Finite Group Databasebeta

← #10796819

Subgroups — #10796819

Order 768.

2126 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5493C211yesmaximal, characteristic
2C2×#5486C211yesmaximal, characteristic, complemented
3#82121C211yesmaximal, characteristic, complemented
4#82121C211yesmaximal, characteristic, complemented
5C22×#806C211yesmaximal, characteristic, complemented
6C2×C3×#342C211yesmaximal, characteristic, complemented
7C2×#4527C211yesmaximal, characteristic, complemented
8#68963C214yesmaximal, complemented
9#68962C214yesmaximal, complemented
10#20960—31nomaximal, Sylow
11C23×#67C2211yescharacteristic
12C23×#67C2211yescharacteristic
13C22×C3×C22⋊C4C2211yescharacteristic
14C22×C3×C22⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×#217C2211yescharacteristic
17C22×#217C2211yescharacteristic
18C2×#930—22no—
19C2×C4×#67—22no—
20#5493—24no—
21#5493C418yescomplemented
22C2×#886—21no—
23C2×#886C2212yes—
24C2×#882—21no—
25C2×#882C2212yes—
26#5486—22no—
27#5486—22no—
28#5486—22no—
29#5486C2214yes—
30C2×#67⋊C4—22no—
31C2×D3×C22⋊C4—21no—
32C2×#877—21no—
33#5213—22no—
34#5213—22no—
35#4958—22no—
36#4958—22no—
37#4955C2212yescomplemented
38#4955C2212yescomplemented
39C2×#806—24no—
40C2×#806C2214yes—
41#4943C2212yescomplemented
42#4943C2212yescomplemented
43C3×#342C2214yescomplemented
44#4527C2214yescomplemented
45C2×#534—31no—
46C2×#518—31no—
47C22×#99—31no—
48#2308—31no—
49#2308—31no—
50#1890—34no—
51#1889—34no—
52C2×#342—31no—
53C2×#342D311yescharacteristic, complemented
54C25×C3C2311yescharacteristic
55C24×D3D411yescharacteristic
56C24×D3C2311yescharacteristic
57C23×C3×C4—21no—
58C23×C3×C4—21no—
59C23×C3×C4D412yescomplemented
60C22×#67—21no—
61C22×#67—21no—
62C22×#67—21no—
63C22×#67—21no—
64C22×#67—22no—
65C22×#67—22no—
66C22×#67—21no—
67C22×#67—21no—
68C22×#67—21no—
69C22×#67—21no—
70C22×#67—21no—
71C22×#67—22no—
72C22×#67—21no—
73C22×#67—22no—
74C22×#67—22no—
75C22×#67C2×C414yes—
76C22×#67C2×C414yescomplemented
77C22×#67D414yes—
78C22×#67D412yes—
79C22×#67C2312yes—
80C23×Dic3—21no—
81C23×Dic3D411yescharacteristic
82C23×Dic3D412yescomplemented
83C23×Dic3C2311yescharacteristic
84C22×D12—22no—
85C22×C4×D3—22no—
86C2×C3×C22⋊C4—21no—
87C2×C3×C22⋊C4—21no—
88C2×C3×C22⋊C4—21no—
89C2×C3×C22⋊C4—21no—
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C22⋊C4C2×C414yescomplemented
96C2×C3×C22⋊C4D412yescomplemented
97C2×C3×C22⋊C4C2312yes—
98C2×C3×C22⋊C4C2312yes—
99C2×C3×C22⋊C4C2312yes—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—21no—
107C2×#217D412yescomplemented
108C2×#217C2312yes—
109C2×#217C2312yes—
110#930—216no—
111C4×#67—28no—
112C4×#67—28no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×C4⋊Dic3—22no—
119C2×Dic3⋊C4—22no—
120C2×C4×Dic3—22no—
121#886—24no—
122#886—28no—
123#886C2×C418yescomplemented
124#882—28no—
125#882—24no—
126#882C2×C418yescomplemented
127#67⋊C4—28no—
128#67⋊C4—28no—
129D3×C22⋊C4—24no—
130D3×C22⋊C4—24no—
131#877—24no—
132#877—24no—
133C3⋊#95—24no—
134C3⋊#95—24no—
135#806—28no—
136C23×D4—31no—
137C23×D4—31no—
138#534—38no—
139#534—64no—
140C2×#123—32no—
141C2×#123—61no—
142C2×#121—62no—
143C2×#120—32no—
144C2×#120—61no—
145#518—34no—
146#518—62no—
147#518—62no—
148#518—62no—
149C2×C4×D4—62no—
150C2×C4×D4—62no—
151C2×#117—61no—
152C22×C22⋊C4—31no—
153C22×C22⋊C4—31no—
154C22×C22⋊C4—61no—
155C22×C22⋊C4C2×D311yescharacteristic
156C22×C22⋊C4C2×D311yescharacteristic
157C22×C22⋊C4C2×D311yescharacteristic
158C2×#99—34no—
159C2×#99—64no—
160#386—62no—
161#386—62no—
162#386—62no—
163#386—62no—
164#381—32no—
165#381—32no—
166#379—32no—
167#379—32no—
