Finite Group Databasebeta

← #10826218

Subgroups — #10826218

Order 768.

2096 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5829C211yesmaximal, characteristic, complemented
2C22×D3×D8C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5169C211yesmaximal, characteristic, complemented
6#82640C211yesmaximal, characteristic, complemented
7#72055C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70277C211yesmaximal, characteristic, complemented
11#70270C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#70172C211yesmaximal, characteristic, complemented
14#69961C211yesmaximal, characteristic, complemented
15#69957C211yesmaximal, characteristic, complemented
16#23851—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18C22×D3×D4C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic, complemented
21C22×C3×D8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic, complemented
23#5829—24no—
24#5829—24no—
25C2×#947C2211yescharacteristic, complemented
26C2×#946C2211yescharacteristic
27C22×#215C2211yescharacteristic, complemented
28C2×#939—21no—
29C2×#937—21no—
30C2×#937—21no—
31C2×D4×Dic3C2211yescharacteristic, complemented
32C22×#213C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×#930C2211yescharacteristic, complemented
35C2×#930C2211yescharacteristic, complemented
36C2×#929—21no—
37C2×C4×#67C2211yescharacteristic
38C22×(C2×D3)⋊C4—21no—
39C2×D3×D8—24no—
40C2×D3×D8—24no—
41C2×D3×D8—24no—
42C22×D24C2211yescharacteristic
43C22×D3×C8C2211yescharacteristic
44C3×#449—24no—
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×C22⋊C8C2211yescharacteristic, complemented
48#5238—24no—
49C2×#835C2211yescharacteristic, complemented
50#5223—21no—
51#5221C2211yescharacteristic, complemented
52C2×#832C2211yescharacteristic, complemented
53C2×#832C2211yescharacteristic, complemented
54C2×#830C2211yescharacteristic, complemented
55#5169—24no—
56C2×#821C2211yescharacteristic, complemented
57C2×#821C2211yescharacteristic, complemented
58C2×(C2×D3)⋊C8C2211yescharacteristic
59#4988C2211yescharacteristic, complemented
60#4987C2211yescharacteristic
61C2×#809C2211yescharacteristic, complemented
62#4959—21no—
63#4955—21no—
64#4551C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C23×D8—31no—
69C2×#546—31no—
70C2×#449—31no—
71C2×#449D311yescharacteristic, complemented
72C2×#450—31no—
73#2408—31no—
74#2012—31no—
75#2012—31no—
76#1999—31no—
77#1999—31no—
78#1892—31no—
79#1879—31no—
80#1879—31no—
81#1869—31no—
82#1786—31no—
83C24×D3—21no—
84C24×D3—21no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67D411yescharacteristic
103C23×Dic3—21no—
104C2×D3×D4—22no—
105C2×D3×D4—22no—
106C2×D3×D4—22no—
107C2×D3×D4—22no—
108C2×D3×D4—22no—
109C2×D3×D4—22no—
110C2×D3×D4—22no—
111C2×D3×D4—41no—
112C2×D3×D4—41no—
113C2×D3×D4—41no—
114C2×D3×D4—41no—
115C2×D3×D4D414yescomplemented
116C22×D12C2311yescharacteristic
117C22×D12C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—41no—
122C2×C3×D8—22no—
123C2×C3×D8—22no—
124C2×C3×D8D414yescomplemented
125C22×C3×C8C2311yescharacteristic
126C22×C3×C8C2311yescharacteristic
127C3×#121—22no—
128C3×#121—41no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217D411yescharacteristic
135#947—22no—
136#947—22no—
137#946—22no—
138#946D414yescomplemented
139C2×#215—22no—
140C2×#215—22no—
141C2×#215—41no—
142#939—28no—
143#937—28no—
144#937—44no—
145D4×Dic3—22no—
146D4×Dic3—22no—
147C2×#213—22no—
148C2×#213—22no—
149C2×#213—22no—
150C2×#213—22no—
151C2×#213—22no—
152C2×#213D414yescomplemented
153#930—22no—
154#930—22no—
155#930—22no—
156#930—41no—
157#929—28no—
