Finite Group Databasebeta

← #10828460

Subgroups — #10828460

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic
2C2×#4863C211yesmaximal, characteristic, complemented
3C2×#4777C211yesmaximal, characteristic, complemented
4D3×#389C211yesmaximal, characteristic, complemented
5C3×#1864C211yesmaximal, characteristic, complemented
6#71607C211yesmaximal, characteristic, complemented
7#70565C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70200C211yesmaximal, characteristic, complemented
10#70177C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68827C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15#68664C211yesmaximal, characteristic, complemented
16#24061—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×C4×D4C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×C4×#67—21no—
22#5548—24no—
23#5548—24no—
24C2×#895C2211yescharacteristic
25C2×D3×C4⋊C4—21no—
26C2×D3×C4⋊C4C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C2×#888C2211yescharacteristic
29C2×#885—21no—
30C2×#884—21no—
31C2×C4×D12C2211yescharacteristic
32C2×C42×D3C2211yescharacteristic
33C2×C3×#106C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#817C2211yescharacteristic
44#4984C2211yescharacteristic
45#4976—21no—
46#4972C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#808C2211yescharacteristic
51#4928C2211yescharacteristic
52#4863—24no—
53#4777—24no—
54D3×#95—21no—
55#4647—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#532—31no—
65C2×#481—31no—
66C2×#481—31no—
67C2×#389—31no—
68#2058—31no—
69#2058—31no—
70#2041—31no—
71#2041—31no—
72#1874—31no—
73#1874—31no—
74#1864—31no—
75#1864—31no—
76#1864—31no—
77#1864D311yescharacteristic, complemented
78#1817—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C2×#235—28no—
85C2×#235—44no—
86C2×#235—44no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C4×D3—21no—
92C22×C4×D3D411yescharacteristic
93C22×C4×D3D411yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107#940—22no—
108#940—22no—
109#938—22no—
110#938D414yes—
111C4×#67—28no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×C4×Dic3D411yescharacteristic
124C2×C4×Dic3D411yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128#895—22no—
129#895D414yes—
130D3×C4⋊C4—22no—
131D3×C4⋊C4—22no—
132D3×C4⋊C4—22no—
133D3×C4⋊C4—22no—
134D3×C4⋊C4—44no—
135#888—22no—
136#888—22no—
137#885—28no—
138#884—28no—
139C4×D12—22no—
140C4×D12—22no—
141C42×D3—22no—
142C42×D3—22no—
143C3×#106—22no—
144C3×#102—22no—
145C3×#102—22no—
146C3×#95—21no—
147#832—22no—
148#832—22no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#821—22no—
153#821—22no—
154(C2×D3)⋊C8—22no—
155(C2×D3)⋊C8—22no—
156#817—22no—
157#809—22no—
158#809—22no—
159#808—22no—
160#808—22no—
161C22×#41—61no—
162#532—64no—
163#532—64no—
164C2×C4⋊Q8—31no—
165C2×#127—31no—
166C2×#124—61no—
167C2×#121—31no—
168C2×#121—31no—
169C2×#121—61no—
170C2×C4×D4—31no—
171C2×C4×D4—61no—
172C2×C4×D4C2×D311yescharacteristic
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—61no—
176C22×C42—31no—
177#481—64no—
178#481—64no—
179C2×#106—31no—
180C2×#106—31no—
181C2×#106—31no—
182C2×#106C2×D311yescharacteristic
183C2×#102—31no—
184C2×#102—31no—
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102C2×D311yescharacteristic
190C2×#102C2×D311yescharacteristic
191C2×C22⋊C8—31no—
192C2×C22⋊C8—31no—
193#389—31no—
194#389—31no—
195#389—31no—
196#389—61no—
197#389—61no—
198#389C2×D311yescharacteristic
199C2×#95—61no—
200#340—31no—
201#340—31no—
202#340—31no—
203#340C2×D311yescharacteristic
204#336—31no—
205#336—31no—
206#336—31no—
207#336C2×D311yescharacteristic
208C24×C3—21no—
209C23×D3—21no—
210C23×D3C2×D411yescharacteristic
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4C2×D412yes—
217C22×C3×C4—24no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2411yescharacteristic
226C2×#67—24no—
227C2×#67—24no—
228C2×#67—24no—
