Finite Group Databasebeta

← C2×#81859 #11670247

Subgroups — C2×#81859 #11670247

Order 768.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#915C211yesmaximal, characteristic, complemented
2C22×#912C211yesmaximal, characteristic, complemented
3C2×#5718C211yesmaximal, characteristic, complemented
4C2×#5677C211yesmaximal, characteristic, complemented
5C2×C3×#496C211yesmaximal, characteristic, complemented
6C2×#5171C211yesmaximal, characteristic, complemented
7C2×#5173C211yesmaximal, characteristic, complemented
8C2×#5170C211yesmaximal, characteristic, complemented
9C2×#5159C211yesmaximal, characteristic, complemented
10C2×#5158C211yesmaximal, characteristic, complemented
11C2×#5158C211yesmaximal, characteristic, complemented
12C2×#5075C211yesmaximal, characteristic, complemented
13C2×#5054C211yesmaximal, characteristic, complemented
14#81859C2116yesmaximal, direct product factor
15C2×#4716C211yesmaximal, characteristic, complemented
16C2×#4706C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×D3×Q8C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×#237C2211yescharacteristic
21C22×#237C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×D8C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C22×#216C2211yescharacteristic
30C2×#940—21no—
31C2×#939—21no—
32C2×#939—21no—
33C2×#938C2211yescharacteristic
34C2×#938C2211yescharacteristic
35C2×#938C2211yescharacteristic
36C2×D4×Dic3—21no—
37C22×#214C2211yescharacteristic
38C22×#214C2211yescharacteristic
39C22×#214C2211yescharacteristic
40C2×#915—28no—
41C2×#915C2218yescomplemented
42C2×#912—28no—
43C2×#912C2218yescomplemented
44C22×Dic12C2211yescharacteristic
45C22×ΓL(1,𝔽25)C2211yescharacteristic
46C22×D3×C8C2211yescharacteristic
47#5718—24no—
48#5718C2218yescomplemented
49#5677—24no—
50#5677C2218yescomplemented
51C2×#885—21no—
52C2×#884—21no—
53C2×#67⋊C4—21no—
54C2×#878—21no—
55C2×C4×D12C2211yescharacteristic
56C2×C4×Dic6C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58C3×#496C2218yescomplemented
59C2×C3×#97C2211yescharacteristic
60C2×#835C2211yescharacteristic
61C2×#832C2211yescharacteristic
62C2×#832C2211yescharacteristic
63C2×#832C2211yescharacteristic
64#5173C2218yescomplemented
65#5171C2218yescomplemented
66#5170C2218yescomplemented
67#5159C2218yescomplemented
68#5158C2218yescomplemented
69#5158C2218yescomplemented
70C2×(C2×D3)⋊C8C2211yescharacteristic
71C2×(C2×D3)⋊C8C2211yescharacteristic
72C2×#817C2211yescharacteristic
73C2×#816C2211yescharacteristic
74C2×#816C2211yescharacteristic
75#5075C2218yescomplemented
76#5054C2218yescomplemented
77C2×C4⋊(C3⋊C8)C2211yescharacteristic
78#4716C2218yescomplemented
79#4706C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#548—31no—
84#3271—316no—
85C2×#496D311yescharacteristic, complemented
86C2×#469—31no—
87C2×#465—31no—
88C2×#464—31no—
89C2×#460—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C22×#67—21no—
106C22×#67—21no—
107C22×#67—21no—
108C23×Dic3—21no—
109C23×Dic3—21no—
110C23×Dic3—21no—
111C2×D3×Q8—22no—
112C2×D3×Q8—24no—
113C2×D3×Q8—42no—
114C2×D3×Q8C2314yes—
115C2×#237—22no—
116C2×#237—22no—
117C2×#237—22no—
118C2×#237—24no—
119C2×#237—24no—
120C2×#237—24no—
121C2×#237—42no—
122C2×#237—42no—
123C2×#237—42no—
124C2×#237C2314yes—
