Finite Group Databasebeta

← #10729059

Subgroups — #10729059

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#5213C212yesmaximal, complemented
4C2×#4960C211yesmaximal, characteristic
5C2×#4947C211yesmaximal, characteristic, complemented
6#71550C212yesmaximal, complemented
7#71537C212yesmaximal, complemented
8#71534C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal, complemented
10#69426C211yesmaximal, characteristic, complemented
11#69424C211yesmaximal, characteristic, complemented
12#14915—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2212yes—
15C23×D12C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×#217C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C2×#875—24no—
28C2×#875—28no—
29C3×C4×C22⋊C4—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32#5213—28no—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4960—24no—
41#4947—24no—
42C22×#124—31no—
43C2×#393—31no—
44C2×#392—31no—
45C2×#386—32no—
46C2×C4×C22⋊C4D311yescharacteristic, complemented
47#1446—31no—
48#1440—32no—
49#1438—31no—
50#1438—32no—
51#1437—32no—
52#1434—31no—
53C25×C3C2311yescharacteristic
54C24×D3C2312yes—
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—24no—
59C23×C3×C4—42no—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—42no—
72C22×#67—42no—
73C23×Dic3C2312yes—
74C23×Dic3C2312yes—
75C23×Dic3C2312yes—
76C22×D12—24no—
77C22×D12—22no—
78C22×D12—22no—
79C22×D12—22no—
80C22×D12—42no—
81C22×Dic6—22no—
82C22×Dic6—24no—
83C22×Dic6—22no—
84C22×Dic6—22no—
85C22×Dic6—42no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4D414yes—
92C2×C3×C42—24no—
93C2×C3×C42—22no—
94C2×C3×C42—42no—
95C2×C3×C42D414yescomplemented
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—42no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4D418yescomplemented
114#875—232no—
115C3×#95—22no—
116C3×#95—22no—
117C3⋊#95—24no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
124C23×Q8—31no—
125C23×D4—32no—
126C23×D4—31no—
127C24×C4C2×D311yescharacteristic
128C2×#124—68no—
129C2×#124—64no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D311yescharacteristic
137C22×C22⋊C4C2×D311yescharacteristic
138C22×C42C2×D311yescharacteristic
139C22×C42C2×D311yescharacteristic
140#393—64no—
141#392—64no—
142#386—68no—
143C4×C22⋊C4—24no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95C2×D311yescharacteristic
152C2×#95C2×D311yescharacteristic
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—22no—
158C24×C3—21no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3C2×D412yes—
162C24×C3#4112yes—
163C24×C3#4112yes—
164C24×C3C2411yescharacteristic
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3C2×D414yes—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—28no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
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—22no—
201C22×C3×C4—22no—
202C22×C3×C4—48no—
203C22×C3×C4—48no—
204C22×C3×C4—44no—
205C22×C3×C4—44no—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4#4112yes—
213C22×C3×C4#4112yes—
214C22×C3×C4#4112yes—
215C2×#67—216no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C2×#67—48no—
221C2×#67—48no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
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×Dic3C2×D414yes—
242C22×Dic3#4114yes—
243C2×D12—28no—
244C2×D12—48no—
245C2×D12—48no—
246C2×D12—44no—
247C2×D12—44no—
248C2×Dic6—28no—
249C2×Dic6—48no—
250C2×Dic6—48no—
251C2×Dic6—44no—
252C2×Dic6—44no—
253C3×C22⋊C4—28no—
254C3×C22⋊C4—28no—
255C3×C42—28no—
256C3×C42—44no—
257#217—48no—
258(C2×D3)⋊C4—216no—
259(C2×D3)⋊C4—216no—
260(C2×D3)⋊C4—48no—
261(C2×D3)⋊C4—48no—
262(C2×D3)⋊C4—48no—
263C25—32no—
264C25C22×D311yescharacteristic
265C22×Q8—64no—
266C22×Q8—62no—
267C22×Q8—62no—
268C22×Q8—62no—
269C22×Q8—122no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—64no—
276C22×D4—62no—
277C22×D4—62no—
278C22×D4—62no—
279C22×D4—122no—
280C22×D4—122no—
281C22×D4—122no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—32no—
287C23×C4—32no—
288C23×C4—32no—
289C23×C4—42no—
290C23×C4C22×D311yescharacteristic
291C23×C4C22×D311yescharacteristic
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D311yescharacteristic
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296#124—632no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—38no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4—122no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4D1214yes—
321C2×C42—24no—
322C2×C42—22no—
323C2×C42—42no—
324C2×C42#6714yescomplemented
325#95—22no—
326#95—22no—
327#95—64no—
328#95—64no—
329#95—62no—
330#95—64no—
331#95—62no—
332#95—64no—
333#95—122no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3#12414yescomplemented
357C23×C3C22×D411yescharacteristic
358C23×C3C22×D412yes—
359C23×C3C22×D411yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3C2×#4111yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4112yes—
366C23×C3H(5,𝔽2)12yes—
367C23×C3H(5,𝔽2)12yes—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—416no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—41no—
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—42no—
432C2×C3×C4#12014yes—
433C2×C3×C4#12114yes—
434#67—432no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—42no—
442C2×Dic3—42no—
