Finite Group Databasebeta

← #10826263

Subgroups — #10826263

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5817C211yesmaximal, characteristic, complemented
2C22×#919C211yesmaximal, characteristic, complemented
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5187C211yesmaximal, characteristic, complemented
6#82812C211yesmaximal, characteristic, complemented
7#72072C211yesmaximal, characteristic, complemented
8#72065C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#70277C211yesmaximal, characteristic, complemented
11#70270C211yesmaximal, characteristic, complemented
12#70267C211yesmaximal, characteristic, complemented
13#70240C211yesmaximal, characteristic, complemented
14#69961C211yesmaximal, characteristic, complemented
15#69957C211yesmaximal, characteristic, complemented
16#23854—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×#239C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23#5817—24no—
24#5817—24no—
25C2×#947—21no—
26C2×#947C2211yescharacteristic
27C2×#946—21no—
28C2×#946C2211yescharacteristic
29C2×Q8×Dic3C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C2×#930—21no—
34C2×#930C2211yescharacteristic
35C2×#930C2211yescharacteristic
36C2×C4×#67—21no—
37C2×C4×#67C2211yescharacteristic
38C2×#919—24no—
39C2×#919—24no—
40C2×#919—24no—
41C22×D24C2211yescharacteristic
42C22×D3×C8C2211yescharacteristic
43C3×#451—24no—
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47#5229C2211yescharacteristic
48#5227—24no—
49C2×#835C2211yescharacteristic
50C2×#835C2211yescharacteristic
51C2×#835C2211yescharacteristic
52C2×#830C2211yescharacteristic
53#5187—24no—
54C2×#821C2211yescharacteristic
55C2×#821C2211yescharacteristic
56C2×(C2×D3)⋊C8C2211yescharacteristic
57#4991—21no—
58#4989—21no—
59#4988C2211yescharacteristic
60#4987C2211yescharacteristic
61C2×#809C2211yescharacteristic
62#4960—21no—
63#4956—21no—
64#4551C2211yescharacteristic
65#4550C2211yescharacteristic
66#4550C2211yescharacteristic
67#4529C2211yescharacteristic
68C22×#135—31no—
69C2×#548—31no—
70C2×#452—31no—
71C2×#451D311yescharacteristic, complemented
72C2×#448—31no—
73#2407—31no—
74#2015—31no—
75#2012—31no—
76#2000—31no—
77#1999—31no—
78#1892—31no—
79#1880—31no—
80#1878—31no—
81#1869—31no—
82#1788—31no—
83C22×C3×Q8—22no—
84C22×C3×Q8—22no—
85C22×C3×Q8—21no—
86C22×C3×Q8—22no—
87C22×C3×Q8—22no—
88C22×C3×Q8—41no—
89C22×C3×Q8—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×Q8C2311yescharacteristic
92C22×C3×Q8C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C22×#67—21no—
96C22×#67—21no—
97C22×#67D411yescharacteristic
98C2×#239—22no—
99C2×#239—22no—
100C2×#239—22no—
101C2×#239—22no—
102C2×#239—22no—
103C2×#239—22no—
104C2×#239—22no—
105C2×#239—41no—
106C2×#239—41no—
107C2×#239—41no—
108C2×#239—41no—
109C2×#239D414yescomplemented
110C22×D12—21no—
111C22×D12—21no—
112C22×D12C2311yescharacteristic
113C22×D12C2311yescharacteristic
114C22×C4×D3—21no—
115C22×C4×D3—21no—
116C22×C4×D3C2311yescharacteristic
117C2×C3×Q16—22no—
118C2×C3×Q16—22no—
119C2×C3×Q16—22no—
120C2×C3×Q16—22no—
121C2×C3×Q16—41no—
122C2×C3×Q16D414yescomplemented
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—41no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×#217D411yescharacteristic
131#947—28no—
132#947—22no—
