Finite Group Databasebeta

← #10826270

Subgroups — #10826270

Order 768.

1930 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#67C211yesmaximal, characteristic, complemented
2C22×D3×SD16C211yesmaximal, characteristic, complemented
3C2×C3×#448C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5169C211yesmaximal, characteristic, complemented
6#82640C211yesmaximal, characteristic
7#72057C211yesmaximal, characteristic, complemented
8#72048C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#70282C211yesmaximal, characteristic, complemented
11#70270C211yesmaximal, characteristic, complemented
12#70266C211yesmaximal, characteristic, complemented
13#70240C211yesmaximal, characteristic, complemented
14#69962C211yesmaximal, characteristic, complemented
15#69957C211yesmaximal, characteristic, complemented
16#23855—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C22×D3×Q8C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23Q8×#67—24no—
24Q8×#67—24no—
25C2×#946—21no—
26C2×#946C2211yescharacteristic
27C2×Q8×Dic3C2211yescharacteristic, complemented
28C2×#944—21no—
29C2×#944C2211yescharacteristic, complemented
30C22×#215C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C2×#937—21no—
33C22×#214C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×C4×#67—21no—
36C2×C4×#67C2211yescharacteristic
37C2×#924—21no—
38C2×#924C2211yescharacteristic, complemented
39C2×D3×SD16—24no—
40C2×D3×SD16—24no—
41C2×D3×SD16—24no—
42C22×#204C2211yescharacteristic
43C22×D3×C8C2211yescharacteristic
44C3×#448—24no—
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×C22⋊C8C2211yescharacteristic, complemented
48#5227—24no—
49C2×#835C2211yescharacteristic, complemented
50C2×#835C2211yescharacteristic, complemented
51#5223—21no—
52#5221C2211yescharacteristic
53C2×#832C2211yescharacteristic
54C2×#830C2211yescharacteristic, complemented
55#5169—24no—
56C2×#821C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×#816C2211yescharacteristic, complemented
59#4988C2211yescharacteristic
60#4987C2211yescharacteristic
61C2×#810C2211yescharacteristic, complemented
62#4959—21no—
63#4955—21no—
64#4551C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C23×SD16—31no—
69C2×D4×Q8—31no—
70C2×#448—31no—
71C2×#448D311yescharacteristic, complemented
72C2×#450—31no—
73#2408—31no—
74#2013—31no—
75#2013—31no—
76#2000—31no—
77#2000—31no—
78#1892—31no—
79#1880—31no—
80#1880—31no—
81#1869—31no—
82#1787—31no—
83C24×D3—21no—
84C22×C3×Q8—22no—
85C22×C3×Q8—22no—
86C22×C3×Q8—21no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—41no—
90C22×C3×Q8—41no—
91C22×C3×Q8C2311yescharacteristic
92C22×C3×Q8C2311yescharacteristic
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67D411yescharacteristic
100C2×D3×Q8—22no—
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—41no—
104C2×D3×Q8—41no—
105C2×D3×Q8D414yescomplemented
106C2×D3×D4—22no—
107C2×D3×D4—22no—
108C2×D3×D4—22no—
109C2×D3×D4—22no—
110C2×D3×D4—41no—
111C2×D3×D4—41no—
112C22×D12C2311yescharacteristic
113C22×C4×D3—21no—
114C22×C4×D3C2311yescharacteristic
115C22×Dic6—21no—
116C22×Dic6C2311yescharacteristic
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—41no—
122C2×C3×SD16D414yescomplemented
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#121—22no—
126C3×#121—41no—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4—21no—
129C2×#217—21no—
130C2×#217—21no—
131C2×#217—21no—
132C2×#217D411yescharacteristic
133#946—28no—
134#946—22no—
135#946D414yescomplemented
136Q8×Dic3—22no—
