Finite Group Databasebeta

← #10828164

Subgroups — #10828164

Order 768.

1364 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5633C211yesmaximal, characteristic
2C2×#4882C211yesmaximal, characteristic, complemented
3C2×D3×#103C211yesmaximal, characteristic, complemented
4#73911C211yesmaximal, characteristic, complemented
5C3×#2036C211yesmaximal, characteristic, complemented
6#71695C211yesmaximal, characteristic, complemented
7#70642C211yesmaximal, characteristic, complemented
8#70279C211yesmaximal, characteristic, complemented
9#70266C211yesmaximal, characteristic, complemented
10#70245C211yesmaximal, characteristic, complemented
11#69960C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69522C211yesmaximal, characteristic, complemented
14#68906C211yesmaximal, characteristic, complemented
15#68883C211yesmaximal, characteristic, complemented
16#24035—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×C4×#67C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23#5633—24no—
24#5633—24no—
25C2×#896—21no—
26C2×#895C2211yescharacteristic
27C2×#893—21no—
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×#885—21no—
31C2×#884—21no—
32C2×#883—21no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic
49#4972C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4952—21no—
56#4882—24no—
57D3×#103—24no—
58#4664—21no—
59#4657—21no—
60C3×#340C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#548—31no—
65C2×#480—31no—
66C22×#103—31no—
67#2486—31no—
68#2042—31no—
69#2042—31no—
70#2036—31no—
71#2036D311yescharacteristic, complemented
72#1893—31no—
73#1869—31no—
74#1863—31no—
75#1863—31no—
76#1788—31no—
77#1788—31no—
78#1787—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×D3×Q8—22no—
84C2×D3×Q8—22no—
85C2×D3×Q8—22no—
86C2×D3×Q8—41no—
87C2×D3×Q8—41no—
88C2×D3×Q8D414yes—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—41no—
94C2×#235—41no—
95C22×D12—21no—
96C22×D12C2311yescharacteristic
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C22×Dic6—21no—
102C22×Dic6C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×#217—21no—
114C2×#217D411yescharacteristic
115#947—22no—
116#947—22no—
117C4×#67—22no—
118C4×#67—22no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4D411yescharacteristic
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×D3×C8—22no—
136C2×D3×C8—41no—
137C2×D3×C8—41no—
138#896—28no—
139#895—22no—
140#895D414yes—
141#893—28no—
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144#887—22no—
145#887—22no—
146#885—28no—
147#884—28no—
148#883—44no—
149C3×#107—22no—
150C3×#103—22no—
151C3×#103—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154#835—22no—
155#835—41no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#830—41no—
161#821—22no—
162#821—41no—
163(C2×D3)⋊C8—22no—
164#816—22no—
165#816—22no—
166#810—22no—
167#810—22no—
168#809—22no—
169#809—41no—
170#807—22no—
171C22×#41—31no—
172C23×Q8—31no—
173C23×C8—31no—
174#548—64no—
175#548—64no—
176C2×#124—31no—
177C2×#124—61no—
178C2×#123—61no—
179C2×C22⋊Q8—61no—
180C2×C22⋊Q8C2×D311yescharacteristic
181C2×#121—31no—
182C2×#121—61no—
183C2×C4×Q8—31no—
184C2×C4×D4—31no—
185C2×C4×D4—61no—
186C22×C4⋊C4—31no—
187#480—64no—
188C2×#107—31no—
189C2×#107C2×D311yescharacteristic
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—64no—
197C2×#103C2×D311yescharacteristic
198C2×#103C2×D311yescharacteristic
199C2×#102—31no—
200C2×#102—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8C2×D311yescharacteristic
206#398—61no—
207#397—61no—
208#389—31no—
209#389—31no—
210#381—61no—
211#380—31no—
212#380—31no—
213#380C2×D311yescharacteristic
214#340—31no—
215#340C2×D311yescharacteristic
216#336—31no—
217#336—31no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8C2×D412yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C2×#67—24no—
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—42no—
