Finite Group Databasebeta

← C2×#81628 #11664912

Subgroups — C2×#81628 #11664912

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5691C211yesmaximal, characteristic, complemented
2C2×#5680C211yesmaximal, characteristic, complemented
3C2×C3×#488C211yesmaximal, characteristic, complemented
4C2×#5065C211yesmaximal, characteristic, complemented
5C2×#5059C211yesmaximal, characteristic, complemented
6#81628C2116yesmaximal, direct product factor
7C2×#4813C211yesmaximal, characteristic, complemented
8C2×#4807C211yesmaximal, characteristic, complemented
9C2×#4790C211yesmaximal, characteristic, complemented
10C2×#4788C211yesmaximal, characteristic, complemented
11C2×#4775C211yesmaximal, characteristic
12C2×#4778C211yesmaximal, characteristic, complemented
13C2×#4758C211yesmaximal, characteristic, complemented
14C2×#4756C211yesmaximal, characteristic, complemented
15C2×#4697C211yesmaximal, characteristic, complemented
16C2×C4×D3×C8C211yesmaximal, characteristic, complemented
17C2×#3168—31nomaximal, Sylow
18C2×C3×#125C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30#5691—24no—
31#5691C2218yescomplemented
32#5680—24no—
33#5680C2218yescomplemented
34C2×#898—21no—
35C2×#897C2211yescharacteristic
36C2×#895C2211yescharacteristic
37C2×#894—21no—
38C2×#893—21no—
39C2×#893C2211yescharacteristic
40C2×#892—21no—
41C2×#887C2211yescharacteristic
42C2×#883—21no—
43C2×#67⋊C4—21no—
44C2×#879—21no—
45C2×#877—21no—
46C2×#875C2211yescharacteristic
47C2×C42×D3C2211yescharacteristic
48C2×#870C2211yescharacteristic
49C3×#488C2218yescomplemented
50C2×C3×#103C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×C4×C8C2211yescharacteristic
55C2×#821C2211yescharacteristic
56C2×#821C2211yescharacteristic
57C2×#816C2211yescharacteristic
58C2×#816C2211yescharacteristic
59C2×C8×Dic3C2211yescharacteristic
60C2×C8×Dic3C2211yescharacteristic
61#5065C2218yescomplemented
62#5059C2218yescomplemented
63C2×#808C2211yescharacteristic
64C2×#808C2211yescharacteristic
65C2×#807C2211yescharacteristic
66C2×#807C2211yescharacteristic
67C2×C4×C3⋊C8C2211yescharacteristic
68#4813C2218yescomplemented
69#4807C2218yescomplemented
70#4790C2218yescomplemented
71#4788C2218yescomplemented
72#4778C2218yescomplemented
73#4775C2218yes—
74#4758C2218yescomplemented
75#4756C2218yescomplemented
76#4697C2218yescomplemented
77C4×D3×C8C2218yescomplemented
78C2×#529—31no—
79C2×#529—31no—
80#3168—316no—
81C2×#499—31no—
82C2×#495—31no—
83C2×#488—31no—
84C2×#488D311yescharacteristic, complemented
85C2×#467—31no—
86C2×#466—31no—
87C2×#465—31no—
88C2×#465—31no—
89C2×C4×Q16—31no—
90C2×C4×SD16—31no—
91C2×C4×SD16—31no—
92C2×C4×D8—31no—
93C22×C4×C8—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C22×#67—21no—
97C23×Dic3—21no—
98C22×D12—21no—
99C22×D12C2311yescharacteristic
100C22×C4×D3—21no—
101C22×C4×D3D411yescharacteristic
102C22×C4×D3D411yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×#125—22no—
108C3×#125C2314yes—
109C3×#124—22no—
110C3×#124C2314yes—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#217—21no—
119C2×#217—21no—
120#946—22no—
121#946C2314yes—
122Q8×Dic3—22no—
123Q8×Dic3C2314yes—
124C2×#216—24no—
125C2×#216C2314yes—
126C2×#215—24no—
127C2×#215C2314yes—
128#938—22no—
129#938C2314yes—
130D4×Dic3—22no—
131D4×Dic3C2314yes—
132C2×#214—24no—
133C2×#214C2314yes—
134C2×#213—24no—
135C2×#213C2314yes—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×C4×Dic3—21no—
