Finite Group Databasebeta

← #10729040

Subgroups — #10729040

Order 768.

2638 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic, complemented
3C2×#5220C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71549C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69413C212yesmaximal, complemented
12#14913—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2212yes—
24C2×#939—24no—
25C2×#939—24no—
26C2×#939—24no—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×Dic3⋊C4C2211yescharacteristic
31C3×#386—24no—
32C2×C3×#95C2212yes—
33#5220—24no—
34#5213—24no—
35C2×C3⋊#95—24no—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4958—24no—
44C22×#121—31no—
45C2×#386—31no—
46C2×#386—31no—
47C2×#386—31no—
48C2×#386D311yescharacteristic, complemented
49C22×#95—31no—
50#1442—32no—
51#1440—32no—
52#1440—32no—
53#1438—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4D414yes—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—42no—
68C23×C3×C4—42no—
69C23×C3×C4D414yescomplemented
70C23×C3×C4C2312yes—
71C23×C3×C4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C22×#67—22no—
74C22×#67—22no—
75C22×#67—22no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—24no—
83C22×#67—42no—
84C22×#67D414yes—
85C23×Dic3—22no—
86C23×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—24no—
89C23×Dic3—24no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—42no—
93C23×Dic3—42no—
94C23×Dic3D414yes—
95C23×Dic3C2312yes—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2312yes—
99C23×Dic3C2311yescharacteristic
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—24no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—24no—
114C2×#217—42no—
115#939—232no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—42no—
123C2×(C2×D3)⋊C4—42no—
124C2×(C2×D3)⋊C4—42no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C3×#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—24no—
134C3⋊#95—24no—
135C3⋊#95—42no—
136C23×D4—31no—
137C23×D4—31no—
138C23×D4C2×D311yescharacteristic
139C24×C4—31no—
140C24×C4—31no—
141C24×C4C2×D311yescharacteristic
142C2×#121—64no—
143C2×#121—64no—
144C2×#121—64no—
145C22×C4⋊C4—31no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4C2×D311yescharacteristic
153C22×C22⋊C4C2×D312yes—
154#386—24no—
155#386—64no—
156#386—64no—
157#386—64no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95—32no—
165C2×#95—64no—
166C2×#95C2×D312yes—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3C2×D412yes—
182C24×C3C2×D412yes—
183C24×C3C2×D412yes—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3#4112yes—
187C24×C3#4112yes—
188C24×C3#4112yes—
189C24×C3C2411yescharacteristic
190C23×D3—21no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—22no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3C2×D412yes—
201C2×C3×D4—28no—
202C2×C3×D4—28no—
203C2×C3×D4—28no—
204C2×C3×D4—44no—
205C2×C3×D4—44no—
206C2×C3×D4—44no—
207C2×C3×D4—44no—
208C22×C3×C4—28no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—48no—
229C22×C3×C4—44no—
230C22×C3×C4—44no—
231C22×C3×C4—48no—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D414yes—
234C2×#67—28no—
235C2×#67—28no—
236C2×#67—28no—
237C2×#67—28no—
238C2×#67—48no—
239C2×#67—48no—
240C2×#67—44no—
241C2×#67—44no—
242C2×#67—44no—
243C2×#67—44no—
244C2×#67—44no—
245C2×#67—44no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249C22×Dic3—28no—
250C22×Dic3—28no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—28no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—44no—
276C22×Dic3—48no—
277C22×Dic3—48no—
278C22×Dic3—48no—
279C22×Dic3—48no—
280C22×Dic3—44no—
281C22×Dic3—44no—
282C22×Dic3C2×D412yes—
283C22×Dic3C2×D412yes—
284C22×Dic3C2×D412yes—
285C22×Dic3#4114yes—
286C22×Dic3#4114yes—
287C3×C22⋊C4—48no—
288C3×C22⋊C4—44no—
289#217—28no—
290#217—48no—
291#217—44no—
292(C2×D3)⋊C4—28no—
293(C2×D3)⋊C4—48no—
294(C2×D3)⋊C4—48no—
295Dic3⋊C4—28no—
296C25—31no—
297C25C22×D311yescharacteristic
298C25C22×D311yescharacteristic
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—34no—