125C2×#237C2314yes—
126C2×#237C2314yes—
127C22×D12D411yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3C2311yescharacteristic
130C22×C4×D3C2311yescharacteristic
131C22×Dic6—21no—
132C22×Dic6C2311yescharacteristic
133C22×Dic6C2311yescharacteristic
134C2×C3×SD16—24no—
135C2×C3×SD16—42no—
136C2×C3×SD16C2314yes—
137C2×C3×SD16C2314yes—
138C2×C3×D8—24no—
139C2×C3×D8—42no—
140C2×C3×D8C2314yes—
141C2×C3×D8C2314yes—
142C22×C3×C8C2311yescharacteristic
143C22×C3×C8C2311yescharacteristic
144C3×#127—22no—
145C3×#127C2314yes—
146C3×#124—22no—
147C3×#124C2314yes—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C42C2311yescharacteristic
151C2×#217—21no—
152C2×#217—21no—
153C2×#217—21no—
154#946—22no—
155#946C2314yes—
156C2×#216—24no—
157C2×#216C2314yes—
158#940—28no—
159#939—28no—
160#939—28no—
161#938—22no—
162#938—22no—
163#938—22no—
164#938C2314yes—
165#938C2314yes—
166#938C2314yes—
167D4×Dic3—28no—
168C2×#214—24no—
169C2×#214—24no—
170C2×#214—24no—
171C2×#214C2314yes—
172C2×#214C2314yes—
173C2×#214C2314yes—
174C2×(C2×D3)⋊C4—21no—
175C2×(C2×D3)⋊C4D411yescharacteristic
176C2×(C2×D3)⋊C4D411yescharacteristic
177C2×C4⋊Dic3D411yescharacteristic
178C2×C4⋊Dic3C2311yescharacteristic
179C2×C4⋊Dic3C2311yescharacteristic
180C2×Dic3⋊C4—21no—
181C2×Dic3⋊C4—21no—
182C2×Dic3⋊C4—21no—
183C2×C4×Dic3—21no—
184C2×C4×Dic3—21no—
185C22×C3⋊C8C2311yescharacteristic
186C22×C3⋊C8C2311yescharacteristic
187#915—232no—
188#912—232no—
189C2×Dic12D418yescomplemented
190C2×Dic12C2314yes—
191C2×ΓL(1,𝔽25)—24no—
192C2×ΓL(1,𝔽25)C2314yes—
193C2×D3×C8—24no—
194C2×D3×C8C2314yes—
195#885—28no—
196#884—28no—
197#67⋊C4—28no—
198#878—28no—
199C4×D12D414yes—
200C4×D12C2314yes—
201C4×Dic6—22no—
202C4×Dic6—22no—
203C4×Dic6C2314yes—
204C4×Dic6C2314yes—
205C3×#97C2314yes—
206#835C2314yes—
207#832C2314yes—
208#832C2314yes—
209#832C2314yes—
210(C2×D3)⋊C8C2314yes—
211(C2×D3)⋊C8C2314yes—
212#817C2314yes—
213#816C2314yes—
214#816C2314yes—
215C4⋊(C3⋊C8)C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C23×Q8—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16C2×D311yescharacteristic
230C22×SD16C2×D311yescharacteristic
231C22×D8C2×D311yescharacteristic
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8—31no—
235#550—38no—
236#550—64no—
237#548—38no—
238#548—64no—
239C2×#127—61no—
240C2×#127C2×D311yescharacteristic
241C2×#124—61no—
242C2×#124C2×D311yescharacteristic
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—61no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#496C2×D318yescomplemented
257#469—38no—
258#465—38no—
259#464—38no—
260#460—38no—
261#452—38no—
262#449—38no—
263#449—38no—
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97C2×D311yescharacteristic
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—21no—
281C23×D3C2×D411yescharacteristic
282C23×D3C2×D411yescharacteristic
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8C2412yes—
287C2×C3×D4—22no—
288C2×C3×D4—22no—
289C2×C3×D4—22no—
290C2×C3×D4—24no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—24no—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—22no—
298C2×C3×D4—44no—
299C2×C3×D4—82no—
300C2×C3×D4C2412yes—
301C2×C3×D4C2412yes—
302C2×C3×D4C2412yes—
303C22×C3×C4—21no—