151C2×C4×Dic3—21no—
152C2×C4×Dic3D411yescharacteristic
153C2×C4×Dic3D411yescharacteristic
154C2×C4×Dic3C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C2×D3×C8—24no—
158C2×D3×C8—24no—
159C2×D3×C8C2314yes—
160C2×D3×C8C2314yes—
161#898—28no—
162#897—22no—
163#897C2314yes—
164#895—22no—
165#895C2314yes—
166#894—28no—
167#893—28no—
168#893—22no—
169#893C2314yes—
170#892—28no—
171#887—22no—
172#887C2314yes—
173#883—28no—
174#67⋊C4—28no—
175#879—28no—
176#877—28no—
177#875—22no—
178#875C2314yes—
179C42×D3D414yes—
180C42×D3C2314yes—
181#870—22no—
182#870C2314yes—
183C3×#103C2314yes—
184C3×#103C2314yes—
185C3×#102C2314yes—
186C3×#102C2314yes—
187C3×C4×C8C2314yes—
188#821C2314yes—
189#821C2314yes—
190#816C2314yes—
191#816C2314yes—
192C8×Dic3C2314yes—
193C8×Dic3C2314yes—
194#808C2314yes—
195#808C2314yes—
196#807C2314yes—
197#807C2314yes—
198C4×C3⋊C8C2314yes—
199C22×Q16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×D8—31no—
203C23×C8—31no—
204C23×C8—31no—
205#529—38no—
206#529—38no—
207#529—64no—
208#529—64no—
209C2×#126—61no—
210C2×#126—61no—
211C2×#125—31no—
212C2×#125C2×D311yescharacteristic
213C2×#124—31no—
214C2×#124C2×D311yescharacteristic
215C2×#123—61no—
216C2×#123—61no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8—31no—
219C2×#121—31no—
220C2×#121—31no—
221C2×C4×Q8—31no—
222C2×C4×Q8—31no—
223C2×C4×D4—31no—
224C2×C4×D4—31no—
225C2×C4×D4—61no—
226C2×C4×D4—61no—
227C2×#117—61no—
228C2×#117—61no—
229C22×C42—31no—
230#499—38no—
231#495—38no—
232#488—38no—
233#488C2×D318yescomplemented
234#467—38no—
235#466—38no—
236#465—38no—
237#465—38no—
238C4×Q16—38no—
239C4×SD16—38no—
240C4×SD16—38no—
241C4×D8—38no—
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×#103—31no—
247C2×#103—31no—
248C2×#103C2×D311yescharacteristic
249C2×#103C2×D311yescharacteristic
250C2×#102—31no—
251C2×#102—31no—
252C2×#102C2×D311yescharacteristic
253C2×#102C2×D311yescharacteristic
254C2×C4×C8—31no—
255C2×C4×C8—31no—
256C2×C4×C8—31no—
257C2×C4×C8—38no—
258C2×C4×C8C2×D311yescharacteristic
259C24×C3—21no—
260C23×D3—21no—
261C23×D3C2×D411yescharacteristic
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8C2412yes—
266C2×C3×D4—21no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4C2412yes—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C2×#67—24no—
277C2×#67—44no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—24no—
282C22×Dic3—44no—
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286C2×D12—22no—
287C2×D12—22no—
288C2×D12—24no—
289C2×D12—21no—
290C2×D12—44no—
291C2×D12C2412yes—
292C2×C4×D3—24no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—44no—
298C2×C4×D3C2×D412yes—
299C2×C4×D3C2×D414yes—
300C2×C4×D3C2×D414yes—
301C2×C4×D3C2412yes—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6C2412yes—
306C2×C3×C8—22no—
307C2×C3×C8—22no—
308C2×C3×C8C2412yes—
309C2×C3×C8C2412yes—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4C2412yes—
315C3×C4⋊C4C2412yes—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C42C2×D412yes—
319C3×C42C2412yes—
320#217—24no—
321#217—24no—
322#216—28no—
323#215—28no—
324#214—28no—
325#213—28no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3C2412yes—
337C4⋊Dic3C2412yes—
338Dic3⋊C4—24no—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342C4×Dic3—24no—
343C4×Dic3—24no—
344C4×Dic3C2×D412yes—
345C4×Dic3C2×D414yes—