158C4×#67—22no—
159C4×#67—22no—
160C2×(C2×D3)⋊C4—28no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169C2×(C2×D3)⋊C4D411yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2311yescharacteristic
172C2×Dic3⋊C4—21no—
173C2×Dic3⋊C4D411yescharacteristic
174C2×C4×Dic3C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177D3×D8—232no—
178C2×D24—22no—
179C2×D24—22no—
180C2×D24—22no—
181C2×D3×C8—22no—
182C2×D3×C8—22no—
183C2×D3×C8—22no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#832—22no—
189#832—22no—
190C3⋊#95—21no—
191#830—22no—
192#821—22no—
193#821—41no—
194(C2×D3)⋊C8—22no—
195#809—41no—
196C22×#41C2×D311yescharacteristic, complemented
197C23×D4—31no—
198C23×D4—31no—
199C22×SD16—31no—
200C22×SD16C2×D311yescharacteristic, complemented
201C22×D8—31no—
202C22×D8—31no—
203C22×D8—31no—
204C22×D8—64no—
205C22×D8—64no—
206C22×D8—64no—
207C22×D8C2×D311yescharacteristic
208C23×C8—31no—
209#546—64no—
210#546—64no—
211C2×#124—31no—
212C2×#123—61no—
213C2×C22⋊Q8—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#121—61no—
217C2×#121C2×D311yescharacteristic, complemented
218C2×#120—61no—
219C2×#120—61no—
220C2×C4×D4—31no—
221C2×C4×D4—31no—
222C22×C22⋊C4—61no—
223#450—64no—
224#449—24no—
225#449—64no—
226C2×#103—31no—
227C2×#103C2×D311yescharacteristic, complemented
228C2×#102—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×#102—31no—
233C2×#102C2×D311yescharacteristic, complemented
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8C2×D311yescharacteristic, complemented
237#394—61no—
238#392—61no—
239#390—31no—
240#390—31no—
241#380—31no—
242#379—61no—
243#340—31no—
244#340—31no—
245#336—31no—
246#336—31no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3C2×D411yescharacteristic
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—24no—
253C23×D3—42no—
254C23×D3—42no—
255C23×D3—42no—
256C23×D3—42no—
257C23×D3—42no—
258C23×D3—42no—
259C23×D3—42no—
260C23×D3—42no—
261C23×D3—42no—
262C23×D3—81no—
263C23×D3—81no—
264C23×D3—81no—
265C23×D3—81no—
266C23×D3C2×D411yescharacteristic
267C3×#41—44no—
268C3×#41—44no—
269C3×#41—44no—
270C3×#41—44no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8C2×D412yes—
277C2×C3×D4—24no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—42no—
290C2×C3×D4—81no—
291C2×C3×D4C2×D412yes—
292C2×C3×D4C2×D412yes—
293C2×C3×D4C2×D412yes—
294C2×C3×D4C2×D412yes—
295C22×C3×C4—24no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C2×#67—22no—
309C2×#67—22no—
310C2×#67—22no—
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—42no—
314C2×#67—42no—
315C2×#67—42no—
316C2×#67—42no—
317C2×#67—42no—
318C2×#67—42no—
319C2×#67—42no—
320C2×#67—81no—
321C2×#67—81no—
322C2×#67—81no—
323C22×Dic3—21no—
324C22×Dic3—24no—
325C22×Dic3—21no—
326C22×Dic3—81no—
327C22×Dic3—81no—
328C22×Dic3C2×D411yescharacteristic
329C22×Dic3C2×D411yescharacteristic
330C22×Dic3C2×D411yescharacteristic
331D3×D4—28no—
332D3×D4—28no—
333D3×D4—44no—
334D3×D4—44no—
335D3×D4—44no—
336D3×D4—44no—
337D3×D4—44no—
338D3×D4—44no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12—21no—
348C2×D12—21no—
349C2×D12C2×D412yes—
350C2×D12C2×D412yes—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3C2×D412yes—
356C2×C4×D3C2×D412yes—
357C3×SD16—44no—
358C3×D8—28no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8C2×D412yes—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C22⋊C4—42no—
368#217—24no—
369#217—22no—
370#217—42no—
371#217—81no—
372#215—44no—
373#213—28no—
374#213—28no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—22no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—42no—
