Finite Group Databasebeta

← #10701942

Subgroups — #10701942

Order 768.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#949C211yesmaximal, characteristic
2C3×#2311C211yesmaximal, characteristic, complemented
3C22×#837C211yesmaximal, characteristic, complemented
4C2×#5001C211yesmaximal, characteristic, complemented
5C2×#4988C211yesmaximal, characteristic, complemented
6C2×#4532C211yesmaximal, characteristic, complemented
7C2×#4530C211yesmaximal, characteristic, complemented
8#11016—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C23×D12C2211yescharacteristic
11C2×C3×#117C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C2×#949—22no—
14C2×#949—22no—
15C2×#949—22no—
16C2×#949—22no—
17C2×#949—22no—
18C2×#949C414yescomplemented
19C22×#215—21no—
20C22×#213—21no—
21C22×(C2×D3)⋊C4—22no—
22C22×C4×Dic3C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C3×#391—21no—
26C3×#390—21no—
27C3×#386—22no—
28C3×#380—22no—
29C2×#837—22no—
30C2×#837—22no—
31C2×#837—22no—
32#5001—22no—
33#5001—22no—
34#4988—22no—
35#4988—22no—
36C2×#809—22no—
37#4532—22no—
38#4530—22no—
39C22×AGL(1,ℤ/8)—31no—
40C22×#104—31no—
41C2×#418—31no—
42#2311D311yescharacteristic, complemented
43C2×#390—31no—
44C2×#343—31no—
45C2×#339—31no—
46C24×D3—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41C2×C412yes—
58C2×C3×#41D412yes—
59C22×C3×Q8D411yescharacteristic
60C22×C3×D4—21no—
61C22×C3×D4D411yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4D412yes—
64C23×C3×C4C2311yescharacteristic
65C23×Dic3—21no—
66C22×D12—21no—
67C22×D12—21no—
68C22×D12—21no—
69C22×D12—21no—
70C22×D12—21no—
71C22×D12—21no—
72C22×D12—21no—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12—21no—
76C22×D12—21no—
77C22×D12C2×C412yes—
78C22×D12D412yes—
79C22×D12D412yes—
80C3×#117—21no—
81C3×#117—21no—
82C3×#117—21no—
83C3×#117—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4D412yes—
91C2×C3×C22⋊C4—21no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C42—21no—
94#949—28no—
95#949—28no—
96#949—28no—
97#949—28no—
98C2×#215—24no—
99C2×#215—24no—
100C2×#215—24no—
101C2×#213—24no—
102C2×#213—24no—
103C2×#213—24no—
104C2×(C2×D3)⋊C4—28no—
105C2×(C2×D3)⋊C4—48no—
106C2×C4×Dic3—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3—21no—
109C2×C4×Dic3—21no—
110C2×C4×Dic3—21no—
111C2×C4×Dic3D412yes—
112C2×#208—21no—
113C2×#208—21no—
114C2×#208—21no—
115C2×#208—21no—
116C2×#208—21no—
117C2×#208—21no—
118C2×#208—21no—
119C2×#208—21no—
120C2×#208C2×C412yes—
121C2×#208D412yes—
122C2×#208D412yes—
123C2×#208D412yes—
124C22×C3⋊C8—21no—
125C22×C3⋊C8—21no—
126C3×#95—24no—
127#837—28no—
128#809—28no—
129C22×#41C2×D311yescharacteristic
130C23×D4—31no—
131C2×AGL(1,ℤ/8)—34no—
132C2×AGL(1,ℤ/8)—62no—
133C2×AGL(1,ℤ/8)—62no—
134C2×AGL(1,ℤ/8)—62no—
135C2×AGL(1,ℤ/8)—62no—
136C2×AGL(1,ℤ/8)—62no—
137C22×SD16—61no—
138C22×D8—61no—
139C22×M16—31no—
140C22×M16—31no—
141C2×#117C2×D311yescharacteristic
142C22×C4⋊C4C2×D311yescharacteristic
143C22×C22⋊C4—62no—
144C22×C42—31no—
145C2×#104—62no—
146C2×#104—62no—
147C2×#104—62no—
148#418—62no—
149#418—62no—
150C2×#102—62no—
151#391—21no—
152#390—21no—
153#390—62no—
154#390—62no—
155#386—22no—
156#380—22no—
157#343—62no—
158#339—62no—
159C24×C3—21no—
160C24×C3C2×D411yescharacteristic
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—44no—
165C23×D3—44no—
166C23×D3—41no—
167C23×D3—41no—
168C23×D3—41no—
169C23×D3—41no—
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C3×#41—41no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8C22⋊C412yescomplemented