137Q8×Dic3—22no—
138#944—28no—
139#944—22no—
140#944—22no—
141C2×#215—22no—
142C2×#215—22no—
143C2×#215—22no—
144C2×#215—22no—
145C2×#215—41no—
146C2×#215D414yescomplemented
147#937—44no—
148C2×#214—22no—
149C2×#214—22no—
150C2×#214—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)⋊C4D411yescharacteristic
162C2×C4⋊Dic3—21no—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165#924—28no—
166#924—22no—
167#924—22no—
168C2×Dic3⋊C4—21no—
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4D411yescharacteristic
173C2×C4×Dic3—21no—
174C2×C4×Dic3C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177D3×SD16—232no—
178C2×#204—22no—
179C2×#204—22no—
180C2×#204—22no—
181C2×D3×C8—22no—
182C2×D3×C8—22no—
183C2×D3×C8—22no—
184C3×#103—22no—
185C3×#103—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#835—22no—
189#832—22no—
190C3⋊#95—21no—
191#830—22no—
192#821—22no—
193(C2×D3)⋊C8—22no—
194#816—41no—
195#810—41no—
196C23×Q8—31no—
197C23×Q8C2×D311yescharacteristic, complemented
198C23×D4—31no—
199C22×SD16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×SD16—31no—
203C22×SD16—64no—
204C22×SD16—64no—
205C22×SD16—64no—
206C22×SD16C2×D311yescharacteristic
207C22×SD16C2×D311yescharacteristic
208C23×C8—31no—
209D4×Q8—64no—
210D4×Q8—64no—
211C2×C4⋊Q8—31no—
212C2×C4⋊Q8—61no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—31no—
215C2×C22⋊Q8—61no—
216C2×C22⋊Q8—61no—
217C2×#121—31no—
218C2×#121C2×D311yescharacteristic
219C2×#120—61no—
220C2×C4×Q8—31no—
221C2×C4×D4—31no—
222C2×C4×D4—61no—
223#450—64no—
224#448—24no—
225#448—64no—
226C2×#103—31no—
227C2×#103—31no—
228C2×#103—31no—
229C2×#103—31no—
230C2×#103C2×D311yescharacteristic, complemented
231C2×#103C2×D311yescharacteristic, complemented
232C2×#102—31no—
233C2×#102—31no—
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8C2×D311yescharacteristic, complemented
237#394—61no—
238#392—61no—
239#390—31no—
240#390—31no—
241#380—31no—
242#379—61no—
243#340—31no—
244#340—31no—
245#336—31no—
246#336—31no—
247C24×C3—21no—
248C24×C3C2×D411yescharacteristic
249C23×D3—21no—
250C23×D3—42no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3—42no—
254C23×D3—42no—
255C23×D3—81no—
256C23×D3—81no—
257C23×D3C2×D411yescharacteristic
258C2×C3×Q8—24no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—42no—
268C2×C3×Q8—42no—
269C2×C3×Q8—44no—
270C2×C3×Q8—44no—
271C2×C3×Q8—44no—
272C2×C3×Q8—44no—
273C2×C3×Q8C2×D412yes—
274C2×C3×Q8C2×D412yes—
275C2×C3×Q8C2×D412yes—
276C2×C3×Q8C2×D412yes—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—81no—
285C2×C3×D4C2×D412yes—
286C22×C3×C4—21no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C2×#67—22no—
301C2×#67—22no—
302C2×#67—42no—
303C2×#67—42no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—81no—
308C2×#67SD1614yescomplemented
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3C2×D411yescharacteristic
313C22×Dic3C2×D411yescharacteristic
314C22×Dic3C2×D411yescharacteristic
315D3×Q8—28no—
316D3×Q8—44no—
317D3×Q8—44no—
318D3×Q8—44no—
319D3×D4—28no—
320D3×D4—44no—
321D3×D4—44no—
322D3×D4—44no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12C2×D412yes—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—24no—
334C2×C4×D3—42no—
335C2×C4×D3—42no—
336C2×C4×D3C2×D412yes—
337C2×C4×D3C2×D412yes—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—21no—
343C2×Dic6—24no—
344C2×Dic6—42no—
345C2×Dic6—42no—
346C2×Dic6C2×D412yes—
347C3×SD16—28no—
348C3×SD16—44no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8—21no—