133#947—22no—
134#946—28no—
135#946—22no—
136#946D414yescomplemented
137Q8×Dic3—22no—
138Q8×Dic3—22no—
139C2×#215—22no—
140C2×#215—22no—
141C2×#215—22no—
142C2×#215—22no—
143C2×#215—22no—
144C2×#215—22no—
145C2×#215—22no—
146C2×#215—41no—
147C2×#215D414yescomplemented
148#930—28no—
149#930—22no—
150#930—22no—
151#930—22no—
152#930—41no—
153C4×#67—28no—
154C4×#67—22no—
155C4×#67—22no—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—21no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4D411yescharacteristic
165C2×C4⋊Dic3—21no—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×Dic3⋊C4—21no—
169C2×Dic3⋊C4D411yescharacteristic
170C2×C4×Dic3—21no—
171C2×C4×Dic3C2311yescharacteristic
172C22×C3⋊C8C2311yescharacteristic
173C22×C3⋊C8C2311yescharacteristic
174#919—232no—
175C2×D24—22no—
176C2×D24—22no—
177C2×D24—22no—
178C2×D3×C8—22no—
179C2×D3×C8—22no—
180C2×D3×C8—22no—
181C3×#103—22no—
182C3×#103—22no—
183C3×C22⋊C8—22no—
184#835—22no—
185#835—22no—
186#835—22no—
187C3⋊#95—21no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190#830—22no—
191#821—22no—
192#821—41no—
193(C2×D3)⋊C8—22no—
194#809—41no—
195C22×#41—31no—
196C22×#41—31no—
197C23×Q8C2×D311yescharacteristic
198C2×#135—64no—
199C2×#135—64no—
200C2×#135—64no—
201C22×Q16C2×D311yescharacteristic
202C22×Q16C2×D311yescharacteristic
203C22×SD16—31no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×D8—31no—
207C23×C8—31no—
208#548—64no—
209#548—64no—
210C2×#124—31no—
211C2×#124—61no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—61no—
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—61no—
218C2×C4×Q8—31no—
219C2×C4×D4—31no—
220C2×C4×D4—61no—
221#452—64no—
222#451—24no—
223#448—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103—31no—
227C2×#103C2×D311yescharacteristic
228C2×#103C2×D311yescharacteristic
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—31no—
234C2×C22⋊C8C2×D311yescharacteristic
235#394—61no—
236#392—61no—
237#391—31no—
238#390—31no—
239#386—61no—
240#385—61no—
241#380—31no—
242#340—31no—
243#340—31no—
244#336—31no—
245#336—31no—
246C24×C3C2×D411yescharacteristic
247C23×D3—21no—
248C23×D3—21no—
249C23×D3C2×D411yescharacteristic
250C2×C3×Q8—24no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—42no—
265C2×C3×Q8—42no—
266C2×C3×Q8—44no—
267C2×C3×Q8—44no—
268C2×C3×Q8—44no—
269C2×C3×Q8—44no—
270C2×C3×Q8C2×D412yes—
271C2×C3×Q8C2×D412yes—
272C2×C3×Q8C2×D412yes—
273C2×C3×Q8C2×D412yes—
274C2×C3×Q8C2×D412yes—
275C22×C3×C4—21no—
276C22×C3×C4—24no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2411yescharacteristic
290C2×#67—24no—
291C2×#67—22no—
292C2×#67—22no—
293C2×#67—41no—
294C2×#67—42no—
295C2×#67—42no—
296C2×#67—42no—
297C2×#67—42no—
298C2×#67—81no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3C2×D411yescharacteristic
302C22×Dic3C2×D411yescharacteristic
303C22×Dic3C2×D411yescharacteristic
304#239—28no—
305#239—28no—
306#239—44no—
307#239—44no—
308#239—44no—
309#239—44no—
310#239—44no—
311#239—44no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12—24no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—42no—
324C2×D12—42no—
325C2×D12—42no—
326C2×D12—42no—
327C2×D12—42no—
328C2×D12C2×D412yes—
329C2×D12C2×D412yes—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—24no—