381(C2×D3)⋊C4—42no—
382(C2×D3)⋊C4—42no—
383(C2×D3)⋊C4—81no—
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3—21no—
387C4⋊Dic3C2×D412yes—
388Dic3⋊C4—24no—
389Dic3⋊C4—22no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8C2×D412yes—
398D24—28no—
399D3×C8—28no—
400C25—61no—
401C25—61no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—41no—
407C2×#41—41no—
408C22×Q8C22×D311yescharacteristic
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—34no—
412C22×D4—31no—
413C22×D4—31no—
414C22×D4—31no—
415C22×D4—62no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—61no—
425C22×D4—61no—
426C22×D4—121no—
427C22×D4—121no—
428C22×D4—121no—
429C22×D4—121no—
430C22×D4C22×D311yescharacteristic
431C22×D4C22×D311yescharacteristic
432C23×C4—21no—
433C23×C4—31no—
434C23×C4—61no—
435C23×C4C22×D311yescharacteristic
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—41no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—121no—
442C2×D8—22no—
443C2×D8—22no—
444C2×D8—34no—
445C2×D8—62no—
446C2×D8—62no—
447C2×D8—62no—
448C2×D8—632no—
449C2×D8—62no—
450C2×D8—62no—
451C2×D8—62no—
452C2×D8—62no—
453C2×D8—62no—
454C2×D8#6714yescomplemented
455C22×C8—31no—
456C22×C8—31no—
457C22×C8—62no—
458C22×C8—62no—
459C22×C8—62no—
460C22×C8C22×D311yescharacteristic
461C22×C8C22×D311yescharacteristic
462#124—62no—
463#124—62no—
464#123—68no—
465C22⋊Q8—34no—
466C22⋊Q8—62no—
467#121—22no—
468#121—41no—
469#121—62no—
470#121—62no—
471#121—68no—
472#121—62no—
473#121—121no—
474#120—68no—
475#120—124no—
476C4×D4—62no—
477C4×D4—62no—
478C4×D4—62no—
479C4×D4—62no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—68no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C22⋊C4—61no—
498C2×C22⋊C4—61no—
499C2×C22⋊C4—61no—
500C2×C42—31no—
501#103—22no—
502#103—62no—
503#102—22no—
504#102—62no—
505#102—62no—
506#102—62no—
507#102—121no—
508#102—121no—
509C22⋊C8—22no—
510C22⋊C8—62no—
511C22⋊C8—62no—
512#95—61no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—22no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3C22×D411yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—48no—
542C22×D3—48no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—48no—
556C22×D3—84no—
557C22×D3—84no—
558C22×D3—84no—
559C22×D3—84no—
560C22×D3—84no—
561C22×D3—84no—
562C22×D3—84no—
563C22×D3—84no—
564C22×D3—84no—
565C22×D3—84no—
566C22×D3—84no—
567C22×D3#12012yes—
568C22×D3#13512yes—
569C22×D3AGL(1,ℤ/8)12yes—
570C3×Q8—22no—
571C3×Q8—22no—
572C3×Q8—41no—
573C3×Q8—41no—
574C3×D4—22no—
575C3×D4—22no—
576C3×D4—22no—
577C3×D4—22no—
578C3×D4—22no—
579C3×D4—48no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—84no—
583C3×D4#12014yescomplemented
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—48no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4H(5,𝔽2)11yescharacteristic
603C2×C3×C4H(5,𝔽2)11yescharacteristic
604#67—48no—
605#67—48no—
606#67—44no—
607#67—84no—
608#67—84no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—22no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—84no—
624C2×Dic3#12012yes—
625D12—22no—
626D12—22no—
627D12—22no—
628D12—22no—
629D12—41no—
630D12—41no—
631D12—41no—
632D12—41no—
633C4×D3—22no—
634C4×D3—22no—
635C4×D3—22no—
636C4×D3—22no—
637C3×C8—22no—
638C3×C8—41no—
639C3⋊C8—22no—
640C3⋊C8—41no—
641C24—21no—
642C24—21no—
643C24—31no—
644C24—64no—
645C24—61no—
646C24—61no—
647C24—122no—
648C24—122no—
649C24—122no—
650C24—122no—
651C24—122no—
652C24—122no—
653C24—122no—
654C24—122no—
655C24—122no—
656C24—241no—
657C24—241no—
658C24—241no—
659C24—241no—
660C24D3×D411yescharacteristic
