Finite Group Databasebeta

← #11069537

Subgroups — #11069537

Order 768.

2238 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5682C212yesmaximal, complemented
2C3×C4×#124C211yesmaximal, characteristic, complemented
3#82500C211yesmaximal, characteristic, complemented
4Q8×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#82417C211yesmaximal, characteristic
6D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#76623C212yesmaximal, complemented
8#76441C212yesmaximal, complemented
9#75696C214yesmaximal, complemented
10#75666C214yesmaximal, complemented
11#74194C212yesmaximal, complemented
12#73516C212yesmaximal, complemented
13#73512C212yesmaximal, complemented
14#73507C212yesmaximal, complemented
15#73493C212yesmaximal, complemented
16#73311C211yesmaximal, characteristic, complemented
17#73299C211yesmaximal, characteristic, complemented
18#39377—31nomaximal, Sylow
19C2×C3×#124C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2212yes—
23C2×Q8×Dic3C2212yes—
24C2×#938C2212yes—
25C2×D4×Dic3C2212yes—
26C2×#930C2212yes—
27C22×C4⋊Dic3C2212yes—
28#5682—216no—
29C2×#886C2214yes—
30C2×#886C2214yes—
31C2×#885C2214yes—
32C2×#879C2214yes—
33C2×#878C2214yes—
34C2×C4×D12C2211yescharacteristic
35C2×#872C2212yes—
36C2×#869C2212yes—
37C2×#869C2212yes—
38C2×#869C2212yes—
39C3×#391C2211yescharacteristic
40C3×#390C2211yescharacteristic
41C3×#388C2212yes—
42C3×#388C2212yes—
43C3×#382C2211yescharacteristic
44C3×C4×C22⋊C4C2212yes—
45C3×C4×C22⋊C4C2212yes—
46C3×C43C2211yescharacteristic
47#5212C2212yes—
48#5212C2212yes—
49#4994C2214yes—
50#4987C2212yes—
51#4987C2212yes—
52#4984C2214yes—
53#4984C2212yes—
54#4984C2212yes—
55#4961C2214yes—
56#4961C2214yes—
57#4953C2214yes—
58#4950C2214yes—
59#4950C2214yes—
60#4940C2212yes—
61#4940C2212yes—
62#4939C2211yescharacteristic
63#4939C2212yes—
64#4939C2211yescharacteristic
65C4×(C2×D3)⋊C4C2212yes—
66#4935C2212yes—
67#4935C2211yescharacteristic
68#4935C2212yes—
69#4935C2211yescharacteristic
70#4935C2212yes—
71#4935C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74#4928C2211yescharacteristic
75#4928C2212yes—
76#4928C2211yescharacteristic
77#4677C2214yes—
78#4677C2214yes—
79#4673C2214yes—
80#4670C2214yes—
81#4661C2214yes—
82#4659C2214yes—
83#4656C2214yes—
84#4653C2214yes—
85C2×#542—32no—
86#2868—31no—
87#2718—34no—
88#2674—34no—
89#2628—32no—
90#2538—31no—
91#2537—31no—
92#2501—32no—
93#2496—32no—
94#2491—32no—
95#2440—32no—
96#2423—32no—
97#2422—32no—
98Q8×C4⋊C4—31no—
99D4×C4⋊C4—31no—
100C4×#124D311yescharacteristic, complemented
101#2293—31no—
102C22×C3×Q8C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C22×#67C2314yes—
106C23×Dic3C2314yes—
107C22×D12C2311yescharacteristic
108C22×C4×D3C2312yes—
109C22×Dic6C2314yes—
110C3×#124D418yescomplemented
111C3×C4×Q8—24no—
112C3×C4×D4—24no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C22⋊C4C2312yes—
117C2×C3×C22⋊C4C2312yes—
118C2×C3×C22⋊C4C2312yes—
119C2×C3×C22⋊C4C2312yes—
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C42C2312yes—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×#217C2314yes—
130C2×#217C2314yes—
131#946—28no—
132Q8×Dic3—28no—
133#938—28no—
134D4×Dic3—28no—
135#930—44no—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×C4⋊Dic3—44no—