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—24no—
310C2×#67—24no—
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—82no—
318C2×#67—82no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—24no—
324C22×Dic3—24no—
325C22×Dic3—24no—
326C22×Dic3—44no—
327C22×Dic3—44no—
328C22×Dic3—44no—
329C22×Dic3C2×D411yescharacteristic
330C22×Dic3C2×D411yescharacteristic
331D3×Q8—28no—
332D3×Q8—44no—
333D3×Q8—48no—
334#237—28no—
335#237—28no—
336#237—28no—
337#237—44no—
338#237—44no—
339#237—44no—
340#237—48no—
341#237—48no—
342#237—48no—
343C2×D12—42no—
344C2×D12C2×D414yes—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—22no—
349C2×C4×D3—24no—
350C2×C4×D3—44no—
351C2×C4×D3C2×D412yes—
352C2×C4×D3C2×D412yes—
353C2×C4×D3C2412yes—
354C2×C4×D3C2412yes—
355C2×Dic6—21no—
356C2×Dic6—21no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—44no—
361C2×Dic6C2×D414yes—
362C2×Dic6C2×D414yes—
363C2×Dic6C2412yes—
364C2×Dic6C2412yes—
365C3×SD16—28no—
366C3×SD16—44no—
367C3×D8—28no—
368C3×D8—44no—
369C2×C3×C8—22no—
370C2×C3×C8C2×D414yes—
371C2×C3×C8C2412yes—
372C2×C3×C8C2412yes—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C42C2×D412yes—
376C3×C42C2412yes—
377#217—24no—
378#217—24no—
379#217—24no—
380#216—28no—
381#214—28no—
382#214—28no—
383#214—28no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4C2×D414yes—
386(C2×D3)⋊C4C2×D414yes—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C2×D414yes—
390C4⋊Dic3C2412yes—
391C4⋊Dic3C2412yes—
392Dic3⋊C4—24no—
393Dic3⋊C4—24no—
394Dic3⋊C4—24no—
395C4×Dic3—24no—
396C4×Dic3—24no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401Dic12C2×D4116yescomplemented
402ΓL(1,𝔽25)—28no—
403D3×C8—28no—
404C2×#41—34no—
405C2×#41—34no—
406C2×#41—34no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—62no—
410C2×#41—64no—
411C2×#41—64no—
412C2×#41—64no—
413C2×#41—122no—
414C2×#41—122no—
415C2×#41—122no—
416C22×Q8—34no—
417C22×Q8—31no—
418C22×Q8—31no—
419C22×Q8—61no—
420C22×Q8—62no—
421C22×Q8—64no—
422C22×Q8—122no—
423C22×Q8C22×D311yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—31no—
427C22×D4—61no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4C22×D311yescharacteristic
434C22×D4C22×D311yescharacteristic
435C22×D4C22×D311yescharacteristic
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4—61no—
442#137—632no—
443#135—632no—
444C2×Q16—34no—
445C2×Q16—38no—
446C2×Q16—34no—
447C2×Q16—64no—
448C2×SD16—24no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—42no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16C22×D314yes—
457C2×SD16C22×D314yes—
458C2×D8—24no—
459C2×D8—42no—
460C2×D8C22×D314yes—
461C2×D8C22×D314yes—
462C2×M16—34no—
463C2×M16—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8—34no—
467C22×C8—64no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#127—22no—
471#127—68no—
472#127C22×D314yes—
473#124—22no—
474#124—68no—
475#124C22×D314yes—
476C22⋊Q8—34no—
477C22⋊Q8—68no—
478C22⋊Q8—62no—
479#121—34no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—68no—
484#121—68no—
485#121—62no—
486#121—62no—
487#121—62no—
488C4×Q8—34no—
489C4×Q8—34no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—68no—
495C4×D4—68no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C42—61no—
511C2×C42—61no—
512C2×C42C22×D311yescharacteristic
