Finite Group Databasebeta

← #10801886

Subgroups — #10801886

Order 768.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#121C211yesmaximal, characteristic, complemented
2C2×#5039C211yesmaximal, characteristic
3C2×#5014C211yesmaximal, characteristic, complemented
4C4×#930C211yesmaximal, characteristic, complemented
5C2×C4×#208C211yesmaximal, characteristic, complemented
6#71682C211yesmaximal, characteristic, complemented
7#71609C211yesmaximal, characteristic, complemented
8#69647C211yesmaximal, characteristic, complemented
9#69644C211yesmaximal, characteristic, complemented
10#69618C211yesmaximal, characteristic, complemented
11#69615C211yesmaximal, characteristic, complemented
12#69517C211yesmaximal, characteristic, complemented
13#69513C211yesmaximal, characteristic, complemented
14#69481C211yesmaximal, characteristic, complemented
15#69474C211yesmaximal, characteristic, complemented
16#21538—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×C4×D4—21no—
19C2×C3×C4×D4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67—21no—
24C22×#208C2211yescharacteristic
25C22×#208C2211yescharacteristic
26C2×C4×D12C2211yescharacteristic
27C3×#390C2211yescharacteristic
28C3×#389C2211yescharacteristic
29C3×#388—21no—
30C3×#386—21no—
31C3×#380C2211yescharacteristic
32C3×C4×C4⋊C4C2211yescharacteristic
33C3×C4×C22⋊C4—21no—
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37#5213—21no—
38#5212C2211yescharacteristic
39#5039C418yescomplemented
40#5014—24no—
41C2×#809C2211yescharacteristic
42C2×#809C2211yescharacteristic
43C2×#809C2211yescharacteristic
44C2×#808C2211yescharacteristic
45C2×#808C2211yescharacteristic
46C2×#807C2211yescharacteristic
47#4940—21no—
48#4939C2211yescharacteristic
49C4×(C2×D3)⋊C4—21no—
50C4×C4⋊Dic3C2211yescharacteristic
51#4928C2211yescharacteristic
52C4×#208—24no—
53C2×#803C2211yescharacteristic
54C2×#803C2211yescharacteristic
55C2×C4×C3⋊C8C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#469—31no—
64C2×#442—31no—
65C2×C4×M16—31no—
66C4×#121—31no—
67C4×#121D311yescharacteristic, complemented
68#1970—31no—
69#1941—31no—
70#1934—31no—
71#1934—31no—
72#1895—31no—
73#1895—31no—
74#1809—31no—
75#1776—31no—
76#1762—31no—
77#1762—31no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4D411yescharacteristic
82C23×C3×C4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C3×#121—22no—
88C3×#121C2×C414yescomplemented
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×C4×D4—44no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—22no—
102C2×C3×C42—22no—
103C2×C3×C42—21no—
104C2×C3×C42D411yescharacteristic
105C2×C3×C42D411yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#213—22no—
110C2×#213—22no—
111C2×#213C2×C414yescomplemented
112#930—22no—
113#930C2×C414yescomplemented
114C4×#67—44no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×Dic3⋊C4—21no—
123C2×C4×Dic3—21no—
124C2×#208—22no—
125C2×#208—22no—
126C2×#208—22no—
127C2×#208—22no—
128C2×#208—22no—
129C2×#208C2×C414yescomplemented
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C4×D12—22no—
135C4×D12—22no—
136C3×#95—21no—
137C3×#95—21no—
138C3×#95—21no—
139#832—22no—
140#832—22no—
141#832C2×C414yescomplemented
142C3⋊#95—21no—
143C3⋊#95—21no—
144C3⋊#95—21no—
145#809—22no—
146#809—22no—
147#809C2×C414yescomplemented
148#808—22no—
149#808C2×C414yescomplemented
150#807—22no—
151#803—22no—
152#803D414yescomplemented
153C4×C3⋊C8—22no—
154C4×C3⋊C8—22no—
155C22×D8—31no—
156C22×M16—31no—
157C22×M16—31no—
158C2×#121—31no—
159C2×#121C2×D311yescharacteristic
160C2×C4×D4—21no—
161C2×C4×D4—31no—
162C2×C4×D4—61no—
163C2×C4×D4C2×D311yescharacteristic
164C22×C42C2×D311yescharacteristic
165#469—38no—
166#442—64no—
167C2×#107—31no—
168C2×#106—31no—
169C2×#106—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102—31no—
173C2×#102—31no—
174C2×#102—31no—
175C2×#102—31no—
176C4×M16—64no—
177C2×#97—31no—
178C2×#97—31no—
179C2×C4×C8—31no—
180C2×C4×C8—31no—
181#390—31no—
182#390C2×D311yescharacteristic
183#389—31no—
184#389C2×D311yescharacteristic
185#388—21no—
186#388—61no—
187#386—21no—
188#386—61no—
189#380—31no—
190#380C2×D311yescharacteristic
191C4×C4⋊C4—31no—
192C4×C4⋊C4C2×D311yescharacteristic
193C4×C22⋊C4—21no—
194C4×C22⋊C4—61no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199#340—31no—
