Finite Group Databasebeta

← #10943995

Subgroups — #10943995

Order 768.

1608 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C2×#5238C211yesmaximal, characteristic, complemented
4C2×#5163C211yesmaximal, characteristic, complemented
5C2×#5150C211yesmaximal, characteristic, complemented
6#82700C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71678C211yesmaximal, characteristic, complemented
10#70240C211yesmaximal, characteristic, complemented
11#70221C211yesmaximal, characteristic, complemented
12#70172C211yesmaximal, characteristic, complemented
13#70153C211yesmaximal, characteristic, complemented
14#69933C211yesmaximal, characteristic, complemented
15#69908C211yesmaximal, characteristic, complemented
16#32904—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21Dic3×#41—24no—
22Dic3×#41—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C22×#215C2211yescharacteristic
26C2×#940C2211yescharacteristic
27C2×#939—21no—
28C2×#939—21no—
29C2×D4×Dic3—21no—
30C2×D4×Dic3—21no—
31C2×D4×Dic3C2211yescharacteristic
32C2×D4×Dic3C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×#926—21no—
36C2×#926C2211yescharacteristic
37C22×C4×Dic3—21no—
38C22×C4×Dic3C2211yescharacteristic
39C3×#449—24no—
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic
43#5238—24no—
44C2×#835C2211yescharacteristic
45#5221C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#830C2211yescharacteristic
50#5163—24no—
51#5150—24no—
52C2×#821C2211yescharacteristic
53C2×#821C2211yescharacteristic
54C2×Dic3⋊C8C2211yescharacteristic
55C2×Dic3⋊C8C2211yescharacteristic
56#4988C2211yescharacteristic
57#4975C2211yescharacteristic
58#4957—21no—
59#4957—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×C4×#41—31no—
67C2×#460—31no—
68C2×#459—31no—
69C2×#449—31no—
70C2×#449D311yescharacteristic, complemented
71#2856—31no—
72#1880—31no—
73#1880—31no—
74#1879—31no—
75#1879—31no—
76#1875—31no—
77#1875—31no—
78#1803—31no—
79#1802—31no—
80#1797—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yescomplemented
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C22×#67—21no—
97C23×Dic3—21no—
98C23×Dic3—21no—
99C23×Dic3D411yescharacteristic
100C23×Dic3D411yescharacteristic
101C22×D12C2311yescharacteristic
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—22no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×#121—22no—
111C3×#121—22no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119Q8×Dic3—22no—
120Q8×Dic3—22no—
121Q8×Dic3—22no—
122Q8×Dic3D414yescomplemented
123C2×#215—22no—
124C2×#215—22no—
125C2×#215—22no—
126#940—22no—
127#940—22no—
128#939—44no—
129#939—44no—
130D4×Dic3—28no—
131D4×Dic3—28no—
132D4×Dic3—22no—
133D4×Dic3—22no—
134D4×Dic3—22no—
135D4×Dic3D414yescomplemented
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—22no—
139#930—22no—
140#930—22no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144#926—28no—
145#926—22no—
146#926—22no—
147C2×C4⋊Dic3—21no—
148C2×C4⋊Dic3—21no—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—21no—
154C2×C4×Dic3—28no—
155C2×C4×Dic3—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3D411yescharacteristic
161C2×C4×Dic3D411yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164C22×C3⋊C8C2311yescharacteristic
165C22×C3⋊C8C2311yescharacteristic
166C3×#103—22no—
167C3×#102—22no—
168C3×C22⋊C8—22no—
169#835—22no—
170#832—22no—
171#832—22no—
172#832—22no—
173#830—22no—
174#821—22no—
175#821—22no—
176Dic3⋊C8—22no—
177Dic3⋊C8—22no—
178C22×#41C2×D311yescharacteristic
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C22×D8—31no—
182C22×D8C2×D311yescharacteristic
183C2×#127—31no—
184C2×#121—31no—
185C2×#121—61no—
186C2×#121—61no—
187C2×#121C2×D311yescharacteristic
188C4×#41—64no—
189C4×#41—64no—
190C2×C4×Q8—31no—
191C2×C4×Q8—31no—
192C2×C4×D4—31no—
193C2×C4×D4—31no—
194C2×C4×D4—61no—
195C2×C4×D4—61no—
196C2×#117—31no—
197C2×#117—61no—
198C22×C42—31no—
199C22×C42—61no—
200#460—64no—
201#459—64no—
202#449—24no—
203#449—64no—
204C2×C4⋊C8—31no—
205C2×C4⋊C8—31no—
206C2×#103—31no—
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102C2×D311yescharacteristic
214C2×C22⋊C8—31no—
215C2×C22⋊C8C2×D311yescharacteristic
216#390—31no—
217#390—31no—
218#390—61no—
219#390—61no—
220#384—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224#340—31no—
225#336—31no—
226#336—31no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3C2×D411yescharacteristic
230C23×D3—21no—
231C3×#41—28no—
232C3×#41—28no—
233C3×#41—28no—
234C3×#41—28no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8C2×D412yes—
