Finite Group Databasebeta

← C2×#81261 #11668011

Subgroups — C2×#81261 #11668011

Order 768.

1962 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×#5580C211yesmaximal, characteristic, complemented
3C2×C3×#479C211yesmaximal, characteristic, complemented
4C2×#5066C211yesmaximal, characteristic, complemented
5C2×#5028C211yesmaximal, characteristic, complemented
6#81261C2116yesmaximal, direct product factor
7C2×#4877C211yesmaximal, characteristic, complemented
8C2×#4883C211yesmaximal, characteristic
9C2×#4871C211yesmaximal, characteristic, complemented
10C2×#4864C211yesmaximal, characteristic, complemented
11C2×#4844C211yesmaximal, characteristic, complemented
12C2×D3×C4⋊C8C211yesmaximal, characteristic, complemented
13C2×#4798C211yesmaximal, characteristic, complemented
14C2×#4819C211yesmaximal, characteristic, complemented
15C2×#4813C211yesmaximal, characteristic, complemented
16C2×#4807C211yesmaximal, characteristic, complemented
17C2×#3250—31nomaximal, Sylow
18C2×C3×#125C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×D24C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5691—24no—
29#5691C2218yescomplemented
30#5580—24no—
31#5580C2218yescomplemented
32C2×#898—21no—
33C2×#898—21no—
34C2×#897C2211yescharacteristic
35C2×#895C2211yescharacteristic
36C2×#895C2211yescharacteristic
37C2×#894—21no—
38C2×#894—21no—
39C2×#893—21no—
40C2×#893C2211yescharacteristic
41C2×#892—21no—
42C2×#890C2211yescharacteristic
43C2×#887C2211yescharacteristic
44C2×#875C2211yescharacteristic
45C2×C4×D12—21no—
46C2×C4×D12C2211yescharacteristic
47C2×#872—21no—
48C2×C42×D3C2211yescharacteristic
49C3×#479C2218yescomplemented
50C2×C3×#107C2211yescharacteristic
51C2×C3×#106C2211yescharacteristic
52C2×C3×C4⋊C8C2211yescharacteristic
53C2×C3×#103C2211yescharacteristic
54C2×C3×#103C2211yescharacteristic
55C2×#821C2211yescharacteristic
56C2×#816C2211yescharacteristic
57C2×Dic3⋊C8C2211yescharacteristic
58C2×Dic3⋊C8C2211yescharacteristic
59#5066C2218yescomplemented
60#5028C2218yescomplemented
61C2×#810C2211yescharacteristic
62C2×#809C2211yescharacteristic
63C2×#809C2211yescharacteristic
64C2×#809C2211yescharacteristic
65C2×#808C2211yescharacteristic
66C2×#807C2211yescharacteristic
67C2×C4⋊(C3⋊C8)C2211yescharacteristic
68#4883C2218yes—
69#4877C2218yescomplemented
70#4871C2218yescomplemented
71#4864C2218yescomplemented
72#4844C2218yescomplemented
73D3×C4⋊C8C2218yescomplemented
74#4819C2218yescomplemented
75#4813C2218yescomplemented
76#4807C2218yescomplemented
77#4798C2218yescomplemented
78C2×#529—31no—
79C2×#529—31no—
80#3250—316no—
81C2×#479—31no—
82C2×#479D311yescharacteristic, complemented
83C2×#478—31no—
84C2×#478—31no—
85C2×#467—31no—
86C2×#466—31no—
87C2×#465—31no—
88C2×#465—31no—
89C2×#464—31no—
90C2×#464—31no—
91C2×#463—31no—
92C2×#463—31no—
93C22×C4⋊C8—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×D12—21no—
96C22×D12—21no—
97C22×D12C2311yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
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×C4×Q8—22no—
110C3×C4×Q8C2314yes—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C42—21no—
118C2×C3×C42C2311yescharacteristic
119#947—22no—
120#947C2314yes—
121#946—22no—
122#946C2314yes—
123C2×#216—42no—
124C2×#216C2314yes—
125C2×#215—42no—
126C2×#215C2314yes—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4—21no—
143C2×C4×Dic3—21no—
144C2×C4×Dic3D411yescharacteristic
145C2×C4×Dic3D411yescharacteristic
146C2×C4×Dic3C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C2×D24—42no—
150C2×D24C2314yes—
151C2×#204—42no—
152C2×#204C2314yes—
153C2×D3×C8—42no—
154C2×D3×C8—42no—
155C2×D3×C8C2314yes—
156C2×D3×C8C2314yes—
157#898—28no—
158#898—28no—
159#897—22no—
160#897C2314yes—
161#895—22no—
162#895—22no—
163#895C2314yes—
164#895C2314yes—
165#894—28no—
166#894—28no—
167#893—28no—
168#893—22no—
169#893C2314yes—
170#892—28no—
171#890—22no—
172#890C2314yes—
173#887—22no—
174#887C2314yes—
175#875—22no—
176#875C2314yes—
177C4×D12—28no—
178C4×D12—22no—
179C4×D12C2314yes—
180#872—28no—
181C42×D3D414yes—
182C42×D3C2314yes—
183C3×#107C2314yes—
184C3×#106C2314yes—
185C3×C4⋊C8C2314yes—
186C3×#103C2314yes—
187C3×#103C2314yes—
188#821C2314yes—
189#816C2314yes—
190Dic3⋊C8C2314yes—
191Dic3⋊C8C2314yes—
192#810C2314yes—
193#809C2314yes—
194#809C2314yes—
195#809C2314yes—
