Finite Group Databasebeta

← #10944105

Subgroups — #10944105

Order 768.

1330 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5572C211yesmaximal, characteristic
2C2×#5186C211yesmaximal, characteristic
3C2×#5182C211yesmaximal, characteristic, complemented
4C2×#4795C211yesmaximal, characteristic, complemented
5C2×#4809C211yesmaximal, characteristic
6#76641C211yesmaximal, characteristic
7C3×#1878C211yesmaximal, characteristic, complemented
8#71632C211yesmaximal, characteristic, complemented
9#70269C211yesmaximal, characteristic
10#70222C211yesmaximal, characteristic, complemented
11#69690C211yesmaximal, characteristic, complemented
12#68905C211yesmaximal, characteristic, complemented
13#68879C211yesmaximal, characteristic
14#68685C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic
16#32915—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×Dic12C2211yescharacteristic
26#5572—24no—
27#5572—24no—
28C2×#897C2211yescharacteristic
29C2×#892—21no—
30C2×#892C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×#872—21no—
34C2×#872C2211yescharacteristic
35C2×C4×Dic6—21no—
36C2×C4×Dic6C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5186—24no—
43#5182—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4977C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53#4929C2211yescharacteristic
54#4809—24no—
55#4795—24no—
56#4675—21no—
57#4675—21no—
58#4657—21no—
59#4657—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×#519—31no—
67C2×#462—31no—
68C2×#462—31no—
69C2×#451—31no—
70C2×#451—31no—
71#2621—31no—
72#1878—31no—
73#1878—31no—
74#1878—31no—
75#1878D311yescharacteristic, complemented
76#1873—31no—
77#1873—31no—
78#1805—31no—
79#1805—31no—
80#1798—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C2×D3×Q8—22no—
84C2×D3×Q8—22no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8D414yes—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×Dic6C2311yescharacteristic
93C22×Dic6C2311yescharacteristic
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4×Q8—22no—
100C3×C4×Q8—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C42—21no—
105C2×C3×C42C2311yescharacteristic
106#946—22no—
107#946—22no—
108Q8×Dic3—22no—
109Q8×Dic3D414yes—
110#944—22no—
111#944—22no—
112C2×#216—22no—
113C2×#216—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C2×Dic12—22no—
142C2×Dic12—22no—
143C2×Dic12—22no—
144#897—22no—
145#897—22no—
146#892—28no—
147#892—22no—
148#892—22no—
149#887—28no—
150#887—22no—
151#887D414yes—
152#872—28no—
153#872—22no—
154#872—22no—
155C4×Dic6—28no—
156C4×Dic6—22no—
157C4×Dic6—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#95—21no—
161C3×#95—21no—
162#835—22no—
163#835—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170#816—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#810—22no—
176C23×Q8—31no—
177C22×Q16—31no—
178C22×Q16—31no—
179C22×Q16—31no—
180C22×Q16C2×D311yescharacteristic
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184#519—64no—
185#519—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×Q8—31no—
189C2×C4×Q8—61no—
190C2×C4×Q8—61no—
191C2×C4×Q8C2×D311yescharacteristic
192C2×#117—31no—
193C2×#117—31no—
194C2×#117—61no—
195C2×#117—61no—
196#462—64no—
197#462—64no—
198#451—64no—
199#451—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#103—31no—
208C2×#103C2×D311yescharacteristic
209C2×#103C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#398—61no—
213#398—61no—
214#397—61no—
215#397—61no—
216#391—31no—
217#391C2×D311yescharacteristic
