Finite Group Databasebeta

← #10826939

Subgroups — #10826939

Order 768.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C22×#930C211yesmaximal, characteristic, complemented
3C2×#5238C212yesmaximal, complemented
4C2×#5046C211yesmaximal, characteristic, complemented
5C2×#5036C211yesmaximal, characteristic, complemented
6#72126C211yesmaximal, characteristic, complemented
7#71699C212yesmaximal, complemented
8#71692C211yesmaximal, characteristic, complemented
9#71684C212yesmaximal, complemented
10#71677C211yesmaximal, characteristic, complemented
11#71586C212yesmaximal, complemented
12#23920—31nomaximal, Sylow
13C22×C3×#41C2211yescharacteristic, complemented
14C24×C3×C4C2211yescharacteristic
15C23×#67—21no—
16C23×D12C2211yescharacteristic
17C3×#525—24no—
18C3×#525—24no—
19C2×C3×#123—21no—
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic, complemented
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic, complemented
24C2×C3×#120—21no—
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4—21no—
27C2×C3×#117C2211yescharacteristic, complemented
28C22×#215C2212yescomplemented
29C22×#213C2212yescomplemented
30C2×#930—21no—
31C2×#930—21no—
32C2×#930—28no—
33C2×#930C2212yes—
34C2×#930C2212yes—
35C22×(C2×D3)⋊C4—21no—
36C22×C4⋊Dic3C2211yescharacteristic
37#5238—28no—
38C2×#835C2212yescomplemented
39C2×#832C2212yescomplemented
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2212yescomplemented
43C2×#830C2212yescomplemented
44#5046—24no—
45#5036—24no—
46C2×#809C2212yescomplemented
47C2×#809C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525D311yescharacteristic, complemented
51C22×#121—31no—
52C2×#449—32no—
53C2×#450—31no—
54C2×#447—31no—
55#2000—32no—
56#1999—32no—
57#1875—32no—
58#1874—31no—
59#1872—31no—
60#1779—31no—
61C25×C3D411yescharacteristic
62C24×D3—21no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—24no—
66C2×C3×#41—42no—
67C22×C3×Q8C2311yescharacteristic
68C22×C3×D4—21no—
69C22×C3×D4—21no—
70C22×C3×D4—21no—
71C22×C3×D4C2311yescharacteristic
72C23×C3×C4—24no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—21no—
76C23×C3×C4—42no—
77C23×C3×C4D411yescharacteristic
78C23×C3×C4D411yescharacteristic
79C23×C3×C4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—28no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—44no—
87C22×#67—44no—
88C23×Dic3—21no—
89C22×D12—21no—
90C22×D12—24no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—42no—
94C22×D12C2312yes—
95C3×#123—28no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8D414yescomplemented
100C3×#121—22no—
101C3×#121—22no—
102C3×#121—22no—
103C3×#121D414yescomplemented
104C3×#120—28no—
105C3×C4×D4—28no—
106C3×C4×D4—28no—
107C3×#117—22no—
108C3×#117—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C42—21no—
119C2×#215—24no—
120C2×#215—24no—
121C2×#215—42no—
122C2×#213—24no—
123C2×#213—24no—
124C2×#213—42no—
125#930—28no—
126#930—28no—
127#930—24no—
128#930—24no—
129#930—24no—
130#930D418yescomplemented
131C2×(C2×D3)⋊C4—28no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—24no—
136C2×C4⋊Dic3C2312yes—
137C22×C3⋊C8C2312yes—
138C22×C3⋊C8C2312yes—
139#835—24no—
140#832—24no—
141#830—22no—
142#830—22no—
143#830—24no—
144#830—42no—
145#809—24no—
146#809—24no—
147C22×#41C2×D311yescharacteristic, complemented
148C23×D4—31no—
149C23×D4—61no—
150C24×C4C2×D311yescharacteristic
151C22×SD16—32no—
152C22×D8—32no—
153#525—24no—
154#525—24no—
155C2×#123—21no—
156C2×C22⋊Q8C2×D311yescharacteristic
157C2×C22⋊Q8C2×D311yescharacteristic, complemented
158C2×#121—32no—
159C2×#121—32no—
160C2×#121—68no—
161C2×#121—61no—
162C2×#121—61no—
163C2×#121C2×D311yescharacteristic
164C2×#121C2×D311yescharacteristic, complemented
165C2×#120—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×#117C2×D311yescharacteristic, complemented
169C22×C4⋊C4—31no—
170C22×C22⋊C4—61no—
171#450—64no—
172#449—68no—
173#447—64no—
174C2×#103—32no—
175C2×#102—32no—
176C2×#102—32no—
177C2×#102—32no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—32no—
181C2×C22⋊C8—32no—
182#340—32no—
183#340—32no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—21no—
190C24×C3—41no—
191C24×C3—41no—
192C24×C3C2×D411yescharacteristic
193C24×C3C2×D411yescharacteristic
194C24×C3C2×D411yescharacteristic
195C23×D3—24no—
196C23×D3—22no—
197C23×D3—42no—
198C23×D3—42no—
199C23×D3—42no—
200C23×D3—42no—
201C23×D3—42no—
202C23×D3—42no—
203C3×#41—48no—
204C3×#41—48no—
205C2×C3×Q8—21no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8C2×D412yescomplemented