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4C22⋊C412yescomplemented
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—44no—
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C22×C3×C4#4111yescharacteristic
229C22×C3×C4#4111yescharacteristic
230C22×Dic3—24no—
231C22×Dic3—22no—
232C22×Dic3—42no—
233C22×Dic3—41no—
234C22×Dic3—41no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—22no—
238C2×D12—22no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—41no—
251C2×D12—41no—
252C2×D12—41no—
253C2×D12—41no—
254C2×D12—41no—
255C2×D12—41no—
256C2×D12—41no—
257C2×D12—41no—
258C2×D12—41no—
259C2×D12—41no—
260C2×D12—41no—
261C2×D12—41no—
262C2×D12C22⋊C414yescomplemented
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—41no—
268C3×C4⋊C4—41no—
269C3×C22⋊C4—41no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—84no—
272C3×C42—41no—
273C3×C42—41no—
274#215—216no—
275#213—216no—
276(C2×D3)⋊C4—416no—
277C4×Dic3—22no—
278C4×Dic3—22no—
279C4×Dic3—41no—
280C4×Dic3—41no—
281#208—22no—
282#208—22no—
283#208—22no—
284#208—22no—
285#208—22no—
286#208—41no—
287#208—41no—
288#208C22⋊C414yescomplemented
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8—41no—
294C2×C3⋊C8—41no—
295C25—61no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41C4×D312yes—
307C2×#41D1212yes—
308C22×Q8#6711yescharacteristic
309C22×D4—21no—
310C22×D4—32no—
311C22×D4—32no—
312C22×D4—32no—
313C22×D4—61no—
314C22×D4—61no—
315C22×D4—61no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4#6711yescharacteristic
325C23×C4—21no—
326C23×C4—61no—
327C23×C4#6712yes—
328C23×C4C22×D311yescharacteristic
329AGL(1,ℤ/8)—68no—
330AGL(1,ℤ/8)—68no—
331AGL(1,ℤ/8)—68no—
332AGL(1,ℤ/8)—68no—
333C2×SD16—64no—
334C2×SD16—64no—
335C2×SD16—64no—
336C2×D8—64no—
337C2×D8—64no—
338C2×D8—64no—
339C2×M16—32no—
340C2×M16—32no—
341C2×M16—32no—
342C2×M16—32no—
343C2×M16—61no—
344C2×M16—61no—
345C2×M16—61no—
346C2×M16—61no—
347C2×M16—61no—
348C2×M16—61no—
349C2×M16—61no—
350C2×M16—61no—
351C22×C8—61no—
352C22×C8—61no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4#6712yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—68no—
367C2×C22⋊C4—128no—
368C2×C42—21no—
369C2×C42—32no—
370C2×C42—61no—
371C2×C42—61no—
372C2×C42—61no—
373C2×C42—61no—
374C2×C42—61no—
375#104—68no—
376#102—68no—
377#95—24no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3C4×D411yescharacteristic
386C23×C3#12011yescharacteristic
387C23×C3#12011yescharacteristic
388C23×C3#12111yescharacteristic
389C23×C3#12111yescharacteristic
390C23×C3#12111yescharacteristic
391C23×C3#12711yescharacteristic
392C22×D3—24no—
393C22×D3—44no—
394C22×D3—48no—
395C22×D3—44no—
396C22×D3—48no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—84no—
404C22×D3—82no—
405C22×D3—82no—
406C22×D3—84no—
407C22×D3—82no—
408C22×D3—82no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×D4—22no—
414C3×D4—22no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—42no—
419C3×D4—41no—
420C3×D4—41no—
421C2×C3×C4—22no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—44no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—44no—
433C2×C3×C4—42no—
434C2×C3×C4—82no—
435C2×C3×C4C2×C22⋊C411yescharacteristic
436C2×C3×C4C2×C22⋊C411yescharacteristic
437C2×C3×C4C2×C22⋊C411yescharacteristic
438C2×C3×C4C4×D411yescharacteristic
439C2×C3×C4C4×D411yescharacteristic
440C2×C3×C4C4×D411yescharacteristic
441C2×C3×C4#12011yescharacteristic
442C2×C3×C4#12011yescharacteristic
443C2×C3×C4#12011yescharacteristic
444C2×C3×C4#12011yescharacteristic
445C2×C3×C4#12011yescharacteristic