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241#235—432no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—24no—
247C2×D12—21no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12C2×D412yes—
251C2×C4×D3—22no—
252C2×C4×D3—22no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—41no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C4×D3SD1614yes—
270C2×C4×D3C2×D412yes—
271C2×C4×D3C2×D412yes—
272C2×Dic6—24no—
273C2×Dic6—42no—
274C2×Dic6—42no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—42no—
286C3×C4⋊C4C2×D412yes—
287C3×C4⋊C4#4112yescomplemented
288C3×C22⋊C4—24no—
289C3×C42—21no—
290C3×C42—21no—
291#217—24no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—42no—
299C4⋊Dic3C2×D412yes—
300C4⋊Dic3#4112yescomplemented
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—22no—
309C4×Dic3—22no—
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×#41—68no—
317C2×#41—124no—
318C2×#41—124no—
319C22×Q8—61no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4C22×D311yescharacteristic
326C23×C4—21no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—61no—
331C23×C4—61no—
332C23×C4—61no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8C22×D311yescharacteristic
336C22×C8C22×D311yescharacteristic
337C4⋊Q8—62no—
338C4⋊Q8—62no—
339#127—62no—
340#127—62no—
341#124—68no—
342#121—34no—
343#121—34no—
344#121—68no—
345#121—62no—
346#121—62no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—68no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—62no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—124no—
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C42—31no—
375C2×C42—31no—
376C2×C42—31no—
377C2×C42—62no—
378C2×C42—62no—
379C2×C42C22×D311yescharacteristic
380#106—22no—
381#106—62no—
382#106—62no—
383#106—62no—
384#102—22no—
385#102—22no—
386#102—62no—
387#102—62no—
388#102—62no—
389#102—62no—
390#102—62no—
391#102—62no—
392C22⋊C8—62no—
393C22⋊C8—62no—
394#95—21no—
395#95—61no—
396#95—61no—
397#95—61no—
398C23×C3—22no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3C22×D411yescharacteristic
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—22no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3#12012yes—
418C22×D3C2×SD1612yes—
419C22×D3AGL(1,ℤ/8)12yes—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—41no—
423C3×D4—41no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—48no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4C2×SD1612yes—
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C42−1+411yescharacteristic
445C2×C3×C42−1+411yescharacteristic
446#67—48no—
447#67—48no—
448#67—48no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3#12012yes—
465C2×Dic3C2×SD1612yes—
466C2×Dic3AGL(1,ℤ/8)12yes—
467D12—22no—
468D12—22no—
469D12—48no—
470D12—41no—
471D12—41no—
472C4×D3—28no—
473C4×D3—22no—
474C4×D3—22no—
475C4×D3—22no—
476C4×D3—22no—
477C4×D3—44no—
478C4×D3—48no—
479C4×D3—48no—
480C4×D3—84no—
481Dic6—48no—
482C3×C8—41no—
483C3×C8—41no—
484C3⋊C8—41no—
485C3⋊C8—41no—
486C24—21no—
487C24—31no—
488C24—61no—
489#41—1232no—
490C2×Q8—64no—
491C2×Q8—122no—
492C2×Q8—122no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—32no—
499C2×D4—64no—
500C2×D4—64no—
501C2×D4—64no—
502C2×D4—64no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—122no—
509C2×D4—122no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4D3×D412yes—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—34no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—64no—
534C22×C4—64no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—121no—
543C22×C4—122no—
544C22×C4—122no—
545C22×C4—122no—
546C22×C4—122no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4D3×D411yescharacteristic
551C22×C4D3×D411yescharacteristic
552C22×C4C23×D311yescharacteristic
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—61no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—32no—