353C2×C3×C8—21no—
354C2×C3×C8C2×D412yes—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C22⋊C4—42no—
358#217—24no—
359#217—22no—
360#217—42no—
361#217—81no—
362#215—28no—
363#215—44no—
364#214—28no—
365(C2×D3)⋊C4—24no—
366(C2×D3)⋊C4—22no—
367(C2×D3)⋊C4—42no—
368(C2×D3)⋊C4—42no—
369(C2×D3)⋊C4—42no—
370(C2×D3)⋊C4—81no—
371C4⋊Dic3—24no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3C2×D412yes—
376Dic3⋊C4—24no—
377Dic3⋊C4—24no—
378Dic3⋊C4—24no—
379Dic3⋊C4—24no—
380Dic3⋊C4—22no—
381C4×Dic3—24no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C2×C3⋊C8—21no—
385C2×C3⋊C8—21no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8C2×D412yes—
390#204—28no—
391D3×C8—28no—
392C25—61no—
393C22×Q8—22no—
394C22×Q8—22no—
395C22×Q8—21no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—34no—
399C22×Q8—31no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8—61no—
403C22×Q8—62no—
404C22×Q8—62no—
405C22×Q8—62no—
406C22×Q8—121no—
407C22×Q8—121no—
408C22×Q8C22×D311yescharacteristic
409C22×Q8C22×D311yescharacteristic
410C22×D4—21no—
411C22×D4—31no—
412C22×D4—31no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—61no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—61no—
419C22×D4—121no—
420C22×D4—121no—
421C22×D4C22×D311yescharacteristic
422C23×C4—21no—
423C23×C4—31no—
424C23×C4—61no—
425C23×C4C22×D311yescharacteristic
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—34no—
431C2×SD16—41no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—62no—
435C2×SD16—632no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—62no—
443C2×SD16—121no—
444C2×SD16#6714yescomplemented
445C22×C8—31no—
446C22×C8—31no—
447C22×C8—62no—
448C22×C8—62no—
449C22×C8—62no—
450C22×C8C22×D311yescharacteristic
451C22×C8C22×D311yescharacteristic
452C4⋊Q8—62no—
453C4⋊Q8—68no—
454C4⋊Q8—62no—
455C22⋊Q8—34no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—68no—
459C22⋊Q8—62no—
460C22⋊Q8—68no—
461#121—22no—
462#121—41no—
463#121—62no—
464#121—121no—
465#120—124no—
466C4×Q8—62no—
467C4×Q8—62no—
468C4×D4—62no—
469C4×D4—62no—
470C4×D4—68no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—61no—
475C2×C4⋊C4—61no—
476C2×C4⋊C4—61no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4—61no—
479C2×C4⋊C4C22×D311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4—61no—
486C2×C22⋊C4—61no—
487C2×C22⋊C4—61no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C42—31no—
492C2×C42—61no—
493#103—22no—
494#103—22no—
495#103—62no—
496#103—62no—
497#103—121no—
498#103—121no—
499#102—62no—
500#102—62no—
501C22⋊C8—22no—
502C22⋊C8—62no—
503C22⋊C8—62no—
504#95—61no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—22no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3C2×SD1612yescomplemented
519C23×C3C22×D411yescharacteristic
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—22no—
525C22×D3—48no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—84no—
533C22×D3—84no—
534C22×D3—84no—
535C22×D3—84no—
536C22×D3—84no—
537C22×D3—84no—
538C22×D3#12012yes—
539C22×D3C2×SD1612yes—
540C22×D3#13712yes—
541C3×Q8—22no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—22no—
545C3×Q8—22no—
546C3×Q8—48no—
547C3×Q8—41no—
548C3×Q8—41no—
549C3×Q8#12014yescomplemented
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—84no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—48no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4H(5,𝔽2)11yescharacteristic
577C2×C3×C4H(5,𝔽2)11yescharacteristic
578#67—28no—
579#67—48no—
