Finite Group Databasebeta

← #10801433

Subgroups — #10801433

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#442C211yesmaximal, characteristic, complemented
2C2×#5150C211yesmaximal, characteristic
3C4×#940C211yesmaximal, characteristic, complemented
4C4×D4×Dic3C211yesmaximal, characteristic, complemented
5C2×#5014C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71609C211yesmaximal, characteristic, complemented
8#70569C211yesmaximal, characteristic, complemented
9#70563C211yesmaximal, characteristic, complemented
10#70174C211yesmaximal, characteristic, complemented
11#70172C211yesmaximal, characteristic, complemented
12#70161C211yesmaximal, characteristic, complemented
13#70153C211yesmaximal, characteristic, complemented
14#69812C211yesmaximal, characteristic, complemented
15#69809C211yesmaximal, characteristic, complemented
16#21503—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C2×D4×Dic3C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×C4×#67—21no—
25C2×C4×#67—21no—
26C22×C4×Dic3—21no—
27C2×C4×D12C2211yescharacteristic
28C3×#442—24no—
29C2×C3×#106C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#97C2211yescharacteristic
33#5221C2211yescharacteristic
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C4×#217—21no—
38#5150C418yescomplemented
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×Dic3⋊C8C2211yescharacteristic
42C2×Dic3⋊C8C2211yescharacteristic
43#5014—24no—
44#4988C2211yescharacteristic
45#4975C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47Dic3×C4⋊C4C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50#4957—21no—
51#4957—21no—
52Dic3×C22⋊C4—21no—
53Dic3×C22⋊C4—21no—
54C4×C4⋊Dic3C2211yescharacteristic
55C42×Dic3C2211yescharacteristic
56C2×#803C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#459—31no—
64C2×#442—31no—
65C2×#442D311yescharacteristic, complemented
66C4×#127—31no—
67C42×D4—31no—
68#1982—31no—
69#1948—31no—
70#1926—31no—
71#1926—31no—
72#1879—31no—
73#1879—31no—
74#1802—31no—
75#1767—31no—
76#1762—31no—
77#1762—31no—
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C23×Dic3—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C2×C3×D8—22no—
89C2×C3×D8—22no—
90C2×C3×D8C2×C414yescomplemented
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C3×C4×D4D414yescomplemented
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106#940—22no—
107#940C2×C414yescomplemented
108D4×Dic3—22no—
109D4×Dic3—22no—
110D4×Dic3—22no—
111D4×Dic3C2×C414yescomplemented
112C2×#213—22no—
113C2×#213—22no—
114C2×#213C2×C414yescomplemented
115C4×#67—44no—
116C4×#67—44no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×C4×Dic3—21no—
126C2×C4×Dic3—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3—44no—
129C2×C4×Dic3D411yescharacteristic
130C2×C4×Dic3D411yescharacteristic
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3C2311yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C4×D12—22no—
138C4×D12—22no—
139C3×#106—22no—
140C3×#102—22no—
141C3×#102—22no—
142C3×#97—22no—
143#832—22no—
144#832—22no—
145#832C2×C414yescomplemented
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149#821—22no—
150#821C2×C414yescomplemented
151Dic3⋊C8—22no—
152Dic3⋊C8C2×C414yescomplemented
153#809—22no—
154#808—22no—
155#803—22no—
156C22×D8—31no—
157C22×D8C2×D311yescharacteristic
158C2×#127—31no—
159C2×C4×D4—31no—
160C2×C4×D4—31no—
161C2×C4×D4—31no—
162C2×C4×D4—61no—
163C2×C4×D4—61no—
164C2×C4×D4C2×D311yescharacteristic
165C2×C4×D4C2×D311yescharacteristic
166C22×C42—61no—
167#459—38no—
168#442—24no—
169#442—64no—
170C2×#106—31no—
171C2×#106C2×D311yescharacteristic
172C2×C4⋊C8—31no—
173C2×C4⋊C8—31no—
174C2×#102—31no—
175C2×#102—31no—
176C2×#102—31no—
177C2×#102—31no—
178C2×#102—31no—
179C2×#102—31no—
180C2×#102C2×D311yescharacteristic
181C2×#102C2×D311yescharacteristic
182C2×#97—31no—
183C2×#97C2×D311yescharacteristic
184#390—31no—
185#390—31no—
186#390—61no—
187#390—61no—
188#384—31no—
189C4×C4⋊C4—31no—
190C4×C4⋊C4—31no—
191C4×C4⋊C4—31no—
192C4×C22⋊C4—61no—
193C4×C22⋊C4—61no—
194C4×C22⋊C4—61no—
195C43—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199#340—31no—
200#336—31no—
201#336—31no—
202C24×C3—21no—
203C24×C3—21no—
204C23×D3—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4C22×C412yes—
214C2×C3×D4C22×C412yes—
215C2×C3×D4C2×D412yes—
216C2×C3×D4#4112yes—
217C22×C3×C4—21no—
218C22×C3×C4—24no—
