Finite Group Databasebeta

← #10729125

Subgroups — #10729125

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#385C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C22×C3⋊#95C211yesmaximal, characteristic, complemented
4C2×#4958C211yesmaximal, characteristic
5C2×#4958C211yesmaximal, characteristic
6C2×#4942C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71566C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11#69418C212yesmaximal, complemented
12#14921—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2212yes—
26C3×#385—24no—
27C2×C3×#95C2212yes—
28#5213—24no—
29C2×C3⋊#95—24no—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39#4958—24no—
40#4958—24no—
41#4942—24no—
42C2×#386—31no—
43C2×#386—31no—
44C2×#386—31no—
45C2×#385D311yescharacteristic, complemented
46C2×#380—31no—
47C22×#95—31no—
48#1443—32no—
49#1441—32no—
50#1439—32no—
51#1439—32no—
52C22⋊#95—31no—
53C25×C3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—42no—
58C23×C3×C4—42no—
59C23×C3×C4D414yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C22×#67—22no—
65C22×#67—22no—
66C22×#67—22no—
67C22×#67—22no—
68C22×#67—22no—
69C22×#67—22no—
70C22×#67Q814yes—
71C23×Dic3—22no—
72C23×Dic3—22no—
73C23×Dic3—22no—
74C23×Dic3—24no—
75C23×Dic3—24no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—42no—
79C23×Dic3—42no—
80C23×Dic3D414yes—
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2312yes—
85C23×Dic3C2311yescharacteristic
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—42no—
88C2×C3×C4⋊C4—42no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4D414yes—
95C2×#217—22no—
96C2×#217—22no—
97C2×#217—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—42no—
105C2×(C2×D3)⋊C4—42no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—42no—
111C3×#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—42no—
121C23×D4—31no—
122C24×C4—31no—
123C24×C4—31no—
124C24×C4C2×D311yescharacteristic
125C22×C4⋊C4—32no—
126C22×C4⋊C4C2×D312yes—
127C22×C22⋊C4—31no—
128C22×C22⋊C4—31no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4C2×D311yescharacteristic
133C22×C22⋊C4C2×D311yescharacteristic
134#386—64no—
135#386—64no—
136#386—64no—
137#385—24no—
138#380—64no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—31no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95—64no—
149C2×#95C2×D312yes—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3C2×D412yes—
155C24×C3C2×D412yes—
156C24×C3C2×D412yes—
157C24×C3C2×Q812yes—
158C24×C3#4112yes—
159C24×C3#4112yes—
160C24×C3#4112yes—
161C24×C3C2411yescharacteristic
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—21no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3C2×Q812yes—
173C22×C3×C4—28no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—48no—
197C22×C3×C4—44no—
198C22×C3×C4—44no—
199C22×C3×C4—48no—
200C22×C3×C4C2×D414yes—
201C22×C3×C4C2×D414yes—
202C2×#67—28no—
203C2×#67—28no—
204C2×#67—28no—
205C2×#67—44no—
206C2×#67—44no—
207C2×#67—44no—
208C2×#67—44no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—28no—
213C22×Dic3—28no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—28no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—44no—
239C22×Dic3—48no—
240C22×Dic3—48no—
241C22×Dic3—48no—
242C22×Dic3—48no—
243C22×Dic3—44no—
244C22×Dic3—44no—
245C22×Dic3C2×D412yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×Q812yes—
248C22×Dic3#4114yes—
249C22×Dic3#4114yes—
250C3×C4⋊C4—48no—
251C3×C22⋊C4—28no—
252C3×C22⋊C4—44no—
253#217—44no—
254(C2×D3)⋊C4—48no—
255(C2×D3)⋊C4—44no—
256(C2×D3)⋊C4—48no—
257(C2×D3)⋊C4—44no—
258Dic3⋊C4—48no—
259C25—31no—
260C25C22×D311yescharacteristic
