Finite Group Databasebeta

← #10728745

Subgroups — #10728745

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#877C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4958C212yesmaximal, complemented
5C2×#4672C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#69428C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11#69402C211yesmaximal, characteristic, complemented
12#14886—31nomaximal, Sylow
13C23×#67C2212yes—
14C24×Dic3C2211yescharacteristic
15C23×D12C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#877—24no—
30C2×#877—24no—
31C2×#877—24no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4988—24no—
40#4960—24no—
41#4958—28no—
42#4672—24no—
43C22×#117—31no—
44C2×#394—31no—
45C2×#392—31no—
46C2×#390—31no—
47C2×#386—32no—
48#1441—31no—
49#1439—32no—
50#1439D311yescharacteristic, complemented
51#1438—32no—
52#1437—32no—
53#1434—31no—
54C25×C3C2311yescharacteristic
55C24×D3C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C22×#67—24no—
61C22×#67—24no—
62C22×#67—24no—
63C22×#67—24no—
64C22×#67—24no—
65C22×#67—42no—
66C22×#67—42no—
67C23×Dic3—22no—
68C23×Dic3—22no—
69C23×Dic3—22no—
70C23×Dic3—22no—
71C23×Dic3—22no—
72C23×Dic3—22no—
73C23×Dic3D414yescomplemented
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12—22no—
83C22×D12—42no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—42no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—42no—
90C2×C3×C22⋊C4—42no—
91C2×C3×C22⋊C4D414yes—
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—22no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
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—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4D414yescomplemented
116C2×C4×Dic3—22no—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3D414yescomplemented
122#877—232no—
123C3×#95—22no—
124C3×#95—42no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—42no—
130C23×D4—32no—
131C23×D4—31no—
132C24×C4—31no—
133C2×#117—64no—
134C2×#117—64no—
135C2×#117—64no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4C2×D311yescharacteristic
139C22×C22⋊C4—31no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4C2×D311yescharacteristic
146C22×C22⋊C4C2×D312yes—
147C22×C42—31no—
148C22×C42—31no—
149#394—64no—
150#392—64no—
151#390—64no—
152#386—68no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95C2×D311yescharacteristic
159C2×#95C2×D312yes—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3C2×D412yes—
169C24×C3C2×D412yes—
170C24×C3#4112yes—
171C24×C3C2411yescharacteristic
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3#4114yes—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
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—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C2×#67—216no—
212C2×#67—48no—
213C2×#67—48no—
214C2×#67—48no—
215C2×#67—48no—
216C2×#67—48no—
217C2×#67—48no—
218C22×Dic3—28no—
219C22×Dic3—28no—
220C22×Dic3—28no—
221C22×Dic3—28no—
222C22×Dic3—28no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—28no—
232C22×Dic3—28no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
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×Dic3—22no—
247C22×Dic3C2×D412yes—
248C22×Dic3C2×D412yes—
249C22×Dic3C2×D412yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C22×Dic3C2×D412yes—
253C22×Dic3#4114yes—
254C22×Dic3#4112yes—
255C22×Dic3#4112yes—
256C2×D12—28no—
257C2×D12—48no—
258C2×D12—48no—
259C2×D12—44no—
260C2×D12—44no—
261C3×C4⋊C4—44no—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—48no—
264#217—28no—
265(C2×D3)⋊C4—48no—
266(C2×D3)⋊C4—48no—
267(C2×D3)⋊C4—48no—
268(C2×D3)⋊C4—48no—
269(C2×D3)⋊C4—48no—
270Dic3⋊C4—28no—
271Dic3⋊C4—28no—
272C4×Dic3—28no—
273C4×Dic3—28no—
274C25—32no—
275C25C22×D311yescharacteristic
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—64no—
282C22×D4—62no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—34no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—32no—
294C23×C4—62no—
295C23×C4—62no—
296C23×C4—62no—
297C23×C4—62no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4C22×D312yes—
301C23×C4C22×D312yes—
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304#117—632no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—34no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—62no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
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—122no—
333C2×C22⋊C4—122no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C22⋊C4D1214yes—
337C2×C42—34no—
338C2×C42—62no—
339C2×C42—62no—
340C2×C42—62no—
341C2×C42—62no—
342C2×C42—62no—
343#95—22no—
344#95—42no—
345#95—64no—
346#95—64no—
347#95—64no—
348#95—62no—
349#95—122no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—41no—
363C23×C3—42no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3#12114yes—
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×D411yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4112yes—
381C23×C3C2×#4112yes—
382C23×C3H(5,𝔽2)12yes—
383C23×C3H(5,𝔽2)12yes—
384C22×D3—24no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
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—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—22no—
424C2×C3×C4—24no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4#12014yes—
443#67—432no—
444C2×Dic3—232no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—24no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—24no—