196#808C2314yes—
197#807C2314yes—
198C4⋊(C3⋊C8)C2314yes—
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×#124—31no—
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×Q8C2×D311yescharacteristic
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#479—38no—
231#479C2×D318yescomplemented
232#478—38no—
233#478—38no—
234#467—38no—
235#466—38no—
236#465—38no—
237#465—38no—
238#464—38no—
239#464—38no—
240#463—38no—
241#463—38no—
242C2×#107—31no—
243C2×#107C2×D311yescharacteristic
244C2×#106—31no—
245C2×#106C2×D311yescharacteristic
246C2×C4⋊C8—31no—
247C2×C4⋊C8—31no—
248C2×C4⋊C8—31no—
249C2×C4⋊C8—38no—
250C2×C4⋊C8C2×D311yescharacteristic
251C2×#103—31no—
252C2×#103—31no—
253C2×#103C2×D311yescharacteristic
254C2×#103C2×D311yescharacteristic
255C2×#102—31no—
256C2×#102—31no—
257C2×#102—31no—
258C2×#102—31no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3C2×D411yescharacteristic
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8C2412yes—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277C22×Dic3C2×D411yescharacteristic
278C2×D12—22no—
279C2×D12—22no—
280C2×D12—22no—
281C2×D12—22no—
282C2×D12—24no—
283C2×D12—24no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—44no—
287C2×D12—44no—
288C2×D12C2412yes—
289C2×D12C2412yes—
290C2×C4×D3—24no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—24no—
294C2×C4×D3—24no—
295C2×C4×D3—42no—
296C2×C4×D3—44no—
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—21no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4C2412yes—
317C3×C4⋊C4C2412yes—
318C3×C4⋊C4C2412yes—
319C3×C42—24no—
320C3×C42C2×D412yes—
321C3×C42C2412yes—
322#216—44no—
323#215—44no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
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—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334C4⋊Dic3—21no—
335C4⋊Dic3—24no—
336C4⋊Dic3—24no—
337C4⋊Dic3C2412yes—
338Dic3⋊C4—24no—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341C4×Dic3—24no—
342C4×Dic3C2×D412yes—
343C4×Dic3C2×D414yes—
344C4×Dic3C2×D414yes—
345C4×Dic3C2412yes—
346C2×C3⋊C8—22no—
347C2×C3⋊C8—22no—
348C2×C3⋊C8C2412yes—
349C2×C3⋊C8C2412yes—
350D24—44no—
351#204—44no—
352D3×C8—44no—
353D3×C8—44no—
354C22×Q8—31no—
355C22×Q8C22×D311yescharacteristic
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—61no—
359C22×D4—61no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—61no—
364C23×C4—61no—
365C2×Q16—34no—
366C2×Q16—122no—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—122no—
370C2×SD16—122no—
371C2×D8—34no—
372C2×D8—122no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8—34no—
376C22×C8—34no—
377C22×C8—122no—
378C22×C8—122no—
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—34no—
388#124—34no—
389#124—62no—
390#124—62no—
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—22no—
402C4×Q8—34no—
403C4×Q8—62no—
404C4×Q8C22×D314yes—
405C4×D4—34no—
406C4×D4—34no—
407C4×D4—68no—
408C4×D4—62no—
409C4×D4—68no—
410C4×D4—62no—
411#117—68no—
412#117—68no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
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⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
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—21no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—34no—
440C2×C42—34no—
441C2×C42—61no—
442C2×C42C22×D311yescharacteristic
443#107—34no—
444#107C22×D314yes—
445#106—34no—
446#106C22×D314yes—
447C4⋊C8—34no—
448C4⋊C8—34no—
449C4⋊C8—34no—
450C4⋊C8C22×D314yes—
451#103—34no—
452#103—34no—
453#103C22×D314yes—
454#103C22×D314yes—
455#102—34no—
456#102—34no—
457#102—34no—
458#102—34no—
459C23×C3C22×D411yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3#13514yes—
471C22×D3C22×D412yes—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—42no—
482C2×C3×C4—42no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4H(5,𝔽2)12yes—
489C2×C3×C42−1+412yes—
490C2×C3×C4C2511yescharacteristic
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3C22×D412yes—
499C2×Dic3C22×D412yes—
500C2×Dic3C22×D412yes—
501D12—22no—
502D12—22no—
503D12—22no—
504D12—22no—
505D12—48no—
506D12—48no—
507D12—42no—
508D12—42no—
509C4×D3—28no—
510C4×D3—24no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—44no—
514C4×D3—48no—
515C4×D3—48no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3×C8—22no—
