44no—
329#217—42no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4C2×D4116yes—
335C4⋊Dic3—24no—
336C4⋊Dic3—44no—
337C4⋊Dic3C2×D4116yes—
338Dic3⋊C4—28no—
339Dic3⋊C4—24no—
340Dic3⋊C4—28no—
341C4×Dic3—28no—
342C4×Dic3—28no—
343C4×Dic3—24no—
344C25—31no—
345C2×#41—68no—
346C2×#41—68no—
347C2×#41—124no—
348C22×Q8—32no—
349C22×Q8—32no—
350C22×Q8—68no—
351C22×Q8—122no—
352C22×D4—32no—
353C22×D4—34no—
354C22×D4—34no—
355C22×D4C22×D312yes—
356C22×D4C22×D314yes—
357C22×D4C22×D314yes—
358C22×D4C22×D312yes—
359C22×D4C22×D312yes—
360C22×D4C22×D311yescharacteristic
361C23×C4—32no—
362C23×C4—31no—
363C23×C4—34no—
364C23×C4—32no—
365C23×C4—32no—
366C23×C4—68no—
367C23×C4—122no—
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#127—28no—
371#127—42no—
372#124—616no—
373#124—68no—
374#123—616no—
375C22⋊Q8—316no—
376C22⋊Q8—616no—
377C22⋊Q8—68no—
378#121—28no—
379#121—28no—
380#121—616no—
381#121—68no—
382#120—616no—
383#120—64no—
384C4×Q8—68no—
385C4×D4—42no—
386C4×D4—616no—
387C4×D4—616no—
388C4×D4—616no—
389C4×D4—68no—
390#117—68no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D312yes—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—31no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4C22×D314yes—
415C2×C22⋊C4C22×D314yes—
416C2×C22⋊C4C22×D311yescharacteristic
417C2×C22⋊C4C22×D311yescharacteristic
418C2×C42—34no—
419C2×C42—32no—
420C2×C42—34no—
421C2×C42C22×D311yescharacteristic
422C2×C42C22×D312yes—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—34no—
427#95—32no—
428#95—34no—
429#95—34no—
430#95C22×D312yes—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3C2×#4112yes—
447C23×C3C2×#4112yes—
448C23×C3C2511yescharacteristic
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—44no—
456C22×D3—48no—
457C22×D3—48no—
458C22×D3—44no—
459C22×D3—44no—
460C22×D3C22×D414yes—
461C3×D4—44no—
462C3×D4—416no—
463C3×D4—416no—
464C3×D4—48no—
465C3×D4—84no—
466C3×D4—84no—
467C2×C3×C4—24no—
468C2×C3×C4—21no—
469C2×C3×C4—24no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—44no—
478C2×C3×C4—44no—
479C2×C3×C4C22×D418yes—
480C2×C3×C4C22×D414yes—
481C2×C3×C4C2×#4112yes—
482C2×C3×C4H(5,𝔽2)12yes—
483#67—416no—
484#67—48no—
485#67—416no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—24no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—48no—
500C2×Dic3—44no—
501C2×Dic3—416no—
502C2×Dic3C22×D414yes—
503C2×Dic3C22×D418yes—
504C4×D3—216no—
505C4×D3—48no—
506Dic6—216no—
507Dic6—48no—
508C24—32no—
509C24—64no—
510C24—62no—
511C24—121no—
512C24—121no—
513C24—122no—
514C24C23×D314yes—
515C24C23×D311yescharacteristic
516C24C23×D311yescharacteristic
517#41—1232no—
518C2×Q8—38no—
519C2×Q8—68no—
520C2×Q8—64no—
521C2×Q8—64no—
522C2×Q8—122no—
523C2×Q8—1216no—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—28no—
527C2×D4—28no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—68no—
541C2×D4—68no—
542C2×D4—64no—
543C2×D4—68no—
544C2×D4—64no—
545C2×D4—124no—
546C2×D4—124no—
547C2×D4—122no—
548C2×D4—124no—
549C2×D4#23714yescomplemented
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—32no—
555C22×C4—34no—
556C22×C4—38no—
557C22×C4—34no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—68no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—122no—
569C22×C4—1216no—
570C22×C4—121no—
571C22×C4—122no—
572C22×C4—124no—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D314yes—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C4⋊C4—316no—
580C4⋊C4—41no—
581C4⋊C4—64no—
582C4⋊C4—68no—
583C4⋊C4—64no—
584C4⋊C4—68no—
585C4⋊C4—124no—
586C4⋊C4D3×D418yes—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—316no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—62no—
599C22⋊C4—68no—
600C22⋊C4—64no—
601C22⋊C4—122no—
602C22⋊C4—121no—
603C22⋊C4—124no—
604C22⋊C4—122no—
605C22⋊C4—124no—