335C2×C4×D3—42no—
336C2×C4×D3—42no—
337C2×C4×D3—42no—
338C2×C4×D3—42no—
339C2×C4×D3—42no—
340C2×C4×D3C2×D412yes—
341C2×C4×D3C2×D412yes—
342C3×Q16—28no—
343C3×Q16—44no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8C2×D412yes—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—42no—
353C3×C22⋊C4—42no—
354#217—22no—
355#215—28no—
356#215—28no—
357#215—44no—
358(C2×D3)⋊C4—24no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4—24no—
361(C2×D3)⋊C4—24no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—42no—
364(C2×D3)⋊C4—42no—
365(C2×D3)⋊C4—81no—
366(C2×D3)⋊C4—81no—
367C4⋊Dic3—24no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3C2×D412yes—
372Dic3⋊C4—24no—
373Dic3⋊C4—22no—
374C4×Dic3—24no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C2×C3⋊C8—21no—
378C2×C3⋊C8—21no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8—21no—
382C2×C3⋊C8C2×D412yes—
383D24—28no—
384D3×C8—28no—
385C2×#41—34no—
386C2×#41—62no—
387C2×#41—62no—
388C2×#41—62no—
389C2×#41—62no—
390C2×#41—62no—
391C2×#41—62no—
392C2×#41—62no—
393C2×#41—121no—
394C2×#41—121no—
395C2×#41—121no—
396C2×#41—121no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—21no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—41no—
403C22×Q8—41no—
404C22×Q8C22×D311yescharacteristic
405C22×Q8C22×D311yescharacteristic
406C22×Q8C22×D311yescharacteristic
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—31no—
410C22×D4—61no—
411C22×D4—61no—
412C22×D4—61no—
413C22×D4—61no—
414C23×C4—21no—
415C23×C4—31no—
416C23×C4—61no—
417C23×C4—61no—
418C23×C4C22×D311yescharacteristic
419#135—632no—
420C2×Q16—22no—
421C2×Q16—22no—
422C2×Q16—22no—
423C2×Q16—22no—
424C2×Q16—41no—
425C2×Q16#6714yescomplemented
426C2×SD16—34no—
427C2×SD16—62no—
428C2×SD16—62no—
429C2×SD16—62no—
430C2×SD16—62no—
431C2×SD16—62no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—121no—
435C2×D8—62no—
436C2×D8—62no—
437C2×D8—62no—
438C22×C8—31no—
439C22×C8—31no—
440C22×C8—62no—
441C22×C8—62no—
442C22×C8—62no—
443C22×C8C22×D311yescharacteristic
444C22×C8C22×D311yescharacteristic
445#124—62no—
446#124—68no—
447#124—62no—
448C22⋊Q8—22no—
449C22⋊Q8—34no—
450C22⋊Q8—41no—
451C22⋊Q8—62no—
452C22⋊Q8—68no—
453#121—62no—
454#121—62no—
455#121—68no—
456#121—62no—
457#121—121no—
458C4×Q8—62no—
459C4×Q8—62no—
460C4×D4—62no—
461C4×D4—62no—
462C4×D4—68no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—61no—
468C2×C4⋊C4—61no—
469C2×C4⋊C4C22×D311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—61no—
474C2×C22⋊C4—61no—
475C2×C22⋊C4—61no—
476C2×C22⋊C4—61no—
477C2×C22⋊C4—61no—
478C2×C22⋊C4—61no—
479C2×C22⋊C4—61no—
480C2×C22⋊C4—61no—
481C2×C42—31no—
482C2×C42—61no—
483#103—22no—
484#103—22no—
485#103—62no—
486#103—62no—
487#103—62no—
488#102—62no—
489#102—121no—
490#102—121no—
491C22⋊C8—22no—
492C22⋊C8—62no—
493C22⋊C8—62no—
494#95—61no—
495#95—61no—
496#95—61no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3#13512yescomplemented
504C23×C3C22×D411yescharacteristic
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3#12012yes—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—22no—
529C3×Q8—22no—
530C3×Q8—22no—
531C3×Q8—22no—
532C3×Q8—22no—
533C3×Q8—48no—
534C3×Q8—41no—
535C3×Q8—41no—
536C3×Q8—41no—
537C3×Q8—41no—
