Finite Group Databasebeta

← #10833978

Subgroups — #10833978

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
1#82678C211yesmaximal, characteristic, complemented
2C2×#5036C211yesmaximal, characteristic
3#82269C211yesmaximal, characteristic, complemented
4C2×#4720C211yesmaximal, characteristic, complemented
5C3×#1875C211yesmaximal, characteristic, complemented
6#71576C211yesmaximal, characteristic, complemented
7#70212C211yesmaximal, characteristic, complemented
8#70212C211yesmaximal, characteristic, complemented
9#70191C211yesmaximal, characteristic, complemented
10#70190C211yesmaximal, characteristic, complemented
11#69959C211yesmaximal, characteristic, complemented
12#68901C211yesmaximal, characteristic, complemented
13#68900C211yesmaximal, characteristic, complemented
14#68856C211yesmaximal, characteristic, complemented
15#68852C211yesmaximal, characteristic, complemented
16#24512—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#926C2211yescharacteristic
23C2×C3×#102C2211yescharacteristic, complemented
24C2×C3×#102C2211yescharacteristic, complemented
25C2×C3×C22⋊C8C2211yescharacteristic
26#5222—21no—
27#5222—21no—
28#5221C2211yescharacteristic, complemented
29#5221C2211yescharacteristic, complemented
30#5212C2211yescharacteristic
31C2×#830C2211yescharacteristic
32C2×#821C2211yescharacteristic
33C2×#821C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×#815C2211yescharacteristic, complemented
37C2×Dic3⋊C8C2211yescharacteristic, complemented
38C2×Dic3⋊C8C2211yescharacteristic, complemented
39C2×C8×Dic3C2211yescharacteristic, complemented
40#5036—24no—
41#4988C2211yescharacteristic
42#4988C2211yescharacteristic
43#4988C2211yescharacteristic
44#4988C2211yescharacteristic
45#4972C2211yescharacteristic, complemented
46#4972C2211yescharacteristic, complemented
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic, complemented
50C2×#807C2211yescharacteristic, complemented
51#4955—21no—
52#4955—21no—
53#4953—21no—
54#4949—21no—
55#4939—21no—
56#4939—21no—
57#4720—24no—
58C3×#340C2211yescharacteristic, complemented
59C3×#340C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62C2×#447—31no—
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#1875D311yescharacteristic, complemented
75#1854—31no—
76#1786—31no—
77C24×D3—21no—
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×D12—21no—
82C22×D12—22no—
83C22×D12—22no—
84C22×D12—22no—
85C22×D12—22no—
86C22×D12—41no—
87C22×D12—41no—
88C22×D12C2311yescharacteristic
89C22×D12C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×#121—22no—
93C3×#121—22no—
94C3×#117—41no—
95C3×#117—41no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108C2×#217D411yescharacteristic
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—22no—
112C2×#213—22no—
113C2×#213—41no—
114C2×#213—41no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123#926—22no—
124#926—22no—
125C2×C4⋊Dic3D411yescharacteristic
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3C2311yescharacteristic
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C3×#102—41no—
136C3×#102—41no—
137C3×C22⋊C8—22no—
138C3⋊#95—21no—
139C3⋊#95—21no—
140C3⋊#95—21no—
141#830D414yes—
142#821—22no—
143#821—22no—
144#821—41no—
145#821—41no—
146#815—22no—
147Dic3⋊C8—22no—
148Dic3⋊C8—22no—
149C8×Dic3—22no—
150#809—22no—
151#809—22no—
152#808—41no—
153#807—41no—
154C23×D4—31no—
155C22×D8—31no—
156C22×D8—31no—
157C2×#121C2×D311yescharacteristic
158C2×#117—31no—
159C2×#117C2×D311yescharacteristic
160#447—64no—
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, complemented
173C2×#102C2×D311yescharacteristic, complemented
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#340C2×D311yescharacteristic, complemented
198#340C2×D311yescharacteristic, complemented
199C24×C3—21no—
200C24×C3C2×D411yescharacteristic
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—24no—
204C23×D3—42no—
205C23×D3—42no—
206C23×D3—81no—
207C23×D3—81no—
208C23×D3—81no—
209C23×D3—81no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—42no—
