Finite Group Databasebeta

← #10815439

Subgroups — #10815439

Order 768.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4889C211yesmaximal, characteristic, complemented
2C2×#4776C211yesmaximal, characteristic
3C2×D3×#102C211yesmaximal, characteristic
4#76431C211yesmaximal, characteristic
5#73773C211yesmaximal, characteristic, complemented
6C3×#1925C211yesmaximal, characteristic, complemented
7#70632C211yesmaximal, characteristic, complemented
8#70213C211yesmaximal, characteristic, complemented
9#70187C211yesmaximal, characteristic, complemented
10#69649C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68894C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68648C211yesmaximal, characteristic, complemented
16#22854—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#214C2211yescharacteristic
19C22×#204C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#893C2211yescharacteristic
23C2×D3×C4⋊C4C2211yescharacteristic
24C2×#887C2211yescharacteristic, complemented
25C2×D3×C22⋊C4—21no—
26C2×C4×D12C2211yescharacteristic
27C2×C3×#107C2211yescharacteristic, complemented
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C3×#390C2211yescharacteristic
31C3×C4×C4⋊C4C2211yescharacteristic, complemented
32#5221C2211yescharacteristic
33C2×#832C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36C2×#816C2211yescharacteristic, complemented
37C2×#815C2211yescharacteristic, complemented
38#4987C2211yescharacteristic
39#4984C2211yescharacteristic, complemented
40C2×#810C2211yescharacteristic, complemented
41C2×#809C2211yescharacteristic
42C2×#809C2211yescharacteristic
43C2×#807C2211yescharacteristic, complemented
44#4956—21no—
45#4956—21no—
46#4955—21no—
47C4×(C2×D3)⋊C4—21no—
48C4×(C2×D3)⋊C4C2211yescharacteristic
49#4929C2211yescharacteristic, complemented
50#4928—21no—
51C2×#803C2211yescharacteristic, complemented
52#4889—24no—
53#4776C418yescomplemented
54D3×#102—24no—
55#4668—21no—
56#4653—21no—
57C3×#340C2211yescharacteristic, complemented
58C3×#336C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63C2×#450—31no—
64C2×#440—31no—
65C22×#102—31no—
66#2360—31no—
67D4×C22⋊C4—31no—
68#1973—31no—
69#1936—31no—
70#1925D311yescharacteristic, complemented
71#1892—31no—
72#1880—31no—
73#1877—31no—
74#1862—31no—
75#1852—31no—
76#1762—31no—
77#1752—31no—
78C24×D3—21no—
79C22×C3×D4C2311yescharacteristic
80C22×#67—21no—
81C2×D3×D4—22no—
82C2×D3×D4—22no—
83C2×D3×D4—22no—
84C2×D3×D4—41no—
85C2×D3×D4—41no—
86C2×D3×D4C2×C414yes—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C4×D3C2311yescharacteristic
92C22×Dic6C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#214—41no—
105C2×#214—41no—
106C2×#214C2×C414yescomplemented
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4D411yescharacteristic
112C2×(C2×D3)⋊C4D411yescharacteristic
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×C4×Dic3—21no—
120C2×C4×Dic3C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C2×#204—22no—
124C2×#204—22no—
125C2×#204C2×C414yescomplemented
126C2×D3×C8—22no—
127C2×D3×C8—22no—
128C2×D3×C8—41no—
129#897—22no—
130#897C2×C414yescomplemented
131#893—22no—
132#893—41no—
133D3×C4⋊C4—22no—
134D3×C4⋊C4—41no—
135#887—22no—
136#887—41no—
137D3×C22⋊C4—44no—
138C4×D12—22no—
139C4×D12—41no—
140C3×#107—22no—
141C3×#102—22no—
142C3×#102C2×C414yescomplemented
143C3×#95—21no—
144#832—22no—
145C3⋊#95—21no—
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149C3⋊#95D411yescharacteristic
