Finite Group Databasebeta

← #10726643

Subgroups — #10726643

Order 768.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C22×#924C211yesmaximal, characteristic, complemented
3C2×#5210C212yesmaximal, complemented
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4947C211yesmaximal, characteristic, complemented
6#72131C212yesmaximal
7#72127C211yesmaximal, characteristic, complemented
8#71565C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71536C212yesmaximal, complemented
12#14723—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C2×C3×C4×D4—24no—
18C2×C3×C4×D4—24no—
19C2×C3×C4×D4—24no—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2212yes—
27C22×#217C2212yes—
28C22×C4⋊Dic3C2211yescharacteristic
29C2×#924—24no—
30C2×#924—28no—
31C22×Dic3⋊C4C2212yes—
32C22×Dic3⋊C4C2212yes—
33#5210—28no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42#4979—24no—
43#4947—24no—
44C22×C22⋊Q8—31no—
45C22×C4×D4D311yescharacteristic
46C2×#395—31no—
47C2×#393—31no—
48C2×#385—32no—
49#1441—31no—
50#1439—31no—
51#1439—32no—
52#1438—32no—
53#1436—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4Q814yescomplemented
64C23×C3×C4—22no—
65C23×C3×C4—24no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—42no—
72C23×C3×C4—42no—
73C23×C3×C4D414yes—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2312yes—
80C23×Dic3C2312yes—
81C23×Dic3C2312yes—
82C23×Dic3C2312yes—
83C22×Dic6—22no—
84C22×Dic6—24no—
85C22×Dic6—22no—
86C22×Dic6—22no—
87C22×Dic6—42no—
88C3×C4×D4—232no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4D414yes—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4D414yes—
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—24no—
108C2×#217—24no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—42no—
112C2×#217—42no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—24no—
115#924—232no—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—42no—
121C2×Dic3⋊C4D418yescomplemented
122C3⋊#95—24no—
123C3⋊#95—22no—
124C3⋊#95—24no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C23×Q8—31no—
131C23×D4C2×D311yescharacteristic
132C24×C4C2×D311yescharacteristic
133C24×C4C2×D311yescharacteristic
134C2×C22⋊Q8—68no—
135C2×C22⋊Q8—64no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4C2×D311yescharacteristic
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4C2×D311yescharacteristic
148C22×C22⋊C4C2×D311yescharacteristic
149C22×C42C2×D311yescharacteristic
150#395—64no—
151#393—64no—
152#385—68no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—31no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3C2×D412yes—
178C24×C3C2×D412yes—
179C24×C3C2×Q812yes—
180C24×C3C2×Q812yes—
181C24×C3#4112yes—
182C24×C3#4112yes—
183C24×C3C2411yescharacteristic
184C2×C3×D4—28no—
185C2×C3×D4—28no—
186C2×C3×D4—28no—
187C2×C3×D4—28no—
188C2×C3×D4—28no—
189C2×C3×D4—28no—
190C2×C3×D4—28no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—28no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—28no—
210C22×C3×C4—28no—
211C22×C3×C4—44no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4—48no—
215C22×C3×C4—48no—
216C22×C3×C4—44no—
217C22×C3×C4—44no—
218C22×C3×C4C2×D414yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×Q812yes—
227C22×C3×C4#4112yes—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3C2×D414yes—
254C22×Dic3C2×D414yes—
255C22×Dic3#4114yes—
256C2×Dic6—28no—
257C2×Dic6—48no—
258C2×Dic6—48no—
259C2×Dic6—44no—
260C2×Dic6—44no—
261C3×C4⋊C4—28no—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—28no—
264C3×C42—28no—
265#217—216no—
266#217—216no—
267#217—48no—
268#217—48no—
269C4⋊Dic3—28no—
270Dic3⋊C4—216no—
271Dic3⋊C4—48no—
272C25C22×D311yescharacteristic
273C25C22×D311yescharacteristic
274C22×Q8—64no—
275C22×Q8—62no—
276C22×Q8—62no—
277C22×Q8—62no—
278C22×Q8—122no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4Dic614yescomplemented
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—32no—
294C23×C4—32no—
295C23×C4—32no—
296C23×C4—32no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4#6714yes—
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304C23×C4C22×D311yescharacteristic
305C22⋊Q8—632no—
306C4×D4—232no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—38no—
310C2×C4⋊C4—64no—
311C2×C4⋊C4—64no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—122no—
317C2×C4⋊C4#6714yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—122no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4#6714yes—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339#95—64no—
340#95—64no—
341#95—64no—
342#95—64no—
343#95—64no—
344#95—62no—
345#95—62no—
346#95—64no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—41no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3C22⋊Q814yes—
392C23×C3C22⋊Q814yescomplemented
393C23×C3C22×D412yes—
394C23×C3C22×D411yescharacteristic
395C23×C3C22×D411yescharacteristic
396C23×C3C22×D411yescharacteristic
397C23×C3C22×Q811yescharacteristic
