Finite Group Databasebeta

← #10827566

Subgroups — #10827566

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5541C211yesmaximal, characteristic, complemented
2C3×#2407C211yesmaximal, characteristic
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5#71700C211yesmaximal, characteristic, complemented
6#71693C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71678C211yesmaximal, characteristic, complemented
9#71611C211yesmaximal, characteristic, complemented
10#69690C211yesmaximal, characteristic, complemented
11#69669C211yesmaximal, characteristic, complemented
12#69660C211yesmaximal, characteristic, complemented
13#69639C211yesmaximal, characteristic, complemented
14#69516C211yesmaximal, characteristic, complemented
15#69502C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#935—21no—
23C22×#214C2211yescharacteristic
24C2×#926C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#208C2211yescharacteristic
29#5541—24no—
30#5541—24no—
31C2×#889—21no—
32C2×#879—21no—
33C2×#877—21no—
34C2×#870C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C3×#394—21no—
37C3×#392—21no—
38C3×#391C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#386—21no—
41C3×#385—21no—
42C3×#380C2211yescharacteristic
43#5239—24no—
44#5232—24no—
45C2×#835C2211yescharacteristic
46C2×#835C2211yescharacteristic
47C2×#835C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#810C2211yescharacteristic
55C2×#810C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#552—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407D311yescharacteristic
68#2026—31no—
69#2025—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1875—31no—
76#1873—31no—
77#1870—31no—
78#1824—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—21no—
94C22×Dic6C2311yescharacteristic
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—41no—
97C3×#121—22no—
98C3×#121—41no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4D411yescharacteristic
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C42C2311yescharacteristic
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—41no—
119#935—28no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—41no—
123#926—22no—
124#926—22no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3D414yescomplemented
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—22no—
133#924—22no—
134#924D414yescomplemented
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×#208—22no—
143C2×#208—41no—
144C2×#208—41no—
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149#889—28no—
150#879—28no—
151#877—28no—
152#870—22no—
153#870—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159#835—22no—
160#835—22no—
161#835—22no—
162#832—22no—
163#832—22no—
164#832—22no—
165#830—22no—
166#830—41no—
167#830—41no—
168#810—41no—
169#810—41no—
170C22×#41C2×D311yescharacteristic
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#552—64no—
175#552—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#125—61no—
179C2×#123—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121C2×D311yescharacteristic
184C2×C4×Q8—31no—
185C2×C4×D4C2×D311yescharacteristic
186C2×#117—31no—
187C2×#117—61no—
188C22×C4⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—21no—
203#392—21no—
204#391C2×D311yescharacteristic
205#390C2×D311yescharacteristic
206#386—21no—
207#385—21no—
208#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C24×C3C2×D411yescharacteristic
220C3×#41—28no—
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8#4112yes—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—41no—
237C2×C3×D4—41no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—81no—
244C2×C3×D4#4112yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×Dic3—24no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—42no—
274C22×Dic3—42no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6C2×D412yes—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—42no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292C3×C22⋊C4—81no—
293C3×C22⋊C4—81no—
294C3×C42—21no—
295C3×C42—21no—
296#217—24no—
297#217—24no—
298#217—24no—
299#216—44no—
300#214—44no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3C2×D412yes—
306C4⋊Dic3C2×D412yes—
307C4⋊Dic3C2×D412yes—
308Dic3⋊C4—24no—
309Dic3⋊C4—24no—
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—24no—
313C4×Dic3—24no—
314C4×Dic3—24no—
315#208—44no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—41no—
333C2×#41—41no—
334C22×Q8—31no—
335C22×Q8C22×D311yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4#6711yescharacteristic
339C22×D4C22×D311yescharacteristic
340C23×C4—21no—
341C23×C4—61no—
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—121no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—121no—
350C2×M16—62no—
351C2×M16—121no—
352C2×M16—121no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—31no—
357#126—68no—
358#125—62no—
359#125—62no—
360#125—68no—
361#123—68no—
362C22⋊Q8—22no—
363C22⋊Q8—34no—
364C22⋊Q8—41no—
365C22⋊Q8—62no—
366C22⋊Q8—62no—
367C22⋊Q8—62no—
368#121—22no—
369#121—41no—
370C4×Q8—62no—
371C4×Q8—62no—
