Finite Group Databasebeta

← #10833968

Subgroups — #10833968

Order 768.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#447C211yesmaximal, characteristic
2#84044C211yesmaximal, characteristic, complemented
3#82678C211yesmaximal, characteristic, complemented
4C2×#4720C211yesmaximal, characteristic, complemented
5#72128C211yesmaximal, characteristic, complemented
6#72040C211yesmaximal, characteristic, complemented
7#72040C211yesmaximal, characteristic, complemented
8#72039C211yesmaximal, characteristic, complemented
9#72038C211yesmaximal, characteristic, complemented
10#71678C211yesmaximal, characteristic, complemented
11#70188C211yesmaximal, characteristic, complemented
12#70186C211yesmaximal, characteristic, complemented
13#70180C211yesmaximal, characteristic, complemented
14#70179C211yesmaximal, characteristic, complemented
15#69929C211yesmaximal, characteristic, complemented
16#24512—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#926C2211yescharacteristic
22C2×#926C2211yescharacteristic
23C3×#447—24no—
24C2×C3×#102C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27#5247—21no—
28#5247—21no—
29#5222—21no—
30#5222—21no—
31#5221—21no—
32#5221—21no—
33#5221C2211yescharacteristic
34#5221C2211yescharacteristic
35#5221C2211yescharacteristic
36#5221C2211yescharacteristic
37#5221C2211yescharacteristic, complemented
38#5221C2211yescharacteristic, complemented
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic, complemented
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#818C2211yescharacteristic, complemented
48C2×#817C2211yescharacteristic, complemented
49C2×#815C2211yescharacteristic, complemented
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×Dic3⋊C8C2211yescharacteristic, complemented
52C2×C8×Dic3C2211yescharacteristic, complemented
53#4972C2211yescharacteristic, complemented
54#4972C2211yescharacteristic, complemented
55#4953—21no—
56#4949—21no—
57#4720—24no—
58#4551C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62C2×#447D311yescharacteristic
63C2×#433—31no—
64#2624—31no—
65#2309—31no—
66#2067—31no—
67#2065—31no—
68#2054—31no—
69#2054—31no—
70#1972—31no—
71#1970—31no—
72#1936—31no—
73#1934—31no—
74#1875—31no—
75#1854—31no—
76#1786—31no—
77C25×C3—21no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—41no—
85C22×C3×D4—41no—
86C22×C3×D4C2311yescharacteristic
87C22×C3×D4C2311yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—41no—
95C2×C3×D8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#121—22no—
99C3×#121—22no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
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×#217D411yescharacteristic
117C2×#217D411yescharacteristic
118#926—22no—
119#926—22no—
120#926—41no—
121#926—41no—
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3C2311yescharacteristic
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C3×#102—22no—
136C3×#102—22no—
137C3×C22⋊C8D414yes—
138#832—22no—
139#832—22no—
140#832—41no—
141#832—41no—
142#832—41no—
143#832—41no—
144C3⋊#95—21no—
145C3⋊#95—21no—
146C3⋊#95—21no—
147#830—22no—
148#818—41no—
149#817—41no—
150#815—22no—
151Dic3⋊C8—22no—
152Dic3⋊C8—22no—
153C8×Dic3—22no—
154C23×D4C2×D311yescharacteristic
155C22×D8C2×D311yescharacteristic
156C22×D8C2×D311yescharacteristic
157C2×#121C2×D311yescharacteristic
158C2×#117—31no—
159C2×#117—31no—
160#447—24no—
161#433—64no—
162C2×#107—31no—
163C2×#106—31no—
164C2×C4⋊C8—31no—
165C2×C4⋊C8—31no—
166C2×#102—31no—
167C2×#102—31no—
168C2×#102—31no—
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102C2×D311yescharacteristic
173C2×#102C2×D311yescharacteristic
174C2×C22⋊C8—31no—
175C2×C22⋊C8C2×D311yescharacteristic
176C2×#97—31no—
177C2×C4×C8—31no—
178#399—61no—
179#397—61no—
180#394—61no—
181#394—61no—
182#390—31no—
183#390—31no—
184#390—31no—
185#390—31no—
186#390—31no—
187#390—31no—
188#390—61no—
189#390—61no—
190#389—31no—
191#389—31no—
192#380—31no—
193#379—61no—
194#379—61no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199C24×C3—24no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—42no—
204C24×C3—42no—
205C24×C3—81no—
206C24×C3—81no—
207C24×C3—81no—
208C24×C3—81no—
209C24×C3C2×D411yescharacteristic
210C2×C3×D4—24no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
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—44no—
228C2×C3×D4—44no—
229C2×C3×D4—44no—
230C2×C3×D4—44no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4#4112yes—
237C2×C3×D4#4112yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D412yes—
245C22×C3×C4#4112yes—
246C22×C3×C4C2411yescharacteristic
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C3×D8—44no—
256C3×D8—44no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8C2×D412yes—
262C2×C3×C8C2×D412yes—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C22⋊C4—42no—
266#217—22no—
267#217—22no—
268#217—42no—
269#217—81no—
270#217—81no—
271#217—81no—
272#217—81no—
273#217—81no—
274#217—81no—
275#217—81no—
276#217—81no—
277#217—81no—
278#217—81no—
279#217—81no—
280#217—81no—
281#217—81no—
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292Dic3⋊C4—81no—
293Dic3⋊C4—81no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—42no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C25—21no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C22×D311yescharacteristic
315C22×D4C22×D311yescharacteristic
316C22×D4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C2×D8—22no—
319C2×D8—22no—
320C2×D8—22no—
321C2×D8—22no—
322C2×D8—41no—
323C2×D8—41no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328#121—22no—
329#121—22no—
