Finite Group Databasebeta

← #10823434

Subgroups — #10823434

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5479C211yesmaximal, characteristic, complemented
2C3×C4×#121C211yesmaximal, characteristic, complemented
3C2×#5014C211yesmaximal, characteristic, complemented
4C2×#5018C211yesmaximal, characteristic, complemented
5#71685C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic
7#71529C211yesmaximal, characteristic, complemented
8#69659C211yesmaximal, characteristic, complemented
9#69639C211yesmaximal, characteristic, complemented
10#69628C211yesmaximal, characteristic, complemented
11#69606C211yesmaximal, characteristic, complemented
12#69526C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69475C211yesmaximal, characteristic, complemented
15#69474C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×C4×D4—21no—
19C2×C3×C4×D4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#929—21no—
25C2×C4×#67—21no—
26C2×#924C2211yescharacteristic
27#5479—24no—
28#5479—24no—
29C2×#876—21no—
30C2×#875C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×#870C2211yescharacteristic
34C2×C4×Dic6C2211yescharacteristic
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#386—21no—
39C3×#380C2211yescharacteristic
40C3×C4×C4⋊C4C2211yescharacteristic
41C3×C4×C22⋊C4—21no—
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5018—24no—
47#5014—24no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#442—31no—
66C2×#440—31no—
67C4×#121D311yescharacteristic, complemented
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4D411yescharacteristic
83C23×C3×C4D411yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×Dic6C2311yescharacteristic
89C3×#121—22no—
90C3×#121—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C3×C4×D4—44no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C42—22no—
104C2×C3×C42—22no—
105C2×C3×C42—21no—
106C2×C3×C42D411yescharacteristic
107C2×C3×C42D411yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#214—22no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—22no—
117#930—22no—
118#930—22no—
119#929—28no—
120C4×#67—28no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—22no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×C4×Dic3—21no—
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#876—28no—
139#875—22no—
140#875—22no—
141C4×D12—22no—
142C4×D12D414yescomplemented
143#872—28no—
144#870—22no—
145#870—22no—
146C4×Dic6—22no—
147C4×Dic6D414yescomplemented
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151#832—22no—
152#832—22no—
153#830—22no—
154#830—22no—
155#810—22no—
156#810—22no—
157#810—22no—
158#809—22no—
159#809—22no—
160#809—22no—
161#808—22no—
162#807—22no—
163#803—22no—
164#803—22no—
165C22×SD16—31no—
166C22×D8—31no—
167#529—64no—
168#529—64no—
169C2×#126—61no—
170C2×#125—31no—
171C2×#124—31no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×C4×Q8—31no—
177C2×C4×D4—21no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4C2×D311yescharacteristic
181C2×#117—61no—
182C22×C42C2×D311yescharacteristic
183#442—64no—
184#440—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97—31no—
199#390C2×D311yescharacteristic
200#389C2×D311yescharacteristic
201#388—21no—
202#386—21no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4C2×D311yescharacteristic
205C4×C22⋊C4—21no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×D4—24no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—42no—
222C2×C3×D4—42no—
223C2×C3×D4#4112yes—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—41no—
237C22×C3×C4—41no—
238C22×C3×C4—41no—
239C22×C3×C4—42no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C2×#67—24no—
249C2×#67—42no—
250C2×#67—42no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12C2×D412yes—
260C2×C4×D3—24no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6C2×D412yes—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4#4112yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C42—22no—
282C3×C42—22no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—42no—
286C3×C42C2×D412yes—
287C3×C42C2×D412yes—
288#217—24no—
289#214—28no—
290#213—28no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303C4×Dic3—24no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8#4112yes—
315C2×C3⋊C8#4112yes—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—21no—
322C23×C4—61no—
323C23×C4#6711yescharacteristic
324C23×C4#6711yescharacteristic
325C23×C4C22×D311yescharacteristic
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×D8—62no—
330C2×D8—62no—
331C2×D8—62no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—31no—
336#126—68no—
337#125—62no—
338#125—62no—
339#124—62no—
340#124—62no—
341#123—68no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344#121—22no—
345#121—22no—
346#121—62no—
347#121—62no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—34no—
