Finite Group Databasebeta

← #10828765

Subgroups — #10828765

Order 768.

1334 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×#5507C211yesmaximal, characteristic
2C2×#4863C211yesmaximal, characteristic, complemented
3C2×D3×#106C211yesmaximal, characteristic, complemented
4#73912C211yesmaximal, characteristic, complemented
5C3×#1853C211yesmaximal, characteristic, complemented
6#71556C211yesmaximal, characteristic, complemented
7#70584C211yesmaximal, characteristic, complemented
8#70565C211yesmaximal, characteristic, complemented
9#69957C211yesmaximal, characteristic, complemented
10#69935C211yesmaximal, characteristic, complemented
11#69524C211yesmaximal, characteristic, complemented
12#68895C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68871C211yesmaximal, characteristic, complemented
15#68827C211yesmaximal, characteristic, complemented
16#24089—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#929—21no—
21C2×C4×#67C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23C2×#896—21no—
24#5507—24no—
25#5507—24no—
26C2×#895C2211yescharacteristic
27C2×#894—21no—
28C2×#893C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#888C2211yescharacteristic
32C2×C3×#106C2211yescharacteristic
33C2×C3×#106C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C3×#380C2211yescharacteristic
36#5212C2211yescharacteristic
37C2×#830C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#817C2211yescharacteristic
42#4987C2211yescharacteristic
43#4984C2211yescharacteristic
44#4972C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#808C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#808C2211yescharacteristic
50#4956—21no—
51#4949—21no—
52#4863—24no—
53D3×#106—24no—
54#4668—21no—
55#4658—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#547—31no—
65C2×#481—31no—
66C22×#106—31no—
67#2487—31no—
68#2058—31no—
69#2058—31no—
70#2034—31no—
71#2034—31no—
72#1893—31no—
73#1869—31no—
74#1864—31no—
75#1864—31no—
76#1853—31no—
77#1853D311yescharacteristic, complemented
78#1823—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×#235—28no—
84C2×#235—44no—
85C2×#235—44no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C4×D3C2311yescharacteristic
92C22×Dic6—21no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104C2×#217D411yescharacteristic
105#930—22no—
106#930—22no—
107#929—28no—
108C4×#67—22no—
109C4×#67—22no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4D411yescharacteristic
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4D411yescharacteristic
124C2×C4×Dic3C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C2×D3×C8—22no—
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130#896—28no—
131#895—22no—
132#895D414yes—
133#894—28no—
134#893—22no—
135#893—22no—
136D3×C4⋊C4—22no—
137D3×C4⋊C4—22no—
138D3×C4⋊C4—22no—
139D3×C4⋊C4D414yes—
140#888—22no—
141#888—22no—
142C3×#106—22no—
143C3×#106—22no—
144C3×C22⋊C8—22no—
145C3×#95—21no—
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149C3⋊#95—21no—
150#830—22no—
151#821—22no—
152#821—22no—
153(C2×D3)⋊C8—22no—
154#817—22no—
155#809—22no—
156#809—22no—
157#808—22no—
158#808—22no—
159#808—22no—
160C22×#41—61no—
161C23×C8—31no—
162#547—64no—
163#547—64no—
164C2×C4⋊Q8—31no—
165C2×#123—61no—
166C2×#123—61no—
167C2×C22⋊Q8—61no—
168C2×#121—31no—
169C2×#121—31no—
170C2×C4×D4—31no—
171C2×C4×D4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4C2×D311yescharacteristic
175#481—64no—
176C2×#106—31no—
177C2×#106—31no—
178C2×#106—31no—
179C2×#106—31no—
180C2×#106—64no—
181C2×#106C2×D311yescharacteristic
182C2×#106C2×D311yescharacteristic
183C2×#102—31no—
184C2×#102—31no—
185C2×#102—31no—
186C2×#102—31no—
187C2×C22⋊C8—31no—
188C2×C22⋊C8—31no—
189C2×C22⋊C8C2×D311yescharacteristic
190#400—61no—
191#399—61no—
192#389—31no—
193#389—31no—
194#386—61no—