538C3×Q8#12014yes—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—48no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4H(5,𝔽2)11yescharacteristic
564C2×C3×C4H(5,𝔽2)11yescharacteristic
565#67—44no—
566#67—48no—
567#67—84no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—22no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3#12012yes—
583D12—22no—
584D12—22no—
585D12—22no—
586D12—22no—
587D12—48no—
588D12—48no—
589D12—41no—
590D12—41no—
591D12—41no—
592D12—41no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—48no—
598C4×D3—48no—
599C3×C8—22no—
600C3×C8—41no—
601C3⋊C8—22no—
602C3⋊C8—41no—
603C24—31no—
604C24—61no—
605C24—61no—
606C24D3×D411yescharacteristic
607#41—68no—
608#41—68no—
609#41—124no—
610#41—124no—
611#41—124no—
612#41—124no—
613#41—124no—
614#41—124no—
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—42no—
630C2×Q8—42no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8D3×D412yes—
636C2×Q8D3×D412yes—
637C2×Q8D3×D412yes—
638C2×Q8C2×#6712yes—
639C2×Q8C2×#6712yes—
640C2×D4—32no—
641C2×D4—32no—
642C2×D4—64no—
643C2×D4—62no—
644C2×D4—64no—
645C2×D4—62no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—61no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—61no—
656C2×D4—122no—
657C2×D4—122no—
658C2×D4—122no—
659C2×D4—122no—
660C2×D4—122no—
661C2×D4—121no—
662C2×D4—122no—
663C2×D4—122no—
664C2×D4—122no—
665C2×D4—122no—
666C2×D4—241no—
667C22×C4—21no—
668C22×C4—24no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—31no—
679C22×C4—32no—
680C22×C4—32no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—64no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—122no—
693C22×C4—122no—
694C22×C4—122no—
695C22×C4—122no—
696C22×C4—122no—
697C22×C4D3×D411yescharacteristic
698C22×C4C23×D311yescharacteristic
699Q16—28no—
700Q16—44no—
701SD16—68no—
702SD16—68no—
703SD16—124no—
704D8—68no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—32no—
711C2×C8—68no—
712C2×C8—61no—
713C2×C8—61no—
714C2×C8—61no—
715C2×C8—61no—
716C2×C8—61no—
717C2×C8C2×#6712yes—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—32no—
721C4⋊C4—42no—
722C4⋊C4—62no—
723C4⋊C4—64no—
724C4⋊C4—64no—
725C4⋊C4—61no—
726C4⋊C4—61no—
727C4⋊C4—61no—
728C22⋊C4—42no—
729C22⋊C4—62no—
730C22⋊C4—64no—
731C22⋊C4—64no—
732C22⋊C4—64no—
733C22⋊C4—64no—
734C22⋊C4—62no—
735C22⋊C4—122no—
736C22⋊C4—122no—
737C22⋊C4—241no—
738C22⋊C4—241no—
739C42—64no—
740C42—61no—
741C42—61no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3C2×#12011yescharacteristic
750C22×C3D4211yescharacteristic
751C22×C3D4211yescharacteristic
752C22×C3C2×#13511yescharacteristic
753C22×C3#57511yescharacteristic
754C22×C3#57711yescharacteristic
755C22×C3#57811yescharacteristic
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—81no—
770C2×D3—81no—
771C2×D3—81no—
772C2×D3—81no—
773C2×D3—81no—
774C2×D3—81no—
775C2×D3—81no—
776C2×D3—81no—
777C3×C4—24no—
778C3×C4—42no—
779C3×C4—41no—
780C3×C4—42no—
781C3×C4—81no—
782C3×C4C2×#12011yescharacteristic
783C3×C4#53411yescharacteristic
784C3×C4D4211yescharacteristic
785C3×C4D4211yescharacteristic
786Dic3—22no—
787Dic3—41no—
788Dic3—42no—
789Dic3—41no—
790Dic3—81no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—32no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—62no—
805C23—62no—
806C23—121no—