219C22×C3×C4—21no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2411yescharacteristic
228C2×#67—24no—
229C2×#67—24no—
230C2×#67—42no—
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—42no—
234C22×Dic3—24no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—24no—
238C22×Dic3—21no—
239C22×Dic3—42no—
240C22×Dic3—42no—
241C22×Dic3—42no—
242C22×Dic3—42no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12C22×C412yes—
253C2×C4×D3—42no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C3×D8—28no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8C22×C412yes—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C2×D412yes—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—42no—
269C3×C42C2×D412yes—
270C3×C42#4112yes—
271#217—24no—
272#217—24no—
273#217—42no—
274#217—42no—
275#213—28no—
276(C2×D3)⋊C4—42no—
277(C2×D3)⋊C4—42no—
278(C2×D3)⋊C4—42no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3C22×C412yes—
284C4⋊Dic3#4112yes—
285Dic3⋊C4—42no—
286Dic3⋊C4—42no—
287C4×Dic3—21no—
288C4×Dic3—21no—
289C4×Dic3—22no—
290C4×Dic3—22no—
291C4×Dic3—22no—
292C4×Dic3—41no—
293C4×Dic3—42no—
294C4×Dic3—42no—
295C4×Dic3—42no—
296C4×Dic3C22×C412yes—
297C4×Dic3#4112yes—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8C22×C412yes—
304C22×D4—31no—
305C22×D4—61no—
306C22×D4—61no—
307C22×D4C22×D311yescharacteristic
308C22×D4C22×D311yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—61no—
312C23×C4—61no—
313C23×C4—61no—
314C2×D8—22no—
315C2×D8—22no—
316C2×D8—34no—
317C2×D8—62no—
318C2×D8—62no—
319C2×D8C4×D314yescomplemented
320C22×C8—31no—
321C22×C8—31no—
322C22×C8C22×D311yescharacteristic
323C22×C8C22×D311yescharacteristic
324#127—34no—
325#127—62no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—34no—
330C4×D4—62no—
331C4×D4—62no—
332C4×D4—62no—
333C4×D4—62no—
334C4×D4—62no—
335C4×D4—124no—
336C4×D4—124no—
337C4×D4#6714yescomplemented
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4C22×D311yescharacteristic
344C2×C4⋊C4C22×D311yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—61no—
349C2×C22⋊C4—61no—
350C2×C22⋊C4—61no—
351C2×C22⋊C4—61no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C42—31no—
355C2×C42—31no—
356C2×C42—31no—
357C2×C42—31no—
358C2×C42—31no—
359C2×C42—31no—
360C2×C42—61no—
361C2×C42—61no—
362C2×C42—61no—
363C2×C42—124no—
364C2×C42C22×D311yescharacteristic
365#106—22no—
366#106—62no—
367C4⋊C8—34no—
368C4⋊C8—62no—
369#102—22no—
370#102—22no—
371#102—34no—
372#102—34no—
373#102—62no—
374#102—62no—
375#102—62no—
376#102—62no—
377#97—22no—
378#97—62no—
379#95—61no—
380#95—61no—
381#95—61no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3C22×D411yescharacteristic
397C22×D3—22no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—22no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—41no—
410C3×D4—41no—
411C3×D4C4×D414yescomplemented
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—48no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—84no—
424C2×C3×C4#12112yes—
425C2×C3×C4#12112yes—
426C2×C3×C4C23×C411yescharacteristic
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432#67—48no—
433#67—48no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—48no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—48no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3C4×D412yes—
453C2×Dic3C4×D412yes—
454C2×Dic3AGL(1,ℤ/8)12yes—
455C2×Dic3AGL(1,ℤ/8)12yes—
456C2×Dic3AGL(1,ℤ/8)12yes—
457D12—22no—
458D12—22no—
459D12—41no—
460D12—41no—
461C4×D3—84no—
462C3×C8—22no—
463C3×C8—41no—
464C3⋊C8—22no—
465C3⋊C8—41no—
466C24—21no—
467C24—21no—
468C24—61no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—32no—
478C2×D4—64no—
479C2×D4—64no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—122no—
486C2×D4—122no—
487C2×D4—122no—
488C2×D4—122no—
489C2×D4C2×C4×D312yes—
490C2×D4C2×C4×D312yes—
491C2×D4#23512yes—
492C2×D4C2×#6712yes—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—64no—
506C22×C4—64no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—122no—
511C22×C4—122no—
512C22×C4—122no—
513C22×C4—122no—
514C22×C4—122no—
515C22×C4—122no—
516C22×C4—122no—
517C22×C4D3×D411yescharacteristic
518C22×C4D3×D411yescharacteristic
519C22×C4C23×D311yescharacteristic
520D8—28no—
521D8—68no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—32no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8C2×C4×D312yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—32no—