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8—34no—
522C22⋊C8—34no—
523#97C22×D314yes—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3C22×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3C22×D412yes—
544C22×D3C22×D412yes—
545C3×Q8—22no—
546C3×Q8—22no—
547C3×Q8—42no—
548C3×D4—22no—
549C3×D4—22no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—22no—
554C3×D4—48no—
555C3×D4—42no—
556C3×D4—42no—
557C3×D4—42no—
558C3×D4—84no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—42no—
563C2×C3×C4C22×D412yes—
564C2×C3×C4C22×D412yes—
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D412yes—
567C2×C3×C4H(5,𝔽2)12yes—
568C2×C3×C4C2511yescharacteristic
569#67—48no—
570#67—48no—
571#67—48no—
572#67—48no—
573#67—84no—
574#67—84no—
575C2×Dic3—24no—
576C2×Dic3—24no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—48no—
584C2×Dic3—48no—
585C2×Dic3—48no—
586C2×Dic3—42no—
587C2×Dic3—42no—
588C2×Dic3C22×D412yes—
589C2×Dic3C22×D412yes—
590D12—44no—
591C4×D3—24no—
592C4×D3—24no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—48no—
598Dic6—24no—
599Dic6—24no—
600Dic6—22no—
601Dic6—22no—
602Dic6—48no—
603Dic6C22×D414yes—
604Dic6C22×D414yes—
605C3×C8—22no—
606C3×C8C22×D414yes—
607C3⋊C8—22no—
608C3⋊C8—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—31no—
613C24—31no—
614#41—68no—
615#41—68no—
616#41—68no—
617#41—124no—
618#41—124no—
619#41—124no—
620#41—128no—
621#41—128no—
622#41—128no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—34no—
627C2×Q8—34no—
628C2×Q8—32no—
629C2×Q8—32no—
630C2×Q8—64no—
631C2×Q8—61no—
632C2×Q8—61no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8—68no—
636C2×Q8—124no—
637C2×Q8—124no—
638C2×Q8—128no—
639C2×Q8C23×D312yes—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—24no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—34no—
652C2×D4—44no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—82no—
660C2×D4—122no—
661C2×D4—124no—
662C2×D4—124no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—242no—
666C2×D4—242no—
667C2×D4C23×D312yes—
668C2×D4C23×D312yes—
669C2×D4C23×D312yes—
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—64no—
680C22×C4—64no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4D3×D411yescharacteristic
694C22×C4D3×D411yescharacteristic
695C22×C4C23×D311yescharacteristic
696Q16—316no—
697Q16—68no—
698SD16—28no—
699SD16—44no—
700SD16—68no—
701SD16—68no—
702SD16—68no—
703D8—28no—
704D8—44no—
705M16—68no—
706C2×C8—22no—
707C2×C8—32no—
708C2×C8—32no—
709C2×C8—62no—
710C2×C8—62no—
711C2×C8—68no—
712C2×C8D3×D414yes—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—34no—
716C4⋊C4—32no—
717C4⋊C4—32no—
718C4⋊C4—64no—
719C4⋊C4—61no—
720C4⋊C4—61no—
721C4⋊C4—64no—
722C4⋊C4—64no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—34no—
726C22⋊C4—34no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C42—64no—
732C42—64no—
733C42D3×D412yes—
734C42C23×D312yes—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—84no—
745C22×C3—84no—
746C22×C3—84no—
747C22×C3D4212yes—
748C22×C3#57512yes—
749C22×C3#57712yes—
750C22×C3C23×D411yescharacteristic
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—44no—
758C2×D3—44no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4D4212yes—
