Finite Group Databasebeta

← #10796987

Subgroups — #10796987

Order 768.

2102 conjugacy classes of subgroups.

The subgroup lattice has 810 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
4C22×#806C211yesmaximal, characteristic, complemented
5C22×#806C211yesmaximal, characteristic, complemented
6C2×C3×#342C211yesmaximal, characteristic, complemented
7C2×#4526C211yesmaximal, characteristic, complemented
8#68970C214yesmaximal, complemented
9#68954C214yesmaximal, complemented
10#20984—31nomaximal, Sylow
11C23×#67C2211yescharacteristic
12C23×#67C2211yescharacteristic
13C22×C3×C22⋊C4C2211yescharacteristic
14C22×C3×C22⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×#217C2211yescharacteristic
17C22×#217C2211yescharacteristic
18C2×#930C414yescomplemented
19C2×C4×#67—22no—
20#5493—22no—
21#5493—22no—
22#5493—22no—
23#5493—22no—
24C2×#886C412yescomplemented
25C2×#886C2212yes—
26C2×#882C412yescomplemented
27C2×#882C2212yes—
28#5486—24no—
29#5486—24no—
30C2×#67⋊C4—22no—
31C2×D3×C22⋊C4C2212yescomplemented
32C2×#877C2212yescomplemented
33#5213—22no—
34#4958—22no—
35#4955C2212yescomplemented
36C2×#806—24no—
37C2×#806—24no—
38C2×#806C2214yes—
39C2×#806C2214yes—
40#4943C2212yescomplemented
41C3×#342C2214yescomplemented
42#4526C2214yescomplemented
43C2×#534—31no—
44C2×#518—31no—
45C22×#99—31no—
46C22×#99—31no—
47#2308—31no—
48#1899—34no—
49#1898—34no—
50C2×#342—31no—
51C2×#342D311yescharacteristic, complemented
52C25×C3C2311yescharacteristic
53C24×D3C2×C411yescharacteristic, complemented
54C24×D3C2311yescharacteristic
55C23×C3×C4—21no—
56C23×C3×C4—21no—
57C23×C3×C4C2×C412yescomplemented
58C22×#67—22no—
59C22×#67—22no—
60C22×#67—22no—
61C22×#67—22no—
62C22×#67—22no—
63C22×#67—22no—
64C22×#67—21no—
65C22×#67—21no—
66C22×#67—21no—
67C22×#67—21no—
68C22×#67—22no—
69C22×#67—22no—
70C22×#67C2×C412yes—
71C22×#67C2×C412yes—
72C22×#67C2×C412yescomplemented
73C22×#67D412yes—
74C22×#67D412yes—
75C22×#67D412yes—
76C22×#67D412yes—
77C22×#67C2312yes—
78C23×Dic3—21no—
79C23×Dic3—21no—
80C23×Dic3C2×C411yescharacteristic, complemented
81C23×Dic3C2311yescharacteristic
82C22×D12C2×C414yescomplemented
83C22×C4×D3—22no—
84C2×C3×C22⋊C4—21no—
85C2×C3×C22⋊C4—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—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4C2×C412yescomplemented
94C2×C3×C22⋊C4D414yescomplemented
95C2×C3×C22⋊C4C2312yes—
96C2×C3×C22⋊C4C2312yes—
97C2×C3×C22⋊C4C2312yes—
98C2×#217—22no—
99C2×#217—21no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—21no—
103C2×#217D414yescomplemented
104C2×#217C2312yes—
105C2×#217C2312yes—
106#930—28no—
107#930—28no—
108C4×#67—216no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4C2×C414yescomplemented
112C2×(C2×D3)⋊C4C2×C414yescomplemented
113C2×C4⋊Dic3C2×C414yescomplemented
114C2×Dic3⋊C4—22no—
115C2×C4×Dic3—22no—
116#886—24no—
117#886—24no—
118#886—24no—
119#886—24no—
120#882—24no—
121#882—24no—
122#882—24no—
123#882—24no—
124#67⋊C4—216no—
125D3×C22⋊C4—24no—
126D3×C22⋊C4—24no—
127#877—24no—
128#877—24no—
129C3⋊#95—24no—
130#806—28no—
131#806—28no—
132C23×D4—31no—
133C23×D4—31no—
134#534—62no—
135#534—62no—
136#534—62no—
137#534—62no—
138C2×#123—32no—
139C2×#123—32no—
140C2×#121—34no—
141C2×#120—32no—
142C2×#120—32no—
143#518—64no—
144#518—64no—
145C2×C4×D4—62no—
146C2×C4×D4—62no—
147C2×#117—32no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4C2×D311yescharacteristic
152C22×C22⋊C4C2×D311yescharacteristic
153C22×C22⋊C4C2×D311yescharacteristic
154C2×#99—34no—