580#67—84no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3#12012yes—
598C2×Dic3C2×SD1612yescomplemented
599D12—22no—
600D12—22no—
601D12—41no—
602D12—41no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—48no—
608Dic6—22no—
609Dic6—22no—
610Dic6—48no—
611Dic6—41no—
612Dic6—41no—
613C3×C8—22no—
614C3×C8—41no—
615C3⋊C8—22no—
616C3⋊C8—41no—
617C24—21no—
618C24—31no—
619C24—61no—
620C24—122no—
621C24—122no—
622C24—122no—
623C24—122no—
624C24—122no—
625C24—241no—
626C24—241no—
627C24D3×D411yescharacteristic
628C2×Q8—24no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—32no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8—64no—
645C2×Q8—61no—
646C2×Q8—68no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—122no—
652C2×Q8—122no—
653C2×Q8—124no—
654C2×Q8—124no—
655C2×Q8—124no—
656C2×Q8D3×D412yes—
657C2×Q8D3×D412yes—
658C2×Q8D3×D412yes—
659C2×Q8C2×#6712yes—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—34no—
666C2×D4—32no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—68no—
670C2×D4—62no—
671C2×D4—62no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—81no—
678C2×D4—122no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—124no—
682C2×D4—122no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—241no—
687C2×D4C2×#6712yes—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—31no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—64no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—122no—
714C22×C4—122no—
715C22×C4D3×D411yescharacteristic
716C22×C4C23×D311yescharacteristic
717SD16—28no—
718SD16—44no—
719SD16—68no—
720SD16—68no—
721SD16—68no—
722SD16—124no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—32no—
729C2×C8—68no—
730C2×C8—61no—
731C2×C8—61no—
732C2×C8—61no—
733C2×C8—61no—
734C2×C8—61no—
735C2×C8C2×#6712yes—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—32no—
739C4⋊C4—62no—
740C4⋊C4—64no—
741C4⋊C4—64no—
742C4⋊C4—64no—
743C4⋊C4—64no—
744C4⋊C4—64no—
745C4⋊C4—61no—
746C4⋊C4—61no—
747C4⋊C4—61no—
748C22⋊C4—42no—
749C22⋊C4—62no—
750C22⋊C4—64no—
751C22⋊C4—62no—
752C22⋊C4—64no—
753C22⋊C4—122no—
754C22⋊C4—122no—
755C22⋊C4—122no—
756C22⋊C4—122no—
757C22⋊C4—241no—
758C22⋊C4—241no—
759C42—64no—
760C42—61no—
761C42—61no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3C2×#12011yescharacteristic
777C22×C3D4211yescharacteristic
778C22×C3D4211yescharacteristic
779C22×C3C22×SD1611yescharacteristic
780C22×C3C2×#13711yescharacteristic
781C22×C3#57711yescharacteristic
782C22×C3#57711yescharacteristic
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—816no—
793C2×D3—81no—
794C2×D3—81no—
795C2×D3—81no—
796C2×D3—81no—
797C2×D3#44814yescomplemented
798C3×C4—24no—
799C3×C4—41no—
800C3×C4—42no—
801C3×C4—81no—
802C3×C4C2×#12011yescharacteristic
803C3×C4#53411yescharacteristic
804C3×C4D4211yescharacteristic
805C3×C4D4211yescharacteristic
806Dic3—22no—
807Dic3—22no—
808Dic3—42no—
809Dic3—41no—
810Dic3—42no—
811Dic3—81no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—22no—
819C23—32no—
820C23—32no—
821C23—32no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—62no—
833C23—128no—
834C23—121no—
835C23—121no—
836C23—121no—
837C23—121no—
838C23—121no—
839C23—121no—
840C23—244no—
841C23—244no—
842C23—244no—
843C23—244no—
844C23—244no—
845C23—244no—
846C23D3×SD1612yescomplemented
847C23C2×D3×D411yescharacteristic
848Q8—22no—
849Q8—22no—
850Q8—22no—
851Q8—22no—
852Q8—22no—
853Q8—48no—
854Q8—41no—
855Q8—41no—
856Q8—62no—
857Q8—62no—
858Q8—128no—
859Q8—121no—
860Q8—121no—