661#41—44no—
662#41—44no—
663#41—44no—
664#41—44no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8D3×D412yes—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—32no—
681C2×D4—32no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—64no—
687C2×D4—68no—
688C2×D4—68no—
689C2×D4—62no—
690C2×D4—62no—
691C2×D4—62no—
692C2×D4—64no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—61no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—81no—
704C2×D4—122no—
705C2×D4—124no—
706C2×D4—124no—
707C2×D4—124no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—122no—
712C2×D4—122no—
713C2×D4—122no—
714C2×D4—122no—
715C2×D4—122no—
716C2×D4—122no—
717C2×D4—241no—
718C2×D4—241no—
719C2×D4—241no—
720C2×D4D3×D412yes—
721C2×D4D3×D412yes—
722C2×D4C2×#6712yes—
723C2×D4C2×#6712yes—
724C22×C4—24no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—31no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—64no—
746C22×C4—61no—
747C22×C4—241no—
748C22×C4—241no—
749C22×C4D3×D411yescharacteristic
750C22×C4C23×D311yescharacteristic
751SD16—44no—
752SD16—124no—
753D8—28no—
754D8—68no—
755D8—68no—
756D8—68no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—32no—
763C2×C8—68no—
764C2×C8—61no—
765C2×C8—61no—
766C2×C8—61no—
767C2×C8—61no—
768C2×C8—61no—
769C2×C8C2×#6712yes—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—32no—
773C4⋊C4—62no—
774C4⋊C4—64no—
775C4⋊C4—61no—
776C4⋊C4—61no—
777C4⋊C4—61no—
778C22⋊C4—42no—
779C22⋊C4—62no—
780C22⋊C4—64no—
781C22⋊C4—64no—
782C22⋊C4—64no—
783C22⋊C4—64no—
784C22⋊C4—62no—
785C22⋊C4—64no—
786C22⋊C4—122no—
787C22⋊C4—122no—
788C22⋊C4—122no—
789C22⋊C4—122no—
790C22⋊C4—241no—
791C22⋊C4—241no—
792C42—61no—
793C42—61no—
794C22×C3—24no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3C2×#12011yescharacteristic
816C22×C3D4211yescharacteristic
817C22×C3D4211yescharacteristic
818C22×C3C2×#13511yescharacteristic
819C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
820C22×C3#57611yescharacteristic
821C22×C3#57611yescharacteristic
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—42no—
832C2×D3—42no—
833C2×D3—42no—
834C2×D3—816no—
835C2×D3—816no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C2×D3—81no—
840C2×D3—81no—
841C2×D3—81no—
842C2×D3—81no—
843C2×D3—81no—
844C2×D3#44914yescomplemented
845C3×C4—41no—
846C3×C4—42no—
847C3×C4—81no—
848C3×C4C2×#12011yescharacteristic
849C3×C4#53411yescharacteristic
850C3×C4D4211yescharacteristic
851C3×C4D4211yescharacteristic
852Dic3—22no—
853Dic3—41no—
854Dic3—41no—
855Dic3—42no—
856Dic3—81no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—32no—
869C23—32no—
870C23—32no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—62no—
886C23—62no—
887C23—128no—
888C23—128no—
889C23—128no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—244no—
903C23—244no—
904C23—244no—
905C23—244no—
906C23—244no—
907C23—244no—
908C23—244no—
909C23—244no—
910C23—244no—
911C23—244no—
912C23—244no—
913C23C2×D3×D411yescharacteristic
914Q8—22no—
915Q8—22no—
916Q8—41no—
917Q8—41no—
918D4—22no—
919D4—22no—
920D4—22no—
921D4—22no—
922D4—22no—
923D4—48no—
924D4—41no—
925D4—41no—
926D4—62no—
927D4—62no—
928D4—62no—
929D4—62no—
930D4—84no—
931D4—128no—
932D4—128no—
933D4—124no—
934D4—121no—
935D4—121no—
936D4—121no—
937D4—121no—
938D4—244no—
939D4—244no—
940D4#93714yescomplemented
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—32no—
946C2×C4—48no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—62no—
969C2×C4—121no—
970C2×C4—121no—
971C2×C4—121no—
972C2×C4—121no—
973C2×C4—121no—
974C2×C4—244no—