155C2×#99—34no—
156C2×#99—64no—
157C2×#99—64no—
158#386—62no—
159#386—62no—
160#381—32no—
161#379—32no—
162#342—34no—
163#342C2×D314yescomplemented
164C24×C3—82no—
165C24×C3C22×C411yescharacteristic
166C24×C3C22×C411yescharacteristic
167C24×C3C2×D412yes—
168C24×C3C2×D411yescharacteristic
169C24×C3C2×D411yescharacteristic
170C24×C3C2×D411yescharacteristic
171C24×C3C2×D411yescharacteristic
172C24×C3C2×D412yes—
173C24×C3#4112yes—
174C24×C3#4112yes—
175C24×C3C2411yescharacteristic
176C23×D3—21no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—82no—
185C23×D3—82no—
186C23×D3C22×C412yes—
187C23×D3C22×C412yes—
188C23×D3C2×D412yes—
189C23×D3C2×D412yes—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—24no—
194C22×C3×C4—22no—
195C22×C3×C4—42no—
196C22×C3×C4—82no—
197C22×C3×C4—82no—
198C22×C3×C4—82no—
199C22×C3×C4C22×C414yes—
200C2×#67—24no—
201C2×#67—24no—
202C2×#67—24no—
203C2×#67—24no—
204C2×#67—24no—
205C2×#67—24no—
206C2×#67—24no—
207C2×#67—24no—
208C2×#67—24no—
209C2×#67—24no—
210C2×#67—24no—
211C2×#67—24no—
212C2×#67—22no—
213C2×#67—22no—
214C2×#67—24no—
215C2×#67—24no—
216C2×#67—22no—
217C2×#67—22no—
218C2×#67—22no—
219C2×#67—22no—
220C2×#67—22no—
221C2×#67—22no—
222C2×#67—42no—
223C2×#67—42no—
224C2×#67—42no—
225C2×#67—42no—
226C2×#67—42no—
227C2×#67—42no—
228C2×#67—42no—
229C2×#67—42no—
230C2×#67C22⋊C414yes—
231C2×#67C22⋊C414yes—
232C2×#67C22⋊C414yes—
233C2×#67C22⋊C414yes—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—24no—
244C22×Dic3—22no—
245C22×Dic3—42no—
246C22×Dic3—82no—
247C22×Dic3—82no—
248C22×Dic3C22×C412yes—
249C22×Dic3C22×C412yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C2×D12—28no—
253C2×D12—84no—
254C2×C4×D3—28no—
255C2×C4×D3—84no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4C2×D414yes—
266#217—24no—
267#217—22no—
268#217—22no—
269#217—22no—
270#217—42no—
271#217C2×D414yes—
272(C2×D3)⋊C4—28no—
273(C2×D3)⋊C4—28no—
274(C2×D3)⋊C4—28no—
275(C2×D3)⋊C4—84no—
276C4⋊Dic3—28no—
277Dic3⋊C4—28no—
278C4×Dic3—28no—
279C25—31no—
280C25—31no—
281C25C22×D311yescharacteristic
282C22×D4—32no—
283C22×D4—32no—
284C22×D4—32no—
285C22×D4—32no—
286C22×D4—32no—
287C22×D4—32no—
288C22×D4—32no—
289C22×D4—32no—
290C22×D4—34no—
291C22×D4—62no—
292C22×D4—62no—
293C22×D4—62no—
294C22×D4—62no—
295C22×D4—62no—
296C22×D4—62no—
297C22×D4—61no—
298C22×D4—61no—
299C22×D4—61no—
300C22×D4—61no—
301C22×D4—62no—
302C22×D4—62no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—62no—
308C23×C4—61no—
309C23×C4—61no—
310C23×C4C4×D312yescomplemented
311#123—64no—
312#123—64no—
313#123—64no—
314#123—64no—
315#121—68no—
316#121—68no—
317#120—64no—
318#120—64no—
319#120—64no—
320#120—64no—
321C4×D4—616no—
322C4×D4—616no—
323#117—64no—
324#117—64no—
325C2×C4⋊C4—34no—
326C2×C4⋊C4—62no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—34no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—34no—
339C2×C22⋊C4—34no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—62no—
344C2×C22⋊C4—61no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—62no—
347C2×C22⋊C4—62no—
348C2×C22⋊C4—61no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4C4×D312yescomplemented
351C2×C22⋊C4D1214yescomplemented
352C2×C22⋊C4C22×D312yes—
353C2×C22⋊C4C22×D312yes—
354C2×C22⋊C4C22×D312yes—
355C2×C42—62no—
356#99—68no—
357#99—68no—
358#95—64no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—82no—
367C23×C3—82no—
368C23×C3—82no—
369C23×C3—82no—
370C23×C3C2×C22⋊C411yescharacteristic
371C23×C3C2×C22⋊C411yescharacteristic
