Finite Group Databasebeta

← #10819902

Subgroups — #10819902

Order 768.

1126 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#496C211yesmaximal, characteristic
2C2×#5164C211yesmaximal, characteristic, complemented
3C2×Dic3×D8C211yesmaximal, characteristic, complemented
4#83173C211yesmaximal, characteristic, complemented
5#82955C211yesmaximal, characteristic, complemented
6#72049C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72047C211yesmaximal, characteristic, complemented
9#72039C211yesmaximal, characteristic, complemented
10#72037C211yesmaximal, characteristic, complemented
11#72037C211yesmaximal, characteristic, complemented
12#71761C211yesmaximal, characteristic, complemented
13#71721C211yesmaximal, characteristic, complemented
14#69814C211yesmaximal, characteristic, complemented
15#69810C211yesmaximal, characteristic, complemented
16#23195—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C2×C3×#127C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×D4×Dic3—21no—
25C2×D4×Dic3C2211yescharacteristic
26C2×D4×Dic3C2211yescharacteristic
27C2×D4×Dic3C2211yescharacteristic
28C3×#496C418yescomplemented
29C2×C3×#97C2211yescharacteristic
30#5229C2211yescharacteristic
31C2×#835C2211yescharacteristic
32C2×#835C2211yescharacteristic
33#5221—21no—
34#5221C2211yescharacteristic
35#5221C2211yescharacteristic
36#5221C2211yescharacteristic
37#5220—21no—
38#5220—21no—
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5164—24no—
46Dic3×D8—24no—
47C2×#818C2211yescharacteristic
48C2×#817C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4951—21no—
52#4951—21no—
53#4950—21no—
54Dic3×C22⋊C4—21no—
55C4×C4⋊Dic3C2211yescharacteristic
56C4×C4⋊Dic3C2211yescharacteristic
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63C2×#496D311yescharacteristic
64C2×#440—31no—
65C2×C4×D8—31no—
66#2367—31no—
67#2366—31no—
68#1983—31no—
69#1982—31no—
70#1972—31no—
71#1968—31no—
72#1880—31no—
73#1879—31no—
74#1879—31no—
75#1877—31no—
76#1776—31no—
77#1771—31no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×Dic3—21no—
85C23×Dic3—21no—
86C23×Dic3—21no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C2×C3×SD16—41no—
91C2×C3×SD16C2×C414yescomplemented
92C2×C3×SD16C2×C414yescomplemented
93C2×C3×D8—22no—
94C2×C3×D8—22no—
95C2×C3×D8—41no—
96C2×C3×D8—41no—
97C2×C3×D8C2×C414yescomplemented
98C2×C3×D8C2×C414yescomplemented
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#127—22no—
102C3×#127C2×C414yescomplemented
103C3×#124—22no—
104C3×#124C2×C414yescomplemented
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117Q8×Dic3—22no—
118Q8×Dic3—41no—
119D4×Dic3—22no—
120D4×Dic3—22no—
121D4×Dic3—22no—
122D4×Dic3—41no—
123D4×Dic3—41no—
124D4×Dic3—41no—
125D4×Dic3—44no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3D411yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3C2311yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C3×#97C2×C414yescomplemented
141#835—22no—
142#835—41no—
143#832—22no—
144#832—22no—
145#832—22no—
146#832—41no—
147#832—41no—
148#832—41no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95D411yescharacteristic
154C3⋊#95D411yescharacteristic
155#818D414yescomplemented
156#817—22no—
157#815—22no—
158C8×Dic3—22no—
159C4⋊(C3⋊C8)—22no—
160C22×SD16C2×D311yescharacteristic
161C22×SD16C2×D311yescharacteristic
162C22×D8C2×D311yescharacteristic
163C22×D8C2×D311yescharacteristic
164C2×#127C2×D311yescharacteristic
165C2×#124C2×D311yescharacteristic
166C2×C4×Q8—31no—
167C2×C4×D4—31no—
168C2×C4×D4—31no—
169C2×C4×D4—31no—
170C2×C4×D4—61no—
171#496Dic318yescomplemented
172#440—64no—
173C4×D8—64no—
174C2×#107—31no—
175C2×#106—31no—
176C2×C4⋊C8—31no—
177C2×#103—31no—
178C2×#103—31no—
179C2×#102—31no—
180C2×#102—31no—
181C2×#102—31no—
182C2×#102—31no—
183C2×#102—31no—
184C2×#102—31no—
185C2×#97—31no—
186C2×#97C2×D311yescharacteristic
187C2×C4×C8—31no—
188#391—31no—
189#390—31no—
190#390—31no—
191#390—31no—
192#390—61no—
193#388—61no—
194#388—61no—
195#386—61no—
196#386—61no—
197#385—61no—