217C2×C3×D4—81no—
218C2×C3×D4—81no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D412yes—
228C22×C3×C4#4112yes—
229C22×C3×C4C2411yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3C2×D411yescharacteristic
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C22×Dic3C2×D411yescharacteristic
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—24no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—44no—
248C2×D12—44no—
249C2×D12—44no—
250C2×D12—44no—
251C2×D12—42no—
252C2×D12—42no—
253C2×D12#4112yes—
254C2×D12#4112yes—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C42—42no—
270#217—22no—
271#217—22no—
272#217—81no—
273#217—81no—
274#217—81no—
275#217—81no—
276#217—81no—
277#213—44no—
278#213—44no—
279(C2×D3)⋊C4—81no—
280(C2×D3)⋊C4—81no—
281(C2×D3)⋊C4—81no—
282(C2×D3)⋊C4—81no—
283(C2×D3)⋊C4—81no—
284(C2×D3)⋊C4—81no—
285(C2×D3)⋊C4—81no—
286(C2×D3)⋊C4—81no—
287C4⋊Dic3—22no—
288C4⋊Dic3—22no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293Dic3⋊C4—81no—
294Dic3⋊C4—81no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8C2×D412yes—
304C2×C3⋊C8C2×D412yes—
305C25—61no—
306C22×D4—21no—
307C22×D4—31no—
308C22×D4—31no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—62no—
312C22×D4—61no—
313C22×D4—62no—
314C22×D4—121no—
315C22×D4—121no—
316C22×D4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C2×D8—62no—
319C2×D8—62no—
320C2×D8—62no—
321C2×D8—62no—
322C2×D8—121no—
323C2×D8—121no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328#121—22no—
329#121—22no—
330#117—41no—
331#117—41no—
332#117—62no—
333#117—62no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—61no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4C22×D311yescharacteristic
341C2×C4⋊C4C22×D311yescharacteristic
342C2×C4⋊C4C22×D311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
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—21no—
361C2×C42—31no—
362C2×C42—31no—
363#107—121no—
364#106—121no—
365C4⋊C8—62no—
366C4⋊C8—62no—
367#102—41no—
368#102—41no—
369#102—62no—
370#102—62no—
371#102—62no—
372#102—62no—
373#102—121no—
374#102—121no—
375C22⋊C8—22no—
376C22⋊C8—34no—
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—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3#12112yes—
396C23×C3C22×D411yescharacteristic
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—48no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—84no—
413C22×D3—84no—
414C22×D3—84no—
415C22×D3—84no—
416C22×D3—84no—
417C22×D3—84no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—84no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4#12112yes—
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4H(5,𝔽2)11yescharacteristic
444C2×C3×C4H(5,𝔽2)11yescharacteristic
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
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—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463D12—22no—
464D12—22no—
465D12—22no—
466D12—22no—
467D12—48no—
468D12—41no—
469D12—41no—
470D12—41no—
471D12—41no—
472C3×C8—41no—
473C3×C8—41no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C24—21no—
477C24—64no—
478C24—61no—
479C24—61no—
480C24—122no—
481C24—122no—
482C24—241no—
483C24—241no—
484C24—241no—
485C24—241no—
486C24D3×D411yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—32no—
494C2×D4—32no—
495C2×D4—42no—
496C2×D4—64no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4—124no—
510C2×D4—124no—
511C2×D4—124no—
512C2×D4—124no—
513C2×D4—122no—
514C2×D4—122no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4#23512yes—
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D412yes—
531C22×C4C23×D311yescharacteristic
532D8—124no—
533D8—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—32no—
541C2×C8—32no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—62no—
553C4⋊C4—62no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—241no—
559C4⋊C4—241no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—62no—
563C22⋊C4—62no—