372C23×C3C2×C22⋊C411yescharacteristic
373C23×C3C2×C22⋊C411yescharacteristic
374C23×C3C4×D412yes—
375C23×C3C4×D412yes—
376C23×C3C4×D412yes—
377C23×C3C4×D412yes—
378C23×C3#12012yes—
379C23×C3#12012yes—
380C23×C3#12112yes—
381C23×C3#12112yes—
382C23×C3#12112yes—
383C23×C3#12112yes—
384C23×C3#12312yes—
385C23×C3#12312yes—
386C23×C3C23×C411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C22×D411yescharacteristic
390C23×C3C22×D411yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—44no—
408C22×D3—82no—
409C22×D3—82no—
410C22×D3—82no—
411C22×D3—82no—
412C22×D3—82no—
413C22×D3—82no—
414C22×D3—84no—
415C22×D3—84no—
416C22×D3C2×C22⋊C414yes—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—44no—
420C2×C3×C4—44no—
421C2×C3×C4—44no—
422C2×C3×C4—42no—
423C2×C3×C4—82no—
424C2×C3×C4—82no—
425C2×C3×C4—84no—
426C2×C3×C4—84no—
427#67—28no—
428#67—28no—
429#67—28no—
430#67—28no—
431#67—42no—
432#67—42no—
433#67—42no—
434#67—42no—
435#67—44no—
436#67—44no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—24no—
447C2×Dic3—44no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—44no—
451C2×Dic3—42no—
452C2×Dic3—84no—
453C2×Dic3—84no—
454C2×Dic3C2×C22⋊C414yes—
455D12—88no—
456C4×D3—88no—
457C24—32no—
458C24—32no—
459C24—32no—
460C24—32no—
461C24—61no—
462C24—61no—
463C24—61no—
464C24—61no—
465C24—62no—
466C24—61no—
467C24—61no—
468C24—62no—
469C24—82no—
470C24—242no—
471C24—242no—
472C24C2×C4×D311yescharacteristic
473C24C2×C4×D311yescharacteristic
474C24C2×D1212yes—
475C24#23512yes—
476C24D3×D411yescharacteristic
477C24D3×D411yescharacteristic
478C24D3×D411yescharacteristic
479C24D3×D411yescharacteristic
480C24D3×D412yes—
481C24#23912yes—
482C24C23×D311yescharacteristic
483C2×D4—34no—
484C2×D4—34no—
485C2×D4—34no—
486C2×D4—34no—
487C2×D4—68no—
488C2×D4—64no—
489C2×D4—64no—
490C2×D4—64no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—64no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—64no—
499C2×D4—64no—
500C2×D4—64no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—64no—
504C2×D4—62no—
505C2×D4—62no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—244no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—42no—
529C22×C4—68no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—64no—
540C22×C4—62no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—122no—
545C22×C4—244no—
546C22×C4—242no—
547C22×C4—242no—
548C22×C4C2×C4×D314yes—
549C4⋊C4—68no—
550C4⋊C4—68no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—24no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—34no—
560C22⋊C4—42no—
561C22⋊C4—68no—
562C22⋊C4—68no—
563C22⋊C4—68no—
564C22⋊C4—64no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—62no—
568C22⋊C4—122no—
569C22⋊C4—244no—
570C22⋊C4C2×D1214yes—
571C42—68no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3#38612yes—
596C22×C3#38612yes—
597C22×C3#38612yes—
598C22×C3#38612yes—
599C22×C3C22×C22⋊C411yescharacteristic
600C22×C3C2×C4×D411yescharacteristic
601C22×C3C2×C4×D411yescharacteristic
602C22×C3C2×#12011yescharacteristic
603C22×C3C2×#12111yescharacteristic
604C22×C3C2×#12111yescharacteristic
605C22×C3C2×#12311yescharacteristic
606C2×D3—28no—
607C2×D3—24no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—44no—
611C2×D3—42no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—84no—
617C2×D3—84no—
618C2×D3—82no—
619C2×D3—82no—
620C3×C4—44no—
621C3×C4—44no—
622C3×C4—82no—
623Dic3—24no—
624Dic3—44no—
625Dic3—42no—
626Dic3—82no—