239C2×C3×Q8C2×D412yes—
240C2×C3×Q8#4112yes—
241C2×C3×D4—24no—
242C2×C3×D4—24no—
243C2×C3×D4—24no—
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×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C2×C3×D4—42no—
256C2×C3×D4C2×D412yes—
257C2×C3×D4C2×D412yes—
258C2×C3×D4#4112yes—
259C22×C3×C4—24no—
260C22×C3×C4—24no—
261C22×C3×C4—21no—
262C22×C3×C4—24no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D412yes—
270C22×C3×C4#4112yes—
271C22×C3×C4C2411yescharacteristic
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—42no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—42no—
281C22×Dic3—24no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—24no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—21no—
291C22×Dic3—41no—
292C22×Dic3—42no—
293C22×Dic3—42no—
294C22×Dic3—42no—
295C22×Dic3—42no—
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299C22×Dic3C2×D411yescharacteristic
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C3×SD16—44no—
307C3×D8—44no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C22⋊C4—42no—
317#217—24no—
318#217—24no—
319#217—24no—
320#217—42no—
321#217—42no—
322#215—44no—
323#213—44no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327C4⋊Dic3—24no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—24no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3C2×D412yes—
334C4⋊Dic3C2×D412yes—
335Dic3⋊C4—42no—
336Dic3⋊C4—42no—
337C4×Dic3—24no—
338C4×Dic3—24no—
339C4×Dic3—21no—
340C4×Dic3—21no—
341C4×Dic3—22no—
342C4×Dic3—24no—
343C4×Dic3—22no—
344C4×Dic3C2×D412yes—
345C4×Dic3C2×D412yes—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41#6714yescomplemented
358C22×Q8C22×D311yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—31no—
362C22×D4—61no—
363C22×D4—61no—
364C22×D4—61no—
365C22×D4C22×D311yescharacteristic
366C22×D4C22×D311yescharacteristic
367C23×C4—21no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4C22×D311yescharacteristic
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—62no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×D8—22no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8—62no—
383C2×D8—62no—
384C2×D8—62no—
385C22×C8—31no—
386C22×C8—31no—
387C22×C8C22×D311yescharacteristic
388C22×C8C22×D311yescharacteristic
389#127—62no—
390#127—62no—
391#121—22no—
392#121—22no—
393#121—62no—
394#121—62no—
395#121—124no—
396#121—124no—
397C4×Q8—34no—
398C4×Q8—62no—
399C4×Q8—62no—
400C4×Q8—62no—
401C4×D4—34no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—68no—
405C4×D4—68no—
406C4×D4—62no—
407#117—62no—
408#117—62no—
409#117—68no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—62no—
433C2×C42—61no—
434C2×C42—61no—
435C2×C42—68no—
436C2×C42—61no—
437C4⋊C8—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—62no—
441#102—22no—
442#102—62no—
443#102—62no—
444#102—62no—
445#102—62no—
446#102—62no—
447C22⋊C8—22no—
448C22⋊C8—62no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3#12112yes—
470C23×C3C22×D411yescharacteristic
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8#12114yescomplemented
482C3×D4—216no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—84no—
491C3×D4#12114yescomplemented
492C2×C3×C4—216no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4#12112yes—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C2×#4111yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512#67—84no—
513#67—84no—
514#67—84no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—44no—
525C2×Dic3—48no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—44no—
531C2×Dic3—48no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3#12012yes—
536C2×Dic3#12012yes—
537C2×Dic3#13512yes—
538C2×Dic3AGL(1,ℤ/8)12yes—
539C2×Dic3AGL(1,ℤ/8)12yes—
540D12—41no—
541D12—41no—
542D12—41no—
543D12—41no—
544C3×C8—41no—
545C3×C8—41no—
546C3⋊C8—41no—
547C3⋊C8—41no—
548C24—21no—
549C24—21no—
550C24—61no—
551C24D3×D411yescharacteristic
552#41—28no—
553#41—28no—
554#41—28no—
555#41—28no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8D3×D412yes—
560C2×Q8#23712yes—
561C2×Q8C2×#6712yes—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4D3×D412yes—
593C2×D4#23712yes—
594C2×D4C2×#6712yes—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—64no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—64no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—121no—
622C22×C4—122no—
623C22×C4D3×D411yescharacteristic
624C22×C4#23712yes—
625C22×C4C2×#6712yes—
626C22×C4C23×D311yescharacteristic