168#342—34no—
169#342C2×D314yescomplemented
170C24×C3—82no—
171C24×C3C22×C412yes—
172C24×C3C2×D411yescharacteristic
173C24×C3C2×D411yescharacteristic
174C24×C3C2×D411yescharacteristic
175C24×C3C2×D411yescharacteristic
176C24×C3C2×D411yescharacteristic
177C24×C3C2×D411yescharacteristic
178C24×C3C2×D412yes—
179C24×C3#4112yes—
180C24×C3#4112yes—
181C24×C3C2411yescharacteristic
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—22no—
185C23×D3—21no—
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—21no—
191C23×D3—82no—
192C23×D3—82no—
193C23×D3C22⋊C414yescomplemented
194C23×D3C22×C412yescomplemented
195C23×D3C2×D412yes—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—24no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—42no—
202C22×C3×C4—82no—
203C22×C3×C4—82no—
204C22×C3×C4—82no—
205C22×C3×C4C2×D414yes—
206C2×#67—24no—
207C2×#67—24no—
208C2×#67—24no—
209C2×#67—24no—
210C2×#67—22no—
211C2×#67—22no—
212C2×#67—24no—
213C2×#67—24no—
214C2×#67—24no—
215C2×#67—24no—
216C2×#67—24no—
217C2×#67—22no—
218C2×#67—22no—
219C2×#67—22no—
220C2×#67—22no—
221C2×#67—24no—
222C2×#67—24no—
223C2×#67—24no—
224C2×#67—24no—
225C2×#67—24no—
226C2×#67—24no—
227C2×#67—41no—
228C2×#67—41no—
229C2×#67—41no—
230C2×#67—41no—
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67C22⋊C418yescomplemented
238C2×#67C22×C414yes—
239C2×#67C2×D414yes—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—42no—
253C22×Dic3—82no—
254C22×Dic3—82no—
255C22×Dic3C22⋊C414yescomplemented
256C22×Dic3C22×C412yescomplemented
257C22×Dic3C2×D412yes—
258C22×Dic3C2×D414yes—
259C2×D12—28no—
260C2×D12—84no—
261C2×C4×D3—28no—
262C2×C4×D3—84no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4C22×C414yescomplemented
273#217—22no—
274#217—22no—
275#217—22no—
276#217—22no—
277#217—22no—
278#217—22no—
279#217—42no—
280(C2×D3)⋊C4—28no—
281(C2×D3)⋊C4—28no—
282(C2×D3)⋊C4—28no—
283(C2×D3)⋊C4—84no—
284(C2×D3)⋊C4—84no—
285C4⋊Dic3—28no—
286Dic3⋊C4—28no—
287C4×Dic3—28no—
288C25—31no—
289C25—31no—
290C25C22×D311yescharacteristic
291C22×D4—34no—
292C22×D4—32no—
293C22×D4—34no—
294C22×D4—32no—
295C22×D4—34no—
296C22×D4—62no—
297C22×D4—61no—
298C22×D4—61no—
299C22×D4—62no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4—62no—
303C22×D4—61no—
304C22×D4—61no—
305C22×D4—62no—
306C22×D4—61no—
307C22×D4—61no—
308C22×D4—62no—
309C22×D4—61no—
310C22×D4—61no—
311C22×D4—62no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—32no—
317C23×C4—62no—
318C23×C4—61no—
319C23×C4D1212yescomplemented
320#123—38no—
321#123—68no—
322#123—64no—
323#121—616no—
324#120—38no—
325#120—64no—
326#120—68no—
327C4×D4—68no—
328C4×D4—68no—
329C4×D4—68no—
330C4×D4—68no—
331#117—64no—
332#117—64no—
333C2×C4⋊C4—62no—
334C2×C4⋊C4—62no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—32no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—62no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4C4×D314yescomplemented
362C2×C22⋊C4D1212yescomplemented
363C2×C22⋊C4C22×D312yes—
364C2×C22⋊C4C22×D312yes—
365C2×C22⋊C4C22×D312yes—
366C2×C42—62no—
367#99—68no—
368#95—64no—
369#95—64no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—82no—
378C23×C3—82no—
379C23×C3—82no—
380C23×C3—82no—
381C23×C3C2×C22⋊C412yes—
382C23×C3C2×C22⋊C412yes—
383C23×C3C4×D412yes—
384C23×C3C4×D412yes—
385C23×C3C4×D412yes—
386C23×C3C4×D412yes—
387C23×C3#12011yescharacteristic
388C23×C3#12011yescharacteristic
389C23×C3#12011yescharacteristic
390C23×C3#12011yescharacteristic
391C23×C3#12112yes—
392C23×C3#12112yes—
393C23×C3#12112yes—
394C23×C3#12112yes—
395C23×C3#12312yes—
396C23×C3#12312yes—
