Finite Group Databasebeta

← #10728133

Subgroups — #10728133

Order 768.

2254 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4993C211yesmaximal, characteristic, complemented
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C212yesmaximal
5C2×#4667C212yesmaximal, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1445C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69421C212yesmaximal, complemented
11#69420C211yesmaximal, characteristic, complemented
12#14836—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×(C2×D3)⋊C4C2212yes—
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2212yes—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2212yes—
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36#4993—24no—
37#4987—24no—
38#4667—28no—
39#4665—28no—
40#4665—24no—
41D3×#95—24no—
42C2×#399—31no—
43C2×#386—32no—
44C2×#386—31no—
45C2×#380—32no—
46C2×#380—31no—
47C22×#95—31no—
48#1445—32no—
49#1445D311yescharacteristic, complemented
50#1444—31no—
51#1439—31no—
52#1439—32no—
53C24×D3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2312yes—
64C22×D12—24no—
65C22×D12—22no—
66C22×D12—24no—
67C22×D12—22no—
68C22×D12Q814yes—
69C22×C4×D3—24no—
70C22×C4×D3—24no—
71C22×C4×D3—24no—
72C22×C4×D3—22no—
73C22×C4×D3—22no—
74C22×C4×D3—24no—
75C22×C4×D3—24no—
76C22×C4×D3—42no—
77C22×C4×D3—42no—
78C22×C4×D3—42no—
79C22×C4×D3D418yes—
80C22×C4×D3D414yes—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×(C2×D3)⋊C4—24no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—42no—
98C2×(C2×D3)⋊C4—42no—
99C2×(C2×D3)⋊C4—42no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—42no—
102C2×Dic3⋊C4—24no—
103C2×Dic3⋊C4—24no—
104C2×Dic3⋊C4—24no—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—42no—
107C2×Dic3⋊C4—42no—
108C3×#95—22no—
109C3×#95—24no—
110C3×#95—22no—
111C3×#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—22no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95D414yescomplemented
118C23×D4—31no—
119C24×C4—32no—
120C24×C4—31no—
121C22×C4⋊C4—32no—
122C22×C4⋊C4—32no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4C2×D311yescharacteristic
125C22×C22⋊C4—32no—
126C22×C22⋊C4—31no—
127C22×C22⋊C4—31no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—31no—
130C22×C22⋊C4—32no—
131#399—64no—
132#386—68no—
133#386—64no—
134#380—68no—
135#380—64no—
136C2×#95—31no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—31no—
142C2×#95—64no—
143C2×#95C2×D311yescharacteristic
144C2×#95C2×D312yes—
145C2×#95C2×D311yescharacteristic
146C2×#95C2×D312yes—
147C24×C3C2411yescharacteristic
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—22no—
151C23×D3—22no—
152C23×D3—21no—
153C23×D3—21no—
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—22no—
157C23×D3—21no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—21no—
161C23×D3—22no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3C2×D414yes—
165C23×D3C2×D412yes—
166C23×D3C2×Q812yes—
167C23×D3C2×Q812yes—
168C23×D3#4114yes—
169C23×D3#4112yes—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4C2×D414yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×Q812yes—
198C22×C3×C4#4112yes—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3C2×D412yes—
220C22×Dic3C2×D414yes—
221C22×Dic3C2×D414yes—
222C22×Dic3#4114yes—
223C2×D12—28no—
224C2×D12—216no—
225C2×D12—44no—
226C2×D12—48no—
227C2×D12—44no—
228C2×C4×D3—216no—
229C2×C4×D3—28no—
230C2×C4×D3—28no—
231C2×C4×D3—216no—
232C2×C4×D3—48no—
233C2×C4×D3—44no—
234C2×C4×D3—48no—
235C2×C4×D3—48no—
236C2×C4×D3—48no—
237C2×C4×D3—48no—
238C2×C4×D3—48no—
239C2×C4×D3—48no—
240C3×C4⋊C4—44no—
241(C2×D3)⋊C4—44no—
242(C2×D3)⋊C4—48no—
243(C2×D3)⋊C4—44no—
244(C2×D3)⋊C4—48no—
245(C2×D3)⋊C4—44no—
246(C2×D3)⋊C4—48no—
247C4⋊Dic3—44no—
248Dic3⋊C4—48no—
249Dic3⋊C4—48no—
250C25—31no—
251C25—31no—
252C22×D4—34no—
253C22×D4—62no—
254C22×D4—64no—
255C22×D4—64no—
256C22×D4—62no—
257C23×C4—32no—
258C23×C4—31no—
259C23×C4—38no—
260C23×C4—34no—
261C23×C4—31no—
262C23×C4—32no—
263C23×C4—64no—
264C23×C4—64no—
265C23×C4—64no—
266C23×C4—64no—
267C23×C4—64no—
268C23×C4—62no—
269C23×C4—62no—
270C23×C4—122no—
271C23×C4—122no—
272C23×C4—122no—