145C2×C4⋊Dic3C2314yes—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2314yes—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2314yes—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2312yes—
165#886—216no—
166#886—48no—
167#885—216no—
168#879—216no—
169#878—216no—
170C4×D12—24no—
171#872—28no—
172#869—28no—
173#869—44no—
174#869—44no—
175C3×#95C2312yes—
176C3×#95C2312yes—
177C3×#95C2312yes—
178C3×#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186#542—616no—
187C2×C4⋊Q8—32no—
188C2×C4⋊Q8—32no—
189C2×C4⋊Q8—32no—
190C2×#126—34no—
191C2×#124—34no—
192C2×#124C2×D311yescharacteristic
193C2×#123—34no—
194C2×#123—34no—
195C2×C22⋊Q8—32no—
196C2×C22⋊Q8—34no—
197C2×#121—32no—
198C2×#121—32no—
199C2×C4×Q8—32no—
200C2×C4×Q8C2×D311yescharacteristic
201C2×C4×D4—32no—
202C2×C4×D4—31no—
203C2×C4×D4C2×D311yescharacteristic
204C2×#117—32no—
205C22×C4⋊C4—32no—
206#400—34no—
207#399—34no—
208#399—34no—
209#398—34no—
210#397—34no—
211#396—34no—
212#395—34no—
213#394—34no—
214#394—34no—
215#393—34no—
216#391C2×D311yescharacteristic
217#390—31no—
218#390—32no—
219#390—31no—
220#390C2×D311yescharacteristic
221#389—32no—
222#389—32no—
223#389—34no—
224#389—31no—
225#389—32no—
226#389—31no—
227#388—32no—
228#388—32no—
229#388—34no—
230#388C2×D312yes—
231#388C2×D312yes—
232#387—34no—
233#385—34no—
234#385—34no—
235#384—31no—
236#384—31no—
237#384—32no—
238#384—32no—
239#384—32no—
240#384—32no—
241#382C2×D311yescharacteristic
242#380—32no—
243#380—32no—
244#380—32no—
245#380—32no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—32no—
248C4×C22⋊C4—32no—
249C4×C22⋊C4C2×D312yes—
250C4×C22⋊C4C2×D312yes—
251C43C2×D311yescharacteristic
252C24×C3C2412yes—
253C23×D3C2412yes—
254C2×C3×Q8—22no—
255C2×C3×Q8—22no—
256C2×C3×Q8C2×D414yes—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4C2×D414yes—
260C22×C3×C4—24no—
261C22×C3×C4—24no—
262C22×C3×C4—24no—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C2×#67—28no—
274C2×#67—44no—
275C2×#67—44no—
276C22×Dic3—28no—
277C22×Dic3—44no—
278C22×Dic3—44no—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C22×Dic3C2414yes—
283C22×Dic3C2414yes—
284C2×D12—22no—
285C2×D12—22no—
286C2×D12—22no—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×Dic6—28no—
291C2×Dic6—44no—
292C2×Dic6—44no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4—22no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4C2×D418yes—
300C3×C22⋊C4C2×D418yes—
301C3×C42—24no—
302C3×C42—22no—
303C3×C42—22no—
304C3×C42—22no—
305C3×C42—22no—
306C3×C42—22no—
307C3×C42C2×D414yes—
308C3×C42#4114yes—
309#217—28no—
310#217—28no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—24no—
317(C2×D3)⋊C4—44no—
318(C2×D3)⋊C4—44no—
319C4⋊Dic3—28no—
320C4⋊Dic3—24no—
321C4⋊Dic3—24no—
322C4⋊Dic3—28no—
323C4⋊Dic3—22no—
324C4⋊Dic3—28no—
325C4⋊Dic3—24no—
326C4⋊Dic3—24no—
327C4⋊Dic3—22no—
328C4⋊Dic3—22no—
329C4⋊Dic3—44no—
330C4⋊Dic3—42no—
331C4⋊Dic3—42no—
332C4⋊Dic3—44no—
333C4⋊Dic3—44no—
334Dic3⋊C4—24no—
335Dic3⋊C4—24no—
336Dic3⋊C4—28no—
337C4×Dic3—24no—
338C4×Dic3—28no—
339C22×Q8—34no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—34no—
342C22×D4—31no—
343C22×D4C22×D311yescharacteristic
344C23×C4—34no—
345C23×C4—32no—
346C23×C4C22×D312yes—
347C4⋊Q8—68no—
348C4⋊Q8—124no—
349C4⋊Q8—124no—
350#126—616no—
351#124—616no—
352#124D1218yescomplemented
353#123—616no—