306C22×D4—62no—
307C22×D4—64no—
308C22×D4—62no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—62no—
312C22×D4—62no—
313C22×D4—62no—
314C22×D4—62no—
315C22×D4—62no—
316C22×D4—122no—
317C22×D4D1214yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—32no—
323C23×C4—31no—
324C23×C4—34no—
325C23×C4—32no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—64no—
329C23×C4—64no—
330C23×C4—62no—
331C23×C4—62no—
332C23×C4—62no—
333C23×C4—62no—
334C23×C4—62no—
335C23×C4—122no—
336C23×C4—122no—
337C23×C4#6714yescomplemented
338C23×C4C22×D312yes—
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D312yes—
341#121—632no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—62no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—62no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—122no—
366C2×C22⋊C4—122no—
367C2×C22⋊C4—122no—
368C2×C22⋊C4—122no—
369#95—24no—
370#95—64no—
371#95—64no—
372#95—64no—
373#95—64no—
374#95—64no—
375#95—64no—
376#95—122no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—22no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3#12014yes—
417C23×C3#12114yes—
418C23×C3#12114yes—
419C23×C3#12114yes—
420C23×C3#12314yes—
421C23×C3#12314yes—
422C23×C3#12414yes—
423C23×C3C22×D411yescharacteristic
424C23×C3C22×D411yescharacteristic
425C23×C3C22×D411yescharacteristic
426C23×C3C22×D411yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4112yes—
431C23×C3C2×#4112yes—
432C23×C3H(5,𝔽2)12yes—
433C23×C3H(5,𝔽2)12yes—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—42no—
457C3×D4—416no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—416no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480#67—416no—
481#67—416no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—416no—
496C2×Dic3—416no—
497C2×Dic3—42no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—42no—
503C2×Dic3—42no—
504C2×Dic3—42no—
505C2×Dic3—42no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3#12314yes—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—21no—
529C24—32no—
530C24—61no—
531C24—61no—
532C24—61no—
533C24—61no—
534C24—61no—
535C24—62no—
536C24—62no—
537C24—62no—
538C24—62no—
539C24—61no—
540C24C2×D1212yes—
541C24C2×D1212yes—
542C24#23512yes—
543C24D3×D412yes—
544C24D3×D412yes—
545C24#23712yes—
546C24#23712yes—
547C24C2×#6712yes—
548C24C23×D311yescharacteristic
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—68no—
557C2×D4—68no—
558C2×D4—68no—
559C2×D4—68no—
560C2×D4—124no—
561C2×D4—128no—
562C2×D4—128no—
563C2×D4—124no—
564C2×D4—124no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—124no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—32no—
589C22×C4—34no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—34no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—68no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—62no—
601C22×C4—68no—
602C22×C4—68no—
603C22×C4—62no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—61no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—124no—
627C22×C4—128no—
628C22×C4—128no—
629C22×C4—128no—
630C22×C4—128no—
631C22×C4—124no—
632C22×C4—124no—
633C22×C4C2×D1212yes—
634C22×C4C2×#6714yes—
635C4⋊C4—68no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—68no—
639C22⋊C4—68no—
640C22⋊C4—128no—
641C22⋊C4—128no—
642C22⋊C4—128no—
643C22⋊C4—124no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—28no—
650C22×C3—28no—
651C22×C3—24no—
652C22×C3—28no—
653C22×C3—28no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—82no—
663C22×C3—81no—
664C22×C3—82no—
665C22×C3#39418yes—
666C22×C3C2×#12011yescharacteristic
667C22×C3C2×#12111yescharacteristic
668C22×C3C2×#12111yescharacteristic
669C22×C3C2×#12111yescharacteristic
670C22×C3C2×#12311yescharacteristic
671C22×C3C2×#12311yescharacteristic
672C22×C3C2×#12311yescharacteristic
673C22×C3#52511yescharacteristic
674C22×C3C2×#12411yescharacteristic
675C22×C3#52912yes—
676C22×C3#53212yes—
677C22×C3#53412yes—
678C22×C3#53411yescharacteristic
679C22×C3#53511yescharacteristic
680C22×C3#53812yes—
681C22×C3#54612yes—