861Q8#93714yescomplemented
862D4—22no—
863D4—22no—
864D4—41no—
865D4—41no—
866D4—68no—
867D4—62no—
868D4—62no—
869D4—84no—
870D4—128no—
871D4—121no—
872D4—121no—
873D4—244no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—48no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—62no—
904C2×C4—61no—
905C2×C4—62no—
906C2×C4—128no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4C2×D3×D411yescharacteristic
915C2×C4C2×D3×D411yescharacteristic
916C2×C4C2×D3×D411yescharacteristic
917C2×C4#100411yescharacteristic
918C2×C4#100411yescharacteristic
919C2×C4C22×#6711yescharacteristic
920C8—22no—
921C8—41no—
922C8—62no—
923C8—121no—
924C2×C3—42no—
925C2×C3—82no—
926C2×C3#240311yescharacteristic
927C2×C3C2×#44811yescharacteristic
928C2×C3#301011yescharacteristic
929C2×C3#326611yescharacteristic
930C2×C3#326611yescharacteristic
931C2×C3D4×SD1611yescharacteristic
932C2×C3D4×SD1611yescharacteristic
933D3—24no—
934D3—82no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—34no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—122no—
957C22—122no—
958C22—122no—
959C22—2416no—
960C22—241no—
961C22—241no—
962C22—241no—
963C22—241no—
964C22D3×#12011yescharacteristic
965C22#559011yescharacteristic
966C22C2×D3×SD1611yescharacteristic
967C22#576211yescharacteristic
968C22D3×#13711yescharacteristic
969C22#577811yescharacteristic
970C22D4×#6711yescharacteristic
971C4—24no—
972C4—41no—
973C4—42no—
974C4—62no—
975C4—62no—
976C4—81no—
977C4—121no—
978C4—122no—
979C4—122no—
980C4—241no—
981C4#558911yescharacteristic
982C4#559011yescharacteristic
983C4C2×#93711yescharacteristic
984C4D4×#6711yescharacteristic
985C3#2385511yescharacteristic, complemented, Sylow
986C2—42no—
987C2—64no—
988C2—82no—
989C2—242no—
990C2D3×#44811yescharacteristic
991C2#8004111yescharacteristic
992C2#8006111yescharacteristic
993C2#8006311yescharacteristic
994C2#8260411yescharacteristic
995C2SD16×#6711yescharacteristic
996C2#8398711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#448C2
socleC23×C3C22×D4
prime radical#82640C2
hypercenterC2×#448D3
hypocenterC3#23855
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#67C2semidirect
2. C22×D3×SD16C2semidirect
3. C2×C3×#448C2semidirect
4. C2×#5227C2semidirect
5. C2×#5169C2semidirect
7. #72057C2semidirect
8. #72048C2semidirect
9. #71685C2semidirect
10. #70282C2semidirect
11. #70270C2semidirect
12. #70266C2semidirect
13. #70240C2semidirect
14. #69962C2semidirect
15. #69957C2semidirect
17. C23×C3×Q8C22semidirect
27. C2×Q8×Dic3C22semidirect
29. C2×#944C22semidirect
38. C2×#924C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×C22⋊C8C22semidirect
49. C2×#835C22semidirect
50. C2×#835C22semidirect
54. C2×#830C22semidirect
58. C2×#816C22semidirect
61. C2×#810C22semidirect
64. #4551C22semidirect
65. #4550C22semidirect
66. #4550C22semidirect
67. #4529C22semidirect
71. C2×#448D3semidirect
105. C2×D3×Q8D4semidirect
122. C2×C3×SD16D4semidirect
135. #946D4semidirect
146. C2×#215D4semidirect
197. C23×Q8C2×D3semidirect
230. C2×#103C2×D3semidirect
231. C2×#103C2×D3semidirect
236. C2×C22⋊C8C2×D3semidirect
308. C2×#67SD16semidirect
444. C2×SD16#67semidirect
518. C23×C3C2×SD16semidirect
549. C3×Q8#120semidirect
598. C2×Dic3C2×SD16semidirect
797. C2×D3#448semidirect
846. C23D3×SD16semidirect
861. Q8#937semidirect
985. C3#23855semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#672
C22×D3×SD162
C2×C3×#4482
C2×#52272
C2×#51692
#826402
#720572
#720482
#716852
#702822
#702702
#702662
#702402
#699622
#699572
#238553