200#340—31no—
201C24×C3—21no—
202C24×C3C2×D411yescharacteristic
203C23×D3—21no—
204C2×C3×D4—24no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—42no—
211C2×C3×D4—42no—
212C2×C3×D4C22×C412yes—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—41no—
225C22×C3×C4—41no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4C22×C412yes—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4#4112yes—
236C22×C3×C4C2411yescharacteristic
237C2×#67—24no—
238C2×#67—42no—
239C2×#67—42no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12C22×C412yes—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—42no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4C22×C412yes—
259C3×C22⋊C4—24no—
260C3×C22⋊C4—42no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—42no—
264C3×C42—22no—
265C3×C42—22no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—42no—
269C3×C42C2×D412yes—
270C3×C42#4112yes—
271#217—42no—
272#213—28no—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—42no—
275(C2×D3)⋊C4—42no—
276(C2×D3)⋊C4—42no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3C22×C412yes—
283Dic3⋊C4—42no—
284C4×Dic3—42no—
285#208—28no—
286#208—28no—
287C2×C3⋊C8—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8C22×C412yes—
294C2×C3⋊C8C22×C412yes—
295C2×C3⋊C8C2×D412yes—
296C2×C3⋊C8C2×D412yes—
297C2×C3⋊C8#4112yes—
298C2×C3⋊C8#4112yes—
299C22×D4—21no—
300C22×D4—31no—
301C22×D4—61no—
302C22×D4C22×D311yescharacteristic
303C23×C4—21no—
304C23×C4—61no—
305C23×C4#6711yescharacteristic
306C23×C4#6711yescharacteristic
307C23×C4C22×D311yescharacteristic
308C2×D8—34no—
309C2×D8—62no—
310C2×D8—62no—
311C2×M16—34no—
312C2×M16—62no—
313C2×M16—62no—
314C2×M16—62no—
315C2×M16—62no—
316C2×M16—62no—
317C22×C8—31no—
318C22×C8—31no—
319C22×C8—31no—
320C22×C8—31no—
321#121—22no—
322#121—34no—
323#121—62no—
324#121C4×D314yescomplemented
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—44no—
328C4×D4—62no—
329C4×D4—62no—
330C4×D4—124no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—61no—
336C2×C4⋊C4C22×D311yescharacteristic
337C2×C4⋊C4C22×D311yescharacteristic
338C2×C4⋊C4C22×D311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—61no—
345C2×C22⋊C4—61no—
346C2×C22⋊C4—61no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—61no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—21no—
352C2×C42—61no—
353C2×C42#6711yescharacteristic
354C2×C42#6711yescharacteristic
355C2×C42C22×D311yescharacteristic
356C2×C42C22×D311yescharacteristic
357#107—62no—
358#106—34no—
359#106—62no—
360#102—34no—
361#102—34no—
362#102—62no—
363#102—62no—
364#102—62no—
365#102—62no—
366#97—34no—
367#97—62no—
368C4×C8—62no—
369C4×C8—62no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—61no—
374#95—61no—
375#95—61no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3C4×D412yes—
390C23×C3C22×D411yescharacteristic
391C22×D3—22no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—48no—
401C3×D4—41no—
402C3×D4—41no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—44no—
419C2×C3×C4—44no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—84no—
429C2×C3×C4C4×D412yes—
430C2×C3×C4#12112yes—
431C2×C3×C4#12112yes—
432C2×C3×C4AGL(1,ℤ/8)12yes—
433C2×C3×C4AGL(1,ℤ/8)12yes—
434C2×C3×C4C23×C411yescharacteristic
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440#67—48no—
441C2×Dic3—22no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450D12—22no—
451D12—22no—
452D12—41no—
453D12—41no—
454C4×D3—84no—
455C3⋊C8—22no—
456C3⋊C8—22no—
457C3⋊C8—22no—
458C3⋊C8C4×D414yescomplemented
459C24—21no—
460C24—61no—
461C24C2×#6711yescharacteristic
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—32no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—64no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—122no—
478C2×D4—122no—
479C2×D4C2×C4×D312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—122no—
500C22×C4—122no—
501C22×C4—122no—
502C22×C4C2×C4×D312yes—
503C22×C4#23512yes—
504C22×C4C2×#6711yescharacteristic
505C22×C4C2×#6711yescharacteristic
506C22×C4C2×#6711yescharacteristic
507C22×C4C2×#6711yescharacteristic
508C22×C4C2×#6711yescharacteristic
509C22×C4C23×D311yescharacteristic
510D8—68no—
511M16—68no—
512M16—68no—
513C2×C8—32no—
514C2×C8—32no—
515C2×C8—32no—
516C2×C8—32no—
517C2×C8—32no—
