Finite Group Databasebeta

← #10943979

Subgroups — #10943979

Order 768.

2008 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic, complemented
3C2×#5150C211yesmaximal, characteristic, complemented
4C2×#4786C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic, complemented
6#76476C211yesmaximal, characteristic, complemented
7C3×#1879C211yesmaximal, characteristic, complemented
8#71613C211yesmaximal, characteristic, complemented
9#70200C211yesmaximal, characteristic, complemented
10#70153C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68880C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32902—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#940C2211yescharacteristic, complemented
22C2×#938C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×C4×#67—21no—
27C22×D24C2211yescharacteristic
28C4×D3×D4—24no—
29C4×D3×D4—24no—
30C2×#895C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#884—21no—
34C2×#884—21no—
35C2×#67⋊C4—21no—
36C2×D3×C22⋊C4—21no—
37C2×C4×D12C2211yescharacteristic
38C2×C42×D3C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic, complemented
41C3×#390C2211yescharacteristic, complemented
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic, complemented
44#5156—24no—
45#5150—24no—
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×Dic3⋊C8C2211yescharacteristic, complemented
52#4975C2211yescharacteristic, complemented
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic, complemented
55#4957—21no—
56#4957—21no—
57#4939C2211yescharacteristic, complemented
58#4786—24no—
59#4773—24no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, complemented
66C22×C4×D4—31no—
67C2×#459—31no—
68C2×#459—31no—
69C2×#447—31no—
70C2×#447—31no—
71#2856—31no—
72#1879—31no—
73#1879—31no—
74#1879—31no—
75#1879D311yescharacteristic, complemented
76#1874—31no—
77#1874—31no—
78#1802—31no—
79#1802—31no—
80#1797—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C23×Dic3—21no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4D414yescomplemented
96C22×D12—21no—
97C22×D12C2311yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—28no—
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3—44no—
104C22×C4×D3—44no—
105C22×C4×D3D411yescharacteristic
106C22×C4×D3D411yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C2×C3×D8—22no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C42C2311yescharacteristic
121C2×#217—21no—
122C2×#217—21no—
123#940—22no—
124#940—22no—
125#938—22no—
126#938—22no—
127D4×Dic3—22no—
128D4×Dic3D414yescomplemented
129C2×#213—22no—
130C2×#213—22no—
131C2×#213—22no—
132C2×#213—22no—
133C2×#213—22no—
134C2×#213—22no—
135C4×#67—28no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×C4×Dic3D411yescharacteristic
147C2×C4×Dic3D411yescharacteristic
148C2×C4×Dic3C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C2×D24—22no—
152C2×D24—22no—
153C2×D24—22no—
154#895—22no—
155#895—22no—
156#893—22no—
157#893D414yescomplemented
158D3×C4⋊C4—22no—
159D3×C4⋊C4—22no—
160#884—44no—
161#884—44no—
162#67⋊C4—28no—
163D3×C22⋊C4—28no—
164C4×D12—22no—
165C4×D12—22no—
166C42×D3—22no—
167C42×D3—22no—
168C3×#102—22no—
169C3×#102—22no—
170#832—22no—
171#832—22no—
172#821—22no—
173#821—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—22no—
176Dic3⋊C8—22no—
177Dic3⋊C8—22no—
178#809—22no—
179#809—22no—
180C23×D4—31no—
181C24×C4—61no—
182C22×D8—31no—
183C22×D8—31no—
184C22×D8—31no—
185C22×D8C2×D311yescharacteristic
186C2×#127—31no—
187C2×#121—31no—
188C2×#121—31no—
189C2×#121—61no—
190C2×#121—61no—
191C2×C4×D4—31no—
192C2×C4×D4—31no—
193C2×C4×D4—31no—
194C2×C4×D4—61no—
195C2×C4×D4—61no—
196C2×C4×D4—64no—
197C2×C4×D4—64no—
198C2×C4×D4C2×D311yescharacteristic
199C22×C4⋊C4—31no—
200C22×C22⋊C4—61no—
201C22×C42—31no—
202#459—64no—
