Finite Group Databasebeta

← #10801011

Subgroups — #10801011

Order 768.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic
2C2×#5239C211yesmaximal, characteristic
3C2×C4×#216C211yesmaximal, characteristic, complemented
4C2×#5018C211yesmaximal, characteristic, complemented
5#82235C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic
7#71632C211yesmaximal, characteristic, complemented
8#71631C211yesmaximal, characteristic, complemented
9#71628C211yesmaximal, characteristic, complemented
10#71612C211yesmaximal, characteristic, complemented
11C4×#832C211yesmaximal, characteristic, complemented
12#71606C211yesmaximal, characteristic, complemented
13#71582C211yesmaximal, characteristic, complemented
14#71559C211yesmaximal, characteristic, complemented
15#71555C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C3×#520—24no—
19C3×#520—24no—
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4—21no—
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×#117—21no—
27C2×C3×#117C2211yescharacteristic
28C22×C3×C4⋊C4—21no—
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34#5239C418yescomplemented
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C4×#216—24no—
45#5018—24no—
46#4978—21no—
47#4976—21no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4945—21no—
53#4944—21no—
54C4×C4⋊Dic3C2211yescharacteristic
55#4929C2211yescharacteristic
56#4928C2211yescharacteristic
57C2×#803C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520D311yescharacteristic
66C2×#452—31no—
67C2×#440—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1877—31no—
72#1872—31no—
73#1863—31no—
74#1862—31no—
75#1852—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41C2×C414yes—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C3×C4×Q8—22no—
96C3×C4×Q8—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8D414yes—
99C3×C4×D4—28no—
100C3×C4×D4—28no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×C4×D4D414yes—
105C3×#117—28no—
106C3×#117—22no—
107C3×#117—22no—
108C2×C3×C4⋊C4—28no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4D411yescharacteristic
115C2×C3×C4⋊C4D411yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×#217—21no—
127C2×#217—21no—
128C2×#216—22no—
129C2×#216—22no—
130C2×#216C2×C414yescomplemented
131C2×#214—22no—
132C2×#214—22no—
133C2×#214C2×C414yescomplemented
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137#924—22no—
138#924C2×C414yescomplemented
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3—21no—
143C2×C4×Dic3—21no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C4×Dic6—22no—
149C4×Dic6—22no—
150#835—22no—
151#835—22no—
152#835C2×C414yescomplemented
153#832—22no—
154#832—22no—
155#832C2×C414yescomplemented
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#830C2×C414yescomplemented
163#810—22no—
164#810—22no—
165#807—22no—
166#807—22no—
167#803—22no—
168C4×C3⋊C8—22no—
169C22×#41C2×D311yescharacteristic
170C22×Q16—31no—
171C22×SD16—31no—
172C2×C22⋊Q8—31no—
173#520—24no—
174#520—24no—
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—21no—
179C2×C4×D4—21no—
180C2×C4×D4C2×D311yescharacteristic
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—21no—
183C2×#117C2×D311yescharacteristic
184C22×C4⋊C4—21no—
185C22×C4⋊C4C2×D311yescharacteristic
186#452—38no—
187#440—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#107—31no—
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×#97—31no—
202C2×C4×C8—31no—
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—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
219C3×#41—28no—
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—28no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8C22×C412yes—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8#4112yes—
229C2×C3×D4—24no—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4C22×C412yes—
236C2×C3×D4C2×D412yes—
237C2×C3×D4#4112yes—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4—81no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4C22×C412yes—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4#4112yes—
264C22×C3×C4C2411yescharacteristic
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6C22×C412yes—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4C2×D412yes—
283C3×C4⋊C4C2×D412yes—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—22no—
288C3×C42—24no—
289C3×C42—24no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294#217—24no—
295#217—81no—
296#216—28no—
297#214—28no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3C22×C412yes—
304Dic3⋊C4—24no—
305Dic3⋊C4—42no—
306Dic3⋊C4—81no—
307C4×Dic3—42no—
308C4×Dic3—81no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8C22×C412yes—
320C2×C3⋊C8C22×C412yes—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41C4×D314yes—
327C22×Q8—31no—
328C22×Q8C22×D311yescharacteristic
329C22×D4—21no—
330C22×D4C22×D311yescharacteristic
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4C22×D311yescharacteristic
336C2×Q16—34no—
337C2×Q16—62no—
338C2×Q16—62no—
339C2×SD16—34no—
340C2×SD16—62no—
341C2×SD16—62no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—31no—
345C22×C8—31no—
346C22⋊Q8—34no—
347C22⋊Q8—62no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8#6714yes—
354C4×D4—28no—
355C4×D4—28no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4#6714yes—
360#117—28no—
361#117—22no—