627SD16—44no—
628SD16—124no—
629D8—44no—
630D8—124no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—61no—
638C2×C8—61no—
639C2×C8—61no—
640C2×C8—61no—
641C2×C8—61no—
642C2×C8—61no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—32no—
646C4⋊C4—32no—
647C4⋊C4—64no—
648C4⋊C4—64no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—122no—
654C4⋊C4—122no—
655C22⋊C4—42no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—122no—
664C42—32no—
665C42—32no—
666C42—62no—
667C42—62no—
668C42—64no—
669C42—64no—
670C42—64no—
671C42—61no—
672C42—61no—
673C22×C3—22no—
674C22×C3—24no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—41no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—42no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—41no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3C2×#12011yescharacteristic
695C22×C3C2×#12111yescharacteristic
696C22×C3#52511yescharacteristic
697C22×C3C2×#13511yescharacteristic
698C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
699C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
700C22×C3#57511yescharacteristic
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3—81no—
706C2×D3—81no—
707C2×D3—81no—
708C3×C4—22no—
709C3×C4—24no—
710C3×C4—81no—
711C3×C4C2×#12111yescharacteristic
712C3×C4C2×#12111yescharacteristic
713C3×C4#52511yescharacteristic
714C3×C4#52511yescharacteristic
715Dic3—22no—
716Dic3—22no—
717Dic3—41no—
718Dic3—42no—
719Dic3—42no—
720Dic3—81no—
721Dic3#44914yescomplemented
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23—121no—
749C23#93912yes—
750C23C2×D3×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8#93914yescomplemented
755D4—216no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—84no—
764D4—121no—
765D4—121no—
766D4—121no—
767D4—121no—
768D4—244no—
769D4—244no—
770D4—244no—
771D4#93914yescomplemented
772C2×C4—216no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—61no—
799C2×C4—124no—
800C2×C4—128no—
801C2×C4—124no—
802C2×C4—128no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4#93912yes—
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×#23711yescharacteristic
814C2×C4C2×#23711yescharacteristic
815C2×C4C2×#23711yescharacteristic
816C2×C4C22×#6711yescharacteristic
817C8—41no—
818C8—41no—
819C8—121no—
820C8—121no—
821C2×C3—42no—
822C2×C3—44no—
823C2×C3—161no—
824C2×C3#284711yescharacteristic
825C2×C3C2×#44911yescharacteristic
826C2×C3#300611yescharacteristic
827C2×C3#303511yescharacteristic
828C2×C3#303811yescharacteristic
829C2×C3#310611yescharacteristic
830C2×C3#311511yescharacteristic
831D3—161no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—22no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—241no—
854C22—241no—
855C22—241no—
856C22—241no—
857C22—241no—
858C22—241no—
859C22—241no—
860C22#558611yescharacteristic
861C22D3×#12011yescharacteristic
862C22D3×#13511yescharacteristic
863C22#576811yescharacteristic
864C22D3×AGL(1,ℤ/8)11yescharacteristic
865C22D3×AGL(1,ℤ/8)11yescharacteristic
866C22C2×#93911yescharacteristic
867C4—22no—
868C4—24no—
869C4—34no—
870C4—62no—
871C4—62no—
872C4—81no—
873C4—121no—
874C4—122no—
875C4—122no—
876C4—241no—
877C4#558611yescharacteristic
878C4#558611yescharacteristic
879C4C2×#93911yescharacteristic
880C4C2×#93911yescharacteristic
881C3#3290411yescharacteristic, complemented, Sylow
882C2—42no—
883C2—44no—
884C2—161no—
885C2—481no—
886C2#8006911yescharacteristic
887C2#8007111yescharacteristic
888C2D3×#44911yescharacteristic
889C2#8008411yescharacteristic
890C2#8260111yescharacteristic
891C2#8390011yescharacteristic
892C2#8393211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#32904
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×#41C2semidirect
2. C2×C3×#449C2semidirect
3. C2×#5238C2semidirect
4. C2×#5163C2semidirect
5. C2×#5150C2semidirect
6. #82700C2semidirect
7. #72048C2semidirect
8. #72037C2semidirect
9. #71678C2semidirect
10. #70240C2semidirect
11. #70221C2semidirect
12. #70172C2semidirect
13. #70153C2semidirect
14. #69933C2semidirect
15. #69908C2semidirect
70. C2×#449D3semidirect
86. C2×C3×#41D4semidirect
122. Q8×Dic3D4semidirect
135. D4×Dic3D4semidirect
357. C2×#41#67semidirect
481. C3×Q8#121semidirect
491. C3×D4#121semidirect
721. Dic3#449semidirect
754. Q8#939semidirect
771. D4#939semidirect
881. C3#32904semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#412
C2×C3×#4492
C2×#52382
C2×#51632
C2×#51502
#827002
#720482
#720372
#716782
#702402
#702212
#701722
#701532
#699332
#699082
#329043