Finite Group Databasebeta

← C2×#80888 #11664959

Subgroups — C2×#80888 #11664959

Order 768.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×#5624C211yesmaximal, characteristic
3C2×C3×#470C211yesmaximal, characteristic, complemented
4C2×#5190C211yesmaximal, characteristic, complemented
5C2×Dic3×Q16C211yesmaximal, characteristic, complemented
6C2×#5134C211yesmaximal, characteristic
7C2×Dic3×M16C211yesmaximal, characteristic, complemented
8C2×#5052C211yesmaximal, characteristic, complemented
9C2×#5049C211yesmaximal, characteristic
10#80888C2116yesmaximal, direct product factor
11C2×#4856C211yesmaximal, characteristic, complemented
12C2×#4852C211yesmaximal, characteristic, complemented
13C2×#4797C211yesmaximal, characteristic, complemented
14C2×#4794C211yesmaximal, characteristic, complemented
15C2×#4790C211yesmaximal, characteristic, complemented
16C2×#4788C211yesmaximal, characteristic, complemented
17C2×#3172—31nomaximal, Sylow
18C22×C3×Q16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#944C2211yescharacteristic
26C22×#216C2211yescharacteristic
27C22×#215C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#924C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×#208C2211yescharacteristic
32C22×#204C2211yescharacteristic
33#5624—24no—
34#5624C2218yes—
35#5622—24no—
36#5622C2218yescomplemented
37C2×#898—21no—
38C2×#893C2211yescharacteristic
39C2×#892—21no—
40C2×#890C2211yescharacteristic
41C2×#889—21no—
42C2×#888C2211yescharacteristic
43C2×#887—21no—
44C2×#887C2211yescharacteristic
45C2×#886—21no—
46C2×#67⋊C4—21no—
47C2×#878—21no—
48C2×#877—21no—
49C3×#470C2218yescomplemented
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#103C2211yescharacteristic
53C2×#835C2211yescharacteristic
54C2×#835C2211yescharacteristic
55#5190C2218yescomplemented
56Dic3×Q16C2218yescomplemented
57#5134C2218yes—
58Dic3×M16C2218yescomplemented
59C2×#821C2211yescharacteristic
60C2×#818C2211yescharacteristic
61C2×#816C2211yescharacteristic
62C2×#815C2211yescharacteristic
63C2×#815C2211yescharacteristic
64C2×C8×Dic3C2211yescharacteristic
65C2×C8×Dic3C2211yescharacteristic
66#5052C2218yescomplemented
67#5049C2218yes—
68C2×#810C2211yescharacteristic
69C2×#809C2211yescharacteristic
70C2×#808C2211yescharacteristic
71C2×#807C2211yescharacteristic
72#4856C2218yescomplemented
73#4852C2218yescomplemented
74#4797C2218yescomplemented
75#4794C2218yescomplemented
76#4790C2218yescomplemented
77#4788C2218yescomplemented
78C2×#533—31no—
79C2×#529—31no—
80#3172—316no—
81C2×#501—31no—
82C2×#497—31no—
83C2×#491—31no—
84C2×#489—31no—
85C2×#470—31no—
86C2×#470D311yescharacteristic, complemented
87C2×#468—31no—
88C2×#468—31no—
89C2×C4×Q16—31no—
90C2×C4×Q16—31no—
91C2×C4×SD16—31no—
92C2×C4×SD16—31no—
93C2×C4×M16—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C23×Dic3D411yescharacteristic
99C23×Dic3D411yescharacteristic
100C22×D12C2311yescharacteristic
101C22×C4×D3—21no—
102C22×Dic6—21no—
103C22×Dic6C2311yescharacteristic
104C2×C3×Q16—24no—
105C2×C3×Q16C2314yes—
106C2×C3×M16—24no—
107C2×C3×M16C2314yes—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8C2314yes—
113C3×C22⋊Q8C2314yes—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×#217—21no—
121#947—22no—
122#947C2314yes—
123Q8×Dic3—22no—
124Q8×Dic3—22no—
125Q8×Dic3C2314yes—
126Q8×Dic3C2314yes—
127#944—22no—
128#944C2314yes—
129C2×#216—24no—
130C2×#216C2314yes—
131C2×#215—24no—
132C2×#215C2314yes—
133#930—22no—