346C4×Dic3C2×D414yes—
347C4×Dic3C2412yes—
348C2×C3⋊C8#4114yes—
349C2×C3⋊C8#4114yes—
350C2×C3⋊C8C2412yes—
351C2×C3⋊C8C2412yes—
352D3×C8—28no—
353D3×C8—28no—
354C22×Q8—31no—
355C22×Q8C22×D311yescharacteristic
356C22×D4—31no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4C22×D311yescharacteristic
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—61no—
364C23×C4—61no—
365C2×Q16—34no—
366C2×Q16—64no—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×D8—34no—
372C2×D8—64no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8—34no—
376C22×C8—34no—
377C22×C8—64no—
378C22×C8—64no—
379C22×C8C22×D311yescharacteristic
380C22×C8C22×D311yescharacteristic
381#126—68no—
382#126—68no—
383#125—22no—
384#125—34no—
385#125—62no—
386#125C22×D314yes—
387#124—22no—
388#124—34no—
389#124—62no—
390#124C22×D314yes—
391#123—68no—
392#123—68no—
393C22⋊Q8—34no—
394C22⋊Q8—34no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397#121—34no—
398#121—34no—
399#121—62no—
400#121—62no—
401C4×Q8—34no—
402C4×Q8—34no—
403C4×Q8—62no—
404C4×Q8—62no—
405C4×D4—34no—
406C4×D4—34no—
407C4×D4—62no—
408C4×D4—62no—
409C4×D4—68no—
410C4×D4—68no—
411#117—68no—
412#117—68no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—34no—
439C2×C42—34no—
440C2×C42—61no—
441C2×C42—61no—
442C2×C42C22×D311yescharacteristic
443#107—34no—
444#107—34no—
445#106—34no—
446#106—34no—
447#103—34no—
448#103—34no—
449#103C22×D314yes—
450#103C22×D314yes—
451#102—34no—
452#102—34no—
453#102C22×D314yes—
454#102C22×D314yes—
455C4×C8—34no—
456C4×C8—34no—
457C4×C8—34no—
458C4×C8C22×D314yes—
459C23×C3—22no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3C22×D411yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3#13514yes—
471C22×D3C22×D412yes—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—42no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C2×#4112yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2511yescharacteristic
492#67—48no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—48no—
502C2×Dic3#13514yes—
503C2×Dic3C22×D412yes—
504C2×Dic3C22×D412yes—
505C2×Dic3C22×D412yes—
506D12—22no—
507D12—22no—
508D12—48no—
509D12—42no—
510C4×D3—28no—
511C4×D3—24no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—28no—
515C4×D3—48no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3×C8—22no—
520C3×C8—22no—
521C3⋊C8C2×#4114yes—
522C3⋊C8C2×#4114yes—
523C24—21no—
524C24—31no—
525C24—61no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—62no—
532C2×Q8—62no—
533C2×Q8C23×D312yes—
534C2×D4—21no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—32no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—61no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4C23×D312yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—34no—
555C22×C4—32no—
556C22×C4—64no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570Q16—68no—
571SD16—68no—
572SD16—68no—
573D8—68no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—34no—
577C2×C8—34no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—68no—
581C2×C8—68no—
582C2×C8C23×D312yes—
583C2×C8C23×D312yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—32no—
589C4⋊C4—32no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4C23×D312yes—
599C4⋊C4C23×D312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C42—34no—
611C42—32no—
612C42—34no—
613C42—32no—
614C42—64no—
615C42—64no—