198C4×C4⋊C4—31no—
199C4×C4⋊C4—31no—
200C4×C4⋊C4—31no—
201C4×C22⋊C4—61no—
202#340—31no—
203#340—31no—
204#336—31no—
205#336—31no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8C22×C412yes—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4C22×C412yes—
237C2×C3×D4C22×C412yes—
238C2×C3×D4C22×C412yes—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—42no—
248C22×Dic3—42no—
249C22×Dic3—42no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3—42no—
253C22×Dic3—81no—
254C22×Dic3—81no—
255C22×Dic3—81no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C3×SD16—28no—
261C3×SD16—44no—
262C3×D8—28no—
263C3×D8—44no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8C22×C412yes—
267C2×C3×C8C22×C412yes—
268C2×C3×C8C2×D412yes—
269C2×C3×C8#4112yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C42C22×C412yes—
273C3×C42#4112yes—
274#217—42no—
275#217—42no—
276#217—42no—
277#217—42no—
278#217—42no—
279#217—42no—
280#217—81no—
281#217—81no—
282#217—81no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—22no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—41no—
291C4⋊Dic3—42no—
292C4⋊Dic3C2×D412yes—
293C4⋊Dic3C2×D412yes—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—42no—
299C4×Dic3—42no—
300C4×Dic3—81no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C22×Q8C22×D311yescharacteristic
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C22×D311yescharacteristic
311C22×D4C22×D311yescharacteristic
312C22×D4C22×D311yescharacteristic
313C23×C4—61no—
314C23×C4—61no—
315C23×C4—61no—
316C2×SD16—22no—
317C2×SD16—22no—
318C2×SD16—41no—
319C2×SD16—41no—
320C2×SD16C2×Dic314yescomplemented
321C2×SD16C2×Dic314yescomplemented
322C2×D8—22no—
323C2×D8—22no—
324C2×D8—41no—
325C2×D8—41no—
326C2×D8C2×Dic314yescomplemented
327C2×D8C2×Dic314yescomplemented
328C22×C8—31no—
329C22×C8—31no—
330C22×C8C22×D311yescharacteristic
331C22×C8C22×D311yescharacteristic
332#127—22no—
333#127C2×Dic314yescomplemented
334#124—22no—
335#124C2×Dic314yescomplemented
336C4×Q8—62no—
337C4×Q8—121no—
338C4×D4—62no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—121no—
342C4×D4—121no—
343C4×D4—121no—
344C4×D4—124no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C42—31no—
364C2×C42—31no—
365C2×C42—61no—
366C2×C42—61no—
367C2×C42—61no—
368C2×C42C22×D311yescharacteristic
369#107—34no—
370#106—62no—
371C4⋊C8—62no—
372#103—62no—
373#103—121no—
374#102—62no—
375#102—62no—
376#102—62no—
377#102—121no—
378#102—121no—
379#102—121no—
380#97—62no—
381#97C2×Dic314yescomplemented
382C4×C8—62no—
383#95—31no—
384#95—31no—
385#95—61no—
386#95—61no—
387#95—61no—
388#95—61no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3C22×D411yescharacteristic
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×D4—22no—
416C3×D4—22no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—48no—
422C3×D4—41no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—84no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4C4×D412yes—
437C2×C3×C4C4×D412yes—
438C2×C3×C4C23×C411yescharacteristic
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C2×C3×C4H(5,𝔽2)11yescharacteristic
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—84no—
468C2×Dic3—84no—
469C2×Dic3—84no—
470C2×Dic3AGL(1,ℤ/8)12yes—
471C3×C8—22no—
472C3×C8C4×D414yescomplemented
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—21no—
476C24—21no—
477C24—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C22×Dic312yes—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4C22×Dic312yes—
506C2×D4C22×Dic312yes—
507C2×D4C22×Dic312yes—
508C22×C4—21no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—122no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4—122no—
521C22×C4—122no—
522C22×C4—122no—
523C22×C4—241no—
524C22×C4—241no—
525C22×C4—241no—
526C22×C4D3×D411yescharacteristic
527C22×C4D3×D411yescharacteristic
528C22×C4C23×D311yescharacteristic
529SD16—28no—
530SD16—44no—
531D8—28no—
532D8—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8D3×D412yes—
542C2×C8#23712yes—
543C2×C8C22×Dic312yes—