627C23—34no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—82no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23—124no—
649C23—124no—
650C23—124no—
651C23—124no—
652C23—122no—
653C23—122no—
654C23—242no—
655C23—242no—
656C23—242no—
657C23—242no—
658C23—242no—
659C23—242no—
660C23—244no—
661C23—244no—
662C23C4×D1212yes—
663C23C4×D1212yes—
664C23D3×C22⋊C411yescharacteristic
665C23D3×C22⋊C411yescharacteristic
666C23D3×C22⋊C411yescharacteristic
667C23D3×C22⋊C411yescharacteristic
668C23#88212yes—
669C23#88212yes—
670C23#88412yes—
671C23#88412yes—
672C23#89312yes—
673C23#89312yes—
674C23#89412yes—
675C23#89412yes—
676C23#89512yes—
677C23#89512yes—
678C23C22×C4×D311yescharacteristic
679C23C22×D1211yescharacteristic
680C23C2×#23511yescharacteristic
681C23C2×D3×D411yescharacteristic
682C23C2×D3×D411yescharacteristic
683C23C2×D3×D411yescharacteristic
684C23C2×#23911yescharacteristic
685D4—68no—
686D4—68no—
687D4—68no—
688D4—68no—
689D4—124no—
690D4—124no—
691D4—122no—
692D4—122no—
693D4—122no—
694D4—122no—
695D4—248no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—34no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—64no—
712C2×C4—62no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—124no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—124no—
721C2×C4—122no—
722C2×C4—248no—
723C2×C4—244no—
724C2×C4—244no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3C2×#38611yescharacteristic
736C2×C3#288312yes—
737D3—44no—
738D3—82no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—68no—
763C22—64no—
764C22—124no—
765C22—124no—
766C22—124no—
767C22—122no—
768C22—242no—
769C22—242no—
770C22—242no—
771C22—242no—
772C22—242no—
773C22—242no—
774C22—244no—
775C22—244no—
776C22#466512yes—
777C22#466512yes—
778C22#466512yes—
779C22#466512yes—
780C22C2×C4×D1211yescharacteristic
781C22C2×D3×C22⋊C411yescharacteristic
782C22C2×#88211yescharacteristic
783C22C2×#88411yescharacteristic
784C22C2×#89311yescharacteristic
785C22C2×#89411yescharacteristic
786C22C2×#89511yescharacteristic
787C4—44no—
788C4—44no—
789C4—64no—
790C4—82no—
791C4—124no—
792C4—122no—
793C4—242no—
794C3#2098411yescharacteristic, complemented, Sylow
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—22no—
802C2—22no—
803C2—22no—
804C2—22no—
805C2—124no—
806C2—242no—
807C2C2×#466511yescharacteristic
808C2#7868812yes—
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×#342C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5493C2
cosocleC24×C3C24
hypercenterC2×#342D3
hypocenterC3#20984
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. C22×#806C2semidirect
5. C22×#806C2semidirect
6. C2×C3×#342C2semidirect
7. C2×#4526C2semidirect
8. #68970C2semidirect
9. #68954C2semidirect
18. C2×#930C4semidirect
24. C2×#886C4semidirect
26. C2×#882C4semidirect
31. C2×D3×C22⋊C4C22semidirect
32. C2×#877C22semidirect
35. #4955C22semidirect
40. #4943C22semidirect
41. C3×#342C22semidirect
42. #4526C22semidirect
51. C2×#342D3semidirect
53. C24×D3C2×C4semidirect
57. C23×C3×C4C2×C4semidirect
72. C22×#67C2×C4semidirect
80. C23×Dic3C2×C4semidirect
82. C22×D12C2×C4semidirect
93. C2×C3×C22⋊C4C2×C4semidirect
94. C2×C3×C22⋊C4D4semidirect
103. C2×#217D4semidirect
111. C2×(C2×D3)⋊C4C2×C4semidirect
112. C2×(C2×D3)⋊C4C2×C4semidirect
113. C2×C4⋊Dic3C2×C4semidirect
163. #342C2×D3semidirect
310. C23×C4C4×D3semidirect
350. C2×C22⋊C4C4×D3semidirect
351. C2×C22⋊C4D12semidirect
794. C3#20984semidirect

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×#45262
#689702
#689542
#209843