397C23×C3C23×C411yescharacteristic
398C23×C3C22×D411yescharacteristic
399C23×C3C22×D411yescharacteristic
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D411yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C22×D3—22no—
405C22×D3—24no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—44no—
412C22×D3—44no—
413C22×D3—44no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—82no—
421C22×D3—84no—
422C22×D3—82no—
423C22×D3—84no—
424C22×D3—82no—
425C22×D3—82no—
426C22×D3—82no—
427C22×D3C2×C22⋊C414yes—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—44no—
433C2×C3×C4—44no—
434C2×C3×C4—42no—
435C2×C3×C4—82no—
436C2×C3×C4—84no—
437C2×C3×C4—84no—
438#67—24no—
439#67—24no—
440#67—24no—
441#67—24no—
442#67—28no—
443#67—28no—
444#67—44no—
445#67—44no—
446#67—44no—
447#67—44no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—24no—
456C2×Dic3—44no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—44no—
462C2×Dic3—44no—
463C2×Dic3—42no—
464C2×Dic3—82no—
465C2×Dic3—84no—
466C2×Dic3C2×C22⋊C414yes—
467D12—88no—
468C4×D3—88no—
469C24—32no—
470C24—34no—
471C24—32no—
472C24—61no—
473C24—61no—
474C24—62no—
475C24—61no—
476C24—61no—
477C24—61no—
478C24—61no—
479C24—61no—
480C24—61no—
481C24—82no—
482C24—242no—
483C24—242no—
484C24C2×C4×D312yes—
485C24C2×D1211yescharacteristic
486C24C2×D1211yescharacteristic
487C24#23512yes—
488C24D3×D411yescharacteristic
489C24D3×D411yescharacteristic
490C24D3×D411yescharacteristic
491C24D3×D411yescharacteristic
492C24D3×D412yes—
493C24#23912yes—
494C24C23×D311yescharacteristic
495C2×D4—38no—
496C2×D4—34no—
497C2×D4—34no—
498C2×D4—68no—
499C2×D4—64no—
500C2×D4—64no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—64no—
504C2×D4—64no—
505C2×D4—64no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—62no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—121no—
521C2×D4—121no—
522C2×D4—121no—
523C2×D4—121no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—244no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—34no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—34no—
540C22×C4—42no—
541C22×C4—68no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—122no—
558C22×C4—244no—
559C22×C4—242no—
560C22×C4—242no—
561C22×C4C2×D1214yes—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C22⋊C4—24no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—42no—
573C22⋊C4—68no—
574C22⋊C4—68no—
575C22⋊C4—68no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—62no—
581C22⋊C4—62no—
582C22⋊C4—122no—
583C22⋊C4—244no—
584C22⋊C4—244no—
585C22⋊C4C2×C4×D314yescomplemented
586C42—68no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3#38612yes—
611C22×C3#38612yes—
612C22×C3#38612yes—
613C22×C3#38612yes—
614C22×C3C22×C22⋊C411yescharacteristic
615C22×C3C2×C4×D411yescharacteristic
616C22×C3C2×C4×D411yescharacteristic
617C22×C3C2×#12011yescharacteristic
618C22×C3C2×#12111yescharacteristic
619C22×C3C2×#12111yescharacteristic
620C22×C3C2×#12311yescharacteristic
621C2×D3—24no—
622C2×D3—48no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—42no—
629C2×D3—82no—
630C2×D3—84no—
631C2×D3—82no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C3×C4—44no—
636C3×C4—44no—
637C3×C4—82no—
638Dic3—24no—
639Dic3—44no—
640Dic3—42no—
641Dic3—82no—
642C23—34no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—64no—
651C23—62no—
652C23—64no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—82no—
658C23—82no—
659C23—82no—
660C23—82no—
661C23—124no—
662C23—124no—
663C23—124no—
664C23—124no—
665C23—124no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—242no—