398C23×C3C2×#4111yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4112yes—
402C23×C3H(5,𝔽2)12yes—
403C23×C32−1+412yes—
404C3×D4—232no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—416no—
424C2×C3×C4—416no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4#12014yes—
432C2×C3×C4#12014yes—
433C2×C3×C4C22⋊Q814yescomplemented
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462Dic6—416no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24C2×Dic612yes—
480C24C2×Dic612yes—
481C24#23512yes—
482C24#23512yes—
483C24C2×#6712yes—
484C24C2×#6712yes—
485C24C23×D311yescharacteristic
486C2×Q8—68no—
487C2×Q8—128no—
488C2×Q8—128no—
489C2×Q8—124no—
490C2×Q8—124no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—34no—
519C22×C4—34no—
520C22×C4—34no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4C2×Dic612yes—
554C22×C4#23512yes—
555C22×C4D3×D414yes—
556C22×C4C2×#6712yes—
557C22×C4C2×#6712yes—
558C22×C4C2×#6712yes—
559C22×C4C2×#6712yes—
560C22×C4C2×#6712yes—
561C22×C4C2×#6712yes—
562C22×C4C2×#6712yes—
563C4⋊C4—28no—
564C4⋊C4—68no—
565C4⋊C4—616no—
566C4⋊C4—128no—
567C22⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—616no—
570C22⋊C4—616no—
571C22⋊C4—128no—
572C22⋊C4—128no—
573C42—28no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—28no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3C2×#12011yescharacteristic
597C22×C3C2×#12011yescharacteristic
598C22×C3C2×C22⋊Q811yescharacteristic
599C22×C3C2×C22⋊Q811yescharacteristic
600C22×C3C2×C22⋊Q811yescharacteristic
601C22×C3#52511yescharacteristic
602C22×C3#52511yescharacteristic
603C22×C3#52511yescharacteristic
604C22×C3#52512yes—
605C22×C3#53212yes—
606C22×C3#53211yescharacteristic
607C22×C3#53411yescharacteristic
608C22×C3#53611yescharacteristic
609C22×C3#53912yes—
610C22×C3#54212yes—
611C22×C3D4212yes—
612C22×C3D4212yes—
613C22×C3#54712yes—
614C22×C3#54812yes—
615C22×C3#54812yes—
616C22×C3D4×Q812yes—
617C22×C3#55112yes—
618C22×C3#55412yes—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—24no—
622C3×C4—42no—
623C3×C4—42no—
624Dic3—44no—
625Dic3—44no—
626Dic3—44no—
627Dic3—82no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23#92414yes—
673C23#92414yescomplemented
674C23C22×Dic611yescharacteristic
675C23C2×#23511yescharacteristic
676C23C2×#23511yescharacteristic
677C23C2×#23511yescharacteristic
678C23C2×D3×D412yes—
679C23#100412yes—
680C23D3×#4112yes—
681C23#101012yes—
682C23C22×#6711yescharacteristic
683C23C22×#6711yescharacteristic
684C23C22×#6711yescharacteristic
685Q8—1216no—
686D4—232no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—416no—
706C2×C4—416no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4#92414yescomplemented
742C2×C4#93714yes—
743C2×C4#95314yes—
744C2×C3—44no—
745C2×C3—44no—
746C2×C3#238811yescharacteristic
747C2×C3#240311yescharacteristic
748C2×C3#240911yescharacteristic
749C2×C3#243211yescharacteristic
750C2×C3#244912yes—
751C2×C3#245212yes—
752C2×C3#246112yes—
753C2×C3#246312yes—
754C2×C3#256411yescharacteristic
755C2×C3#263811yescharacteristic
756C2×C3#284811yescharacteristic
757C22—24no—
758C22—24no—
759C22—24no—
760C22—28no—
761C22—24no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22D4×Dic612yes—
780C22#553912yes—
781C22#554712yes—
782C22#554812yes—
783C22#555212yes—
784C22#555612yes—
785C22#556112yes—
786C22#556412yes—
787C22C2×#92411yescharacteristic
788C22C2×#92411yescharacteristic
789C22C2×#92411yescharacteristic
790C22#579111yescharacteristic
791C22#579111yescharacteristic
792C22#579111yescharacteristic
793C22C2×#93711yescharacteristic
794C22D4×#6712yes—
795C22D4×#6712yes—
796C22#580411yescharacteristic
797C22#582412yes—
798C22#582511yescharacteristic
799C22#583112yes—
800C22#583211yescharacteristic
801C22C2×#95311yescharacteristic
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—42no—
807C4—124no—
808C4—124no—
809C4—124no—
810C4—242no—
811C3#1472311yescharacteristic, complemented, Sylow
812C2—44no—
813C2—44no—
814C2#8234911yescharacteristic
815C2#8236012yes—
816C2#8236212yes—
817C2#8236712yes—
818C2#8236812yes—
819C2#8238511yescharacteristic
820C2#8239211yescharacteristic
821C2#8240011yescharacteristic
822C2#8403111yescharacteristic
823C2#8405211yescharacteristic
824C2#8409311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C4×D4C2
prime radicalC23×C3×D4C22
hypercenterC22×C4×D4D3
hypocenterC3#14723
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#924C2semidirect
3. C2×#5210C2semidirect
4. C2×#4979C2semidirect
5. C2×#4947C2semidirect
7. #72127C2semidirect
8. #71565C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71536C2semidirect
63. C22×C3×D4Q8semidirect
121. C2×Dic3⋊C4D4semidirect
285. C22×D4Dic6semidirect
392. C23×C3C22⋊Q8semidirect
433. C2×C3×C4C22⋊Q8semidirect
673. C23#924semidirect
741. C2×C4#924semidirect
811. C3#14723semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C22×#9242
C2×#52102
C2×#49792
C2×#49472
#721312
#721272
#715652
#715472
#715462
#715362
#147233