209C2×C3×D4—24no—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—42no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4C2×D412yescomplemented
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—41no—
242C22×C3×C4—41no—
243C22×C3×C4—41no—
244C22×C3×C4—48no—
245C22×C3×C4—48no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2411yescharacteristic
255C2×#67—28no—
256C2×#67—28no—
257C2×#67—432no—
258C2×#67—44no—
259C2×#67—44no—
260C2×#67—44no—
261C2×#67—44no—
262C22×Dic3—24no—
263C22×Dic3—22no—
264C22×Dic3—42no—
265C22×Dic3—42no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—22no—
269C2×D12—22no—
270C2×D12—24no—
271C2×D12—22no—
272C2×D12—48no—
273C2×D12—48no—
274C2×D12—42no—
275C2×D12—42no—
276C2×D12C2×D414yes—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4C2×D412yescomplemented
282C3×C4⋊C4C2×D412yescomplemented
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C42—24no—
289#215—48no—
290#213—48no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—28no—
293C4⋊Dic3—24no—
294C4⋊Dic3—22no—
295C4⋊Dic3C2×D414yes—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C25—61no—
303C25#6711yescharacteristic
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—24no—
307C2×#41—42no—
308C22×Q8C22×D311yescharacteristic
309C22×D4—21no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—32no—
313C22×D4—64no—
314C22×D4—68no—
315C22×D4—62no—
316C22×D4—62no—
317C22×D4—61no—
318C22×D4—62no—
319C22×D4—62no—
320C22×D4—122no—
321C22×D4—124no—
322C22×D4—124no—
323C22×D4C22×D311yescharacteristic
324C23×C4—24no—
325C23×C4—21no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—42no—
329C23×C4—61no—
330C23×C4#6711yescharacteristic
331C23×C4#6711yescharacteristic
332C23×C4#6711yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C2×SD16—64no—
337C2×SD16—64no—
338C2×SD16—122no—
339C2×D8—64no—
340C2×D8—64no—
341C2×D8—122no—
342C22×C8—32no—
343C22×C8—32no—
344#123—28no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8#6714yescomplemented
349#121—22no—
350#121—22no—
351#121—22no—
352#121—38no—
353#121—64no—
354#121—64no—
355#121—68no—
356#121—68no—
357#121—64no—
358#121#6714yescomplemented
359#120—28no—
360C4×D4—28no—
361C4×D4—28no—
362#117—22no—
363#117—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—64no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—68no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C42—21no—
380#103—64no—
381#102—64no—
382#102—64no—
383#102—64no—
384C22⋊C8—64no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387C22⋊C8—122no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—28no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—44no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3#12012yes—
419C23×C3#12012yes—
420C23×C3#13512yes—
421C23×C3AGL(1,ℤ/8)12yes—
422C23×C3AGL(1,ℤ/8)12yes—
423C23×C3C22×D411yescharacteristic
424C22×D3—24no—
425C22×D3—48no—
426C22×D3—48no—
427C22×D3—48no—
428C22×D3—42no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3—42no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—84no—
435C22×D3—84no—
436C22×D3—84no—
437C22×D3—84no—
438C3×Q8—24no—
439C3×Q8—42no—
440C3×D4—24no—
441C3×D4—48no—
442C3×D4—48no—
443C3×D4—48no—
444C3×D4—42no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—44no—
460C2×C3×C4—44no—
461C2×C3×C4—44no—
462C2×C3×C4—48no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4#12012yes—
472C2×C3×C4#12012yes—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4H(5,𝔽2)12yes—
477#67—416no—
478#67—416no—
479C2×Dic3—24no—
480C2×Dic3—48no—
481C2×Dic3—42no—
482C2×Dic3—42no—
483D12—24no—
484D12—24no—
485D12—48no—
486D12—42no—
487D12—42no—
488C3⋊C8—42no—
489C3⋊C8—42no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—64no—
499C24—62no—
500C24—122no—
501C24—122no—
502C24—122no—
503C24—122no—
504C24—122no—
505C24—122no—
506C24C2×#6711yescharacteristic
507C24C2×#6711yescharacteristic
508C24C2×#6711yescharacteristic
509#41—48no—
510#41—48no—
511C2×Q8—21no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8C2×#6712yescomplemented
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—34no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—64no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—128no—
537C2×D4—128no—
538C2×D4—122no—
539C2×D4—1232no—
540C2×D4—124no—
541C2×D4—124no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—122no—
545C2×D4C2×#6712yescomplemented
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—64no—
573C22×C4—62no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4D3×D414yes—
577C22×C4C2×#6711yescharacteristic
