Finite Group Databasebeta

← #10731938

Subgroups — #10731938

Order 768.

1922 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#390C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic, complemented
5C2×#4949C212yesmaximal, complemented
6C2×#4928C211yesmaximal, characteristic, complemented
7C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71546C212yesmaximal, complemented
12#15148—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C3×#390—24no—
31#5221—24no—
32#5221—24no—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4984—24no—
40#4949—28no—
41C4×Dic3⋊C4—24no—
42#4928—24no—
43C2×#399—32no—
44C2×#390—31no—
45C2×#390—31no—
46C2×#390D311yescharacteristic
47C2×#389—31no—
48C2×#389—31no—
49C2×C4×C4⋊C4—31no—
50#1439—32no—
51#1439—32no—
52#1439—32no—
53C4⋊#95—31no—
54C25×C3C2312yes—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4Q814yes—
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×Dic3C2312yes—
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C23×Dic3C2311yescharacteristic
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4D414yes—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—42no—
80C2×C3×C22⋊C4—42no—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×C3×C42—22no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—42no—
93C2×#217—42no—
94C2×#217—42no—
95C2×#217—42no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—24no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—24no—
103C2×C4⋊Dic3—42no—
104C2×C4⋊Dic3D414yes—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—42no—
113C2×Dic3⋊C4D414yescomplemented
114C2×C4×Dic3—22no—
115C2×C4×Dic3—22no—
116C2×C4×Dic3—22no—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3D414yes—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—22no—
123C3⋊#95—22no—
124C3⋊#95—24no—
125C3⋊#95—42no—
126C23×D4C2×D311yescharacteristic
127C22×C4⋊C4—31no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4—32no—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4C2×D312yes—
139C22×C22⋊C4C2×D312yes—
140C22×C42—31no—
141C22×C42—31no—
142C22×C42C2×D311yescharacteristic
143#399—68no—
144#390—24no—
145#390—64no—
146#390—64no—
147#389—64no—
148#389—64no—
149C4×C4⋊C4—64no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
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×C3C2×Q814yes—
171C24×C3C2411yescharacteristic
172C2×C3×D4—28no—
173C2×C3×D4—28no—
174C2×C3×D4—28no—
175C2×C3×D4—44no—
176C2×C3×D4—44no—
177C2×C3×D4—44no—
178C2×C3×D4—44no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D414yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×Q812yes—
203C22×C3×C4#4112yes—
204C22×C3×C4#4112yes—
205C22×C3×C4#4112yes—
206C22×C3×C4#4112yes—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3C2×D412yes—
243C22×Dic3C2×D414yes—
244C22×Dic3C2×D412yes—
245C22×Dic3C2×D412yes—
246C22×Dic3C2×D412yes—
247C22×Dic3#4112yes—
248C22×Dic3#4112yes—
249C3×C4⋊C4—28no—
250C3×C22⋊C4—48no—
251C3×C22⋊C4—48no—
252C3×C42—44no—
253#217—48no—
254#217—48no—
255#217—48no—
256#217—48no—
257C4⋊Dic3—28no—
258C4⋊Dic3—48no—
259C4⋊Dic3—44no—
260Dic3⋊C4—28no—
261Dic3⋊C4—28no—
262Dic3⋊C4—48no—
263C4×Dic3—28no—
264C4×Dic3—44no—
265C25C22×D312yes—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4Dic614yes—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4—32no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—32no—
279C23×C4C22×D311yescharacteristic
280C23×C4C22×D311yescharacteristic
281C23×C4C22×D312yes—
282C23×C4C22×D311yescharacteristic
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—34no—
286C2×C4⋊C4—34no—
287C2×C4⋊C4—62no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—62no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—62no—
292C2×C4⋊C4—62no—
293C2×C4⋊C4—62no—
294C2×C4⋊C4—64no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—122no—