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—42no—
578C42—61no—
579C42—61no—
580C42—61no—
581C42—61no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3C2×#12111yescharacteristic
597C22×C3#52511yescharacteristic
598C22×C3#53511yescharacteristic
599C22×C3#57611yescharacteristic
600C22×C3#57611yescharacteristic
601C22×C3#57611yescharacteristic
602C22×C3#57711yescharacteristic
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—816no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C3×C4—22no—
619C3×C4—81no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4#54611yescharacteristic
623C3×C4#54611yescharacteristic
624C3×C4#55111yescharacteristic
625C3×C4#55111yescharacteristic
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—81no—
631Dic3—81no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—62no—
646C23—62no—
647C23—128no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—244no—
661C23—244no—
662C23—244no—
663C23—244no—
664C23—244no—
665C23—244no—
666C23#88412yes—
667C23C2×D3×D411yescharacteristic
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—62no—
673D4—62no—
674D4—62no—
675D4—62no—
676D4—84no—
677D4—128no—
678D4—121no—
679D4—121no—
680D4—121no—
681D4—121no—
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—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4#88412yes—
716C2×C4C2×#23511yescharacteristic
717C2×C4C2×D3×D411yescharacteristic
718C2×C4#100411yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C2×C4D3×#4111yescharacteristic
722C8—41no—
723C8—41no—
724C8—62no—
725C8—62no—
726C2×C3—42no—
727C2×C3—161no—
728C2×C3#241111yescharacteristic
729C2×C3#305811yescharacteristic
730C2×C3#306211yescharacteristic
731C2×C3#311811yescharacteristic
732C2×C3#312211yescharacteristic
733C2×C3#322011yescharacteristic
734C2×C3#322411yescharacteristic
735D3—82no—
736D3—82no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—2416no—
758C22—241no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22C2×#88411yescharacteristic
767C22#559211yescharacteristic
768C22#565611yescharacteristic
769C22#576911yescharacteristic
770C22#577011yescharacteristic
771C22#577411yescharacteristic
772C22#577411yescharacteristic
773C4—22no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—241no—
782C4—241no—
783C4#555611yescharacteristic
784C4#555611yescharacteristic
785C4#561011yescharacteristic
786C4#561011yescharacteristic
787C3#2451211yescharacteristic, complemented, Sylow
788C2—42no—
789C2—161no—
790C2—242no—
791C2—242no—
792C2#7488911yescharacteristic
793C2#7884011yescharacteristic
794C2#7893211yescharacteristic
795C2#8011811yescharacteristic
796C2#8011911yescharacteristic
797C2#8135211yescharacteristic
798C2#8135411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1875C2
socleC23×C3C22×D4
prime radicalC2×#5036C2
hypercenter#1875D3
hypocenterC3#24512
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. #82678C2semidirect
3. #82269C2semidirect
4. C2×#4720C2semidirect
5. C3×#1875C2semidirect
6. #71576C2semidirect
7. #70212C2semidirect
8. #70212C2semidirect
9. #70191C2semidirect
10. #70190C2semidirect
11. #69959C2semidirect
12. #68901C2semidirect
13. #68900C2semidirect
14. #68856C2semidirect
15. #68852C2semidirect
23. C2×C3×#102C22semidirect
24. C2×C3×#102C22semidirect
28. #5221C22semidirect
29. #5221C22semidirect
36. C2×#815C22semidirect
37. C2×Dic3⋊C8C22semidirect
38. C2×Dic3⋊C8C22semidirect
39. C2×C8×Dic3C22semidirect
45. #4972C22semidirect
46. #4972C22semidirect
49. C2×#808C22semidirect
50. C2×#807C22semidirect
58. C3×#340C22semidirect
59. C3×#340C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
74. #1875D3semidirect
172. C2×#102C2×D3semidirect
173. C2×#102C2×D3semidirect
197. #340C2×D3semidirect
198. #340C2×D3semidirect
787. C3#24512semidirect

Maximal subgroups

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

subgroupindex
#826782
C2×#50362
#822692
C2×#47202
C3×#18752
#715762
#702122
#701912
#701902
#699592
#689012
#689002
#688562
#688522
#245123