520C3×C8—22no—
521C3⋊C8—22no—
522C3⋊C8—22no—
523C24—31no—
524C24—61no—
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—32no—
535C2×D4—32no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—124no—
545C2×D4—124no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—34no—
555C22×C4—32no—
556C22×C4—34no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—64no—
564C22×C4—122no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570Q16—124no—
571SD16—124no—
572SD16—124no—
573D8—124no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—32no—
577C2×C8—32no—
578C2×C8—62no—
579C2×C8—62no—
580C2×C8—124no—
581C2×C8—124no—
582C2×C8C23×D312yes—
583C2×C8C23×D312yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—32no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—61no—
597C4⋊C4C23×D312yes—
598C4⋊C4C23×D312yes—
599C4⋊C4C23×D312yes—
600C22⋊C4—64no—
601C22⋊C4—64no—
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—24no—
611C42—34no—
612C42—34no—
613C42—32no—
614C42—32no—
615C42—64no—
616C42D3×D412yes—
617C42C23×D312yes—
618C22×C3#53712yes—
619C22×C3C2×#13512yes—
620C22×C3#57512yes—
621C22×C3C23×D411yescharacteristic
622C2×D3—22no—
623C2×D3—28no—
624C2×D3—22no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—84no—
632C2×D3—84no—
633C2×D3C2×#13514yes—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4#53712yes—
641C3×C4C2×H(5,𝔽2)11yescharacteristic
642C3×C4C2×2−1+411yescharacteristic
643Dic3—22no—
644Dic3—22no—
645Dic3—22no—
646Dic3—42no—
647Dic3—42no—
648C23—32no—
649C23—34no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23C2×D3×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—122no—
667D4—62no—
668D4—62no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—128no—
673D4—122no—
674D4—122no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—68no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—64no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—124no—
698C2×C4—128no—
699C2×C4—128no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4C2×D3×D412yes—
703C2×C4C2×D3×D412yes—
704C2×C4C2×D3×D411yescharacteristic
705C2×C4#100712yes—
706C2×C4#100912yes—
707C2×C4C24×D311yescharacteristic
708C8—22no—
709C8—22no—
710C8—62no—
711C8—62no—
712C2×C3#325014yescomplemented
713C2×C3C2×#53711yescharacteristic
714C2×C3C22×#13511yescharacteristic
715C2×C3C2×#57511yescharacteristic
716D3—24no—
717D3—82no—
718D3—82no—
719C22—34no—
720C22—68no—
721C22—62no—
722C22—62no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22—122no—
727C22—122no—
728C22—122no—
729C22—244no—
730C22—244no—
731C22#562912yes—
732C22D3×#13512yes—
733C22#577712yes—
734C22C22×D3×D411yescharacteristic
735C4—22no—
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—62no—
742C4—62no—
743C4—62no—
744C4—122no—
745C4—122no—
746C4#562912yes—
747C4C2×#100711yescharacteristic
748C4C2×#100911yescharacteristic
749C3C2×#325011yescharacteristic, complemented, Sylow
750C2—64no—
751C2—242no—
752C2—242no—
753C2#8126114yesdirect product factor
754C2C2×#562911yescharacteristic
755C2C2×D3×#13511yescharacteristic
756C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#479C2
socleC23×C3C22×D4
prime radicalC2×#4883C2
hypercenterC2×#479D3
hypocenterC3C2×#3250
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#5691C2semidirect
2. C2×#5580C2semidirect
3. C2×C3×#479C2semidirect
4. C2×#5066C2semidirect
5. C2×#5028C2semidirect
6. #81261C2direct (N × H)
7. C2×#4877C2semidirect
9. C2×#4871C2semidirect
10. C2×#4864C2semidirect
11. C2×#4844C2semidirect
12. C2×D3×C4⋊C8C2semidirect
13. C2×#4798C2semidirect
14. C2×#4819C2semidirect
15. C2×#4813C2semidirect
16. C2×#4807C2semidirect
29. #5691C22semidirect
31. #5580C22semidirect
49. C3×#479C22semidirect
59. #5066C22semidirect
60. #5028C22semidirect
69. #4877C22semidirect
70. #4871C22semidirect
71. #4864C22semidirect
72. #4844C22semidirect
73. D3×C4⋊C8C22semidirect
74. #4819C22semidirect
75. #4813C22semidirect
76. #4807C22semidirect
77. #4798C22semidirect
82. C2×#479D3semidirect
231. #479C2×D3semidirect
712. C2×C3#3250semidirect
749. C3C2×#3250semidirect
753. C2#81261direct (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×#55802
C2×C3×#4792
C2×#50662
C2×#50282
#812612
C2×#48772
C2×#48832
C2×#48712
C2×#48642
C2×#48442
C2×D3×C4⋊C82
C2×#47982
C2×#48192
C2×#48132
C2×#48072
C2×#32503