354#123—128no—
355C22⋊Q8—68no—
356C22⋊Q8—616no—
357#121—68no—
358#121—124no—
359C4×Q8—24no—
360C4×Q8—68no—
361C4×D4—24no—
362C4×D4—68no—
363C4×D4—64no—
364#117—68no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—124no—
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C4⋊C4C22×D312yes—
387C2×C22⋊C4—34no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4C22×D312yes—
398C2×C22⋊C4C22×D312yes—
399C2×C22⋊C4C22×D312yes—
400C2×C22⋊C4C22×D312yes—
401C2×C22⋊C4C22×D312yes—
402C2×C42—32no—
403C2×C42—34no—
404C2×C42C22×D312yes—
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407C2×C42C22×D311yescharacteristic
408C2×C42C22×D311yescharacteristic
409C2×C42C22×D311yescharacteristic
410C2×C42C22×D311yescharacteristic
411C2×C42C22×D311yescharacteristic
412#95—32no—
413#95—32no—
414#95—32no—
415#95—34no—
416#95—34no—
417#95—34no—
418#95—34no—
419#95C22×D312yes—
420#95C22×D312yes—
421#95C22×D312yes—
422#95C22×D312yes—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3C22×D414yes—
430C23×C3C2511yescharacteristic
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C3×Q8—28no—
439C3×D4—28no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—48no—
459C2×C3×C4C22×D414yes—
460C2×C3×C4C22×D412yes—
461C2×C3×C4C22×D412yes—
462C2×C3×C4C22×D412yes—
463C2×C3×C4C2×#4112yes—
464C2×C3×C4C2×#4112yes—
465C2×C3×C4C2×#4112yes—
466C2×C3×C4H(5,𝔽2)12yes—
467C2×C3×C4H(5,𝔽2)12yes—
468C2×C3×C42−1+412yes—
469C2×C3×C42−1+412yes—
470C2×C3×C42−1+412yes—
471#67—88no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—24no—
475C2×Dic3—22no—
476C2×Dic3—24no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—24no—
482C2×Dic3—24no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—88no—
488D12—44no—
489C4×D3—48no—
490Dic6—88no—
491C24—32no—
492C24C23×D312yes—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—68no—
496C2×Q8—124no—
497C2×Q8—124no—
498C2×Q8C2×D1214yes—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—68no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—62no—
505C2×D4—124no—
506C2×D4—124no—
507C2×D4C2×D1214yes—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—32no—
514C22×C4—34no—
515C22×C4—34no—
516C22×C4—68no—
517C22×C4—64no—
518C22×C4—64no—
519C22×C4—64no—
520C22×C4—124no—
521C22×C4—124no—
522C22×C4C23×D312yes—
523C22×C4C23×D312yes—
524C22×C4C23×D312yes—
525C22×C4C23×D311yescharacteristic
526C22×C4C23×D311yescharacteristic
527C22×C4C23×D311yescharacteristic
528C22×C4C23×D311yescharacteristic
529C22×C4C23×D311yescharacteristic
530C22×C4C23×D311yescharacteristic
531C22×C4C23×D311yescharacteristic
532C4⋊C4—22no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—64no—
536C4⋊C4—64no—
537C4⋊C4—64no—
538C4⋊C4—64no—
539C4⋊C4—68no—
540C4⋊C4—68no—
541C4⋊C4—68no—
542C4⋊C4—62no—
543C4⋊C4—62no—
544C4⋊C4—64no—
545C4⋊C4—64no—
546C4⋊C4—68no—
547C4⋊C4—62no—
548C4⋊C4—124no—
549C4⋊C4—124no—
550C4⋊C4—122no—
551C4⋊C4—124no—
552C4⋊C4—122no—
553C22⋊C4—24no—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—68no—
557C22⋊C4—68no—
558C22⋊C4—64no—
559C22⋊C4—64no—
560C22⋊C4—68no—
561C22⋊C4—64no—
562C22⋊C4—64no—
563C22⋊C4—64no—
564C22⋊C4—124no—
565C22⋊C4—124no—
566C22⋊C4C2×D1218yes—
567C22⋊C4C2×D1218yes—
568C42—24no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—64no—
575C42—68no—
576C42C2×D1214yes—