465C2×Dic3—42no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3#12114yes—
475C2×Dic3#12114yes—
476D12—416no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—34no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24C2×D1212yes—
501C24D3×D412yes—
502C24#23912yes—
503C24C23×D311yescharacteristic
504C2×D4—68no—
505C2×D4—616no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—124no—
509C2×D4—128no—
510C2×D4—128no—
511C2×D4—128no—
512C2×D4—128no—
513C2×D4—128no—
514C2×D4—128no—
515C2×D4—124no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—34no—
545C22×C4—68no—
546C22×C4—68no—
547C22×C4—68no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—68no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—62no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4C2×D1212yes—
575C22×C4C2×D1212yes—
576C22×C4D3×D412yes—
577C22×C4D3×D412yes—
578C4⋊C4—44no—
579C4⋊C4—68no—
580C4⋊C4—68no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—68no—
584C22⋊C4—128no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22⋊C4—128no—
588C22⋊C4—128no—
589C42—68no—
590C42—68no—
591C22×C3—24no—
592C22×C3—28no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—44no—
599C22×C3—42no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3C2×#12011yescharacteristic
603C22×C3C2×#12111yescharacteristic
604C22×C3C2×#12111yescharacteristic
605C22×C3C2×#12111yescharacteristic
606C22×C3#52511yescharacteristic
607C22×C3#52512yes—
608C22×C3#52511yescharacteristic
609C22×C3#52511yescharacteristic
610C22×C3#52511yescharacteristic
611C22×C3#52912yes—
612C22×C3#53211yescharacteristic
613C22×C3#53511yescharacteristic
614C22×C3#53511yescharacteristic
615C22×C3#53512yes—
616C22×C3#54012yes—
617C22×C3#54612yes—
618C22×C3#54612yes—
619C22×C3#54612yes—
620C22×C3#55012yes—
621C22×C3#55112yes—
622C22×C3#55112yes—
623C22×C3#55312yes—
624C22×C3#55512yes—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3—82no—
636C2×D3—82no—
637C2×D3—82no—
638C2×D3—82no—
639C2×D3—82no—
640C3×C4—24no—
641C3×C4—42no—
642C3×C4—82no—
643C3×C4—82no—
644Dic3—24no—
645Dic3—24no—
646Dic3—42no—
647Dic3—44no—
648Dic3—42no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—64no—
672C23—64no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23#89514yes—
707C23C22×D1211yescharacteristic
708C23C2×D3×D411yescharacteristic
709C23C2×D3×D411yescharacteristic
710C23C2×D3×D411yescharacteristic
711C23#100412yes—
712C23#100412yes—
713C23C2×#23911yescharacteristic
714C23D3×#4112yes—
715C23D3×#4112yes—
716C23D3×#4111yescharacteristic
717C23D3×#4111yescharacteristic
718D4—1216no—
719D4—1232no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—34no—
727C2×C4—34no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—632no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—64no—
759C2×C4—64no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—122no—
767C2×C4—121no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—121no—
774C2×C4—122no—
775C2×C4#88214yes—
776C2×C3—44no—
777C2×C3#239211yescharacteristic
778C2×C3#240411yescharacteristic
779C2×C3#241112yes—
780C2×C3#241412yes—
781C2×C3#243111yescharacteristic
782C2×C3#247112yes—
783C2×C3#247612yes—
784C2×C3#259811yescharacteristic
785C2×C3#261011yescharacteristic
786C2×C3#261911yescharacteristic
787C2×C3#284711yescharacteristic
788D3—84no—
789C22—24no—
790C22—28no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—124no—
801C22—124no—
802C22—124no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—124no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22—242no—
812C22—242no—
813C22—242no—
814C22—242no—
815C22C2×#88211yescharacteristic
816C22C2×#89511yescharacteristic
817C22#552411yescharacteristic
818C22#555412yes—
819C22#555412yes—
820C22#559211yescharacteristic
821C22#559212yes—
822C22#559912yes—
823C22D3×#12111yescharacteristic
824C22D3×#12111yescharacteristic
825C22#561012yes—
826C22#561512yes—
827C22#562711yescharacteristic
828C22#562711yescharacteristic
829C22#563712yes—
830C22#563712yes—
831C22#565612yes—
832C22#565611yescharacteristic
833C22#566112yes—
834C22#566811yescharacteristic
835C22#567012yes—
836C22#570612yes—
837C22#571511yescharacteristic
838C4—24no—
839C4—42no—
840C4—64no—
841C4—64no—
842C4—82no—
843C4—82no—
844C4—122no—
845C4—124no—
846C4—122no—
847C3#1488611yescharacteristic, complemented, Sylow
848C2—44no—
849C2—244no—
850C2#7404811yescharacteristic
851C2#7460212yes—
852C2#7488511yescharacteristic
853C2#7586312yes—
854C2#7631311yescharacteristic
855C2#7669811yescharacteristic
856C2#7680811yescharacteristic
857C2#7689612yes—
858C2#7730012yes—
859C2#7745711yescharacteristic
860C2#7804411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC2×#4960C2
hypercenter#1439D3
hypocenterC3#14886
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#877C2semidirect
2. C2×#4988C2semidirect
4. C2×#4958C2semidirect
5. C2×#4672C2semidirect
6. C3×#1439C2semidirect
7. #71566C2semidirect
8. #71550C2semidirect
9. #69428C2semidirect
10. #69408C2semidirect
11. #69402C2semidirect
50. #1439D3semidirect
73. C23×Dic3D4semidirect
115. C2×Dic3⋊C4D4semidirect
121. C2×C4×Dic3D4semidirect
847. C3#14886semidirect

Maximal subgroups

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

subgroupindex
C22×#8772
C2×#49882
C2×#49602
C2×#49582
C2×#46722
C3×#14392
#715662
#715502
#694282
#694082
#694022
#148863