Finite Group Databasebeta

← #10728739

Subgroups — #10728739

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×#892C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#5221C211yesmaximal, characteristic, complemented
5C2×#4956C212yesmaximal, complemented
6#71565C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71546C212yesmaximal, complemented
9#71545C212yesmaximal, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69402C211yesmaximal, characteristic, complemented
12#14886—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2212yes—
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#892—24no—
30C2×#892—24no—
31C2×#892—24no—
32C3×#394—24no—
33C2×C3×#95C2211yescharacteristic
34#5223—24no—
35#5221—24no—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42#4956—28no—
43C22×#117—31no—
44C2×#394D311yescharacteristic, complemented
45C2×#392—31no—
46C2×#390—31no—
47C2×#386—32no—
48#1441—31no—
49#1439—31no—
50#1439—32no—
51#1438—32no—
52#1437—32no—
53#1434—31no—
54C25×C3C2312yes—
55C24×D3C2311yescharacteristic
56C22×C3×D4—24no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—42no—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—42no—
71C22×#67—42no—
72C23×Dic3C2312yes—
73C23×Dic3C2311yescharacteristic
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3D414yescomplemented
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4D414yescomplemented
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—42no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—42no—
100C2×#217—42no—
101C2×#217—42no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4D414yes—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3—42no—
116C2×C4×Dic3—22no—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3D414yescomplemented
122#892—232no—
123C3×#95—22no—
124C3⋊#95—24no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4—32no—
131C23×D4C2×D311yescharacteristic
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—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4C2×D312yes—
146C22×C22⋊C4C2×D312yes—
147C22×C42—31no—
148C22×C42—31no—
149#394—24no—
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×#95—32no—
159C2×#95C2×D311yescharacteristic
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3#4114yes—
175C24×C3C2411yescharacteristic
176C23×D3—21no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3C2×D412yes—
185C23×D3C2×D412yes—
186C23×D3#4112yes—
187C2×C3×D4—28no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—44no—
191C2×C3×D4—44no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
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×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4#4112yes—
216C2×#67—216no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C2×#67—48no—
221C2×#67—48no—
222C2×#67—48no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
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×Dic3C2×D412yes—
249C22×Dic3C2×D412yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C22×Dic3#4114yes—
253C22×Dic3#4112yes—
254C2×C4×D3—28no—
255C2×C4×D3—28no—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C2×C4×D3—28no—
259C2×C4×D3—28no—
260C2×C4×D3—28no—
261C3×C4⋊C4—28no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—48no—
264#217—48no—
265#217—48no—
266#217—48no—
267(C2×D3)⋊C4—28no—
268(C2×D3)⋊C4—28no—
269(C2×D3)⋊C4—48no—
270C4⋊Dic3—28no—
271C4⋊Dic3—44no—
272C4×Dic3—28no—
273C4×Dic3—28no—
274C25—31no—
275C25C22×D312yes—
276C22×D4—24no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—42no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—32no—
292C23×C4—34no—
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×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304#117—632no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—122no—
312C2×C4⋊C4#6714yescomplemented
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—62no—
324C2×C22⋊C4—62no—
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⋊C4—122no—
337C2×C42—34no—
338C2×C42—62no—
339C2×C42—62no—
340C2×C42—62no—
341C2×C42—62no—
342C2×C42—62no—
343#95—22no—
344#95—64no—
345#95—64no—
346#95—64no—
347#95—62no—
348#95—122no—
349#95—122no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4112yes—
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4112yes—
394C23×C3H(5,𝔽2)12yes—
395C23×C3H(5,𝔽2)12yes—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3—41no—
409C22×D3—42no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3#12114yes—
419C3×D4—416no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
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—
443C2×C3×C4#12114yes—
444#67—432no—
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—24no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—24no—
459C2×Dic3—42no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3#12114yes—
476C4×D3—232no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—32no—
492C24—32no—
493C24—32no—
494C24—61no—
495C24—61no—
496C24—62no—
497C24—62no—