203#459—64no—
204#447—64no—
205#447—64no—
206C2×C4⋊C8—31no—
207C2×C4⋊C8—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102C2×D311yescharacteristic
215C2×#102C2×D311yescharacteristic, complemented
216C2×C22⋊C8—31no—
217C2×C22⋊C8—31no—
218#390—31no—
219#390—61no—
220#390—61no—
221#390C2×D311yescharacteristic, complemented
222#384—31no—
223#340—31no—
224#340—31no—
225#340—31no—
226#340C2×D311yescharacteristic, complemented
227#336—31no—
228#336C2×D311yescharacteristic, complemented
229C24×C3—21no—
230C24×C3—21no—
231C23×D3—24no—
232C23×D3—24no—
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—21no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3C2×D411yescharacteristic
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C2×D412yes—
251C2×C3×D4C2×D412yes—
252C2×C3×D4#4112yes—
253C22×C3×C4—24no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C2×#67—24no—
262C2×#67—24no—
263C2×#67—24no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—42no—
271C2×#67—42no—
272C2×#67—42no—
273C22×Dic3—21no—
274C22×Dic3—24no—
275C22×Dic3—21no—
276C22×Dic3—42no—
277C22×Dic3—42no—
278C22×Dic3C2×D411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281D3×D4—28no—
282D3×D4—28no—
283D3×D4—28no—
284D3×D4—28no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12C2×D412yes—
298C2×D12C2×D412yes—
299C2×D12#4112yes—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—24no—
311C2×C4×D3—432no—
312C2×C4×D3—41no—
313C2×C4×D3—42no—
314C2×C4×D3—42no—
315C2×C4×D3—42no—
316C2×C4×D3—42no—
317C2×C4×D3—42no—
318C2×C4×D3—42no—
319C2×C4×D3D814yescomplemented
320C2×C4×D3C2×D412yes—
321C2×C4×D3#4112yes—
322C3×D8—44no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4C2×D412yes—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C42—21no—
337C3×C42—21no—
338#217—24no—
339#217—42no—
340#213—44no—
341#213—44no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—42no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—42no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3C2×D412yes—
351Dic3⋊C4—24no—
352Dic3⋊C4—42no—
353Dic3⋊C4—42no—
354C4×Dic3—22no—
355C4×Dic3—22no—
356C4×Dic3C2×D412yes—
357C4×Dic3C2×D412yes—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8—21no—
364D24—44no—
365C25—61no—
366C22×D4—34no—
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—61no—
372C22×D4—61no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4C22×D311yescharacteristic
380C22×D4C22×D311yescharacteristic
381C23×C4—21no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—61no—
386C23×C4—61no—
387C23×C4—68no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4—124no—
391C23×C4—124no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—62no—
400C2×D8—62no—
401C2×D8—62no—
402C2×D8—62no—
403C2×D8—62no—
404C22×C8—31no—
405C22×C8—31no—
406C22×C8C22×D311yescharacteristic
407C22×C8C22×D311yescharacteristic
408#127—62no—
409#127—62no—
410#121—62no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—124no—
415#121—124no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—34no—
419C4×D4—34no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C4×D4—62no—
424C4×D4—68no—
425C4×D4—68no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4C22×D311yescharacteristic
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—68no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C22⋊C4—61no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445C2×C22⋊C4—61no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—62no—
450C2×C42—62no—
451C2×C42C22×D311yescharacteristic
452C4⋊C8—62no—
453C4⋊C8—62no—
454#102—22no—
455#102—22no—
456#102—62no—
457#102—62no—
458#102—62no—
459#102—62no—
460#102—62no—
461#102—62no—
462C22⋊C8—62no—