372C4×D4—22no—
373C4×D4—22no—
374#117—68no—
375#117—62no—
376#117—62no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4#6711yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4#6711yescharacteristic
401C2×C22⋊C4#6711yescharacteristic
402C2×C42—61no—
403C2×C42—61no—
404C2×C42C22×D311yescharacteristic
405#103—62no—
406#103—62no—
407#103—62no—
408#103—121no—
409#103—121no—
410#102—62no—
411#102—62no—
412#102—62no—
413C22⋊C8—62no—
414C22⋊C8—121no—
415C22⋊C8—121no—
416#95—21no—
417#95—21no—
418#95—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3#12012yes—
440C23×C3C22×D411yescharacteristic
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—44no—
448C3×D4—48no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—84no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—48no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4#12012yes—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4H(5,𝔽2)11yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—48no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501Dic6—22no—
502Dic6—22no—
503Dic6—41no—
504Dic6—41no—
505C3⋊C8—41no—
506C3⋊C8—41no—
507C3⋊C8—41no—
508C3⋊C8—41no—
509C24—21no—
510C24C2×#6711yescharacteristic
511C24C2×#6711yescharacteristic
512#41—28no—
513#41—44no—
514#41—44no—
515#41—44no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—32no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8#23712yes—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4#23712yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—64no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4D3×D412yes—
567C22×C4D3×D412yes—
568C22×C4C2×#6711yescharacteristic
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6711yescharacteristic
571C22×C4C2×#6711yescharacteristic
572C22×C4C23×D311yescharacteristic
573Q16—124no—
574SD16—124no—
575M16—124no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—32no—
594C4⋊C4—32no—
595C4⋊C4—32no—
596C4⋊C4—42no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C42—21no—
617C42—21no—
618C42—64no—
619C42—64no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—42no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3C2×#12011yescharacteristic
642C22×C3#54611yescharacteristic
643C22×C3#54611yescharacteristic
644C22×C3#57511yescharacteristic
645C22×C3#57511yescharacteristic
646C22×C3#57711yescharacteristic
647C22×C3#57811yescharacteristic
648C3×C4—22no—
649C3×C4—41no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4#52511yescharacteristic
656C3×C4#53511yescharacteristic
657C3×C4#54611yescharacteristic
658C3×C4#54611yescharacteristic
659Dic3—42no—
660Dic3—42no—
661Dic3—42no—
662Dic3—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23#93712yes—
684C23C22×#6711yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—62no—
690Q8—62no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
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—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—128no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4#93712yes—
743C2×C4C2×D3×D411yescharacteristic
744C2×C4C2×D3×D411yescharacteristic
745C2×C4C2×#23711yescharacteristic
746C2×C4C2×#23711yescharacteristic
747C2×C4#100411yescharacteristic
748C2×C4#100411yescharacteristic
749C8—121no—
750C8—121no—
751C8—121no—
752C8—121no—
753C2×C3—42no—
754C2×C3—81no—
755C2×C3—82no—
756C2×C3#240411yescharacteristic
757C2×C3#300511yescharacteristic
758C2×C3#301311yescharacteristic
759C2×C3#331511yescharacteristic
760C2×C3#331711yescharacteristic
761C2×C3#332311yescharacteristic
762C2×C3#332711yescharacteristic
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22C2×#93711yescharacteristic
785C22#580611yescharacteristic
786C22#580611yescharacteristic
787C22#582211yescharacteristic
788C22#582211yescharacteristic
789C22#583611yescharacteristic
790C22#583811yescharacteristic
791C4—22no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—41no—
796C4—81no—
797C4—81no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4—122no—
802C4#558611yescharacteristic
803C4#559111yescharacteristic
804C4#559111yescharacteristic
805C4#559211yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—42no—
808C2—81no—
809C2—82no—
810C2#8258111yescharacteristic
811C2#8292811yescharacteristic
812C2#8342711yescharacteristic
813C2#8350111yescharacteristic
814C2#8351311yescharacteristic
815C2#8354111yescharacteristic
816C2#8357311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#5541C2semidirect
3. C2×#5239C2semidirect
4. C2×#5232C2semidirect
5. #71700C2semidirect
6. #71693C2semidirect
7. #71685C2semidirect
8. #71678C2semidirect
9. #71611C2semidirect
10. #69690C2semidirect
11. #69669C2semidirect
12. #69660C2semidirect
13. #69639C2semidirect
14. #69516C2semidirect
15. #69502C2semidirect
127. C2×C4⋊Dic3D4semidirect
134. #924D4semidirect
806. C3#23978semidirect

Maximal subgroups

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

subgroupindex
C2×#55412
C3×#24072
C2×#52392
C2×#52322
#717002
#716932
#716852
#716782
#716112
#696902
#696692
#696602
#696392
#695162
#695022
#239783