671C23—242no—
672C23—244no—
673C23—244no—
674C23—242no—
675C23—242no—
676C23—242no—
677C23C4×D1212yes—
678C23C4×D1212yes—
679C23D3×C22⋊C412yes—
680C23D3×C22⋊C412yes—
681C23#88211yescharacteristic
682C23#88211yescharacteristic
683C23#88211yescharacteristic
684C23#88211yescharacteristic
685C23#88412yes—
686C23#88412yes—
687C23#89312yes—
688C23#89312yes—
689C23#89412yes—
690C23#89412yes—
691C23#89512yes—
692C23#89512yes—
693C23C22×C4×D311yescharacteristic
694C23C22×D1211yescharacteristic
695C23C2×#23511yescharacteristic
696C23C2×D3×D411yescharacteristic
697C23C2×D3×D411yescharacteristic
698C23C2×D3×D411yescharacteristic
699C23C2×#23911yescharacteristic
700D4—68no—
701D4—68no—
702D4—64no—
703D4—64no—
704D4—64no—
705D4—64no—
706D4—124no—
707D4—124no—
708D4—124no—
709D4—124no—
710D4—248no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—34no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—82no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—124no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—124no—
736C2×C4—124no—
737C2×C4—122no—
738C2×C4—248no—
739C2×C4—242no—
740C2×C4—244no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—22no—
747C2×C3—21no—
748C2×C3—22no—
749C2×C3—22no—
750C2×C3—22no—
751C2×C3C2×#38611yescharacteristic
752C2×C3#302612yes—
753D3—44no—
754D3—82no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—64no—
779C22—124no—
780C22—128no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—122no—
786C22—242no—
787C22—244no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22—242no—
792C22#466512yes—
793C22#466512yes—
794C22#466512yes—
795C22#466512yes—
796C22C2×C4×D1211yescharacteristic
797C22C2×D3×C22⋊C411yescharacteristic
798C22C2×#88211yescharacteristic
799C22C2×#88411yescharacteristic
800C22C2×#89311yescharacteristic
801C22C2×#89411yescharacteristic
802C22C2×#89511yescharacteristic
803C4—44no—
804C4—44no—
805C4—64no—
806C4—82no—
807C4—124no—
808C4—122no—
809C4—242no—
810C3#2096011yescharacteristic, complemented, Sylow
811C2—21no—
812C2—21no—
813C2—21no—
814C2—22no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—22no—
819C2—22no—
820C2—22no—
821C2—124no—
822C2—242no—
823C2C2×#466511yescharacteristic
824C2#7868612yes—
subgroupG/H
centerC22C2×#882
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×#342C2
socleC22×C3C2×#120
prime radicalC2×#5493C2
cosocleC24×C3C24
hypercenterC2×#342D3
hypocenterC3#20960
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C2×#5486C2semidirect
3. #82121C2semidirect
4. #82121C2semidirect
5. C22×#806C2semidirect
6. C2×C3×#342C2semidirect
7. C2×#4527C2semidirect
8. #68963C2semidirect
9. #68962C2semidirect
21. #5493C4semidirect
37. #4955C22semidirect
38. #4955C22semidirect
41. #4943C22semidirect
42. #4943C22semidirect
43. C3×#342C22semidirect
44. #4527C22semidirect
53. C2×#342D3semidirect
59. C23×C3×C4D4semidirect
76. C22×#67C2×C4semidirect
82. C23×Dic3D4semidirect
95. C2×C3×C22⋊C4C2×C4semidirect
96. C2×C3×C22⋊C4D4semidirect
107. C2×#217D4semidirect
123. #886C2×C4semidirect
126. #882C2×C4semidirect
169. #342C2×D3semidirect
193. C23×D3C22⋊C4semidirect
194. C23×D3C22×C4semidirect
237. C2×#67C22⋊C4semidirect
255. C22×Dic3C22⋊C4semidirect
256. C22×Dic3C22×C4semidirect
272. C3×C22⋊C4C22×C4semidirect
319. C23×C4D12semidirect
361. C2×C22⋊C4C4×D3semidirect
362. C2×C22⋊C4D12semidirect
585. C22⋊C4C2×C4×D3semidirect
810. C3#20960semidirect

Maximal subgroups

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

subgroupindex
C2×#54932
C2×#54862
#821212
C22×#8062
C2×C3×#3422
C2×#45272
#689632
#689622
#209603