273C23×C4C22×D311yescharacteristic
274C23×C4C22×D312yes—
275C23×C4C22×D312yes—
276C23×C4C22×D311yescharacteristic
277C23×C4C22×D311yescharacteristic
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—64no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4—64no—
284C2×C4⋊C4—64no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—122no—
287C2×C4⋊C4—122no—
288C2×C4⋊C4—122no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—64no—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—62no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—62no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—62no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305#95—22no—
306#95—24no—
307#95—24no—
308#95—22no—
309#95—34no—
310#95—64no—
311#95—64no—
312#95—64no—
313#95—62no—
314#95—64no—
315C23×C3C22×D411yescharacteristic
316C23×C3C22×D411yescharacteristic
317C23×C3C22×D412yes—
318C23×C3C22×Q811yescharacteristic
319C23×C3C2×#4111yescharacteristic
320C23×C3C2×#4112yes—
321C23×C3C2×#4112yes—
322C23×C3C2×#4111yescharacteristic
323C23×C3H(5,𝔽2)12yes—
324C23×C3H(5,𝔽2)11yescharacteristic
325C23×C32−1+411yescharacteristic
326C22×D3—22no—
327C22×D3—24no—
328C22×D3—22no—
329C22×D3—24no—
330C22×D3—22no—
331C22×D3—24no—
332C22×D3—22no—
333C22×D3—24no—
334C22×D3—24no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—24no—
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—24no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—24no—
346C22×D3—22no—
347C22×D3—24no—
348C22×D3—22no—
349C22×D3—41no—
350C22×D3—42no—
351C22×D3—41no—
352C22×D3—42no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—42no—
356C22×D3—41no—
357C22×D3—42no—
358C22×D3—41no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—41no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—41no—
367C22×D3C22⋊Q814yes—
368C22×D3C22⋊Q818yes—
369C22×D3#12314yes—
370C22×D3#12318yes—
371C22×D3#12714yes—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—41no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4#12114yes—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—24no—
406C2×Dic3—24no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412C2×Dic3—42no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—42no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3#12118yes—
425D12—416no—
426C4×D3—432no—
427C4×D3—416no—
428C24—32no—
429C24—34no—
430C24—32no—
431C24—34no—
432C24—32no—
433C24—32no—
434C24—61no—
435C24—61no—
436C24—61no—
437C24—62no—
438C24—62no—
439C24—61no—
440C24—61no—
441C24—61no—
442C24—61no—
443C24—62no—
444C24—61no—
445C24—62no—
446C24—62no—
447C24—61no—
448C24—62no—
449C24—61no—
450C24C23×D311yescharacteristic
451C2×D4—68no—
452C2×D4—616no—
453C2×D4—124no—
454C2×D4—128no—
455C2×D4—124no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—34no—
481C22×C4—34no—
482C22×C4—34no—
483C22×C4—32no—
484C22×C4—616no—
485C22×C4—68no—
486C22×C4—616no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—68no—
496C22×C4—61no—
497C22×C4—62no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—124no—
509C22×C4—128no—
510C22×C4—128no—
511C22×C4—128no—
512C22×C4—128no—
513C22×C4—128no—
514C22×C4—128no—
515C22×C4—128no—
516C22×C4#23512yes—
517C22×C4D3×D414yes—
518C22×C4D3×D412yes—
519C22×C4D3×D412yes—
520C22×C4D3×Q812yes—
521C4⋊C4—44no—
522C4⋊C4—124no—
523C4⋊C4—128no—
524C4⋊C4—128no—
525C22⋊C4—128no—
526C22⋊C4—128no—
527C22⋊C4—124no—
528C22⋊C4—124no—
529C22⋊C4—128no—
530C22⋊C4—124no—
531C22×C3C2×#12111yescharacteristic
532C22×C3C2×#12112yes—
533C22×C3C2×C22⋊Q811yescharacteristic
534C22×C3C2×C22⋊Q812yes—
535C22×C3C2×#12311yescharacteristic
536C22×C3C2×#12312yes—
537C22×C3C2×#12711yescharacteristic
538C22×C3#53211yescharacteristic
539C22×C3#53212yes—
540C22×C3#53411yescharacteristic
541C22×C3#53412yes—
542C22×C3#53711yescharacteristic
543C22×C3#53712yes—
544C22×C3#54612yes—
545C22×C3#54611yescharacteristic
546C22×C3D4×Q811yescharacteristic
547C22×C3#55112yes—
548C22×C3#55112yes—
549C22×C3#55112yes—
550C22×C3#55212yes—
551C22×C3#55211yescharacteristic
552C22×C3#55412yes—
553C22×C3#55411yescharacteristic
554C2×D3—24no—
555C2×D3—28no—
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—28no—