150C3⋊#95D411yescharacteristic
151#821—22no—
152(C2×D3)⋊C8C2×C414yescomplemented
153#816—41no—
154#815—22no—
155#810—22no—
156#809C2×C414yescomplemented
157#809D414yes—
158#807—41no—
159#803—41no—
160C23×D4—31no—
161C22×SD16—31no—
162C22×SD16—31no—
163C23×C8—31no—
164C2×C22⋊Q8—31no—
165C2×C4×Q8—31no—
166C2×C4×D4—31no—
167C2×C4×D4—31no—
168C22×C4⋊C4—31no—
169C22×C22⋊C4—61no—
170#450—38no—
171#440—64no—
172C2×#107—31no—
173C2×#107C2×D311yescharacteristic, complemented
174C2×#103—31no—
175C2×#103—31no—
176C2×#102—31no—
177C2×#102—31no—
178C2×#102—31no—
179C2×#102—31no—
180C2×#102—64no—
181C2×#102C2×D311yescharacteristic
182C2×#102C2×D311yescharacteristic
183C2×C22⋊C8—31no—
184C2×#97—31no—
185C2×#97—31no—
186#391—31no—
187#390—31no—
188#390C2×D311yescharacteristic
189#389—31no—
190#389—61no—
191#387—61no—
192#386—61no—
193#386—61no—
194#385—61no—
195#380—31no—
196#379—61no—
197C4×C4⋊C4C2×D311yescharacteristic, complemented
198C4×C22⋊C4—31no—
199C4×C22⋊C4—61no—
200#340—31no—
201#340—31no—
202#340—31no—
203#340C2×D311yescharacteristic, complemented
204#336—31no—
205#336C2×D311yescharacteristic, complemented
206C24×C3—21no—
207C23×D3—21no—
208C23×D3—24no—
209C23×D3—42no—
210C23×D3—42no—
211C23×D3—42no—
212C23×D3—42no—
213C23×D3—81no—
214C23×D3—81no—
215C23×D3C2×D411yescharacteristic
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4C22×C412yes—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2411yescharacteristic
228C2×#67—24no—
229C2×#67—42no—
230C2×#67—42no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3C2×D411yescharacteristic
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237D3×D4—28no—
238D3×D4—44no—
239D3×D4—44no—
240D3×D4—44no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12C22×C412yes—
245C2×D12C2×D412yes—
246C2×D12#4112yes—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—42no—
252C2×C4×D3—42no—
253C2×C4×D3—42no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—81no—
258C2×C4×D3—81no—
259C2×C4×D3—81no—
260C2×C4×D3C22×C412yes—
261C2×C4×D3#4112yes—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6C22×C412yes—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8C22×C412yes—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4C22×C412yes—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—81no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—81no—
285#217—42no—
286#217—81no—
287#214—44no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294C4⋊Dic3—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—81no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—42no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8C22×C412yes—
310C2×C3⋊C8C2×D412yes—
311#204—28no—
312D3×C8—44no—
313C25—61no—
314C22×Q8—31no—
315C22×D4—34no—
316C22×D4—31no—
317C22×D4—62no—
318C22×D4—61no—
319C22×D4—62no—
320C22×D4—62no—
321C22×D4—121no—
322C22×D4—121no—
323C22×D4C22×D311yescharacteristic
324C23×C4—31no—
325C23×C4—61no—
326C23×C4—61no—
327C23×C4—61no—
328C2×SD16—34no—
329C2×SD16—34no—
330C2×SD16—62no—
331C2×SD16—62no—
332C2×SD16—121no—
333C2×SD16—121no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341C22⋊Q8—34no—
342C22⋊Q8—62no—
343C4×Q8—62no—
344C4×Q8—121no—
345C4×D4—62no—
346C4×D4—62no—
347C4×D4—121no—
348C4×D4—121no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—121no—
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C4⋊C4C22×D311yescharacteristic