353C4×D4—44no—
354C4×D4—68no—
355C4×D4—62no—
356#117—68no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—21no—
380C2×C42—61no—
381C2×C42#6711yescharacteristic
382C2×C42#6711yescharacteristic
383C2×C42C22×D311yescharacteristic
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#97—62no—
398#97—62no—
399#95—21no—
400#95—21no—
401#95—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3AGL(1,ℤ/8)12yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—22no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—48no—
427C3×D4—41no—
428C3×D4—41no—
429C2×C3×C4—21no—
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—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
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×C4—84no—
458C2×C3×C4#12012yes—
459C2×C3×C4#12012yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466#67—48no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476D12—22no—
477D12—22no—
478D12—41no—
479D12—41no—
480C4×D3—48no—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3⋊C8—22no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C3⋊C8—41no—
489C24—21no—
490C24—61no—
491C24C2×#6711yescharacteristic
492C2×Q8—32no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—32no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—64no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4#23512yes—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—64no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4C2×#6711yescharacteristic
541C22×C4C2×#6711yescharacteristic
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—68no—
547D8—68no—
548C2×C8—32no—
549C2×C8—32no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—32no—
566C4⋊C4—32no—
567C4⋊C4—42no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4#23512yes—
575C22⋊C4—24no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C42—22no—
586C42—22no—
587C42—21no—
588C42—21no—
589C42—42no—
590C42—64no—
591C42D3×D412yes—
592C42D3×D412yes—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57511yescharacteristic
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4#52511yescharacteristic
630C3×C4#52511yescharacteristic
631C3×C4#53211yescharacteristic
632C3×C4#53211yescharacteristic
633Dic3—42no—
634Dic3—42no—
635Dic3—42no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—62no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23#93212yes—
657C23C22×#6711yescharacteristic
658Q8—62no—
659Q8—62no—
660Q8—121no—
661Q8—121no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—62no—
668D4—62no—
669D4—128no—
670D4—121no—
671D4—121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—84no—
704C2×C4—128no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4#93712yes—
712C2×C4#93712yes—
713C2×C4C2×#23511yescharacteristic
714C2×C4C2×#23511yescharacteristic
715C2×C4C2×D3×D411yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4D3×#4111yescharacteristic
718C2×C4D3×#4111yescharacteristic
719C8—62no—
720C8—62no—
721C8—121no—
722C8—121no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3#238811yescharacteristic
726C2×C3#300511yescharacteristic
727C2×C3#300611yescharacteristic
728C2×C3#311111yescharacteristic
729C2×C3#311411yescharacteristic
730C2×C3#318011yescharacteristic
731C2×C3#318311yescharacteristic
732D3—82no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22#579111yescharacteristic
755C22C2×#93211yescharacteristic
756C22C2×#93711yescharacteristic
757C22#582211yescharacteristic
758C22#582211yescharacteristic
759C22#582211yescharacteristic
760C22#583211yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—122no—
770C4—122no—
771C4—122no—
772C4#554711yescharacteristic
773C4#554711yescharacteristic
774C4#554811yescharacteristic
775C4#554811yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—42no—
778C2—82no—
779C2—242no—
780C2#8231111yescharacteristic
781C2#8240011yescharacteristic
782C2#8253011yescharacteristic
783C2#8262411yescharacteristic
784C2#8292811yescharacteristic
785C2#8313911yescharacteristic
786C2#8329311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×#121C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenterC4×#121D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5479C2semidirect
2. C3×C4×#121C2semidirect
3. C2×#5014C2semidirect
4. C2×#5018C2semidirect
5. #71685C2semidirect
7. #71529C2semidirect
8. #69659C2semidirect
9. #69639C2semidirect
10. #69628C2semidirect
11. #69606C2semidirect
12. #69526C2semidirect
13. #69523C2semidirect
14. #69475C2semidirect
15. #69474C2semidirect
67. C4×#121D3semidirect
142. C4×D12D4semidirect
147. C4×Dic6D4semidirect
776. C3#23575semidirect

Maximal subgroups

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

subgroupindex
C2×#54792
C3×C4×#1212
C2×#50142
C2×#50182
#716852
#716842
#715292
#696592
#696392
#696282
#696062
#695262
#695232
#694752
#694742
#235753