577C42#23714yes—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3C23×D411yescharacteristic
586C22×C3C22×#4111yescharacteristic
587C22×C3C2×H(5,𝔽2)11yescharacteristic
588C22×C3C2×H(5,𝔽2)11yescharacteristic
589C22×C3C2×2−1+411yescharacteristic
590C22×C3C2×2−1+411yescharacteristic
591C22×C3C2×2−1+411yescharacteristic
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—42no—
599C3×C4—24no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4#54214yescomplemented
608C3×C4#54714yes—
609Dic3—42no—
610Dic3—44no—
611Dic3—44no—
612Dic3—42no—
613Dic3—42no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23C22×D1214yes—
628C23C24×D311yescharacteristic
629Q8—28no—
630Q8—248no—
631D4—28no—
632D4—124no—
633D4—248no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—64no—
656C2×C4—62no—
657C2×C4—64no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—64no—
661C2×C4—64no—
662C2×C4—62no—
663C2×C4—64no—
664C2×C4—64no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—128no—
669C2×C4—248no—
670C2×C4C22×D1214yes—
671C2×C4C22×D1212yes—
672C2×C4C22×D1212yes—
673C2×C4C22×D1212yes—
674C2×C4C2×#23712yes—
675C2×C4C2×#23712yes—
676C2×C4C2×#23712yes—
677C2×C4#100912yes—
678C2×C4#100912yes—
679C2×C4#101012yes—
680C2×C4#101012yes—
681C2×C4#101012yes—
682C2×C3—44no—
683C2×C3C2×#54211yescharacteristic
684C2×C3C2×#54711yescharacteristic
685C2×C3#349811yescharacteristic
686C2×C3#349911yescharacteristic
687C2×C3#351111yescharacteristic
688C2×C3#354411yescharacteristic
689C2×C3#355211yescharacteristic
690D3—82no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—122no—
699C22—122no—
700C22—122no—
701C22—122no—
702C22—122no—
703C22—122no—
704C22—122no—
705C22C23×D1211yescharacteristic
706C22C22×#23711yescharacteristic
707C22C2×#100911yescharacteristic
708C22C2×#100911yescharacteristic
709C22C2×#101011yescharacteristic
710C22C2×#101011yescharacteristic
711C22C2×#101011yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—122no—
721C4—122no—
722C4—124no—
723C4—124no—
724C4—122no—
725C4#555514yes—
726C4#568214yescomplemented
727C3#3937711yescharacteristic, complemented, Sylow
728C2—44no—
729C2—242no—
730C2C2×#555511yescharacteristic
731C2#8582711yescharacteristic
732C2#8584611yescharacteristic
733C2C2×#568211yescharacteristic
734C2#8613311yescharacteristic
735C2#8613511yescharacteristic
736C2#8622511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#124C2
prime radical#82417C2
hypercenterC4×#124D3
hypocenterC3#39377
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. C2×#5682C2semidirect
2. C3×C4×#124C2semidirect
3. #82500C2semidirect
4. Q8×C4⋊Dic3C2semidirect
6. D4×C4⋊Dic3C2semidirect
7. #76623C2semidirect
8. #76441C2semidirect
9. #75696C2semidirect
10. #75666C2semidirect
11. #74194C2semidirect
12. #73516C2semidirect
13. #73512C2semidirect
14. #73507C2semidirect
15. #73493C2semidirect
16. #73311C2semidirect
17. #73299C2semidirect
100. C4×#124D3semidirect
110. C3×#124D4semidirect
352. #124D12semidirect
607. C3×C4#542semidirect
726. C4#5682semidirect
727. C3#39377semidirect

Maximal subgroups

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

subgroupindex
C2×#56822
C3×C4×#1242
#825002
Q8×C4⋊Dic32
#824172
D4×C4⋊Dic32
#766232
#764412
#756962
#756662
#741942
#735162
#735122
#735072
#734932
#733112
#732992
#393773