616C42D3×D412yes—
617C42C23×D312yes—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—84no—
622C22×C3#53212yes—
623C22×C3C2×#13512yes—
624C22×C3C2×#13512yes—
625C22×C3C23×D411yescharacteristic
626C2×D3—28no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—84no—
633C2×D3C2×#13514yes—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4#53212yes—
640C3×C4C22×#4111yescharacteristic
641C3×C4C22×#4111yescharacteristic
642Dic3—22no—
643Dic3—22no—
644Dic3—42no—
645Dic3—42no—
646Dic3—42no—
647Dic3C2×#13514yes—
648C23—22no—
649C23—32no—
650C23—34no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23C2×D3×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—122no—
667D4—22no—
668D4—22no—
669D4—42no—
670D4—62no—
671D4—62no—
672D4—128no—
673D4—128no—
674D4—122no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—32no—
681C2×C4—34no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—68no—
688C2×C4—68no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—128no—
698C2×C4—128no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4C2×D3×D412yes—
703C2×C4C2×D3×D412yes—
704C2×C4C2×D3×D411yescharacteristic
705C2×C4D3×#4112yes—
706C2×C4D3×#4112yes—
707C2×C4C24×D311yescharacteristic
708C8—22no—
709C8—22no—
710C8—34no—
711C8—34no—
712C2×C3—82no—
713C2×C3#316814yescomplemented
714C2×C3C2×#53211yescharacteristic
715C2×C3C22×#13511yescharacteristic
716C2×C3C22×#13511yescharacteristic
717D3—24no—
718D3—82no—
719C22—34no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—62no—
724C22—62no—
725C22—68no—
726C22—84no—
727C22—122no—
728C22—122no—
729C22—122no—
730C22—244no—
731C22#566812yes—
732C22D3×#13512yes—
733C22D3×#13512yes—
734C22C22×D3×D411yescharacteristic
735C4—22no—
736C4—22no—
737C4—34no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—62no—
742C4—62no—
743C4—122no—
744C4—122no—
745C4—122no—
746C4#566812yes—
747C4C2×D3×#4111yescharacteristic
748C4C2×D3×#4111yescharacteristic
749C3C2×#316811yescharacteristic, complemented, Sylow
750C2—64no—
751C2—82no—
752C2—242no—
753C2#8162814yesdirect product factor
754C2C2×#566811yescharacteristic
755C2C2×D3×#13511yescharacteristic
756C2C2×D3×#13511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#488C2
socleC23×C3C22×D4
prime radicalC2×#4775C2
hypercenterC2×#488D3
hypocenterC3C2×#3168
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#5691C2semidirect
2. C2×#5680C2semidirect
3. C2×C3×#488C2semidirect
4. C2×#5065C2semidirect
5. C2×#5059C2semidirect
6. #81628C2direct (N × H)
7. C2×#4813C2semidirect
8. C2×#4807C2semidirect
9. C2×#4790C2semidirect
10. C2×#4788C2semidirect
12. C2×#4778C2semidirect
13. C2×#4758C2semidirect
14. C2×#4756C2semidirect
15. C2×#4697C2semidirect
16. C2×C4×D3×C8C2semidirect
31. #5691C22semidirect
33. #5680C22semidirect
49. C3×#488C22semidirect
61. #5065C22semidirect
62. #5059C22semidirect
68. #4813C22semidirect
69. #4807C22semidirect
70. #4790C22semidirect
71. #4788C22semidirect
72. #4778C22semidirect
74. #4758C22semidirect
75. #4756C22semidirect
76. #4697C22semidirect
77. C4×D3×C8C22semidirect
84. C2×#488D3semidirect
233. #488C2×D3semidirect
713. C2×C3#3168semidirect
749. C3C2×#3168semidirect
753. C2#81628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56912
C2×#56802
C2×C3×#4882
C2×#50652
C2×#50592
#816282
C2×#48132
C2×#48072
C2×#47902
C2×#47882
C2×#47752
C2×#47782
C2×#47582
C2×#47562
C2×#46972
C2×C4×D3×C82
C2×#31683