544C2×C8C22×Dic312yes—
545C4⋊C4—32no—
546C4⋊C4—32no—
547C4⋊C4—62no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—121no—
555C4⋊C4—122no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—122no—
559C22⋊C4—122no—
560C22⋊C4—122no—
561C22⋊C4—122no—
562C22⋊C4—122no—
563C22⋊C4—122no—
564C22⋊C4—241no—
565C22⋊C4—241no—
566C22⋊C4—241no—
567C42—61no—
568C42—61no—
569C42—61no—
570C42—61no—
571C42—122no—
572C42—122no—
573C42—241no—
574C42#23712yes—
575C42C22×Dic312yes—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3C2×C4×D411yescharacteristic
598C22×C3D4211yescharacteristic
599C22×C3#55011yescharacteristic
600C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
601C22×C3#57511yescharacteristic
602C22×C3#57611yescharacteristic
603C22×C3#57711yescharacteristic
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—42no—
607C3×C4C2×C4×D411yescharacteristic
608C3×C4#51811yescharacteristic
609C3×C4#55011yescharacteristic
610C3×C4#55911yescharacteristic
611Dic3—22no—
612Dic3—41no—
613Dic3—42no—
614Dic3—42no—
615Dic3—41no—
616Dic3—41no—
617Dic3—81no—
618Dic3—81no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23C2×D3×D411yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—84no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—244no—
691C2×C4—244no—
692C2×C4—244no—
693C2×C4D4×Dic312yes—
694C2×C4D4×Dic312yes—
695C2×C4C2×D3×D411yescharacteristic
696C2×C4C2×#23711yescharacteristic
697C2×C4C2×#23711yescharacteristic
698C2×C4#100411yescharacteristic
699C2×C4#100411yescharacteristic
700C2×C4C23×Dic311yescharacteristic
701C8—22no—
702C8—121no—
703C8—121no—
704C8D4×Dic314yescomplemented
705C2×C3—82no—
706C2×C3—82no—
707C2×C3—82no—
708C2×C3#236611yescharacteristic
709C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
710C2×C3#294611yescharacteristic
711C2×C3#326411yescharacteristic
712C2×C3#327111yescharacteristic
713C2×C3#339711yescharacteristic
714C2×C3#340311yescharacteristic
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#571711yescharacteristic
737C22#571811yescharacteristic
738C22D3×AGL(1,ℤ/8)11yescharacteristic
739C22#577311yescharacteristic
740C22#577411yescharacteristic
741C22#577511yescharacteristic
742C22C2×D4×Dic311yescharacteristic
743C4—22no—
744C4—22no—
745C4—42no—
746C4—62no—
747C4—121no—
748C4—122no—
749C4—122no—
750C4—121no—
751C4—121no—
752C4—241no—
753C4—241no—
754C4#571311yescharacteristic
755C4#571811yescharacteristic
756C4C2×D4×Dic311yescharacteristic
757C4#579811yescharacteristic
758C3#2319511yescharacteristic, complemented, Sylow
759C2—82no—
760C2—82no—
761C2—82no—
762C2#8183911yescharacteristic
763C2#8184211yescharacteristic
764C2#8185611yescharacteristic
765C2#8185911yescharacteristic
766C2#8317311yescharacteristic
767C2Dic3×AGL(1,ℤ/8)11yescharacteristic
768C2#8393011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#496C2
socleC23×C3C22×D4
cosocleC22×C3×C4C24
hypercenterC2×#496D3
hypocenterC3#23195
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
2. C2×#5164C2semidirect
3. C2×Dic3×D8C2semidirect
4. #83173C2semidirect
5. #82955C2semidirect
6. #72049C2semidirect
7. #72048C2semidirect
8. #72047C2semidirect
9. #72039C2semidirect
10. #72037C2semidirect
11. #72037C2semidirect
12. #71761C2semidirect
13. #71721C2semidirect
14. #69814C2semidirect
15. #69810C2semidirect
28. C3×#496C4semidirect
91. C2×C3×SD16C2×C4semidirect
92. C2×C3×SD16C2×C4semidirect
97. C2×C3×D8C2×C4semidirect
98. C2×C3×D8C2×C4semidirect
102. C3×#127C2×C4semidirect
104. C3×#124C2×C4semidirect
140. C3×#97C2×C4semidirect
155. #818D4semidirect
171. #496Dic3semidirect
320. C2×SD16C2×Dic3semidirect
321. C2×SD16C2×Dic3semidirect
326. C2×D8C2×Dic3semidirect
327. C2×D8C2×Dic3semidirect
333. #127C2×Dic3semidirect
335. #124C2×Dic3semidirect
381. #97C2×Dic3semidirect
472. C3×C8C4×D4semidirect
704. C8D4×Dic3semidirect
758. C3#23195semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4962
C2×#51642
C2×Dic3×D82
#831732
#829552
#720492
#720482
#720472
#720392
#720372
#717612
#717212
#698142
#698102
#231953