134#930C2314yes—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144#924—22no—
145#924C2314yes—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×C4×Dic3—21no—
153C2×C4×Dic3—21no—
154C2×C4×Dic3—21no—
155C2×C4×Dic3D411yescharacteristic
156C2×C4×Dic3D411yescharacteristic
157C2×C4×Dic3D414yes—
158C2×C4×Dic3C2311yescharacteristic
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2314yes—
161C2×#208—24no—
162C2×#208C2314yes—
163C22×C3⋊C8C2311yescharacteristic
164C22×C3⋊C8C2311yescharacteristic
165C2×#204—24no—
166C2×#204C2314yes—
167#898—28no—
168#893—22no—
169#893C2314yes—
170#892—28no—
171#890—22no—
172#890C2314yes—
173#889—28no—
174#888—22no—
175#888C2314yes—
176#887—28no—
177#887—22no—
178#887C2314yes—
179#886—28no—
180#67⋊C4—28no—
181#878—28no—
182#877—28no—
183C3×#106C2314yes—
184C3×#103C2314yes—
185C3×#103C2314yes—
186#835C2314yes—
187#835C2314yes—
188#821C2314yes—
189#818C2314yes—
190#816C2314yes—
191#815C2314yes—
192#815C2314yes—
193C8×Dic3C2314yes—
194C8×Dic3C2314yes—
195#810C2314yes—
196#809C2314yes—
197#808C2314yes—
198#807C2314yes—
199C22×Q16—31no—
200C22×Q16C2×D311yescharacteristic
201C22×SD16—31no—
202C22×SD16—31no—
203C22×M16—31no—
204C22×M16C2×D311yescharacteristic
205#533—38no—
206#533—64no—
207C2×C4⋊Q8—31no—
208C2×C4⋊Q8—31no—
209#529—38no—
210#529—64no—
211C2×#126—61no—
212C2×#125—31no—
213C2×#125—61no—
214C2×#124—31no—
215C2×#123—61no—
216C2×C22⋊Q8—31no—
217C2×C22⋊Q8—61no—
218C2×C22⋊Q8C2×D311yescharacteristic
219C2×C22⋊Q8C2×D311yescharacteristic
220C2×#121—31no—
221C2×C4×Q8—31no—
222C2×C4×Q8—31no—
223C2×C4×Q8—31no—
224C2×C4×Q8—61no—
225C2×C4×D4—31no—
226C2×C4×D4—61no—
227C2×#117—61no—
228C2×#117—61no—
229C22×C42—31no—
230#501—38no—
231#497—38no—
232#491—38no—
233#489—38no—
234#470—38no—
235#470C2×D318yescomplemented
236#468—38no—
237#468—38no—
238C4×Q16—38no—
239C4×Q16—38no—
240C4×SD16—38no—
241C4×SD16—38no—
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106C2×D311yescharacteristic
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103—31no—
250C2×#103C2×D311yescharacteristic
251C2×#103C2×D311yescharacteristic
252C2×#102—31no—
253C2×#102—31no—
254C4×M16—38no—
255C2×#97—31no—
256C2×#97—31no—
257C2×C4×C8—31no—
258C2×C4×C8—31no—
259C24×C3C2×D411yescharacteristic
260C23×D3—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C2412yes—
268C2×C3×Q8C2412yes—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C2×#67—24no—
280C2×#67—44no—
281C22×Dic3—24no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—42no—
286C22×Dic3C2×D414yes—
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C22×Dic3C2×D414yes—
291C22×Dic3C2×D411yescharacteristic
292C2×D12—22no—
293C2×D12—22no—
294C2×D12—21no—
295C2×D12C2412yes—
296C2×C4×D3—24no—
297C2×C4×D3—44no—
298C2×Dic6—22no—
299C2×Dic6—22no—
300C2×Dic6—21no—
301C2×Dic6—24no—
302C2×Dic6—44no—
303C2×Dic6C2412yes—
304C3×Q16—28no—
305C3×M16—28no—
306C2×C3×C8—22no—
307C2×C3×C8#4114yes—
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—
318#217—24no—
319#216—28no—
320#215—28no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—24no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—24no—
330C4⋊Dic3C2412yes—
331C4⋊Dic3C2412yes—
332Dic3⋊C4—24no—
333Dic3⋊C4—24no—
334Dic3⋊C4—24no—
335Dic3⋊C4—24no—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338C4×Dic3—24no—
339C4×Dic3—24no—
340C4×Dic3—24no—
341C4×Dic3C2×D414yes—
342C4×Dic3C2×D412yes—
343C4×Dic3C2×D412yes—
344C4×Dic3C2×D414yes—
345C4×Dic3C2412yes—
346C4×Dic3C2412yes—
347#208—28no—
348C2×C3⋊C8—22no—