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—
456D12—416no—
457Dic6—416no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—34no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24C2×D1212yes—
482C24#23512yes—
483C24#23512yes—
484C24C23×D311yescharacteristic
485C2×Q8—68no—
486C2×Q8—128no—
487C2×Q8—128no—
488C2×Q8—124no—
489C2×Q8—124no—
490C2×D4—68no—
491C2×D4—616no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—124no—
495C2×D4—128no—
496C2×D4—128no—
497C2×D4—128no—
498C2×D4—128no—
499C2×D4—128no—
500C2×D4—128no—
501C2×D4—124no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—34no—
525C22×C4—34no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
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×C4C2×D1212yes—
550C22×C4C2×D1212yes—
551C22×C4#23512yes—
552C22×C4#23512yes—
553C22×C4#23512yes—
554C22×C4D3×D414yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6712yes—
557C22×C4C2×#6712yes—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—616no—
561C22⋊C4—616no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C22⋊C4—128no—
565C22⋊C4—128no—
566C42—28no—
567C42—44no—
568C22×C3—24no—
569C22×C3—28no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—44no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3C2×#12011yescharacteristic
580C22×C3C2×#12111yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3#52511yescharacteristic
583C22×C3#52512yes—
584C22×C3C2×#12411yescharacteristic
585C22×C3#52911yescharacteristic
586C22×C3#52911yescharacteristic
587C22×C3#53211yescharacteristic
588C22×C3#53212yes—
589C22×C3#53211yescharacteristic
590C22×C3#53511yescharacteristic
591C22×C3#53511yescharacteristic
592C22×C3#53812yes—
593C22×C3#53812yes—
594C22×C3D4212yes—
595C22×C3#54612yes—
596C22×C3#54612yes—
597C22×C3#54612yes—
598C22×C3#54612yes—
599C22×C3#55112yes—
600C22×C3#55512yes—
601C22×C3#55912yes—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—82no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623Dic3—44no—
624Dic3—44no—
625Dic3—82no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—42no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—64no—
649C23—64no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—64no—
654C23—64no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23#87514yescomplemented
684C23C22×D1211yescharacteristic
685C23C2×#23511yescharacteristic
686C23C2×#23511yescharacteristic
687C23C2×#23511yescharacteristic
688C23C2×#23511yescharacteristic
689C23C2×#23511yescharacteristic
690C23C2×D3×D412yes—
691C23#100412yes—
692C23D3×#4112yes—
693C23#100912yes—
694C23C22×#6711yescharacteristic
695Q8—1216no—
696D4—1216no—
697D4—1232no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—64no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—64no—
732C2×C4—64no—
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—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4#93014yes—
749C2×C4#93714yes—
750C2×C3—44no—
751C2×C3#238811yescharacteristic
752C2×C3#240411yescharacteristic
753C2×C3#240811yescharacteristic
754C2×C3#245912yes—
755C2×C3#247212yes—
756C2×C3#254411yescharacteristic
757C2×C3#255512yes—
758C2×C3#255712yes—
759C2×C3#261011yescharacteristic
760C2×C3#263111yescharacteristic
761C2×C3#285011yescharacteristic
762D3—84no—
763C22—28no—
764C22—24no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—124no—
775C22—124no—
776C22—124no—
777C22—124no—
778C22—124no—
779C22—124no—
780C22—124no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22C2×#87511yescharacteristic
790C22#547711yescharacteristic
791C22#547911yescharacteristic
792C22#547911yescharacteristic
793C22#549012yes—
794C22#549012yes—
795C22#552712yes—
796C22#553212yes—
797C22#554712yes—
798C22#554812yes—
799C22D4×D1212yes—
800C22#555012yes—
801C22#555412yes—
802C22#555912yes—
803C22#556012yes—
804C22#556012yes—
805C22C2×#93011yescharacteristic
806C22#579111yescharacteristic
807C22#579111yescharacteristic
808C22C2×#93711yescharacteristic
809C22#580511yescharacteristic
810C22#583011yescharacteristic
811C22#583211yescharacteristic
812C4—24no—
813C4—24no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—124no—
819C4—124no—
820C4—242no—
821C3#1491511yescharacteristic, complemented, Sylow
822C2—44no—
823C2—244no—
824C2#7359012yes—
825C2#7359412yes—
826C2#7360012yes—
827C2#7360112yes—
828C2#8207711yescharacteristic
829C2#8212511yescharacteristic
830C2#8226011yescharacteristic
831C2#8238111yescharacteristic
832C2#8240011yescharacteristic
833C2#8240311yescharacteristic
834C2#8242111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×C4×C22⋊C4C2
prime radicalC2×#4960C2
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#14915
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#875C2semidirect
2. C2×C3×C4×C22⋊C4C2semidirect
3. C2×#5213C2semidirect
5. C2×#4947C2semidirect
6. #71550C2semidirect
7. #71537C2semidirect
8. #71534C2semidirect
9. #69429C2semidirect
10. #69426C2semidirect
11. #69424C2semidirect
46. C2×C4×C22⋊C4D3semidirect
95. C2×C3×C42D4semidirect
113. C2×(C2×D3)⋊C4D4semidirect
324. C2×C42#67semidirect
356. C23×C3#124semidirect
683. C23#875semidirect
821. C3#14915semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×C3×C4×C22⋊C42
C2×#52132
C2×#49602
C2×#49472
#715502
#715372
#715342
#694292
#694262
#694242
#149153