330#117—62no—
331#117—62no—
332#117—121no—
333#117—121no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4C22×D311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—61no—
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×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C42—31no—
361C2×C42—31no—
362C2×C42—61no—
363#107—121no—
364#106—121no—
365C4⋊C8—62no—
366C4⋊C8—62no—
367#102—22no—
368#102—22no—
369#102—62no—
370#102—62no—
371#102—121no—
372#102—121no—
373#102—121no—
374#102—121no—
375C22⋊C8—62no—
376C22⋊C8#6714yes—
377#97—62no—
378C4×C8—62no—
379#95—61no—
380#95—61no—
381#95—61no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—48no—
391C23×C3—41no—
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×C3—84no—
411C23×C3—84no—
412C23×C3—84no—
413C23×C3—84no—
414C23×C3—84no—
415C23×C3—84no—
416C23×C3#12112yes—
417C23×C3C22×D411yescharacteristic
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—48no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4#12112yes—
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4H(5,𝔽2)11yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C3×C8—22no—
473C3×C8—22no—
474C3⋊C8—41no—
475C3⋊C8—41no—
476C24—24no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—42no—
481C24—42no—
482C24—81no—
483C24—81no—
484C24—81no—
485C24—81no—
486C24D3×D411yescharacteristic
487C2×D4—24no—
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—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4#23712yes—
514C2×D4#23712yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4D3×D411yescharacteristic
529C22×C4#23712yes—
530C22×C4C2×#6712yes—
531C22×C4C23×D311yescharacteristic
532D8—44no—
533D8—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8C2×#6712yes—
545C2×C8C2×#6712yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—62no—
549C4⋊C4—62no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—241no—
559C4⋊C4—241no—
560C22⋊C4—42no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C22⋊C4—122no—
564C22⋊C4—241no—
565C22⋊C4—241no—
566C22⋊C4—241no—
567C22⋊C4—241no—
568C22⋊C4—241no—
569C22⋊C4—241no—
570C22⋊C4—241no—
571C22⋊C4—241no—
572C22⋊C4—241no—
573C22⋊C4—241no—
574C22⋊C4—241no—
575C22⋊C4—241no—
576C22⋊C4—241no—
577C42—61no—
578C42—61no—
579C42—61no—
580C42—61no—
581C42—122no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—816no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3C2×#12111yescharacteristic
612C22×C3#52511yescharacteristic
613C22×C3#53511yescharacteristic
614C22×C3#57611yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57611yescharacteristic
617C22×C3#57711yescharacteristic
618C3×C4—22no—
619C3×C4—81no—
620C3×C4#54611yescharacteristic
621C3×C4#54611yescharacteristic
622C3×C4#55111yescharacteristic
623C3×C4#55111yescharacteristic
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3—41no—
628Dic3—81no—
629Dic3—81no—
630Dic3—81no—
631Dic3—81no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—48no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23—84no—
666C23#93812yes—
667C23C2×D3×D411yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4#93812yes—
716C2×C4C2×#23711yescharacteristic
717C2×C4C2×#23711yescharacteristic
718C2×C4C2×#23711yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4#100411yescharacteristic
721C2×C4C22×#6711yescharacteristic
722C8—22no—
723C8—22no—
724C8—121no—
725C8—121no—
726C2×C3—42no—
727C2×C3—82no—
728C2×C3—82no—
729C2×C3—161no—
730C2×C3#241111yescharacteristic
731C2×C3#305811yescharacteristic
732C2×C3#306211yescharacteristic
733C2×C3#311811yescharacteristic
734C2×C3#312211yescharacteristic
735C2×C3#322011yescharacteristic
736C2×C3#322411yescharacteristic
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—816no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#558611yescharacteristic
767C22#559211yescharacteristic
768C22#575711yescharacteristic
769C22#575711yescharacteristic
770C22#577411yescharacteristic
771C22#577511yescharacteristic
772C22C2×#93811yescharacteristic
773C4—22no—
774C4—81no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—241no—
780C4—241no—
781C4—241no—
782C4—241no—
783C4#558711yescharacteristic
784C4#558711yescharacteristic
785C4#580611yescharacteristic
786C4#580611yescharacteristic
787C3#2451211yescharacteristic, complemented, Sylow
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2#7999211yescharacteristic
793C2#7999311yescharacteristic
794C2#7999811yescharacteristic
795C2#7999911yescharacteristic
796C2#8258311yescharacteristic
797C2#8383611yescharacteristic
798C2#8395111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#447C2
socleC23×C3C22×D4
hypercenterC2×#447D3
hypocenterC3#24512
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
2. #84044C2semidirect
3. #82678C2semidirect
4. C2×#4720C2semidirect
5. #72128C2semidirect
6. #72040C2semidirect
7. #72040C2semidirect
8. #72039C2semidirect
9. #72038C2semidirect
10. #71678C2semidirect
11. #70188C2semidirect
12. #70186C2semidirect
13. #70180C2semidirect
14. #70179C2semidirect
15. #69929C2semidirect
37. #5221C22semidirect
38. #5221C22semidirect
43. C2×#832C22semidirect
44. C2×#832C22semidirect
47. C2×#818C22semidirect
48. C2×#817C22semidirect
49. C2×#815C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×Dic3⋊C8C22semidirect
52. C2×C8×Dic3C22semidirect
53. #4972C22semidirect
54. #4972C22semidirect
58. #4551C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
787. C3#24512semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4472
#840442
#826782
C2×#47202
#721282
#720402
#720392
#720382
#716782
#701882
#701862
#701802
#701792
#699292
#245123