349C2×C3⋊C8#4114yes—
350C2×C3⋊C8C2412yes—
351C2×C3⋊C8C2412yes—
352#204—28no—
353C22×Q8—31no—
354C22×Q8—61no—
355C22×Q8C22×D311yescharacteristic
356C22×Q8C22×D311yescharacteristic
357C22×D4—31no—
358C22×D4—61no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—61no—
362C23×C4C22×D311yescharacteristic
363C2×Q16—24no—
364C2×Q16—34no—
365C2×Q16—64no—
366C2×Q16C22×D314yes—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×M16—24no—
372C2×M16—34no—
373C2×M16—64no—
374C2×M16C22×D314yes—
375C22×C8—31no—
376C22×C8—31no—
377C22×C8C22×D311yescharacteristic
378C22×C8C22×D311yescharacteristic
379C4⋊Q8—34no—
380C4⋊Q8—34no—
381C4⋊Q8—62no—
382C4⋊Q8—62no—
383#126—68no—
384#125—34no—
385#125—62no—
386#125—68no—
387#124—34no—
388#124—62no—
389#123—68no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—34no—
393C22⋊Q8—68no—
394C22⋊Q8—62no—
395C22⋊Q8C22×D314yes—
396C22⋊Q8C22×D314yes—
397#121—34no—
398#121—62no—
399C4×Q8—34no—
400C4×Q8—34no—
401C4×Q8—34no—
402C4×Q8—62no—
403C4×Q8—68no—
404C4×Q8—62no—
405C4×Q8—62no—
406C4×D4—34no—
407C4×D4—62no—
408C4×D4—68no—
409#117—68no—
410#117—68no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
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⋊C4—61no—
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C42—31no—
434C2×C42—31no—
435C2×C42—34no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—34no—
439C2×C42—61no—
440C2×C42—61no—
441C2×C42—61no—
442#107—34no—
443#107—34no—
444#106—34no—
445#106C22×D314yes—
446#103—34no—
447#103—34no—
448#103—34no—
449#103—34no—
450#103C22×D314yes—
451#103C22×D314yes—
452#102—34no—
453#102—34no—
454#97—34no—
455#97—34no—
456C4×C8—34no—
457C4×C8—34no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3C22×D412yes—
462C23×C3C22×D411yescharacteristic
463C22×D3—22no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3—42no—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—42no—
472C3×Q8—42no—
473C2×C3×C4—22no—
474C2×C3×C4—24no—
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×D411yescharacteristic
487C2×C3×C4C2×#4112yes—
488C2×C3×C4C2×#4112yes—
489C2×C3×C4C2511yescharacteristic
490#67—48no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—28no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—44no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C2×Dic3#13714yes—
503C2×Dic3C22×D412yes—
504C2×Dic3C22×D412yes—
505C2×Dic3C22×D412yes—
506C2×Dic3C22×D412yes—
507D12—22no—
508D12—22no—
509D12—42no—
510C4×D3—48no—
511Dic6—22no—
512Dic6—22no—
513Dic6—48no—
514Dic6—42no—
515C3×C8—22no—
516C3×C8C2×#4114yes—
517C3⋊C8—22no—
518C3⋊C8C2×#4114yes—
519C24—61no—
520C24D3×D411yescharacteristic
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—32no—
528C2×Q8—64no—
529C2×Q8—61no—
530C2×Q8—62no—
531C2×Q8—62no—
532C2×Q8—124no—
533C2×Q8C23×D312yes—
534C2×Q8C23×D312yes—
535C2×D4—32no—
536C2×D4—64no—
537C2×D4—61no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—124no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—31no—
548C22×C4—34no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—34no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—124no—
559C22×C4—122no—
560C22×C4D3×D412yes—
561C22×C4D3×D411yescharacteristic
562C22×C4C23×D312yes—
563C22×C4C23×D311yescharacteristic
564Q16—28no—
565Q16—68no—
566SD16—68no—
567SD16—68no—
568M16—28no—
569M16—68no—
570C2×C8—22no—
571C2×C8—34no—
572C2×C8—32no—
573C2×C8—32no—
574C2×C8—62no—
575C2×C8#23714yes—
576C2×C8C23×D312yes—