446C2×C3×C4#12011yescharacteristic
447C2×C3×C4#12111yescharacteristic
448C2×C3×C4#12111yescharacteristic
449C2×C3×C4#12111yescharacteristic
450C2×C3×C4#12111yescharacteristic
451C2×C3×C4#12111yescharacteristic
452C2×C3×C4#12111yescharacteristic
453C2×C3×C4#12111yescharacteristic
454C2×C3×C4#12111yescharacteristic
455C2×C3×C4#12111yescharacteristic
456C2×C3×C4#12311yescharacteristic
457C2×C3×C4#12311yescharacteristic
458C2×C3×C4#12311yescharacteristic
459C2×C3×C4#12311yescharacteristic
460C2×C3×C4#12411yescharacteristic
461C2×C3×C4#12411yescharacteristic
462C2×C3×C4#12711yescharacteristic
463C2×Dic3—24no—
464C2×Dic3—44no—
465C2×Dic3—42no—
466C2×Dic3—44no—
467C2×Dic3—42no—
468D12—24no—
469D12—24no—
470D12—42no—
471D12—42no—
472D12—42no—
473D12—42no—
474D12—42no—
475D12—42no—
476C3⋊C8—24no—
477C3⋊C8—42no—
478C24—21no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24—124no—
483C24—124no—
484C24—121no—
485C24—121no—
486C24—121no—
487C24—121no—
488C24C2×#6711yescharacteristic
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8(C2×D3)⋊C412yescomplemented
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—34no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—62no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4—121no—
539C2×D4—121no—
540C2×D4—121no—
541C2×D4—121no—
542C2×D4—121no—
543C2×D4—121no—
544C2×D4—121no—
545C2×D4—121no—
546C2×D4—121no—
547C2×D4—121no—
548C2×D4—121no—
549C2×D4—121no—
550C2×D4(C2×D3)⋊C412yescomplemented
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—44no—
563C22×C4—64no—
564C22×C4—62no—
565C22×C4—122no—
566C22×C4—121no—
567C22×C4—121no—
568C22×C4C2×C4×D311yescharacteristic
569C22×C4C2×D1211yescharacteristic
570C22×C4#23511yescharacteristic
571C22×C4#23511yescharacteristic
572C22×C4D3×D411yescharacteristic
573C22×C4D3×D411yescharacteristic
574C22×C4D3×D411yescharacteristic
575C22×C4D3×D411yescharacteristic
576C22×C4D3×D411yescharacteristic
577C22×C4D3×D411yescharacteristic
578C22×C4#23711yescharacteristic
579C22×C4#23711yescharacteristic
580C22×C4C2×#6711yescharacteristic
581C22×C4C2×#6711yescharacteristic
582SD16—616no—
583D8—616no—
584M16—34no—
585M16—62no—
586M16—62no—
587M16—62no—
588M16—62no—
589M16—62no—
590M16—121no—
591M16—121no—
592C2×C8—62no—
593C2×C8—62no—
594C2×C8—62no—
595C2×C8—62no—
596C2×C8—121no—
597C2×C8—121no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—84no—
607C22⋊C4—1216no—
608C42—41no—
609C42—41no—
610C42—62no—
611C42—62no—
612C42—121no—
613C42—121no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—44no—
623C22×C3—42no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—82no—
627C22×C3#38611yescharacteristic
628C22×C3#38611yescharacteristic
629C22×C3#39011yescharacteristic
630C22×C3#39211yescharacteristic
631C22×C3#39211yescharacteristic
632C22×C3#39211yescharacteristic
633C22×C3#39411yescharacteristic
634C22×C3#45312yes—
635C22×C3#45412yes—
636C2×D3—48no—
637C2×D3—44no—
638C2×D3—84no—
639C2×D3—84no—
640C2×D3—84no—
641C2×D3—84no—
642C2×D3—82no—
643C2×D3—82no—
644C2×D3—84no—
645C3×C4—42no—
646C3×C4—82no—
647C3×C4—82no—
648C3×C4#37911yescharacteristic
649C3×C4#38611yescharacteristic
650C3×C4#38611yescharacteristic
651C3×C4#39011yescharacteristic
652C3×C4#39211yescharacteristic
653C3×C4#39411yescharacteristic
654C3×C4#39411yescharacteristic
655C3×C4#39411yescharacteristic
656Dic3—44no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—64no—
665C23—124no—
666C23—124no—
667C23—128no—
668C23—128no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—242no—
676C23—242no—
677C23—244no—
