Finite Group Databasebeta

← #10746861

Subgroups — #10746861

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#929C211yesmaximal, characteristic
3C2×#5231C211yesmaximal, characteristic, complemented
4C2×#5230C211yesmaximal, characteristic, complemented
5C2×#4959C212yesmaximal
6#72127C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71568C212yesmaximal, complemented
10#71566C211yesmaximal, characteristic, complemented
11#71548C212yesmaximal, complemented
12#16251—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—28no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C2×#929—24no—
24C2×#929—24no—
25C2×#929—24no—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2212yes—
32C22×Dic3⋊C4C2211yescharacteristic
33#5231—24no—
34#5230—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4959—28no—
44C22×#123—31no—
45C22×C22⋊Q8D311yescharacteristic, complemented
46C2×#395—31no—
47C2×#394—32no—
48C2×#393—31no—
49#1444—32no—
50#1441—31no—
51#1440—32no—
52#1439—31no—
53#1439—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C22×C3×Q8—24no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—42no—
62C23×C3×C4—24no—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—42no—
66C23×C3×C4D414yes—
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C22×#67—22no—
72C22×#67—22no—
73C22×#67—24no—
74C22×#67—22no—
75C22×#67—42no—
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2312yes—
81C3×C22⋊Q8—232no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4D418yes—
90C2×#217—22no—
91C2×#217—22no—
92C2×#217—22no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—42no—
96#929—232no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×(C2×D3)⋊C4D414yes—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—42no—
117C2×Dic3⋊C4D414yes—
118C3⋊#95—24no—
119C3⋊#95—22no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—42no—
125C3⋊#95—42no—
126C23×Q8C2×D311yescharacteristic
127C23×D4—31no—
128C24×C4C2×D311yescharacteristic
129C2×#123—64no—
130C2×#123—64no—
131C2×#123—64no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—28no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4—31no—
136C22×C4⋊C4—32no—
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C4⋊C4C2×D312yes—
139C22×C22⋊C4—31no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4C2×D312yes—
146#395—64no—
147#394—68no—
148#393—64no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3C2×D412yes—
167C24×C3C2×D414yes—
168C24×C3C2411yescharacteristic
169C23×D3—21no—
170C23×D3—21no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—21no—
176C23×D3—21no—
177C23×D3—22no—
178C23×D3—21no—
179C23×D3C2×D412yes—
180C2×C3×Q8—28no—
181C2×C3×Q8—48no—
182C2×C3×Q8—48no—
183C2×C3×Q8—44no—
184C2×C3×Q8—44no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—28no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—28no—
205C22×C3×C4—44no—
206C22×C3×C4—48no—
207C22×C3×C4—48no—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D414yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C2×#67—28no—
215C2×#67—48no—
216C2×#67—48no—
217C2×#67—44no—
218C2×#67—44no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—21no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D412yes—
248C22×Dic3C2×D412yes—
249C22×Dic3#4114yes—
250C3×C4⋊C4—28no—
251C3×C4⋊C4—216no—
252C3×C22⋊C4—216no—
253#217—28no—
254#217—48no—
255(C2×D3)⋊C4—28no—
256(C2×D3)⋊C4—28no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—48no—
259Dic3⋊C4—28no—
260Dic3⋊C4—28no—
261Dic3⋊C4—48no—
262C25—31no—
263C25C22×D311yescharacteristic
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—24no—
267C22×Q8—22no—
268C22×Q8—42no—
269C22×D4—62no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—64no—
273C22×D4—122no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—32no—
280C23×C4—31no—
281C23×C4—32no—
282C23×C4—42no—
283C23×C4#6714yes—
284C23×C4C22×D312yes—
285C23×C4C22×D312yes—
286C23×C4C22×D311yescharacteristic
287C23×C4C22×D311yescharacteristic
288#123—632no—
289C22⋊Q8—232no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—34no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—122no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—62no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C22⋊C4—122no—
324C2×C22⋊C4#6718yes—
325#95—64no—
326#95—64no—
327#95—64no—
328#95—62no—
329#95—62no—
330#95—64no—
331#95—122no—
332#95—122no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3#12014yes—
356C23×C3C22×D411yescharacteristic
357C23×C3C22×D411yescharacteristic
358C23×C3C22×D411yescharacteristic
359C23×C3C22×D412yes—
360C23×C3C2×#4112yes—
361C23×C3H(5,𝔽2)12yes—
362C23×C3H(5,𝔽2)11yescharacteristic
363C23×C32−1+411yescharacteristic
364C23×C32−1+411yescharacteristic
365C23×C32−1+412yes—
366C23×C32−1+411yescharacteristic