218#382—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C23×D3C2×D411yescharacteristic
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8C2×D412yes—
236C2×C3×Q8C2×D412yes—
237C2×C3×Q8#4112yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252D3×Q8—28no—
253D3×Q8—28no—
254D3×Q8—28no—
255D3×Q8—28no—
256C2×C4×D3—24no—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3C2×D412yes—
264C2×C4×D3#4112yes—
265C2×Dic6—24no—
266C2×Dic6—24no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—24no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6C2×D412yes—
278C2×Dic6C2×D412yes—
279C2×Dic6#4112yes—
280C3×Q16—44no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D412yes—
292C3×C42—24no—
293C3×C42—21no—
294C3×C42—21no—
295#216—44no—
296#216—44no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302C4⋊Dic3—21no—
303C4⋊Dic3—24no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—42no—
307C4⋊Dic3C2×D412yes—
308Dic3⋊C4—24no—
309Dic3⋊C4—22no—
310Dic3⋊C4—22no—
311Dic3⋊C4—24no—
312Dic3⋊C4—42no—
313Dic3⋊C4—42no—
314Dic3⋊C4—42no—
315C4×Dic3—24no—
316C4×Dic3—24no—
317C4×Dic3—24no—
318C4×Dic3—24no—
319C4×Dic3C2×D412yes—
320C4×Dic3C2×D412yes—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327Dic12—44no—
328C22×Q8—34no—
329C22×Q8—31no—
330C22×Q8—31no—
331C22×Q8—61no—
332C22×Q8—62no—
333C22×Q8—62no—
334C22×Q8—62no—
335C22×Q8—62no—
336C22×Q8—62no—
337C22×Q8C22×D311yescharacteristic
338C22×Q8C22×D311yescharacteristic
339C23×C4—31no—
340C23×C4—61no—
341C2×Q16—22no—
342C2×Q16—22no—
343C2×Q16—22no—
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—62no—
347C2×Q16—62no—
348C2×Q16—62no—
349C2×Q16—62no—
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—62no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8C22×D311yescharacteristic
356C22×C8C22×D311yescharacteristic
357C4⋊Q8—62no—
358C4⋊Q8—62no—
359C22⋊Q8—62no—
360C22⋊Q8—62no—
361C22⋊Q8—62no—
362C22⋊Q8—62no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—34no—
366C4×Q8—34no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×Q8—68no—
370C4×Q8—62no—
371C4×Q8—62no—
372C4×Q8—68no—
373#117—62no—
374#117—62no—
375#117—68no—
376#117—62no—
377#117—68no—
378#117—62no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C4⋊C4C22×D311yescharacteristic
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—21no—
399C2×C42—31no—
400C2×C42—61no—
401C2×C42—61no—
402C2×C42—61no—
403C2×C42—61no—
404C2×C42C22×D311yescharacteristic
405C4⋊C8—62no—
406C4⋊C8—62no—
407#103—22no—
408#103—22no—
409#103—62no—
410#103—62no—
411#103—62no—
412#103—62no—
413#103—62no—
414#103—62no—
415C22⋊C8—62no—
416C22⋊C8—62no—
417#95—21no—
418#95—21no—
419#95—61no—
420#95—61no—
421#95—61no—
422#95—61no—
423C23×C3C22×D411yescharacteristic
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3#12112yes—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C3×Q8#12114yes—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3#12012yes—
482C2×Dic3#12012yes—
483C2×Dic3#12112yes—
484C4×D3—216no—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—22no—
488C4×D3—22no—
489Dic6—216no—
490Dic6—22no—
491Dic6—22no—
492Dic6—22no—
493Dic6—41no—
494Dic6—41no—
495Dic6—41no—
496Dic6—41no—
497Dic6#12114yes—
498C3×C8—41no—
499C3×C8—41no—
500C3⋊C8—41no—
501C3⋊C8—41no—
502C24—31no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—32no—
513C2×Q8—32no—
514C2×Q8—32no—
515C2×Q8—64no—
516C2×Q8—64no—
517C2×Q8—64no—
518C2×Q8—68no—
519C2×Q8—68no—
520C2×Q8—68no—
521C2×Q8—68no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8#23512yes—
532C2×Q8D3×D412yes—