463C22⋊C8—62no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3C22×D411yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—216no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—48no—
488C22×D3—48no—
489C22×D3—48no—
490C22×D3—48no—
491C22×D3—48no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—48no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3#12112yes—
505C22×D3C2×D812yes—
506C22×D3AGL(1,ℤ/8)12yes—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4#12114yescomplemented
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—48no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4C2×D812yes—
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C2×#4111yescharacteristic
532C2×C3×C4C2×#4111yescharacteristic
533C2×C3×C4C2×#4111yescharacteristic
534#67—216no—
535#67—84no—
536#67—84no—
537#67—84no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—22no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—48no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3#12012yes—
550C2×Dic3#12012yes—
551C2×Dic3#12112yes—
552C2×Dic3C2×D812yes—
553C2×Dic3AGL(1,ℤ/8)12yes—
554D12—22no—
555D12—22no—
556D12—22no—
557D12—41no—
558D12—41no—
559D12—41no—
560D12—41no—
561D12—84no—
562D12#12114yescomplemented
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—22no—
566C4×D3—22no—
567C4×D3—28no—
568C4×D3—44no—
569C4×D3—48no—
570C4×D3—48no—
571C4×D3—48no—
572C3×C8—41no—
573C3×C8—41no—
574C3⋊C8—41no—
575C3⋊C8—41no—
576C24—21no—
577C24—21no—
578C24—31no—
579C24—64no—
580C24—64no—
581C24—64no—
582C24—61no—
583C24—61no—
584C24—122no—
585C24—122no—
586C24—122no—
587C24—122no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—32no—
600C2×D4—64no—
601C2×D4—68no—
602C2×D4—68no—
603C2×D4—68no—
604C2×D4—64no—
605C2×D4—64no—
606C2×D4—68no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—122no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4#23512yes—
629C2×D4D3×D412yes—
630C2×D4D3×D412yes—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—34no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—64no—
646C22×C4—62no—
647C22×C4—64no—
648C22×C4—64no—
649C22×C4—64no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—121no—
657C22×C4—122no—
658C22×C4—122no—
659C22×C4—122no—
660C22×C4—122no—
661C22×C4—122no—
662C22×C4—1232no—
663C22×C4—122no—
664C22×C4—122no—
665C22×C4—122no—
666C22×C4D3×D411yescharacteristic
667C22×C4D3×D411yescharacteristic
668C22×C4C23×D311yescharacteristic
669D8—44no—
670D8—124no—
671D8—124no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—32no—
689C4⋊C4—64no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—122no—
694C4⋊C4—122no—
695C4⋊C4D3×D412yes—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—122no—
706C42—21no—
707C42—21no—
708C42—32no—
709C42—32no—
710C42—62no—
711C42—62no—
712C22×C3—24no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3C2×#12011yescharacteristic
727C22×C3C2×#12111yescharacteristic
728C22×C3#52511yescharacteristic
729C22×C3C22×D811yescharacteristic
730C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
731C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
732C22×C3#57511yescharacteristic
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—24no—
740C2×D3—432no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C2×D3—81no—
753C2×D3—81no—
754C2×D3#45914yescomplemented
755C3×C4—22no—
756C3×C4—42no—
757C3×C4—41no—
758C3×C4—81no—
759C3×C4C2×#12111yescharacteristic
760C3×C4C2×#12111yescharacteristic
761C3×C4#52511yescharacteristic
762C3×C4#52511yescharacteristic
763Dic3—22no—
764Dic3—22no—
765Dic3—42no—
766Dic3—81no—
767Dic3#44714yescomplemented
768C23—22no—
769C23—22no—
770C23—22no—
771C23—32no—
772C23—32no—
773C23—32no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—616no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—128no—
794C23—128no—
795C23—128no—