362#117—22no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4#6711yescharacteristic
376C2×C4⋊C4#6711yescharacteristic
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4#6711yescharacteristic
384C2×C22⋊C4#6711yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42C22×D311yescharacteristic
390C2×C42C22×D311yescharacteristic
391#107—62no—
392#107—62no—
393#103—34no—
394#103—62no—
395#103—62no—
396#103—62no—
397#103—62no—
398#102—34no—
399#102—62no—
400#102—62no—
401C22⋊C8—34no—
402C22⋊C8—62no—
403#97—62no—
404C4×C8—62no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409#95—61no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3C4×D412yes—
424C23×C3C22×D411yescharacteristic
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8C4×D414yes—
429C3×D4—216no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4C4×D414yes—
434C2×C3×C4—216no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
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—84no—
461C2×C3×C4—84no—
462C2×C3×C4—84no—
463C2×C3×C4C4×D412yes—
464C2×C3×C4#12012yes—
465C2×C3×C4#12012yes—
466C2×C3×C4C23×C411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484Dic6—22no—
485Dic6—22no—
486Dic6—41no—
487Dic6—41no—
488C3⋊C8—22no—
489C3⋊C8—22no—
490C3⋊C8—41no—
491C3⋊C8—41no—
492C24—21no—
493C24C2×#6711yescharacteristic
494#41—28no—
495#41—28no—
496#41—28no—
497#41—28no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8C2×C4×D312yes—
508C2×Q8#23512yes—
509C2×Q8C2×#6712yes—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4C2×C4×D312yes—
517C2×D4#23512yes—
518C2×D4C2×#6712yes—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4C2×C4×D312yes—
543C22×C4#23512yes—
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C22×C4C2×#6711yescharacteristic
549C22×C4C23×D311yescharacteristic
550Q16—68no—
551SD16—68no—
552C2×C8—32no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—32no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—122no—
579C4⋊C4—241no—
580C4⋊C4C2×#6712yes—
581C4⋊C4C2×#6712yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—64no—
587C22⋊C4—241no—
588C42—24no—
589C42—24no—
590C42—21no—
591C42—21no—
592C42—122no—
593C42—241no—
594C42C2×#6712yes—
595C42C2×#6712yes—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—24no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—42no—
610C22×C3C2×C4×D411yescharacteristic
611C22×C3C2×#12011yescharacteristic
612C22×C3#52511yescharacteristic
613C22×C3#57611yescharacteristic
614C22×C3#57711yescharacteristic
615C22×C3#57811yescharacteristic
616C22×C3#57811yescharacteristic
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4C2×C4×D411yescharacteristic
626C3×C4C2×C4×D411yescharacteristic
627C3×C4#52511yescharacteristic
628C3×C4#52511yescharacteristic
629Dic3—42no—
630Dic3—42no—
631Dic3—81no—
632Dic3—81no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C4×#6712yes—
647C23C22×#6711yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—62no—
652Q8—62no—
653Q8—121no—
654Q8—121no—
655Q8C4×#6714yes—
656D4—216no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4C4×#6714yes—
661C2×C4—216no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4C4×#6712yes—
703C2×C4#95312yes—
704C2×C4#95312yes—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×#23511yescharacteristic
708C2×C4C2×#23511yescharacteristic
709C2×C4C22×#6711yescharacteristic
710C2×C4C22×#6711yescharacteristic
711C8—62no—
712C8—62no—
713C8—121no—
714C8—121no—
715C2×C3—42no—
716C2×C3—44no—
717C2×C3C4×#12011yescharacteristic
718C2×C3#294711yescharacteristic
719C2×C3#295111yescharacteristic
720C2×C3#301111yescharacteristic
721C2×C3#301211yescharacteristic
722C2×C3#312011yescharacteristic
723C2×C3#312411yescharacteristic
724C22—22no—
725C22—24no—
726C22—22no—
727C22—22no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22C2×C4×#6711yescharacteristic
739C22#579111yescharacteristic
740C22#583511yescharacteristic
741C22#583611yescharacteristic
742C22#583811yescharacteristic
743C22#583811yescharacteristic
744C22C2×#95311yescharacteristic
745C4—22no—
746C4—24no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—122no—
754C4—122no—
755C4—241no—
756C4—241no—
757C4C2×C4×#6711yescharacteristic
758C4C2×C4×#6711yescharacteristic
759C4#579111yescharacteristic
760C4#579111yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—42no—
763C2—44no—
764C2#8255711yescharacteristic
765C2#8256911yescharacteristic
766C2#8257111yescharacteristic
767C2#8257511yescharacteristic
768C2C4×#95311yescharacteristic
769C2#8410211yescharacteristic
770C2#8411711yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#520C2
socleC23×C3C22×D4
prime radicalC22×C3×#41C22
cosocleC22×C3×C4C24
hypercenterC2×#520D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
3. C2×C4×#216C2semidirect
4. C2×#5018C2semidirect
5. #82235C2semidirect
7. #71632C2semidirect
8. #71631C2semidirect
9. #71628C2semidirect
10. #71612C2semidirect
11. C4×#832C2semidirect
12. #71606C2semidirect
13. #71582C2semidirect
14. #71559C2semidirect
15. #71555C2semidirect
34. #5239C4semidirect
130. C2×#216C2×C4semidirect
133. C2×#214C2×C4semidirect
138. #924C2×C4semidirect
152. #835C2×C4semidirect
155. #832C2×C4semidirect
162. #830C2×C4semidirect
761. C3#21465semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×#52392
C2×C4×#2162
C2×#50182
#822352
#721352
#716322
#716312
#716282
#716122
C4×#8322
#716062
#715822
#715592
#715552
#214653