807C23—121no—
808C23—121no—
809C23—121no—
810C23—121no—
811C23—121no—
812C23—121no—
813C23—121no—
814C23—121no—
815C23—121no—
816C23—121no—
817C23—121no—
818C23#91912yescomplemented
819C23C2×D3×D411yescharacteristic
820Q8—22no—
821Q8—22no—
822Q8—22no—
823Q8—22no—
824Q8—22no—
825Q8—22no—
826Q8—22no—
827Q8—48no—
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—41no—
832Q8#93714yes—
833D4—62no—
834D4—62no—
835D4—62no—
836D4—62no—
837D4—128no—
838D4—128no—
839D4—124no—
840D4—128no—
841D4—121no—
842D4—121no—
843D4—121no—
844D4—121no—
845D4—244no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—32no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—62no—
879C2×C4—61no—
880C2×C4—128no—
881C2×C4—128no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4C2×D3×D411yescharacteristic
888C2×C4C2×D3×D411yescharacteristic
889C2×C4C2×D3×D411yescharacteristic
890C2×C4#100411yescharacteristic
891C2×C4#100411yescharacteristic
892C2×C4C22×#6711yescharacteristic
893C8—22no—
894C8—41no—
895C8—62no—
896C8—121no—
897C2×C3—42no—
898C2×C3#240311yescharacteristic
899C2×C3#300211yescharacteristic
900C2×C3#301311yescharacteristic
901C2×C3#326911yescharacteristic
902C2×C3#327111yescharacteristic
903C2×C3#328211yescharacteristic
904C2×C3#328511yescharacteristic
905D3—42no—
906D3—82no—
907D3—82no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—122no—
923C22—122no—
924C22—122no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—241no—
929C22—241no—
930C22—241no—
931C22—241no—
932C22—241no—
933C22—241no—
934C22—241no—
935C22—241no—
936C22D3×#12011yescharacteristic
937C22#559011yescharacteristic
938C22C2×#91911yescharacteristic
939C22#576611yescharacteristic
940C22#577711yescharacteristic
941C22#577811yescharacteristic
942C22D4×#6711yescharacteristic
943C4—24no—
944C4—41no—
945C4—42no—
946C4—42no—
947C4—62no—
948C4—81no—
949C4—121no—
950C4—122no—
951C4—121no—
952C4—241no—
953C4#558911yescharacteristic
954C4#559011yescharacteristic
955C4C2×#93711yescharacteristic
956C4D4×#6711yescharacteristic
957C3#2385411yescharacteristic, complemented, Sylow
958C2—42no—
959C2—122no—
960C2—242no—
961C2—242no—
962C2#8018211yescharacteristic
963C2#8018611yescharacteristic
964C2#8020511yescharacteristic
965C2#8020711yescharacteristic
966C2#8260411yescharacteristic
967C2#8388911yescharacteristic
968C2#8399011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
hypercenterC2×#451D3
hypocenterC3#23854
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C22×#919C2semidirect
3. C2×C3×#451C2semidirect
4. C2×#5227C2semidirect
5. C2×#5187C2semidirect
6. #82812C2semidirect
7. #72072C2semidirect
8. #72065C2semidirect
9. #71699C2semidirect
10. #70277C2semidirect
11. #70270C2semidirect
12. #70267C2semidirect
13. #70240C2semidirect
14. #69961C2semidirect
15. #69957C2semidirect
71. C2×#451D3semidirect
109. C2×#239D4semidirect
122. C2×C3×Q16D4semidirect
136. #946D4semidirect
147. C2×#215D4semidirect
425. C2×Q16#67semidirect
503. C23×C3#135semidirect
818. C23#919semidirect
957. C3#23854semidirect

Maximal subgroups

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

subgroupindex
C2×#58172
C22×#9192
C2×C3×#4512
C2×#52272
C2×#51872
#828122
#720722
#720652
#716992
#702772
#702702
#702672
#702402
#699612
#699572
#238543