682C22×C3#54612yes—
683C22×C3#54612yes—
684C22×C3#54612yes—
685C22×C3#55312yes—
686C22×C3#55312yes—
687C22×C3#55312yes—
688C22×C3#55312yes—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—44no—
693C2×D3—44no—
694C2×D3—81no—
695C2×D3—81no—
696C2×D3—81no—
697C2×D3—82no—
698C2×D3—81no—
699C2×D3—82no—
700C3×C4—44no—
701C3×C4—42no—
702C3×C4—82no—
703Dic3—24no—
704Dic3—42no—
705Dic3—44no—
706Dic3—42no—
707Dic3—82no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—64no—
751C23—64no—
752C23—122no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—122no—
759C23—122no—
760C23—121no—
761C23—122no—
762C23—122no—
763C23—122no—
764C23—122no—
765C23—121no—
766C23—121no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23#88214yes—
771C23#88314yes—
772C23#88514yes—
773C23#88614yes—
774C23#93014yes—
775C23#93814yes—
776C23#93914yes—
777C23C22×D1211yescharacteristic
778C23C2×#23511yescharacteristic
779C23C2×D3×D411yescharacteristic
780C23C2×D3×D411yescharacteristic
781C23C2×#23711yescharacteristic
782C23C2×#23711yescharacteristic
783C23#100412yes—
784C23#100412yes—
785C23D3×#4112yes—
786C23D3×#4112yes—
787C23C22×#6711yescharacteristic
788D4—416no—
789D4—1216no—
790D4—1216no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—34no—
798C2×C4—416no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—62no—
815C2×C4—64no—
816C2×C4—62no—
817C2×C4—64no—
818C2×C4—62no—
819C2×C4—64no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—64no—
825C2×C4—62no—
826C2×C4—64no—
827C2×C4—1216no—
828C2×C4—1216no—
829C2×C4—122no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—122no—
840C2×C4—122no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C3—28no—
847C2×C3—82no—
848C2×C3C2×#39411yescharacteristic
849C2×C3#240411yescharacteristic
850C2×C3#240511yescharacteristic
851C2×C3#244412yes—
852C2×C3#244412yes—
853C2×C3#250411yescharacteristic
854C2×C3#254312yes—
855C2×C3#254312yes—
856C2×C3#259111yescharacteristic
857C2×C3#261711yescharacteristic
858C2×C3#285411yescharacteristic
859D3—82no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—28no—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—44no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—81no—
881C22—122no—
882C22—122no—
883C22—122no—
884C22—124no—
885C22—124no—
886C22—241no—
887C22—241no—
888C22—241no—
889C22—242no—
890C22—242no—
891C22—241no—
892C22#496118yes—
893C22C2×#88211yescharacteristic
894C22C2×#88311yescharacteristic
895C22C2×#88511yescharacteristic
896C22C2×#88611yescharacteristic
897C22#554012yes—
898C22#554012yes—
899C22#555412yes—
900C22#555412yes—
901C22#558911yescharacteristic
902C22#559211yescharacteristic
903C22#559312yes—
904C22#560112yes—
905C22#560112yes—
906C22#561012yes—
907C22#561012yes—
908C22#564912yes—
909C22D3×#12311yescharacteristic
910C22#565611yescharacteristic
911C22C2×#93011yescharacteristic
912C22C2×#93811yescharacteristic
913C22C2×#93911yescharacteristic
914C22#580412yes—
915C22#583212yes—
916C4—44no—
917C4—42no—
918C4—64no—
919C4—82no—
920C4—124no—
921C4—122no—
922C4—122no—
923C4—242no—
924C3#1491311yescharacteristic, complemented, Sylow
925C2—28no—
926C2—82no—
927C2—242no—
928C2#7468611yescharacteristic
929C2#7470612yes—
930C2#7470712yes—
931C2#7474211yescharacteristic
932C2#7477211yescharacteristic
933C2#7488511yescharacteristic
934C2C2×#496111yescharacteristic
935C2#8238012yes—
936C2#8259211yescharacteristic
937C2#8267112yes—
938C2#8289111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#14913
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×#386C2semidirect
3. C2×#5220C2semidirect
4. C2×#5213C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4958C2semidirect
7. #71550C2semidirect
8. #71549C2semidirect
9. #71544C2semidirect
10. #69429C2semidirect
11. #69413C2semidirect
48. C2×#386D3semidirect
69. C23×C3×C4D4semidirect
337. C23×C4#67semidirect
924. C3#14913semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C2×C3×#3862
C2×#52202
C2×#52132
C22×C3⋊#952
C2×#49582
#715502
#715492
#715442
#694292
#694132
#149133