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C3×Q8—416no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—416no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4#12014yes—
416#67—416no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—42no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—32no—
458C24—61no—
459C24—62no—
460C24—61no—
461C24—61no—
462C24—62no—
463C24—62no—
464C24—61no—
465C24—61no—
466C24—61no—
467C24—62no—
468C24C2×#6712yes—
469C24C2×#6714yes—
470C24C23×D311yescharacteristic
471C2×Q8—28no—
472C2×Q8—48no—
473C2×Q8—48no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×D4—68no—
477C2×D4—128no—
478C2×D4—128no—
479C2×D4—124no—
480C2×D4—124no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—34no—
505C22×C4—44no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—62no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4D3×D412yes—
536C22×C4D3×D412yes—
537C22×C4C2×#6714yes—
538C22×C4C2×#6714yes—
539C22×C4C2×#6712yes—
540C22×C4C2×#6712yes—
541C4⋊C4—28no—
542C4⋊C4—216no—
543C4⋊C4—68no—
544C4⋊C4—68no—
545C4⋊C4—128no—
546C22⋊C4—216no—
547C22⋊C4—68no—
548C22⋊C4—68no—
549C22⋊C4—68no—
550C22⋊C4—128no—
551C22⋊C4—128no—
552C22⋊C4—128no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3C2×#12011yescharacteristic
565C22×C3C2×#12011yescharacteristic
566C22×C3#53211yescharacteristic
567C22×C3#53411yescharacteristic
568C22×C3#53611yescharacteristic
569C22×C3#53612yes—
570C22×C3#53612yes—
571C22×C3#53611yescharacteristic
572C22×C3#53611yescharacteristic
573C22×C3#53611yescharacteristic
574C22×C3#53711yescharacteristic
575C22×C3#53711yescharacteristic
576C22×C3#53711yescharacteristic
577C22×C3#53912yes—
578C22×C3#54212yes—
579C22×C3D4212yes—
580C22×C3D4212yes—
581C22×C3#54612yes—
582C22×C3#54712yes—
583C22×C3#54712yes—
584C22×C3#54812yes—
585C22×C3#56212yes—
586C22×C3#56312yes—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—42no—
592C2×D3—81no—
593C2×D3—81no—
594C2×D3—82no—
595C2×D3—82no—
596C2×D3—81no—
597C2×D3—81no—
598C3×C4—24no—
599C3×C4—42no—
600C3×C4—44no—
601C3×C4—44no—
602Dic3—42no—
603Dic3—42no—
604Dic3—44no—
605Dic3—42no—
606Dic3—82no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—62no—
630C23—64no—
631C23—62no—
632C23—62no—
633C23—64no—
634C23—122no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23#95314yes—
653C23C2×D3×D411yescharacteristic
654C23C2×D3×D411yescharacteristic
655C23#100412yes—
656C23#100712yes—
657C23#100711yescharacteristic
658C23#100711yescharacteristic
659C23D3×#4112yes—
660C23#100911yescharacteristic
661C23#101011yescharacteristic
662C23C22×#6711yescharacteristic
663C23C22×#6712yes—
664Q8—416no—
665D4—1216no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—122no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—121no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4#93714yes—
722C2×C3—44no—
723C2×C3#240311yescharacteristic
724C2×C3#243011yescharacteristic
725C2×C3#243211yescharacteristic
726C2×C3#261411yescharacteristic
727C2×C3#261611yescharacteristic
728C2×C3#266311yescharacteristic
729C2×C3#267212yes—
730C2×C3#267412yes—
731C2×C3#268012yes—
732C2×C3#268112yes—
733C2×C3#281411yescharacteristic
734D3—82no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—124no—
750C22—124no—
751C22—241no—
752C22—242no—
753C22—242no—
754C22—241no—
755C22—241no—
756C22—241no—
757C22#562811yescharacteristic
758C22#562811yescharacteristic
759C22#562911yescharacteristic
760C22#562911yescharacteristic
761C22#563112yes—
762C22#563312yes—
763C22#563812yes—
764C22#564012yes—
765C22#564612yes—
766C22#564712yes—
767C22C2×#93711yescharacteristic
768C22D4×#6712yes—
769C22D4×#6712yes—
770C22#580411yescharacteristic
771C22#581611yescharacteristic
772C22#581612yes—
773C22#581612yes—
774C22#581611yescharacteristic
775C22#582412yes—
776C22#582912yes—
777C22#583211yescharacteristic
778C22#583311yescharacteristic
779C22C2×#95311yescharacteristic
780C4—24no—
781C4—42no—
782C4—44no—
783C4—44no—
784C4—122no—
785C4—122no—
786C4—124no—
787C4—122no—
788C4—242no—
789C3#1625111yescharacteristic, complemented, Sylow
790C2—44no—
791C2—242no—
792C2#8275911yescharacteristic
793C2#8279012yes—
794C2#8279212yes—
795C2#8282011yescharacteristic
796C2#8282511yescharacteristic
797C2#8282612yes—
798C2#8282812yes—
799C2#8283211yescharacteristic
800C2#8405211yescharacteristic
801C2#8406911yescharacteristic
802C2#8409111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#16251
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
3. C2×#5231C2semidirect
4. C2×#5230C2semidirect
6. #72127C2semidirect
7. #71570C2semidirect
8. #71570C2semidirect
9. #71568C2semidirect
10. #71566C2semidirect
11. #71548C2semidirect
45. C22×C22⋊Q8D3semidirect
789. C3#16251semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9292
C2×#52312
C2×#52302
C2×#49592
#721272
#715702
#715682
#715662
#715482
#162513