302C2×C4⋊C4—122no—
303C2×C4⋊C4#6714yes—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—34no—
326C2×C42—62no—
327C2×C42—62no—
328C2×C42—62no—
329C2×C42—62no—
330C2×C42—62no—
331#95—62no—
332#95—62no—
333#95—64no—
334#95—64no—
335#95—64no—
336#95—122no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
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×C3C22×D411yescharacteristic
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×Q811yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4111yescharacteristic
381C23×C3C2×#4111yescharacteristic
382C23×C3C2×#4111yescharacteristic
383C23×C3H(5,𝔽2)11yescharacteristic
384C23×C3H(5,𝔽2)11yescharacteristic
385C23×C3H(5,𝔽2)11yescharacteristic
386C23×C32−1+411yescharacteristic
387C3×D4—416no—
388C2×C3×C4—22no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—42no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—42no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409C2×C3×C4C22⋊Q814yes—
410C2×C3×C4C22⋊Q814yes—
411C2×C3×C4C22⋊Q814yes—
412C2×C3×C4#12314yes—
413C2×C3×C4#12314yes—
414C2×C3×C4#12314yes—
415C2×C3×C4#12714yes—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—24no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—42no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3#12114yes—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C2×Dic614yes—
473C24C23×D311yescharacteristic
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—32no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—34no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—62no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—62no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4C2×Dic612yes—
542C22×C4#23512yes—
543C22×C4D3×D412yes—
544C22×C4D3×D412yes—
545C22×C4D3×D412yes—
546C22×C4#23712yes—
547C22×C4#23712yes—
548C22×C4#23712yes—
549C22×C4C2×#6714yes—
550C22×C4C2×#6712yes—
551C4⋊C4—28no—
552C4⋊C4—68no—
553C4⋊C4—68no—
554C4⋊C4—68no—
555C4⋊C4—128no—
556C4⋊C4—128no—
557C4⋊C4—124no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—128no—
561C22⋊C4—128no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C42—44no—
565C42—68no—
566C42—124no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—82no—
575C22×C3—82no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3C2×#12111yescharacteristic
583C22×C3C2×C22⋊Q811yescharacteristic
584C22×C3C2×C22⋊Q811yescharacteristic
585C22×C3C2×C22⋊Q811yescharacteristic
586C22×C3C2×#12311yescharacteristic
587C22×C3C2×#12311yescharacteristic
588C22×C3C2×#12311yescharacteristic
589C22×C3#52511yescharacteristic
590C22×C3#52911yescharacteristic
591C22×C3#52911yescharacteristic
592C22×C3C2×#12711yescharacteristic
593C22×C3#53211yescharacteristic
594C22×C3#53211yescharacteristic
595C22×C3#53511yescharacteristic
596C22×C3#53711yescharacteristic
597C22×C3#54011yescharacteristic
598C22×C3#54011yescharacteristic
599C22×C3#54211yescharacteristic
600C22×C3#54211yescharacteristic
601C22×C3D4211yescharacteristic
602C22×C3D4211yescharacteristic
603C22×C3#54611yescharacteristic
604C22×C3#54611yescharacteristic
605C22×C3#54811yescharacteristic
606C22×C3#54811yescharacteristic
607C22×C3D4×Q811yescharacteristic
608C22×C3#55011yescharacteristic
609C22×C3#55011yescharacteristic
610C22×C3#55011yescharacteristic
611C22×C3#55411yescharacteristic
612C22×C3#55411yescharacteristic
613C22×C3#55411yescharacteristic
614C22×C3#55611yescharacteristic
615C22×C3#55911yescharacteristic
616C22×C3#55911yescharacteristic
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4#39918yescomplemented
621Dic3—24no—
622Dic3—42no—
623Dic3—44no—
624Dic3—42no—
625Dic3—42no—
626Dic3—82no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23C22×Dic611yescharacteristic
663C23C2×#23511yescharacteristic
664C23C2×D3×D411yescharacteristic
665C23C2×D3×D411yescharacteristic