244C2×#67—42no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251D3×Q8—28no—
252D3×Q8—44no—
253D3×Q8—44no—
254D3×Q8—44no—
255#235—44no—
256#235—44no—
257#235—44no—
258#235—44no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—24no—
264C2×D12—21no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12C2×D412yes—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—24no—
273C2×C4×D3—24no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×C4×D3C2×D412yes—
282C2×C4×D3C2×D412yes—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—24no—
287C2×Dic6—42no—
288C2×Dic6—42no—
289C2×Dic6C2×D412yes—
290C2×Dic6#4112yes—
291C2×Dic6#4112yes—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C3×C4⋊C4—24no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4C2×D412yes—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—42no—
307#217—22no—
308#217—42no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—42no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—42no—
319Dic3⋊C4—24no—
320Dic3⋊C4—22no—
321Dic3⋊C4—42no—
322Dic3⋊C4—42no—
323C4×Dic3—24no—
324C4×Dic3—21no—
325C4×Dic3—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332D3×C8—44no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—121no—
338C2×#41—121no—
339C22×Q8—34no—
340C22×Q8—31no—
341C22×Q8—61no—
342C22×Q8—62no—
343C22×Q8—62no—
344C22×Q8—62no—
345C22×Q8—121no—
346C22×Q8—121no—
347C22×Q8C22×D311yescharacteristic
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4—61no—
352C23×C4—31no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4C22×D311yescharacteristic
357C22×C8—31no—
358C22×C8—31no—
359C22×C8—62no—
360C22×C8—121no—
361C22×C8—121no—
362C22×C8C22×D311yescharacteristic
363C22×C8C22×D311yescharacteristic
364#124—68no—
365#124—62no—
366#124—62no—
367#123—124no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—68no—
371#121—34no—
372#121—68no—
373#121—62no—
374C4×Q8—62no—
375C4×Q8—62no—
376C4×D4—68no—
377C4×D4—62no—
378C4×D4—62no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C42—31no—
402C2×C42—61no—
403#107—22no—
404#107—62no—
405#103—22no—
406#103—41no—
407#103—62no—
408#103—62no—
409#103—62no—
410#103—62no—
411#103—62no—
412#103—121no—
413#102—62no—
414#102—62no—
415#102—121no—
416#102—121no—
417C22⋊C8—41no—
418C22⋊C8—62no—
419C22⋊C8—121no—
420#95—21no—
421#95—61no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3#12012yes—
445C22×D3#13512yes—
446C22×D3AGL(1,ℤ/8)12yes—
447C3×Q8—22no—
448C3×Q8—22no—
449C3×Q8—41no—
450C3×Q8—41no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4H(5,𝔽2)11yescharacteristic
475C2×C3×C4H(5,𝔽2)11yescharacteristic
476#67—48no—
477#67—44no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3#12012yes—
496D12—22no—
497D12—22no—
498D12—48no—
499D12—41no—
500D12—41no—
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—22no—
505C4×D3—48no—
506C4×D3—48no—
507C4×D3—84no—
508Dic6—22no—
509Dic6—22no—
510Dic6—22no—
511Dic6—48no—
512Dic6#12314yescomplemented
513C3×C8—41no—
514C3×C8—41no—
515C3⋊C8—41no—
516C3⋊C8—41no—
517C24—31no—
518C24—61no—
519C24D3×D411yescharacteristic
520#41—124no—
521#41—124no—
522#41—124no—
523#41—124no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—32no—
530C2×Q8—32no—
531C2×Q8—32no—
532C2×Q8—64no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—68no—
537C2×Q8—122no—
538C2×Q8—122no—
539C2×Q8—124no—
540C2×Q8—124no—
541C2×Q8—124no—
542C2×Q8D3×D412yes—
543C2×D4—32no—
544C2×D4—64no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—64no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—31no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—122no—
585C22×C4—122no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4D3×D411yescharacteristic
590C22×C4C23×D311yescharacteristic
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—124no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—62no—