975C2×C4C2×D3×D411yescharacteristic
976C2×C4C2×D3×D411yescharacteristic
977C2×C4C2×D3×D411yescharacteristic
978C2×C4#100411yescharacteristic
979C2×C4#100411yescharacteristic
980C2×C4C22×#6711yescharacteristic
981C8—22no—
982C8—41no—
983C8—62no—
984C8—121no—
985C2×C3—44no—
986C2×C3—82no—
987C2×C3—81no—
988C2×C3#240311yescharacteristic
989C2×C3C2×#44911yescharacteristic
990C2×C3#300811yescharacteristic
991C2×C3#326411yescharacteristic
992C2×C3#326411yescharacteristic
993C2×C3#328011yescharacteristic
994C2×C3#328011yescharacteristic
995D3—24no—
996D3—82no—
997D3—82no—
998C22—24no—
999C22—34no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—41no—
1007C22—42no—
1008C22—41no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—42no—
1015C22—41no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—81no—
1026C22—122no—
1027C22—122no—
1028C22—122no—
1029C22—122no—
1030C22—122no—
1031C22—122no—
1032C22—2416no—
1033C22—2416no—
1034C22—241no—
1035C22—241no—
1036C22—241no—
1037C22—241no—
1038C22—241no—
1039C22—241no—
1040C22—241no—
1041C22—241no—
1042C22D3×#12011yescharacteristic
1043C22#559011yescharacteristic
1044C22D3×#13511yescharacteristic
1045C22#576911yescharacteristic
1046C22D3×AGL(1,ℤ/8)11yescharacteristic
1047C22#577411yescharacteristic
1048C22D4×#6711yescharacteristic
1049C4—41no—
1050C4—42no—
1051C4—62no—
1052C4—81no—
1053C4—121no—
1054C4—121no—
1055C4—122no—
1056C4—241no—
1057C4#558911yescharacteristic
1058C4#559011yescharacteristic
1059C4C2×#93711yescharacteristic
1060C4D4×#6711yescharacteristic
1061C3#2385111yescharacteristic, complemented, Sylow
1062C2—44no—
1063C2—64no—
1064C2—81no—
1065C2—82no—
1066C2—242no—
1067C2—242no—
1068C2D3×#44911yescharacteristic
1069C2#8008511yescharacteristic
1070C2#8010111yescharacteristic
1071C2#8012011yescharacteristic
1072C2#8260411yescharacteristic
1073C2#8391811yescharacteristic
1074C2#8395211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23851
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×#5829C2semidirect
2. C22×D3×D8C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5238C2semidirect
5. C2×#5169C2semidirect
6. #82640C2semidirect
7. #72055C2semidirect
8. #72037C2semidirect
9. #71684C2semidirect
10. #70277C2semidirect
11. #70270C2semidirect
12. #70198C2semidirect
13. #70172C2semidirect
14. #69961C2semidirect
15. #69957C2semidirect
17. C22×C3×#41C22semidirect
20. C22×C3×SD16C22semidirect
22. C2×C3×#121C22semidirect
25. C2×#947C22semidirect
27. C22×#215C22semidirect
31. C2×D4×Dic3C22semidirect
34. C2×#930C22semidirect
35. C2×#930C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×C22⋊C8C22semidirect
49. C2×#835C22semidirect
51. #5221C22semidirect
52. C2×#832C22semidirect
53. C2×#832C22semidirect
54. C2×#830C22semidirect
56. C2×#821C22semidirect
57. C2×#821C22semidirect
59. #4988C22semidirect
61. C2×#809C22semidirect
64. #4551C22semidirect
65. #4550C22semidirect
66. #4550C22semidirect
67. #4529C22semidirect
71. C2×#449D3semidirect
115. C2×D3×D4D4semidirect
124. C2×C3×D8D4semidirect
138. #946D4semidirect
152. C2×#213D4semidirect
196. C22×#41C2×D3semidirect
200. C22×SD16C2×D3semidirect
217. C2×#121C2×D3semidirect
227. C2×#103C2×D3semidirect
233. C2×#102C2×D3semidirect
236. C2×C22⋊C8C2×D3semidirect
454. C2×D8#67semidirect
583. C3×D4#120semidirect
844. C2×D3#449semidirect
940. D4#937semidirect
1061. C3#23851semidirect

Maximal subgroups

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

subgroupindex
C2×#58292
C22×D3×D82
C2×C3×#4492
C2×#52382
C2×#51692
#826402
#720552
#720372
#716842
#702772
#702702
#701982
#701722
#699612
#699572
#238513