666C23C2×D3×D411yescharacteristic
667C23C2×#23711yescharacteristic
668C23C2×#23711yescharacteristic
669C23C2×#23711yescharacteristic
670C23#100411yescharacteristic
671C23#100411yescharacteristic
672C23D3×#4111yescharacteristic
673C23D3×#4111yescharacteristic
674C23#100911yescharacteristic
675C23#101011yescharacteristic
676C23C22×#6711yescharacteristic
677D4—416no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—34no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—64no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—64no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—122no—
719C2×C4—121no—
720C2×C4—122no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—122no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—122no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4#87814yes—
742C2×C4#87814yes—
743C2×C4#88314yes—
744C2×C4#88314yes—
745C2×C4#92414yes—
746C2×C4#93514yes—
747C2×C4#94014yes—
748C2×C3—84no—
749C2×C3C2×#39911yescharacteristic
750C2×C3#244511yescharacteristic
751C2×C3#244511yescharacteristic
752C2×C3#244811yescharacteristic
753C2×C3#244811yescharacteristic
754C2×C3#245211yescharacteristic
755C2×C3#245211yescharacteristic
756C2×C3#245411yescharacteristic
757C2×C3#245411yescharacteristic
758C2×C3#253811yescharacteristic
759C2×C3#254011yescharacteristic
760C2×C3#254111yescharacteristic
761C2×C3#258011yescharacteristic
762C2×C3#262411yescharacteristic
763C2×C3#285411yescharacteristic
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22C2×#87811yescharacteristic
780C22C2×#87811yescharacteristic
781C22C2×#88311yescharacteristic
782C22C2×#88311yescharacteristic
783C22D4×Dic611yescharacteristic
784C22#553911yescharacteristic
785C22#553911yescharacteristic
786C22#554311yescharacteristic
787C22#554811yescharacteristic
788C22#555711yescharacteristic
789C22#556111yescharacteristic
790C22#556211yescharacteristic
791C22#559811yescharacteristic
792C22#559911yescharacteristic
793C22D3×#12111yescharacteristic
794C22#560611yescharacteristic
795C22#560711yescharacteristic
796C22#560811yescharacteristic
797C22#560911yescharacteristic
798C22#561211yescharacteristic
799C22#567111yescharacteristic
800C22#568011yescharacteristic
801C22#568111yescharacteristic
802C22#568211yescharacteristic
803C22#571311yescharacteristic
804C22#571611yescharacteristic
805C22#571811yescharacteristic
806C22#571911yescharacteristic
807C22C2×#92411yescharacteristic
808C22C2×#93511yescharacteristic
809C22D4×#6711yescharacteristic
810C22C2×#94011yescharacteristic
811C22#580611yescharacteristic
812C22#583111yescharacteristic
813C22#583411yescharacteristic
814C4—44no—
815C4—42no—
816C4—42no—
817C4—64no—
818C4—124no—
819C4—122no—
820C4—122no—
821C4—122no—
822C4—242no—
823C4#494918yescomplemented
824C3#1514811yescharacteristic, complemented, Sylow
825C2—84no—
826C2#7631611yescharacteristic
827C2#7632011yescharacteristic
828C2#7632211yescharacteristic
829C2#7632411yescharacteristic
830C2#7634611yescharacteristic
831C2#7636411yescharacteristic
832C2#7645811yescharacteristic
833C2#7647511yescharacteristic
834C2C2×#494911yescharacteristic
835C2#8236211yescharacteristic
836C2#8236311yescharacteristic
837C2#8266811yescharacteristic
838C2#8266911yescharacteristic
839C2#8296311yescharacteristic
840C2#8317611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#15148
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#4984C2semidirect
5. C2×#4949C2semidirect
6. C2×#4928C2semidirect
7. C2×C4×Dic3⋊C4C2semidirect
8. #71563C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71546C2semidirect
113. C2×Dic3⋊C4D4semidirect
620. C3×C4#399semidirect
823. C4#4949semidirect
824. C3#15148semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×#52212
C2×#49842
C2×#49492
C2×#49282
C2×C4×Dic3⋊C42
#715632
#715472
#715462
#151483