570C4⋊C4—32no—
571C4⋊C4—42no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—122no—
579C4⋊C4—122no—
580C4⋊C4—122no—
581C4⋊C4—122no—
582C4⋊C4#23512yescomplemented
583C4⋊C4D3×D412yes—
584C22⋊C4—24no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C42—21no—
589C42—21no—
590C42—62no—
591C42—62no—
592C42—61no—
593C42—61no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3C2×#12011yescharacteristic
602C22×C3#52511yescharacteristic
603C22×C3#53611yescharacteristic
604C22×C3C22×SD1611yescharacteristic
605C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
606C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
607C22×C3#57511yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C2×D3#45014yes—
622C3×C4—22no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—81no—
627C3×C4#54711yescharacteristic
628C3×C4#54711yescharacteristic
629C3×C4#54711yescharacteristic
630C3×C4#54711yescharacteristic
631Dic3—22no—
632Dic3—22no—
633Dic3—22no—
634Dic3—42no—
635Dic3—42no—
636Dic3—81no—
637C23—22no—
638C23—32no—
639C23—32no—
640C23—32no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—62no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23C2×D3×D411yescharacteristic
659Q8—128no—
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—62no—
665D4—62no—
666D4—128no—
667D4—128no—
668D4—128no—
669D4—128no—
670D4—121no—
671D4—121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—68no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—128no—
704C2×C4—124no—
705C2×C4—128no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—244no—
714C2×C4D3×SD1612yes—
715C2×C4C2×#23511yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4C2×D3×D411yescharacteristic
718C2×C4#100711yescharacteristic
719C2×C4D3×#4111yescharacteristic
720C2×C4#101011yescharacteristic
721C8—41no—
722C8—41no—
723C8—121no—
724C8—121no—
725C2×C3—82no—
726C2×C3#240611yescharacteristic
727C2×C3C2×#45011yescharacteristic
728C2×C3#300611yescharacteristic
729C2×C3#310311yescharacteristic
730C2×C3#310911yescharacteristic
731C2×C3#322711yescharacteristic
732C2×C3#323411yescharacteristic
733D3—24no—
734D3—82no—
735C22—34no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—241no—
753C22—241no—
754C22—241no—
755C22—241no—
756C22#554711yescharacteristic
757C22D3×#12011yescharacteristic
758C22#562811yescharacteristic
759C22C2×D3×SD1611yescharacteristic
760C22#576811yescharacteristic
761C22D3×AGL(1,ℤ/8)11yescharacteristic
762C22D3×AGL(1,ℤ/8)11yescharacteristic
763C4—22no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—62no—
768C4—62no—
769C4—62no—
770C4—81no—
771C4—122no—
772C4—122no—
773C4—241no—
774C4#550711yescharacteristic
775C4#555111yescharacteristic
776C4#563111yescharacteristic
777C4#565511yescharacteristic
778C3#2406111yescharacteristic, complemented, Sylow
779C2—64no—
780C2—82no—
781C2—242no—
782C2#7460011yescharacteristic
783C2#7965311yescharacteristic
784C2#7986911yescharacteristic
785C2#8008411yescharacteristic
786C2D3×#45011yescharacteristic
787C2#8106411yescharacteristic
788C2#8117411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1864C2
socleC23×C3C22×D4
prime radicalC2×#5548C2
hypercenter#1864D3
hypocenterC3#24061
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#4863C2semidirect
3. C2×#4777C2semidirect
4. D3×#389C2semidirect
5. C3×#1864C2semidirect
6. #71607C2semidirect
7. #70565C2semidirect
8. #70211C2semidirect
9. #70200C2semidirect
10. #70177C2semidirect
11. #69626C2semidirect
12. #68880C2semidirect
13. #68827C2semidirect
14. #68671C2semidirect
15. #68664C2semidirect
77. #1864D3semidirect
287. C3×C4⋊C4#41semidirect
300. C4⋊Dic3#41semidirect
582. C4⋊C4#235semidirect
778. C3#24061semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×#48632
C2×#47772
D3×#3892
C3×#18642
#716072
#705652
#702112
#702002
#701772
#696262
#688802
#688272
#686712
#686642
#240613