559C2×D3—24no—
560C2×D3—24no—
561C2×D3—28no—
562C2×D3—24no—
563C2×D3—28no—
564C2×D3—42no—
565C2×D3—44no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3—44no—
569C2×D3—81no—
570C2×D3—81no—
571C2×D3—82no—
572C2×D3—81no—
573C2×D3—81no—
574C2×D3—82no—
575C2×D3#39918yescomplemented
576C3×C4—24no—
577C3×C4—42no—
578C3×C4—44no—
579C3×C4—82no—
580C3×C4—81no—
581Dic3—28no—
582Dic3—42no—
583Dic3—81no—
584Dic3—82no—
585C23—34no—
586C23—38no—
587C23—34no—
588C23—34no—
589C23—38no—
590C23—62no—
591C23—64no—
592C23—64no—
593C23—62no—
594C23—62no—
595C23—64no—
596C23—64no—
597C23—64no—
598C23—64no—
599C23—62no—
600C23—62no—
601C23—64no—
602C23—64no—
603C23—62no—
604C23—62no—
605C23—64no—
606C23—62no—
607C23—64no—
608C23—64no—
609C23—62no—
610C23—62no—
611C23—62no—
612C23—64no—
613C23—121no—
614C23—122no—
615C23—121no—
616C23—122no—
617C23—122no—
618C23—121no—
619C23—121no—
620C23—122no—
621C23—122no—
622C23—122no—
623C23—121no—
624C23—121no—
625C23—122no—
626C23—122no—
627C23—121no—
628C23—122no—
629C23—121no—
630C23—122no—
631C23C2×#23511yescharacteristic
632C23C2×D3×D411yescharacteristic
633C23C2×D3×D412yes—
634C23C2×D3×D411yescharacteristic
635C23C2×D3×Q811yescharacteristic
636C23#100711yescharacteristic
637C23D3×#4112yes—
638C23D3×#4111yescharacteristic
639C23D3×#4112yes—
640C23#100912yes—
641C23#100911yescharacteristic
642D4—1216no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—38no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—64no—
673C2×C4—64no—
674C2×C4—64no—
675C2×C4—64no—
676C2×C4—64no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—1216no—
682C2×C4—1232no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—121no—
689C2×C4—122no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4#88414yes—
698C2×C3C2×#39911yescharacteristic
699C2×C3#241212yes—
700C2×C3#241211yescharacteristic
701C2×C3#241711yescharacteristic
702C2×C3#241712yes—
703C2×C3#249811yescharacteristic
704C2×C3#249812yes—
705C2×C3#256411yescharacteristic
706C2×C3#256412yes—
707C2×C3#265611yescharacteristic
708C2×C3#285611yescharacteristic
709D3—28no—
710D3—82no—
711C22—38no—
712C22—64no—
713C22—64no—
714C22—64no—
715C22—68no—
716C22—64no—
717C22—68no—
718C22—68no—
719C22—64no—
720C22—68no—
721C22—64no—
722C22—122no—
723C22—122no—
724C22—122no—
725C22—124no—
726C22—124no—
727C22—241no—
728C22—241no—
729C22—242no—
730C22—242no—
731C22—241no—
732C22—241no—
733C22C2×#88411yescharacteristic
734C22#552712yes—
735C22#554812yes—
736C22#557911yescharacteristic
737C22#558111yescharacteristic
738C22D3×#12112yes—
739C22D3×C22⋊Q811yescharacteristic
740C22D3×C22⋊Q812yes—
741C22#562911yescharacteristic
742C22#562912yes—
743C22D3×#12311yescharacteristic
744C22D3×#12312yes—
745C22#565311yescharacteristic
746C22#565312yes—
747C22#565412yes—
748C22#566811yescharacteristic
749C22#567611yescharacteristic
750C22#569012yes—
751C22#569312yes—
752C22#570512yes—
753C22#570512yes—
754C22D3×#12711yescharacteristic
755C22#572711yescharacteristic
756C4—24no—
757C4—42no—
758C4—44no—
759C4—68no—
760C4—81no—
761C4—82no—
762C4—122no—
763C4—242no—
764C4—241no—
765C3#1483611yescharacteristic, complemented, Sylow
766C2—68no—
767C2—242no—
768C2#7412611yescharacteristic
769C2#7533912yes—
770C2#7536012yes—
771C2#7647611yescharacteristic
772C2#7662111yescharacteristic
773C2#7766812yes—
774C2#7774212yes—
775C2D3×#39911yescharacteristic
776C2#7811111yescharacteristic
777C2#7835111yescharacteristic
778C2#7835611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1445C2
prime radicalC23×D12C22
hypercenter#1445D3
hypocenterC3#14836
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C2×#4993C2semidirect
2. C2×#4987C2semidirect
5. C2×#4667C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1445C2semidirect
8. #69428C2semidirect
9. #69427C2semidirect
10. #69421C2semidirect
11. #69420C2semidirect
49. #1445D3semidirect
117. C3⋊#95D4semidirect
575. C2×D3#399semidirect
765. C3#14836semidirect

Maximal subgroups

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

subgroupindex
C2×#49932
C2×#49872
C2×#46652
C2×#46672
C2×D3×#952
C3×#14452
#694282
#694272
#694212
#694202
#148363