498C24—61no—
499C24—62no—
500C24—62no—
501C24—61no—
502C24#23714yes—
503C24C23×D311yescharacteristic
504C2×D4—28no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—616no—
510C2×D4—128no—
511C2×D4—128no—
512C2×D4—128no—
513C2×D4—128no—
514C2×D4—128no—
515C2×D4—128no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
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—32no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—34no—
539C22×C4—68no—
540C22×C4—68no—
541C22×C4—68no—
542C22×C4—68no—
543C22×C4—68no—
544C22×C4—68no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—68no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4D3×D412yes—
572C22×C4D3×D412yes—
573C22×C4D3×D412yes—
574C22×C4#23712yes—
575C22×C4C2×#6712yes—
576C22×C4C2×#6712yes—
577C22×C4C2×#6712yes—
578C4⋊C4—28no—
579C4⋊C4—68no—
580C4⋊C4—124no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22⋊C4—128no—
588C22⋊C4—128no—
589C42—68no—
590C42—68no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—82no—
603C22×C3—82no—
604C22×C3—82no—
605C22×C3—82no—
606C22×C3C2×#12011yescharacteristic
607C22×C3C2×#12111yescharacteristic
608C22×C3C2×#12111yescharacteristic
609C22×C3C2×#12111yescharacteristic
610C22×C3#52511yescharacteristic
611C22×C3#52511yescharacteristic
612C22×C3#52511yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#52512yes—
615C22×C3#52912yes—
616C22×C3#53211yescharacteristic
617C22×C3#53511yescharacteristic
618C22×C3#53511yescharacteristic
619C22×C3#53512yes—
620C22×C3#54012yes—
621C22×C3#54612yes—
622C22×C3#54612yes—
623C22×C3#54612yes—
624C22×C3#55012yes—
625C22×C3#55112yes—
626C22×C3#55112yes—
627C22×C3#55312yes—
628C22×C3#55512yes—
629C2×D3—24no—
630C2×D3—28no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—44no—
637C2×D3—42no—
638C2×D3—44no—
639C2×D3—44no—
640C3×C4—24no—
641C3×C4—24no—
642C3×C4—42no—
643C3×C4—82no—
644Dic3—24no—
645Dic3—44no—
646Dic3—42no—
647Dic3—42no—
648Dic3—82no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—34no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—64no—
686C23—64no—
687C23—64no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—64no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—64no—
696C23—64no—
697C23—122no—
698C23—122no—
699C23—121no—
700C23—121no—
701C23—122no—
702C23—122no—
703C23—121no—
704C23—121no—
705C23—122no—
706C23—122no—
707C23C2×D3×D411yescharacteristic
708C23C2×D3×D411yescharacteristic
709C23C2×D3×D411yescharacteristic
710C23C2×#23712yes—
711C23C2×#23711yescharacteristic
712C23#100412yes—
713C23D3×#4111yescharacteristic
714C23D3×#4112yes—
715C23D3×#4111yescharacteristic
716C23#100912yes—
717C23C22×#6711yescharacteristic
718D4—416no—
719D4—1232no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—34no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—632no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—122no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4#93714yes—
775C2×C4#93814yes—
776C2×C3—84no—
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—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—64no—
797C22—68no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—122no—
807C22—124no—
808C22—122no—
809C22—124no—
810C22—122no—
811C22—122no—
812C22—124no—
813C22—122no—
814C22—122no—
815C22#558611yescharacteristic
816C22#559112yes—
817C22#559211yescharacteristic
818C22D3×#12111yescharacteristic
819C22D3×#12111yescharacteristic
820C22#560612yes—
821C22#560611yescharacteristic
822C22#560611yescharacteristic
823C22#560712yes—
824C22#561612yes—
825C22#561812yes—
826C22#564912yes—
827C22#565812yes—
828C22#565912yes—
829C22#566312yes—
830C22#566811yescharacteristic
831C22#567411yescharacteristic
832C22#567612yes—
833C22C2×#93711yescharacteristic
834C22C2×#93811yescharacteristic
835C22#580612yes—
836C22#582811yescharacteristic
837C22#583412yes—
838C4—24no—
839C4—24no—
840C4—42no—
841C4—64no—
842C4—82no—
843C4—122no—
844C4—122no—
845C4—124no—
846C4—242no—
847C3#1488611yescharacteristic, complemented, Sylow
848C2—84no—
849C2—124no—
850C2#7689111yescharacteristic
851C2#7692912yes—
852C2#7696211yescharacteristic
853C2#7696911yescharacteristic
854C2#7697111yescharacteristic
855C2#7710912yes—
856C2#8258111yescharacteristic
857C2#8270312yes—
858C2#8272311yescharacteristic
859C2#8285512yes—
860C2#8295811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3#14886
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#892C2semidirect
2. C2×C3×#394C2semidirect
4. C2×#5221C2semidirect
5. C2×#4956C2semidirect
6. #71565C2semidirect
7. #71550C2semidirect
8. #71546C2semidirect
9. #71545C2semidirect
10. #69427C2semidirect
11. #69402C2semidirect
44. C2×#394D3semidirect
83. C22×C4×D3D4semidirect
86. C2×C3×C4⋊C4D4semidirect
121. C2×C4×Dic3D4semidirect
312. C2×C4⋊C4#67semidirect
847. C3#14886semidirect

Maximal subgroups

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

subgroupindex
C22×#8922
C2×C3×#3942
C2×#52232
C2×#52212
C2×#49562
#715652
#715502
#715462
#715452
#694272
#694022
#148863