763C3×C4C23×D411yescharacteristic
764C3×C4C2×H(5,𝔽2)11yescharacteristic
765Dic3—24no—
766Dic3—24no—
767Dic3—22no—
768Dic3—22no—
769Dic3—42no—
770Dic3—42no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—32no—
775C23—32no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—34no—
795Q8—34no—
796Q8—42no—
797Q8—62no—
798Q8—62no—
799Q8—64no—
800Q8—64no—
801Q8—128no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—42no—
810D4—42no—
811D4—42no—
812D4—84no—
813D4—124no—
814D4—128no—
815D4—128no—
816D4—128no—
817D4—128no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—42no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—64no—
831C2×C4—64no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—64no—
837C2×C4—64no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—128no—
841C2×C4—128no—
842C2×C4—128no—
843C2×C4—128no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C4C2×D3×D412yes—
847C2×C4C2×D3×D412yes—
848C2×C4C2×D3×D412yes—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4#100412yes—
851C2×C4C24×D311yescharacteristic
852C8—22no—
853C8—62no—
854C8—62no—
855C8C2×D3×D414yes—
856C2×C3—82no—
857C2×C3—82no—
858C2×C3—82no—
859C2×C3#327114yescomplemented
860C2×C3C2×D4211yescharacteristic
861C2×C3C2×#57511yescharacteristic
862C2×C3C2×#57711yescharacteristic
863D3—42no—
864D3—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—84no—
881C22—84no—
882C22—84no—
883C22—124no—
884C22—124no—
885C22#571712yes—
886C22#577312yes—
887C22#577512yes—
888C22C22×D3×D411yescharacteristic
889C4—22no—
890C4—22no—
891C4—42no—
892C4—62no—
893C4—62no—
894C4—64no—
895C4—64no—
896C4—122no—
897C4—122no—
898C4#571712yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100411yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—82no—
903C2—82no—
904C2—82no—
905C2—122no—
906C2—122no—
907C2#8185914yesdirect product factor
908C2C2×#571711yescharacteristic
909C2C2×#577311yescharacteristic
910C2C2×#577511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#496C2
socleC23×C3C22×D4
hypercenterC2×#496D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C22×#915C2semidirect
2. C22×#912C2semidirect
3. C2×#5718C2semidirect
4. C2×#5677C2semidirect
5. C2×C3×#496C2semidirect
6. C2×#5171C2semidirect
7. C2×#5173C2semidirect
8. C2×#5170C2semidirect
9. C2×#5159C2semidirect
10. C2×#5158C2semidirect
11. C2×#5158C2semidirect
12. C2×#5075C2semidirect
13. C2×#5054C2semidirect
14. #81859C2direct (N × H)
15. C2×#4716C2semidirect
16. C2×#4706C2semidirect
41. C2×#915C22semidirect
43. C2×#912C22semidirect
48. #5718C22semidirect
50. #5677C22semidirect
58. C3×#496C22semidirect
64. #5173C22semidirect
65. #5171C22semidirect
66. #5170C22semidirect
67. #5159C22semidirect
68. #5158C22semidirect
69. #5158C22semidirect
75. #5075C22semidirect
76. #5054C22semidirect
78. #4716C22semidirect
79. #4706C22semidirect
85. C2×#496D3semidirect
189. C2×Dic12D4semidirect
256. #496C2×D3semidirect
401. Dic12C2×D4semidirect
859. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#81859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9152
C22×#9122
C2×#57182
C2×#56772
C2×C3×#4962
C2×#51712
C2×#51732
C2×#51702
C2×#51592
C2×#51582
C2×#50752
C2×#50542
#818592
C2×#47162
C2×#47062
C2×#32713