533C2×Q8D3×D412yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4D3×D411yescharacteristic
555C22×C4D3×D411yescharacteristic
556C22×C4C23×D311yescharacteristic
557Q16—44no—
558Q16—124no—
559Q16—124no—
560Q16—124no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—32no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4—64no—
581C4⋊C4—64no—
582C4⋊C4—64no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4—122no—
590C4⋊C4D3×D412yes—
591C22⋊C4—62no—
592C22⋊C4—62no—
593C22⋊C4—64no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C42—24no—
597C42—21no—
598C42—21no—
599C42—32no—
600C42—32no—
601C42—64no—
602C42—64no—
603C42—64no—
604C42—64no—
605C22×C3C2×#12011yescharacteristic
606C22×C3C2×#12111yescharacteristic
607C22×C3#52511yescharacteristic
608C22×C3#57811yescharacteristic
609C22×C3#57811yescharacteristic
610C22×C3#57811yescharacteristic
611C22×C3#57811yescharacteristic
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C3×C4—24no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4C2×#12111yescharacteristic
626C3×C4C2×#12111yescharacteristic
627C3×C4#52511yescharacteristic
628C3×C4#52511yescharacteristic
629Dic3—22no—
630Dic3—24no—
631Dic3—22no—
632Dic3—22no—
633Dic3—42no—
634Dic3—81no—
635Dic3—81no—
636C23—32no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23C2×D3×D411yescharacteristic
644Q8—22no—
645Q8—22no—
646Q8—22no—
647Q8—34no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—616no—
653Q8—62no—
654Q8—62no—
655Q8—62no—
656Q8—121no—
657Q8—121no—
658Q8—121no—
659Q8—121no—
660Q8#88414yes—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—616no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4C2×#23511yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—41no—
712C8—41no—
713C8—121no—
714C8—121no—
715C2×C3#284711yescharacteristic
716C2×C3#301111yescharacteristic
717C2×C3#301111yescharacteristic
718C2×C3#304411yescharacteristic
719C2×C3#304411yescharacteristic
720C2×C3#312711yescharacteristic
721C2×C3#312711yescharacteristic
722D3—42no—
723C22—62no—
724C22—62no—
725C22—62no—
726C22—121no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22#554711yescharacteristic
731C22D3×#12011yescharacteristic
732C22D3×#12111yescharacteristic
733C22#576611yescharacteristic
734C22#577111yescharacteristic
735C22#577911yescharacteristic
736C22#577911yescharacteristic
737C4—24no—
738C4—41no—
739C4—41no—
740C4—42no—
741C4—62no—
742C4—62no—
743C4—62no—
744C4—64no—
745C4—81no—
746C4—81no—
747C4—122no—
748C4—241no—
749C4—241no—
750C4C2×#88411yescharacteristic
751C4#554711yescharacteristic
752C4D3×#12111yescharacteristic
753C4#565611yescharacteristic
754C3#3291511yescharacteristic, complemented, Sylow
755C2—122no—
756C2#7493511yescharacteristic
757C2#7972411yescharacteristic
758C2#7983611yescharacteristic
759C2#8018511yescharacteristic
760C2#8023011yescharacteristic
761C2#8047811yescharacteristic
762C2#8060111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC23×D3C2×D4
hypercenter#1878D3
hypocenterC3#32915
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
3. C2×#5182C2semidirect
4. C2×#4795C2semidirect
7. C3×#1878C2semidirect
8. #71632C2semidirect
10. #70222C2semidirect
11. #69690C2semidirect
12. #68905C2semidirect
14. #68685C2semidirect
75. #1878D3semidirect
754. C3#32915semidirect

Maximal subgroups

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

subgroupindex
C2×#55722
C2×#51862
C2×#51822
C2×#47952
C2×#48092
#766412
C3×#18782
#716322
#702692
#702222
#696902
#689052
#688792
#686852
#686632
#329153