195#385—61no—
196#380—31no—
197#380—31no—
198#380C2×D311yescharacteristic
199#340—31no—
200#340—31no—
201#340—31no—
202#340—31no—
203#340C2×D311yescharacteristic
204#340C2×D311yescharacteristic
205#336—31no—
206#336—31no—
207C24×C3C2×D411yescharacteristic
208C23×D3—21no—
209C23×D3C2×D411yescharacteristic
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2411yescharacteristic
225C2×#67—22no—
226C2×#67—22no—
227C2×#67—24no—
228C2×#67—42no—
229C2×#67—42no—
230C2×#67SD1614yes—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3C2×D411yescharacteristic
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237#235—432no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—24no—
243C2×D12—21no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12C2×D412yes—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—24no—
252C2×C4×D3—24no—
253C2×C4×D3—42no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—81no—
259C2×C4×D3—81no—
260C2×C4×D3C2×D412yes—
261C2×C4×D3C2×D412yes—
262C2×Dic6—24no—
263C2×Dic6—42no—
264C2×Dic6—42no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8#4112yescomplemented
271C3×C4⋊C4—24no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4C2×D412yes—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—81no—
281#217—22no—
282#217—81no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—42no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—81no—
294C4⋊Dic3C2×D412yes—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—22no—
298Dic3⋊C4—42no—
299Dic3⋊C4—81no—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8#4112yescomplemented
308D3×C8—28no—
309C2×#41—68no—
310C2×#41—124no—
311C2×#41—124no—
312C22×Q8—61no—
313C22×D4—31no—
314C22×D4—31no—
315C22×D4—61no—
316C22×D4—61no—
317C23×C4—21no—
318C23×C4—31no—
319C23×C4—61no—
320C23×C4—61no—
321C23×C4—61no—
322C23×C4C22×D311yescharacteristic
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—62no—
326C22×C8—62no—
327C22×C8—62no—
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C4⋊Q8—62no—
331C4⋊Q8—62no—
332#123—68no—
333#123—68no—
334C22⋊Q8—68no—
335#121—34no—
336#121—62no—
337#121—62no—
338#121—62no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—62no—
342C4×D4—62no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—34no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—62no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4C22×D311yescharacteristic
360C2×C4⋊C4C22×D311yescharacteristic
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C42—31no—
372#106—22no—
373#106—22no—
374#106—62no—
375#106—62no—
376#106—62no—
377#106—62no—
378#102—62no—
379#102—62no—
380#102—62no—
381#102—62no—
382C22⋊C8—22no—
383C22⋊C8—62no—
384C22⋊C8—62no—
385#95—21no—
386#95—61no—
387#95—61no—
388#95—61no—
389#95—61no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3C2×SD1612yes—
397C23×C3C22×D411yescharacteristic
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—22no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3#12012yes—
410C22×D3C2×SD1612yes—
411C22×D3AGL(1,ℤ/8)12yes—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
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—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C42−1+411yescharacteristic
437C2×C3×C42−1+411yescharacteristic
438#67—28no—
439#67—48no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—22no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3#12012yes—
457C2×Dic3C2×SD1612yes—
458D12—22no—
459D12—22no—
460D12—48no—
461D12—41no—
462D12—41no—
463C4×D3—22no—
464C4×D3—22no—
465C4×D3—22no—
466C4×D3—22no—
467C4×D3—48no—
468C4×D3—48no—
469C4×D3—84no—
470Dic6—48no—
471C3×C8—22no—
472C3×C8—41no—
473C3⋊C8—22no—
474C3⋊C8—41no—
475C24—31no—
476C24—61no—
477C24D3×D411yescharacteristic
478#41—1232no—
479C2×Q8—64no—
480C2×Q8—122no—
481C2×Q8—122no—
482C2×D4—34no—