796C23—128no—
797C23—128no—
798C23—128no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—121no—
803C23—121no—
804C23—121no—
805C23—121no—
806C23—121no—
807C23—121no—
808C23—121no—
809C23—121no—
810C23C2×D3×D411yescharacteristic
811D4—22no—
812D4—22no—
813D4—22no—
814D4—34no—
815D4—41no—
816D4—41no—
817D4—41no—
818D4—41no—
819D4—616no—
820D4—62no—
821D4—62no—
822D4—62no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4—244no—
830D4—244no—
831D4#88414yescomplemented
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—48no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—68no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—128no—
860C2×C4—128no—
861C2×C4—128no—
862C2×C4—124no—
863C2×C4—128no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4D3×D812yes—
870C2×C4C2×#23511yescharacteristic
871C2×C4C2×D3×D411yescharacteristic
872C2×C4C2×D3×D411yescharacteristic
873C2×C4C2×D3×D411yescharacteristic
874C2×C4D3×#4111yescharacteristic
875C2×C4D3×#4111yescharacteristic
876C8—41no—
877C8—41no—
878C8—121no—
879C8—121no—
880C2×C3—44no—
881C2×C3—161no—
882C2×C3#284711yescharacteristic
883C2×C3C2×#44711yescharacteristic
884C2×C3#300611yescharacteristic
885C2×C3C2×#45911yescharacteristic
886C2×C3#303611yescharacteristic
887C2×C3#310011yescharacteristic
888C2×C3#310911yescharacteristic
889D3—24no—
890D3—44no—
891D3—161no—
892C22—24no—
893C22—34no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—64no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—1232no—
915C22—122no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—241no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22—241no—
927C22—241no—
928C22#554711yescharacteristic
929C22D3×#12011yescharacteristic
930C22D3×#12111yescharacteristic
931C22C2×D3×D811yescharacteristic
932C22#576811yescharacteristic
933C22D3×AGL(1,ℤ/8)11yescharacteristic
934C22D3×AGL(1,ℤ/8)11yescharacteristic
935C4—22no—
936C4—34no—
937C4—42no—
938C4—41no—
939C4—62no—
940C4—62no—
941C4—81no—
942C4—122no—
943C4—241no—
944C4C2×#88411yescharacteristic
945C4#554711yescharacteristic
946C4D3×#12111yescharacteristic
947C4#565611yescharacteristic
948C3#3290211yescharacteristic, complemented, Sylow
949C2—44no—
950C2—64no—
951C2—124no—
952C2—161no—
953C2—481no—
954C2#7493511yescharacteristic
955C2#7959011yescharacteristic
956C2#7986911yescharacteristic
957C2D3×#44711yescharacteristic
958C2#8008411yescharacteristic
959C2D3×#45911yescharacteristic
960C2#8053411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
hypercenter#1879D3
hypocenterC3#32902
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×#5156C2semidirect
3. C2×#5150C2semidirect
4. C2×#4786C2semidirect
5. C2×#4773C2semidirect
6. #76476C2semidirect
7. C3×#1879C2semidirect
8. #71613C2semidirect
9. #70200C2semidirect
10. #70153C2semidirect
11. #69657C2semidirect
12. #68892C2semidirect
13. #68880C2semidirect
14. #68673C2semidirect
15. #68662C2semidirect
21. C2×#940C22semidirect
40. C2×C3×#102C22semidirect
41. C3×#390C22semidirect
43. C2×#832C22semidirect
47. C2×#821C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×Dic3⋊C8C22semidirect
52. #4975C22semidirect
54. C2×#809C22semidirect
57. #4939C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
75. #1879D3semidirect
95. C2×D3×D4D4semidirect
128. D4×Dic3D4semidirect
157. #893D4semidirect
215. C2×#102C2×D3semidirect
221. #390C2×D3semidirect
226. #340C2×D3semidirect
228. #336C2×D3semidirect
319. C2×C4×D3D8semidirect
514. C3×D4#121semidirect
562. D12#121semidirect
754. C2×D3#459semidirect
767. Dic3#447semidirect
831. D4#884semidirect
948. C3#32902semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
C2×#51562
C2×#51502
C2×#47862
C2×#47732
#764762
C3×#18792
#716132
#702002
#701532
#696572
#688922
#688802
#686732
#686622
#329023