261C22×D4—34no—
262C22×D4—62no—
263C22×D4—62no—
264C22×D4—62no—
265C22×D4—62no—
266C22×D4—62no—
267C22×D4—62no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—31no—
271C23×C4—31no—
272C23×C4—32no—
273C23×C4—31no—
274C23×C4—34no—
275C23×C4—32no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—64no—
279C23×C4—64no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4—62no—
285C23×C4—122no—
286C23×C4—122no—
287C23×C4#6714yes—
288C23×C4C22×D311yescharacteristic
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D312yes—
291C23×C4C22×D312yes—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—64no—
297C2×C4⋊C4—122no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—62no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—122no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4D1214yes—
317#95—24no—
318#95—64no—
319#95—64no—
320#95—64no—
321#95—62no—
322#95—62no—
323#95—64no—
324#95—64no—
325#95—64no—
326#95—122no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3#12114yes—
344C23×C3#12114yes—
345C23×C3#12114yes—
346C23×C3C22⋊Q814yes—
347C23×C3C22⋊Q814yes—
348C23×C3C22⋊Q814yes—
349C23×C3#12614yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C22×Q811yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4112yes—
358C23×C3C2×#4112yes—
359C23×C3H(5,𝔽2)12yes—
360C23×C3H(5,𝔽2)12yes—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—416no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409#67—416no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—416no—
424C2×Dic3—416no—
425C2×Dic3—42no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3#12314yes—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—32no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24—61no—
452C24—62no—
453C24—62no—
454C24—61no—
455C24—62no—
456C24—62no—
457C24—61no—
458C24C2×D1212yes—
459C24#23512yes—
460C24D3×D412yes—
461C24#23712yes—
462C24D3×Q812yes—
463C24#23912yes—
464C24C2×#6712yes—
465C24C23×D311yescharacteristic
466C2×D4—68no—
467C2×D4—68no—
468C2×D4—68no—
469C2×D4—124no—
470C2×D4—124no—
471C2×D4—124no—
472C2×D4—124no—
473C22×C4—28no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—32no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—32no—
500C22×C4—34no—
501C22×C4—48no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—68no—
506C22×C4—61no—
507C22×C4—62no—
508C22×C4—61no—
509C22×C4—68no—
510C22×C4—68no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—62no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—124no—
535C22×C4—128no—
536C22×C4—128no—
537C22×C4—128no—
538C22×C4—128no—
539C22×C4—124no—
540C22×C4—124no—
541C22×C4C2×D1214yes—
542C22×C4C2×#6714yes—
543C4⋊C4—48no—
544C4⋊C4—128no—
545C22⋊C4—28no—
546C22⋊C4—44no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C22⋊C4—124no—
550C22⋊C4—124no—
551C22⋊C4—124no—
552C22×C3—28no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—28no—
559C22×C3—24no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3#39618yes—
563C22×C3C2×#12111yescharacteristic
564C22×C3C2×#12111yescharacteristic
565C22×C3C2×#12111yescharacteristic
566C22×C3C2×C22⋊Q811yescharacteristic
567C22×C3C2×C22⋊Q811yescharacteristic
568C22×C3C2×C22⋊Q811yescharacteristic
569C22×C3C2×#12311yescharacteristic
570C22×C3#52511yescharacteristic
571C22×C3C2×#12611yescharacteristic
572C22×C3#52912yes—
573C22×C3#53212yes—
574C22×C3#53412yes—
575C22×C3#53411yescharacteristic
576C22×C3#53511yescharacteristic
577C22×C3#53812yes—
578C22×C3#54612yes—
579C22×C3#54612yes—
580C22×C3#55112yes—
581C22×C3#55112yes—
582C22×C3#55312yes—
583C22×C3#55312yes—
584C22×C3#55412yes—
585C22×C3#55412yes—