606C42—24no—
607C42—22no—
608C42—68no—
609C42—68no—
610C42—64no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3C23×D412yes—
629C22×C3C22×#4111yescharacteristic
630C22×C3C2×H(5,𝔽2)11yescharacteristic
631C22×C3#58511yescharacteristic
632C22×C3#58512yes—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—24no—
636C2×D3—416no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C3×C4—28no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4D4214yes—
647Dic3—28no—
648Dic3—24no—
649Dic3—42no—
650Dic3—42no—
651Dic3—44no—
652C23—22no—
653C23—22no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—34no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—128no—
675C23—124no—
676C23—124no—
677C23—128no—
678C23—124no—
679C23C2×#23712yes—
680C23C2×#23712yes—
681C23C24×D311yescharacteristic
682Q8—616no—
683Q8—128no—
684D4—44no—
685D4—416no—
686D4—416no—
687D4—48no—
688D4—84no—
689D4—84no—
690D4—1216no—
691D4—128no—
692D4—1216no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—38no—
704C2×C4—34no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—616no—
712C2×C4—62no—
713C2×C4—64no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—128no—
722C2×C4—124no—
723C2×C4—128no—
724C2×C4—1216no—
725C2×C4C2×D3×D418yes—
726C2×C4C2×D3×D414yes—
727C2×C4C2×#23712yes—
728C2×C4#100412yes—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—84no—
732C2×C3C2×D4211yescharacteristic
733C2×C3D4×#4112yes—
734C2×C3#348712yes—
735C2×C3#350511yescharacteristic
736C2×C3#354011yescharacteristic
737D3—44no—
738C22—24no—
739C22—24no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—64no—
756C22—64no—
757C22—64no—
758C22—1216no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22C22×D3×D412yes—
764C22C22×#23711yescharacteristic
765C22C2×#100411yescharacteristic
766C22#596411yescharacteristic
767C22#596612yes—
768C4—28no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—64no—
774C4—68no—
775C4—122no—
776C4—124no—
777C4—122no—
778C4#571714yes—
779C3#5900111yescharacteristic, complemented, Sylow
780C2—42no—
781C2—42no—
782C2—84no—
783C2—124no—
784C2#8593711yescharacteristic
785C2C2×#571711yescharacteristic
786C2#8632211yescharacteristic
787C2D4×#23712yes—
788C2#8678312yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2541C2
hypercenter#2541D3
hypocenterC3#59001
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#5598C2semidirect
2. C2×#5606C2semidirect
3. C3×#2541C2semidirect
4. #83190C2semidirect
5. #83187C2semidirect
6. #83173C2semidirect
7. #82703C2semidirect
8. #82646C2semidirect
9. C4×#937C2semidirect
10. #82349C2semidirect
11. #76767C2semidirect
12. #76681C2semidirect
13. #76677C2semidirect
14. #76327C2semidirect
15. #73647C2semidirect
19. C23×Dic6C22semidirect
21. C2×C3×#127C22semidirect
23. C2×C3×#121C22semidirect
29. C2×#936C22semidirect
31. C2×D4×Dic3C22semidirect
38. C2×#887C22semidirect
42. C2×#878C22semidirect
44. C3×#392C22semidirect
45. C3×#390C22semidirect
46. C3×C4×C4⋊C4C22semidirect
52. #5221C22semidirect
53. #5221C22semidirect
56. #5220C22semidirect
57. #5220C22semidirect
58. #5212C22semidirect
61. #4984C22semidirect
62. #4979C22semidirect
66. #4948C22semidirect
69. #4946C22semidirect
70. #4944C22semidirect
71. #4944C22semidirect
74. C4×C4⋊Dic3C22semidirect
75. #4929C22semidirect
77. #4653C22semidirect
82. #2541D3semidirect
165. #897D4semidirect
185. C2×#127C2×D3semidirect
196. C2×#121C2×D3semidirect
215. #392C2×D3semidirect
220. #390C2×D3semidirect
238. C4×C4⋊C4C2×D3semidirect
266. C2×C3×D4#41semidirect
549. C2×D4#237semidirect
779. C3#59001semidirect

Maximal subgroups

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

subgroupindex
C2×#55982
C2×#56062
C3×#25412
#831902
#831872
#831732
#827032
#826462
C4×#9372
#823492
#767672
#766812
#766772
#763272
#736472
#590013