Finite Group Databasebeta

← #10729038

Subgroups — #10729038

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#71548C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69414C212yesmaximal, 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—24no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—42no—
70C23×C3×C4C2312yes—
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2312yes—
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—22no—
89C23×Dic3—24no—
90C23×Dic3—42no—
91C23×Dic3—42no—
92C23×Dic3—42no—
93C23×Dic3D414yes—
94C23×Dic3D414yescomplemented
95C23×Dic3C2312yes—
96C23×Dic3C2312yes—
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—42no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—24no—
113C2×#217—42no—
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—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
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—48no—
230C22×C3×C4—44no—
231C22×C3×C4—44no—
232C22×C3×C4C2×D412yes—
233C22×C3×C4#4114yes—
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—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—22no—
263C22×Dic3—22no—
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—44no—
280C22×Dic3—44no—
281C22×Dic3—48no—
282C22×Dic3C2×D412yes—
283C22×Dic3C2×D412yes—
284C22×Dic3C2×D414yes—
285C22×Dic3C2×D412yes—
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×D4#6714yes—
318C23×C4—22no—
319C23×C4—24no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—31no—
323C23×C4—32no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—34no—
327C23×C4—34no—
328C23×C4—32no—
329C23×C4—42no—
330C23×C4—64no—
331C23×C4—62no—
332C23×C4—62no—
333C23×C4—62no—
334C23×C4—62no—
335C23×C4—122no—
336C23×C4—122no—
337C23×C4—122no—
338C23×C4C22×D312yes—
339C23×C4C22×D312yes—
340C23×C4C22×D311yescharacteristic
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—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
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—62no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—122no—
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—22no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—416no—
465C2×C3×C4—42no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
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—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—22no—
495C2×Dic3—416no—
496C2×Dic3—416no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—42no—
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—21no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—32no—
530C24—61no—
531C24—61no—
532C24—61no—
533C24—61no—
534C24—62no—
535C24—61no—
536C24—62no—
537C24—62no—
538C24—62no—
539C24—61no—
540C24#23512yes—
541C24#23512yes—
542C24D3×D412yes—
543C24D3×D412yes—
544C24D3×D412yes—
545C24#23712yes—
546C24C2×#6712yes—
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—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
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—34no—
592C22×C4—32no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—68no—
598C22×C4—61no—
599C22×C4—62no—
600C22×C4—61no—
601C22×C4—68no—
602C22×C4—68no—
603C22×C4—62no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—62no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—61no—
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—124no—
631C22×C4—128no—
632C22×C4—124no—
633C22×C4#23714yes—
634C22×C4C2×#6712yes—
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#53411yescharacteristic
678C22×C3#53412yes—
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—42no—
701C3×C4—44no—
702C3×C4—82no—
703Dic3—24no—
704Dic3—44no—
705Dic3—42no—
706Dic3—42no—
707Dic3—82no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—41no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—64no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—64no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—122no—
758C23—122no—
759C23—121no—
760C23—122no—
761C23—122no—
762C23—122no—
763C23—122no—
764C23—121no—
765C23—121no—
766C23—122no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23#88314yes—
771C23#88414yes—
772C23#88414yes—
773C23#88514yes—
774C23#92914yes—
775C23#93714yes—
776C23#93914yes—
777C23C2×#23511yescharacteristic
778C23C2×#23511yescharacteristic
779C23C2×D3×D411yescharacteristic
780C23C2×D3×D411yescharacteristic
781C23C2×D3×D411yescharacteristic
782C23C2×#23711yescharacteristic
783C23C2×#23712yes—
784C23#100412yes—
785C23D3×#4112yes—
786C23#100912yes—
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—62no—
820C2×C4—62no—
821C2×C4—64no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—64no—
826C2×C4—64no—
827C2×C4—1216no—
828C2×C4—1216no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
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—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—28no—
866C22—24no—
867C22—28no—
868C22—28no—
869C22—24no—
870C22—42no—
871C22—44no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—82no—
880C22—81no—
881C22—124no—
882C22—122no—
883C22—122no—
884C22—122no—
885C22—124no—
886C22—241no—
887C22—241no—
888C22—241no—
889C22—242no—
890C22—242no—
891C22—241no—
892C22#495918yes—
893C22C2×#88311yescharacteristic
894C22C2×#88411yescharacteristic
895C22C2×#88411yescharacteristic
896C22C2×#88511yescharacteristic
897C22#553812yes—
898C22#554012yes—
899C22#556012yes—
900C22#556512yes—
901C22#558611yescharacteristic
902C22#559112yes—
903C22#559211yescharacteristic
904C22#559612yes—
905C22#560112yes—
906C22#560512yes—
907C22#561812yes—
908C22D3×#12311yescharacteristic
909C22#565311yescharacteristic
910C22#565412yes—
911C22C2×#92911yescharacteristic
912C22C2×#93711yescharacteristic
913C22C2×#93911yescharacteristic
914C22#580612yes—
915C22#582912yes—
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#7470512yes—
929C2#7474211yescharacteristic
930C2#7475212yes—
931C2#7477111yescharacteristic
932C2#7487211yescharacteristic
933C2#7490511yescharacteristic
934C2C2×#495911yescharacteristic
935C2#8235712yes—
936C2#8258111yescharacteristic
937C2#8267012yes—
938C2#8289311yescharacteristic
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. #71548C2semidirect
9. #71544C2semidirect
10. #69429C2semidirect
11. #69414C2semidirect
48. C2×#386D3semidirect
94. C23×Dic3D4semidirect
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
#715482
#715442
#694292
#694142
#149133