586C2×D3—44no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—44no—
590C2×D3—42no—
591C2×D3—81no—
592C2×D3—81no—
593C2×D3—81no—
594C2×D3—81no—
595C2×D3—82no—
596C2×D3—82no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—81no—
600C3×C4—81no—
601Dic3—24no—
602Dic3—42no—
603Dic3—44no—
604Dic3—42no—
605Dic3—82no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—64no—
623C23—64no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23—122no—
628C23—122no—
629C23—122no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—122no—
636C23—122no—
637C23—121no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—121no—
643C23—121no—
644C23—122no—
645C23#89514yes—
646C23#89614yes—
647C23#89714yes—
648C23#89814yes—
649C23#93014yes—
650C23#93914yes—
651C23#94614yes—
652C23C22×D1211yescharacteristic
653C23C2×#23511yescharacteristic
654C23C2×D3×D411yescharacteristic
655C23C2×#23711yescharacteristic
656C23#100412yes—
657C23#100412yes—
658C23C2×D3×Q811yescharacteristic
659C23C2×#23911yescharacteristic
660C23D3×#4112yes—
661C23D3×#4112yes—
662C23C22×#6711yescharacteristic
663D4—1216no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—34no—
671C2×C4—416no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—64no—
695C2×C4—62no—
696C2×C4—64no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—1216no—
704C2×C4—1216no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C3—28no—
723C2×C3C2×#39611yescharacteristic
724C2×C3#241111yescharacteristic
725C2×C3#241211yescharacteristic
726C2×C3#245012yes—
727C2×C3#248711yescharacteristic
728C2×C3#251012yes—
729C2×C3#254312yes—
730C2×C3#256412yes—
731C2×C3#257911yescharacteristic
732C2×C3#261711yescharacteristic
733C2×C3#285411yescharacteristic
734D3—82no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—28no—
740C22—24no—
741C22—28no—
742C22—24no—
743C22—28no—
744C22—24no—
745C22—122no—
746C22—124no—
747C22—124no—
748C22—122no—
749C22—122no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22—242no—
755C22—242no—
756C22#499418yes—
757C22C2×#89511yescharacteristic
758C22C2×#89611yescharacteristic
759C22C2×#89711yescharacteristic
760C22C2×#89811yescharacteristic
761C22#554012yes—
762C22#554012yes—
763C22#555412yes—
764C22#555412yes—
765C22#558911yescharacteristic
766C22#559211yescharacteristic
767C22#559312yes—
768C22#563612yes—
769C22#563612yes—
770C22#563712yes—
771C22#563712yes—
772C22#564912yes—
773C22D3×#12311yescharacteristic
774C22#565611yescharacteristic
775C22C2×#93011yescharacteristic
776C22C2×#93911yescharacteristic
777C22#580412yes—
778C22C2×#94611yescharacteristic
779C22#583212yes—
780C4—44no—
781C4—44no—
782C4—64no—
783C4—81no—
784C4—81no—
785C4—122no—
786C4—124no—
787C4—122no—
788C4—242no—
789C3#1492111yescharacteristic, complemented, Sylow
790C2—28no—
791C2—242no—
792C2#7440611yescharacteristic
793C2#7442412yes—
794C2#7445711yescharacteristic
795C2#7446512yes—
796C2#7448611yescharacteristic
797C2#7460211yescharacteristic
798C2C2×#499411yescharacteristic
799C2#8238012yes—
800C2#8259211yescharacteristic
801C2#8278412yes—
802C2#8289111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#385C2
prime radicalC23×#67C22
hypercenterC2×#385D3
hypocenterC3#14921
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×C3×#385C2semidirect
3. C22×C3⋊#95C2semidirect
6. C2×#4942C2semidirect
7. #71570C2semidirect
8. #71566C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. #69418C2semidirect
45. C2×#385D3semidirect
789. C3#14921semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3852
C2×#52132
C22×C3⋊#952
C2×#49582
C2×#49422
#715702
#715662
#715442
#694282
#694182
#149213