577C2×C8C23×D312yes—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—32no—
583C4⋊C4—32no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—64no—
595C4⋊C4C23×D312yes—
596C4⋊C4C23×D312yes—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C42—34no—
605C42—32no—
606C42—32no—
607C42—34no—
608C42—32no—
609C42—32no—
610C42—64no—
611C42—64no—
612C42—64no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—44no—
617C22×C3#53212yes—
618C22×C3C2×#13712yes—
619C22×C3#57512yes—
620C22×C3C23×D411yescharacteristic
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—84no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4#53212yes—
631C3×C4C22×#4111yescharacteristic
632C3×C4C22×#4111yescharacteristic
633Dic3—22no—
634Dic3—22no—
635Dic3—22no—
636Dic3—42no—
637Dic3—42no—
638Dic3—42no—
639Dic3C2×#13714yes—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—62no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23C2×D3×D412yes—
648C23C2×D3×D411yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—42no—
654Q8—42no—
655Q8—62no—
656Q8—62no—
657Q8—128no—
658Q8—122no—
659D4—62no—
660D4—62no—
661D4—128no—
662D4—122no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—32no—
672C2×C4—34no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—68no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—128no—
688C2×C4—124no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4C2×D3×D412yes—
693C2×C4C2×D3×D411yescharacteristic
694C2×C4C2×#23712yes—
695C2×C4D3×#4112yes—
696C2×C4C24×D311yescharacteristic
697C8—22no—
698C8—34no—
699C8—62no—
700C8C2×#23714yes—
701C2×C3—42no—
702C2×C3#317214yescomplemented
703C2×C3C2×#53211yescharacteristic
704C2×C3C22×#13711yescharacteristic
705C2×C3C2×#57511yescharacteristic
706D3—82no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—44no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—244no—
715C22#559612yes—
716C22D3×#13712yes—
717C22#577712yes—
718C22C22×D3×D411yescharacteristic
719C4—22no—
720C4—34no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—62no—
726C4—62no—
727C4—62no—
728C4—122no—
729C4—122no—
730C4—122no—
731C4#559612yes—
732C4C22×#23711yescharacteristic
733C4C2×D3×#4111yescharacteristic
734C3C2×#317211yescharacteristic, complemented, Sylow
735C2—42no—
736C2—242no—
737C2#8088814yesdirect product factor
738C2C2×#559611yescharacteristic
739C2C2×D3×#13711yescharacteristic
740C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#470C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenterC2×#470D3
hypocenterC3C2×#3172
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
3. C2×C3×#470C2semidirect
4. C2×#5190C2semidirect
5. C2×Dic3×Q16C2semidirect
7. C2×Dic3×M16C2semidirect
8. C2×#5052C2semidirect
10. #80888C2direct (N × H)
11. C2×#4856C2semidirect
12. C2×#4852C2semidirect
13. C2×#4797C2semidirect
14. C2×#4794C2semidirect
15. C2×#4790C2semidirect
16. C2×#4788C2semidirect
36. #5622C22semidirect
49. C3×#470C22semidirect
55. #5190C22semidirect
56. Dic3×Q16C22semidirect
58. Dic3×M16C22semidirect
66. #5052C22semidirect
72. #4856C22semidirect
73. #4852C22semidirect
74. #4797C22semidirect
75. #4794C22semidirect
76. #4790C22semidirect
77. #4788C22semidirect
86. C2×#470D3semidirect
235. #470C2×D3semidirect
702. C2×C3#3172semidirect
734. C3C2×#3172semidirect
737. C2#80888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#56242
C2×C3×#4702
C2×#51902
C2×Dic3×Q162
C2×#51342
C2×Dic3×M162
C2×#50522
C2×#50492
#808882
C2×#48562
C2×#48522
C2×#47972
C2×#47942
C2×#47902
C2×#47882
C2×#31723