538C4⋊C4—32no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—122no—
544C4⋊C4—122no—
545C4⋊C4C2×#6712yes—
546C22⋊C4—24no—
547C22⋊C4—42no—
548C22⋊C4—64no—
549C22⋊C4—64no—
550C22⋊C4—122no—
551C22⋊C4—122no—
552C22⋊C4—122no—
553C22⋊C4—122no—
554C22⋊C4—122no—
555C42—32no—
556C42—32no—
557C42—62no—
558C42—62no—
559C42—62no—
560C42—61no—
561C42—61no—
562C42—121no—
563C42—122no—
564C42—122no—
565C42—122no—
566C42#23712yes—
567C42C2×#6712yes—
568C22×C3—24no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3C2×C4×D411yescharacteristic
583C22×C3C2×#12111yescharacteristic
584C22×C3#52511yescharacteristic
585C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
586C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
587C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
588C22×C3#57511yescharacteristic
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—81no—
593C2×D3—81no—
594C2×D3—81no—
595C2×D3—81no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—42no—
599C3×C4—81no—
600C3×C4C2×C4×D411yescharacteristic
601C3×C4C4×#4111yescharacteristic
602C3×C4#52911yescharacteristic
603C3×C4#53211yescharacteristic
604Dic3—22no—
605Dic3—22no—
606Dic3—42no—
607Dic3—41no—
608Dic3—42no—
609Dic3—81no—
610Dic3#44214yescomplemented
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—62no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23C2×D3×D411yescharacteristic
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—62no—
641D4—62no—
642D4—128no—
643D4—128no—
644D4—121no—
645D4—121no—
646D4C4×#6714yescomplemented
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—48no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—84no—
673C2×C4—128no—
674C2×C4—128no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—244no—
683C2×C4#93912yes—
684C2×C4#93912yes—
685C2×C4C22×C4×D311yescharacteristic
686C2×C4C2×#23511yescharacteristic
687C2×C4C2×#23711yescharacteristic
688C2×C4D3×#4111yescharacteristic
689C2×C4D3×#4111yescharacteristic
690C2×C4C22×#6711yescharacteristic
691C8—22no—
692C8—41no—
693C8—62no—
694C8—121no—
695C2×C3—44no—
696C2×C3—82no—
697C2×C3C4×#12111yescharacteristic
698C2×C3C2×#44211yescharacteristic
699C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
700C2×C3#303611yescharacteristic
701C2×C3#303811yescharacteristic
702C2×C3#310911yescharacteristic
703C2×C3#311511yescharacteristic
704D3—82no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—122no—
720C22—122no—
721C22—122no—
722C22—241no—
723C22—241no—
724C22—241no—
725C22—241no—
726C22C4×D3×D411yescharacteristic
727C22#554711yescharacteristic
728C22D3×AGL(1,ℤ/8)11yescharacteristic
729C22D3×AGL(1,ℤ/8)11yescharacteristic
730C22D3×AGL(1,ℤ/8)11yescharacteristic
731C22#577311yescharacteristic
732C22C2×#93911yescharacteristic
733C4—22no—
734C4—22no—
735C4—34no—
736C4—42no—
737C4—62no—
738C4—62no—
739C4—81no—
740C4—121no—
741C4—122no—
742C4—122no—
743C4—241no—
744C4C4×#23711yescharacteristic
745C4#553811yescharacteristic
746C4C2×C4×#6711yescharacteristic
747C4#583211yescharacteristic
748C3#2150311yescharacteristic, complemented, Sylow
749C2—44no—
750C2—82no—
751C2—242no—
752C2D3×#44211yescharacteristic
753C2#7986511yescharacteristic
754C2#7986911yescharacteristic
755C2#7987211yescharacteristic
756C2C4×#93911yescharacteristic
757C2#8393111yescharacteristic
758C2#8393211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
prime radicalC2×#5150C2
cosocleC22×C3×C4C24
hypercenterC2×#442D3
hypocenterC3#21503
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×C3×#442C2semidirect
3. C4×#940C2semidirect
4. C4×D4×Dic3C2semidirect
5. C2×#5014C2semidirect
6. #72037C2semidirect
7. #71609C2semidirect
8. #70569C2semidirect
9. #70563C2semidirect
10. #70174C2semidirect
11. #70172C2semidirect
12. #70161C2semidirect
13. #70153C2semidirect
14. #69812C2semidirect
15. #69809C2semidirect
38. #5150C4semidirect
65. C2×#442D3semidirect
90. C2×C3×D8C2×C4semidirect
96. C3×C4×D4D4semidirect
107. #940C2×C4semidirect
111. D4×Dic3C2×C4semidirect
114. C2×#213C2×C4semidirect
145. #832C2×C4semidirect
150. #821C2×C4semidirect
152. Dic3⋊C8C2×C4semidirect
319. C2×D8C4×D3semidirect
337. C4×D4#67semidirect
411. C3×D4C4×D4semidirect
610. Dic3#442semidirect
646. D4C4×#67semidirect
748. C3#21503semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4422
C2×#51502
C4×#9402
C4×D4×Dic32
C2×#50142
#720372
#716092
#705692
#705632
#701742
#701722
#701612
#701532
#698122
#698092
#215033