359C2×C4⋊C4C22×D311yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—124no—
371C2×C42—21no—
372C2×C42—31no—
373C2×C42—61no—
374C2×C42C22×D311yescharacteristic
375#107—22no—
376#107—121no—
377#103—62no—
378#103—121no—
379#102—22no—
380#102—34no—
381#102—34no—
382#102—62no—
383#102—62no—
384#102C4×D314yescomplemented
385C22⋊C8—34no—
386#97—62no—
387#97—121no—
388#95—21no—
389#95—31no—
390#95—31no—
391#95—61no—
392#95—61no—
393#95—61no—
394#95—61no—
395C23×C3—22no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3C22×D411yescharacteristic
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—48no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—48no—
416C22×D3—84no—
417C22×D3—84no—
418C22×D3—84no—
419C22×D3—84no—
420C22×D3—84no—
421C22×D3C4×D412yes—
422C22×D3AGL(1,ℤ/8)12yes—
423C22×D3#13712yes—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—41no—
427C3×D4—41no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4C23×C411yescharacteristic
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448C2×C3×C4H(5,𝔽2)11yescharacteristic
449#67—48no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—22no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3C4×D412yes—
468D12—22no—
469D12—22no—
470D12—22no—
471D12C4×D414yes—
472C4×D3—22no—
473C4×D3—22no—
474C4×D3—22no—
475C4×D3—22no—
476C4×D3—84no—
477C4×D3—84no—
478C4×D3—84no—
479Dic6—22no—
480Dic6—22no—
481Dic6—41no—
482Dic6—41no—
483C3×C8—22no—
484C3×C8—41no—
485C3⋊C8—22no—
486C3⋊C8—22no—
487C24—21no—
488C24—31no—
489C24—64no—
490C24—61no—
491C24—122no—
492C24—122no—
493C24—122no—
494C24—122no—
495C24—241no—
496C24—241no—
497C2×Q8—32no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—32no—
509C2×D4—32no—
510C2×D4—32no—
511C2×D4—64no—
512C2×D4—68no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—124no—
517C2×D4—124no—
518C2×D4—124no—
519C2×D4—122no—
520C2×D4—122no—
521C2×D4C2×C4×D312yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4—241no—
546C22×C4D3×D411yescharacteristic
547C22×C4D3×D411yescharacteristic
548C22×C4C23×D311yescharacteristic
549SD16—68no—
550SD16—124no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—32no—
557C2×C8—32no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—124no—
563C2×C8C2×C4×D312yes—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—64no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—241no—
576C4⋊C4C2×C4×D312yes—
577C4⋊C4D3×D412yes—
578C22⋊C4—42no—
579C22⋊C4—62no—
580C22⋊C4—62no—
581C22⋊C4—64no—
582C22⋊C4—81no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—241no—
588C42—21no—
589C42—21no—
590C42—61no—
591C42—61no—
592C42—81no—
593C42—122no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3C2×C4×D411yescharacteristic
602C22×C3D4211yescharacteristic
603C22×C3#54611yescharacteristic
604C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
605C22×C3C2×#13711yescharacteristic
606C22×C3#57611yescharacteristic
607C22×C3#57711yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—24no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—816no—
622C2×D3#44014yescomplemented
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—81no—
628C3×C4C2×C4×D411yescharacteristic
629C3×C4#51811yescharacteristic
630C3×C4#54611yescharacteristic
631C3×C4#55111yescharacteristic
632Dic3—22no—
633Dic3—42no—
634Dic3—41no—
635Dic3—41no—
636Dic3—81no—
637Dic3—81no—
638C23—22no—
639C23—32no—
640C23—32no—
641C23—32no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—128no—