518C2×C8—32no—
519C2×C8—61no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—32no—
531C4⋊C4—42no—
532C4⋊C4—61no—
533C4⋊C4—61no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—122no—
538C4⋊C4C2×C4×D312yes—
539C22⋊C4—24no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—64no—
545C22⋊C4—122no—
546C22⋊C4—122no—
547C22⋊C4—122no—
548C22⋊C4—122no—
549C42—22no—
550C42—22no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—122no—
555C42D3×D412yes—
556C42#23712yes—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3C2×C4×D411yescharacteristic
572C22×C3C2×#12111yescharacteristic
573C22×C3#53211yescharacteristic
574C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
575C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
576C22×C3#57511yescharacteristic
577C22×C3#57511yescharacteristic
578C2×D3—42no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—81no—
582C2×D3—81no—
583C2×D3—81no—
584C2×D3—81no—
585C3×C4—22no—
586C3×C4—22no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—81no—
592C3×C4—81no—
593C3×C4C2×C4×D411yescharacteristic
594C3×C4C4×#4111yescharacteristic
595C3×C4#52511yescharacteristic
596C3×C4#52911yescharacteristic
597Dic3—42no—
598Dic3—81no—
599Dic3—81no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—62no—
614C23—121no—
615C23—121no—
616C23—121no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23C4×#6712yes—
621C23C22×#6711yescharacteristic
622D4—22no—
623D4—22no—
624D4—48no—
625D4—41no—
626D4—41no—
627D4—62no—
628D4—62no—
629D4—128no—
630D4—121no—
631D4—121no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—62no—
658C2×C4—84no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—244no—
668C2×C4C4×#6712yes—
669C2×C4#93212yes—
670C2×C4#93912yes—
671C2×C4#93912yes—
672C2×C4#94912yes—
673C2×C4C22×C4×D311yescharacteristic
674C2×C4C2×#23511yescharacteristic
675C2×C4C2×D3×D411yescharacteristic
676C2×C4C2×#23711yescharacteristic
677C2×C4D3×#4111yescharacteristic
678C2×C4D3×#4111yescharacteristic
679C8—34no—
680C8—62no—
681C8—62no—
682C8—62no—
683C2×C3—42no—
684C2×C3—82no—
685C2×C3C4×#12111yescharacteristic
686C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
687C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
688C2×C3#305511yescharacteristic
689C2×C3#305511yescharacteristic
690C2×C3#318311yescharacteristic
691C2×C3#318411yescharacteristic
692D3—82no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—241no—
711C22—241no—
712C22—241no—
713C22—241no—
714C22C2×C4×#6711yescharacteristic
715C22C2×#93211yescharacteristic
716C22C2×#93911yescharacteristic
717C22C2×#94911yescharacteristic
718C22#582211yescharacteristic
719C22#582211yescharacteristic
720C22#583211yescharacteristic
721C4—22no—
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—122no—
730C4—241no—
731C4—241no—
732C4C4×#23711yescharacteristic
733C4#553811yescharacteristic
734C4C4×D3×D411yescharacteristic
735C4#554711yescharacteristic
736C3#2153811yescharacteristic, complemented, Sylow
737C2—42no—
738C2—82no—
739C2—242no—
740C2C4×#93211yescharacteristic
741C2C4×#93911yescharacteristic
742C2C4×#94911yescharacteristic
743C2#8262111yescharacteristic
744C2#8292411yescharacteristic
745C2#8313911yescharacteristic
746C2#8329511yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×C4×#121C2
socleC23×C3C22×D4
prime radicalC2×#5039C2
cosocleC22×C3×C4C24
hypercenterC4×#121D3
hypocenterC3#21538
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C3×C4×#121C2semidirect
3. C2×#5014C2semidirect
4. C4×#930C2semidirect
5. C2×C4×#208C2semidirect
6. #71682C2semidirect
7. #71609C2semidirect
8. #69647C2semidirect
9. #69644C2semidirect
10. #69618C2semidirect
11. #69615C2semidirect
12. #69517C2semidirect
13. #69513C2semidirect
14. #69481C2semidirect
15. #69474C2semidirect
39. #5039C4semidirect
67. C4×#121D3semidirect
88. C3×#121C2×C4semidirect
111. C2×#213C2×C4semidirect
113. #930C2×C4semidirect
129. C2×#208C2×C4semidirect
141. #832C2×C4semidirect
147. #809C2×C4semidirect
149. #808C2×C4semidirect
152. #803D4semidirect
324. #121C4×D3semidirect
458. C3⋊C8C4×D4semidirect
736. C3#21538semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#1212
C2×#50392
C2×#50142
C4×#9302
C2×C4×#2082
#716822
#716092
#696472
#696442
#696182
#696152
#695172
#695132
#694812
#694742
#215383