611C4⋊C4—64no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—122no—
617C4⋊C4—122no—
618C4⋊C4—122no—
619C4⋊C4D3×D412yes—
620C22⋊C4—24no—
621C22⋊C4—42no—
622C22⋊C4—64no—
623C22⋊C4—62no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—62no—
627C22⋊C4—122no—
628C22⋊C4—122no—
629C42—64no—
630C42—61no—
631C42—61no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3C2×#12011yescharacteristic
640C22×C3#54611yescharacteristic
641C22×C3#54611yescharacteristic
642C22×C3C2×#13511yescharacteristic
643C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
644C22×C3#57811yescharacteristic
645C22×C3#57811yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3#44914yes—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—42no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4C2×#12311yescharacteristic
666C3×C4#53411yescharacteristic
667C3×C4#54611yescharacteristic
668C3×C4#54611yescharacteristic
669Dic3—24no—
670Dic3—22no—
671Dic3—41no—
672Dic3—41no—
673Dic3—81no—
674Dic3—81no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—32no—
683C23—32no—
684C23—32no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—62no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23C2×D3×D411yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—34no—
700Q8—41no—
701Q8—41no—
702Q8—62no—
703Q8—62no—
704Q8—62no—
705Q8—128no—
706D4—62no—
707D4—62no—
708D4—128no—
709D4—128no—
710D4—124no—
711D4—121no—
712D4—121no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—32no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—128no—
749C2×C4—128no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—244no—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4#100411yescharacteristic
760C2×C4D3×#4111yescharacteristic
761C2×C4D3×#4111yescharacteristic
762C2×C4#100911yescharacteristic
763C8—41no—
764C8—41no—
765C8—121no—
766C8—121no—
767C2×C3—81no—
768C2×C3#240511yescharacteristic
769C2×C3C2×#44911yescharacteristic
770C2×C3#301111yescharacteristic
771C2×C3#330011yescharacteristic
772C2×C3#330011yescharacteristic
773C2×C3#330811yescharacteristic
774C2×C3#330811yescharacteristic
775D3—24no—
776D3—82no—
777C22—34no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—62no—
791C22—122no—
792C22—122no—
793C22—122no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22D3×#12011yescharacteristic
799C22#561011yescharacteristic
800C22#565411yescharacteristic
801C22#576611yescharacteristic
802C22D3×#13511yescharacteristic
803C22D3×AGL(1,ℤ/8)11yescharacteristic
804C22#577911yescharacteristic
805C4—41no—
806C4—42no—
807C4—42no—
808C4—62no—
809C4—64no—
810C4—81no—
811C4—81no—
812C4—121no—
813C4—121no—
814C4—241no—
815C4—241no—
816C4#560511yescharacteristic
817C4#561211yescharacteristic
818C4D3×#12311yescharacteristic
819C4#567611yescharacteristic
820C3#2403511yescharacteristic, complemented, Sylow
821C2—64no—
822C2—81no—
823C2—242no—
824C2#7710611yescharacteristic
825C2D3×#44911yescharacteristic
826C2#8018511yescharacteristic
827C2#8076911yescharacteristic
828C2#8082011yescharacteristic
829C2#8147311yescharacteristic
830C2#8152411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
prime radicalC2×#5633C2
hypercenter#2036D3
hypocenterC3#24035
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#4882C2semidirect
3. C2×D3×#103C2semidirect
4. #73911C2semidirect
5. C3×#2036C2semidirect
6. #71695C2semidirect
7. #70642C2semidirect
8. #70279C2semidirect
9. #70266C2semidirect
10. #70245C2semidirect
11. #69960C2semidirect
12. #69957C2semidirect
13. #69522C2semidirect
14. #68906C2semidirect
15. #68883C2semidirect
71. #2036D3semidirect
512. Dic6#123semidirect
820. C3#24035semidirect

Maximal subgroups

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

subgroupindex
C2×#56332
C2×#48822
C2×D3×#1032
#739112
C3×#20362
#716952
#706422
#702792
#702662
#702452
#699602
#699572
#695222
#689062
#688832
#240353