678C23—244no—
679C23—242no—
680C23—242no—
681C23C4×#6711yescharacteristic
682C23#93011yescharacteristic
683C23#93711yescharacteristic
684C23#93811yescharacteristic
685C23#93911yescharacteristic
686C23#94011yescharacteristic
687C23#95311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—41no—
699D4—41no—
700D4—64no—
701D4—64no—
702D4—122no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—122no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—64no—
722C2×C4—82no—
723C2×C4—122no—
724C2×C4—124no—
725C2×C4—124no—
726C2×C4—122no—
727C2×C4D3×C22⋊C411yescharacteristic
728C2×C4D3×C22⋊C411yescharacteristic
729C2×C4#67⋊C411yescharacteristic
730C2×C4#67⋊C411yescharacteristic
731C2×C4#88211yescharacteristic
732C2×C4#88211yescharacteristic
733C2×C4#88211yescharacteristic
734C2×C4#88311yescharacteristic
735C2×C4#88311yescharacteristic
736C2×C4#88411yescharacteristic
737C2×C4#88411yescharacteristic
738C2×C4#88411yescharacteristic
739C2×C4#88411yescharacteristic
740C2×C4#88511yescharacteristic
741C2×C4#88511yescharacteristic
742C2×C4#88611yescharacteristic
743C2×C4C2×(C2×D3)⋊C411yescharacteristic
744C2×C4C4×#6711yescharacteristic
745C2×C4#92911yescharacteristic
746C2×C4#93011yescharacteristic
747C2×C4#93711yescharacteristic
748C2×C4#93711yescharacteristic
749C2×C4#93711yescharacteristic
750C2×C4#93811yescharacteristic
751C2×C4#93911yescharacteristic
752C2×C4#93911yescharacteristic
753C2×C4#93911yescharacteristic
754C2×C4#94011yescharacteristic
755C8—64no—
756C8—122no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—82no—
762C2×C3#143811yescharacteristic
763C2×C3#188312yes—
764C2×C3#200211yescharacteristic
765C2×C3#200311yescharacteristic
766C2×C3#200612yes—
767D3—84no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—42no—
777C22—44no—
778C22—81no—
779C22—81no—
780C22—82no—
781C22—128no—
782C22—124no—
783C22—244no—
784C22—244no—
785C22—244no—
786C22—242no—
787C22—242no—
788C22—244no—
789C22—244no—
790C22#495611yescharacteristic
791C22#495711yescharacteristic
792C22#496011yescharacteristic
793C22#496111yescharacteristic
794C22#521311yescharacteristic
795C22#522311yescharacteristic
796C22#522311yescharacteristic
797C22#524112yes—
798C22#524512yes—
799C4—42no—
800C4—82no—
801C4—82no—
802C4—124no—
803C4#495511yescharacteristic
804C4#495611yescharacteristic
805C4#495711yescharacteristic
806C4#495811yescharacteristic
807C4#495911yescharacteristic
808C4#495911yescharacteristic
809C4#496011yescharacteristic
810C4#496111yescharacteristic
811C3#1101611yescharacteristic, complemented, Sylow
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—244no—
818C2#7155011yescharacteristic
819C2#7166712yes—
820C2#7185611yescharacteristic
821C2#7186711yescharacteristic
822C2#7187912yes—
subgroupG/H
centerC23#953
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC3×#2311C2
socleC23×C3#120
prime radicalC22×#949C2
cosocleC23×C3×C4C23
hypercenter#2311D3
hypocenterC3#11016
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C3×#2311C2semidirect
3. C22×#837C2semidirect
4. C2×#5001C2semidirect
5. C2×#4988C2semidirect
6. C2×#4532C2semidirect
7. C2×#4530C2semidirect
18. C2×#949C4semidirect
42. #2311D3semidirect
191. C2×C3×Q8C22⋊C4semidirect
203. C2×C3×D4C22⋊C4semidirect
262. C2×D12C22⋊C4semidirect
288. #208C22⋊C4semidirect
510. C2×Q8(C2×D3)⋊C4semidirect
550. C2×D4(C2×D3)⋊C4semidirect
811. C3#11016semidirect

Maximal subgroups

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

subgroupindex
C22×#9492
C3×#23112
C22×#8372
C2×#50012
C2×#49882
C2×#45322
C2×#45302
#110163