656C23—128no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—244no—
662C23—244no—
663C23—244no—
664C23—244no—
665C23—244no—
666C23C2×D3×D411yescharacteristic
667Q8—62no—
668Q8—62no—
669Q8—121no—
670Q8—121no—
671D4—22no—
672D4—22no—
673D4—34no—
674D4—41no—
675D4—41no—
676D4—62no—
677D4—62no—
678D4—62no—
679D4—128no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—32no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—244no—
718C2×C4—244no—
719C2×C4—244no—
720C2×C4C22×C4×D311yescharacteristic
721C2×C4C2×D3×D411yescharacteristic
722C2×C4D3×#4111yescharacteristic
723C2×C4D3×#4111yescharacteristic
724C2×C4#100911yescharacteristic
725C2×C4#100911yescharacteristic
726C8—22no—
727C8—41no—
728C8—62no—
729C8—62no—
730C2×C3—82no—
731C2×C3#235811yescharacteristic
732C2×C3C2×#44011yescharacteristic
733C2×C3#294611yescharacteristic
734C2×C3#326411yescharacteristic
735C2×C3#326611yescharacteristic
736C2×C3#331011yescharacteristic
737C2×C3#331411yescharacteristic
738D3—24no—
739D3—44no—
740C22—34no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—64no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—2416no—
762C22C4×D3×D411yescharacteristic
763C22#560911yescharacteristic
764C22#565411yescharacteristic
765C22#575711yescharacteristic
766C22#577011yescharacteristic
767C22D3×AGL(1,ℤ/8)11yescharacteristic
768C22D3×#13711yescharacteristic
769C4—41no—
770C4—42no—
771C4—42no—
772C4—41no—
773C4—62no—
774C4—81no—
775C4—122no—
776C4—121no—
777C4—121no—
778C4—241no—
779C4—241no—
780C4#552111yescharacteristic
781C4C4×D3×D411yescharacteristic
782C4#567611yescharacteristic
783C4#570511yescharacteristic
784C3#2285411yescharacteristic, complemented, Sylow
785C2—64no—
786C2—82no—
787C2—124no—
788C2#7583611yescharacteristic
789C2#7958711yescharacteristic
790C2D3×#44011yescharacteristic
791C2#8035811yescharacteristic
792C2#8062711yescharacteristic
793C2#8128911yescharacteristic
794C2#8138311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1925C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
cosocleC22×C3×C4C24
hypercenter#1925D3
hypocenterC3#22854
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
1. C2×#4889C2semidirect
5. #73773C2semidirect
6. C3×#1925C2semidirect
7. #70632C2semidirect
8. #70213C2semidirect
9. #70187C2semidirect
10. #69649C2semidirect
11. #69474C2semidirect
12. #68894C2semidirect
13. #68882C2semidirect
14. #68672C2semidirect
15. #68648C2semidirect
24. C2×#887C22semidirect
27. C2×C3×#107C22semidirect
31. C3×C4×C4⋊C4C22semidirect
36. C2×#816C22semidirect
37. C2×#815C22semidirect
39. #4984C22semidirect
40. C2×#810C22semidirect
43. C2×#807C22semidirect
49. #4929C22semidirect
51. C2×#803C22semidirect
53. #4776C4semidirect
57. C3×#340C22semidirect
58. C3×#336C22semidirect
59. #4551C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
70. #1925D3semidirect
106. C2×#214C2×C4semidirect
125. C2×#204C2×C4semidirect
130. #897C2×C4semidirect
142. C3×#102C2×C4semidirect
152. (C2×D3)⋊C8C2×C4semidirect
156. #809C2×C4semidirect
173. C2×#107C2×D3semidirect
197. C4×C4⋊C4C2×D3semidirect
203. #340C2×D3semidirect
205. #336C2×D3semidirect
384. #102C4×D3semidirect
622. C2×D3#440semidirect
784. C3#22854semidirect

Maximal subgroups

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

subgroupindex
C2×#48892
C2×#47762
C2×D3×#1022
#764312
#737732
C3×#19252
#706322
#702132
#701872
#696492
#694742
#688942
#688822
#686722
#686482
#228543