578C22×C4C2×#6711yescharacteristic
579C22×C4C2×#6711yescharacteristic
580C22×C4C2×#6712yes—
581C22×C4C2×#6712yes—
582C22×C4C23×D311yescharacteristic
583SD16—128no—
584D8—128no—
585C2×C8—62no—
586C2×C8—62no—
587C2×C8—62no—
588C2×C8—62no—
589C2×C8—62no—
590C2×C8—62no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—34no—
596C4⋊C4—64no—
597C4⋊C4—62no—
598C4⋊C4C2×#6712yescomplemented
599C4⋊C4C2×#6712yescomplemented
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C42—24no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—416no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3#44914yescomplemented
637C22×C3C2×#12011yescharacteristic
638C22×C3C2×#12011yescharacteristic
639C22×C3#53411yescharacteristic
640C22×C3C2×#13511yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
643C22×C3#57511yescharacteristic
644C2×D3—44no—
645C2×D3—44no—
646C2×D3—44no—
647C2×D3—816no—
648C2×D3—82no—
649C2×D3—82no—
650C2×D3—82no—
651C2×D3—82no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4D4212yes—
659C3×C4D4212yes—
660Dic3—44no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—28no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—64no—
692C23—128no—
693C23—128no—
694C23—128no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—244no—
702C23—244no—
703C23—244no—
704C23—244no—
705C23#93712yes—
706C23#94912yes—
707C23#94912yes—
708C23#95012yes—
709C23#95312yes—
710C23C22×#6711yescharacteristic
711Q8—24no—
712Q8—42no—
713D4—24no—
714D4—48no—
715D4—48no—
716D4—48no—
717D4—42no—
718D4—64no—
719D4—64no—
720D4—128no—
721D4—1216no—
722D4—1216no—
723D4—122no—
724D4—122no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—64no—
752C2×C4—128no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4#93712yes—
756C2×C4#95312yes—
757C2×C4C2×D3×D412yes—
758C2×C4#100412yes—
759C2×C4C22×#6711yescharacteristic
760C2×C4C22×#6711yescharacteristic
761C8—122no—
762C8—122no—
763C2×C3—24no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—82no—
767C2×C3#240311yescharacteristic
768C2×C3C2×#44911yescharacteristic
769C2×C3#300211yescharacteristic
770C2×C3#300311yescharacteristic
771C2×C3#300611yescharacteristic
772C2×C3#318811yescharacteristic
773C2×C3#319411yescharacteristic
774D3—84no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—416no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—2416no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22#523814yescomplemented
812C22C2×#93711yescharacteristic
813C22#580411yescharacteristic
814C22C2×#94911yescharacteristic
815C22C2×#94911yescharacteristic
816C22C2×#95011yescharacteristic
817C22#582211yescharacteristic
818C22C2×#95311yescharacteristic
819C4—22no—
820C4—22no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—124no—
826C4D4×#6712yes—
827C4D4×#6712yes—
828C3#2392011yescharacteristic, complemented, Sylow
829C2—24no—
830C2—42no—
831C2—42no—
832C2—82no—
833C2—244no—
834C2#8292611yescharacteristic
835C2#8292711yescharacteristic
836C2#8292911yescharacteristic
837C2#8293111yescharacteristic
838C2#8405211yescharacteristic
839C2C2×#523811yescharacteristic
840C2#8408211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#525C2
socleC23×C3C22×D4
hypercenterC2×#525D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×C3×#525C2semidirect
2. C22×#930C2semidirect
3. C2×#5238C2semidirect
4. C2×#5046C2semidirect
5. C2×#5036C2semidirect
6. #72126C2semidirect
7. #71699C2semidirect
8. #71692C2semidirect
9. #71684C2semidirect
10. #71677C2semidirect
11. #71586C2semidirect
13. C22×C3×#41C22semidirect
21. C2×C3×C22⋊Q8C22semidirect
23. C2×C3×#121C22semidirect
27. C2×C3×#117C22semidirect
28. C22×#215C22semidirect
29. C22×#213C22semidirect
38. C2×#835C22semidirect
39. C2×#832C22semidirect
42. C2×#830C22semidirect
43. C2×#830C22semidirect
46. C2×#809C22semidirect
47. C2×#809C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
50. C2×#525D3semidirect
99. C3×C22⋊Q8D4semidirect
103. C3×#121D4semidirect
130. #930D4semidirect
147. C22×#41C2×D3semidirect
157. C2×C22⋊Q8C2×D3semidirect
164. C2×#121C2×D3semidirect
168. C2×#117C2×D3semidirect
208. C2×C3×Q8C2×D4semidirect
221. C2×C3×D4C2×D4semidirect
281. C3×C4⋊C4C2×D4semidirect
282. C3×C4⋊C4C2×D4semidirect
348. C22⋊Q8#67semidirect
358. #121#67semidirect
514. C2×Q8C2×#67semidirect
545. C2×D4C2×#67semidirect
598. C4⋊C4C2×#67semidirect
599. C4⋊C4C2×#67semidirect
636. C22×C3#449semidirect
811. C22#5238semidirect
828. C3#23920semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C22×#9302
C2×#52382
C2×#50462
C2×#50362
#721262
#716992
#716922
#716842
#716772
#715862
#239203