483C2×D4—32no—
484C2×D4—64no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—64no—
488C2×D4—61no—
489C2×D4—61no—
490C2×D4—61no—
491C2×D4—61no—
492C2×D4—61no—
493C2×D4—122no—
494C2×D4—122no—
495C2×D4—122no—
496C2×D4—122no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—31no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—64no—
516C22×C4—64no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—122no—
525C22×C4—122no—
526C22×C4—122no—
527C22×C4—122no—
528C22×C4—122no—
529C22×C4—241no—
530C22×C4—241no—
531C22×C4D3×D411yescharacteristic
532C22×C4C23×D311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—32no—
539C2×C8—68no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8#23512yescomplemented
546C4⋊C4—24no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—32no—
554C4⋊C4—64no—
555C4⋊C4—62no—
556C4⋊C4—64no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—122no—
563C4⋊C4—241no—
564C4⋊C4—241no—
565C4⋊C4D3×D412yes—
566C4⋊C4D3×D412yes—
567C22⋊C4—64no—
568C22⋊C4—62no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—62no—
572C22⋊C4—81no—
573C22⋊C4—122no—
574C22⋊C4—241no—
575C42—61no—
576C42—61no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3C2×#12011yescharacteristic
585C22×C3#54711yescharacteristic
586C22×C3#54711yescharacteristic
587C22×C3C22×SD1611yescharacteristic
588C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
589C22×C3#57711yescharacteristic
590C22×C3#57711yescharacteristic
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—81no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C2×D3#45014yes—
605C3×C4—41no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—81no—
609C3×C4—81no—
610C3×C4#52511yescharacteristic
611C3×C4#53611yescharacteristic
612C3×C4#54711yescharacteristic
613C3×C4#54711yescharacteristic
614Dic3—22no—
615Dic3—22no—
616Dic3—42no—
617Dic3—41no—
618Dic3—81no—
619Dic3—81no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—32no—
627C23—32no—
628C23—32no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—62no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23D3×SD1612yes—
641C23C2×D3×D411yescharacteristic
642Q8—128no—
643D4—68no—
644D4—62no—
645D4—62no—
646D4—128no—
647D4—128no—
648D4—121no—
649D4—121no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
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—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—128no—
685C2×C4—128no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—244no—
695C2×C4C2×#23511yescharacteristic
696C2×C4C2×D3×D411yescharacteristic
697C2×C4C2×D3×D411yescharacteristic
698C2×C4#100711yescharacteristic
699C2×C4D3×#4111yescharacteristic
700C2×C4#101011yescharacteristic
701C8—22no—
702C8—41no—
703C8—62no—
704C8—121no—
705C2×C3—42no—
706C2×C3#240611yescharacteristic
707C2×C3C2×#45011yescharacteristic
708C2×C3#301011yescharacteristic
709C2×C3#333511yescharacteristic
710C2×C3#333511yescharacteristic
711C2×C3#334511yescharacteristic
712C2×C3#334511yescharacteristic
713D3—24no—
714D3—82no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—34no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—62no—
724C22—62no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—62no—
729C22—122no—
730C22—122no—
731C22—122no—
732C22—241no—
733C22—241no—
734C22—241no—
735C22—241no—
736C22#550711yescharacteristic
737C22D3×#12011yescharacteristic
738C22#565511yescharacteristic
739C22C2×D3×SD1611yescharacteristic
740C22#576211yescharacteristic
741C22D3×AGL(1,ℤ/8)11yescharacteristic
742C22#577811yescharacteristic
743C4—42no—
744C4—42no—
745C4—41no—
746C4—62no—
747C4—62no—
748C4—81no—
749C4—81no—
750C4—122no—
751C4—121no—
752C4—241no—
753C4—241no—
754C4#554711yescharacteristic
755C4#555111yescharacteristic
756C4#562811yescharacteristic
757C4#563111yescharacteristic
758C3#2408911yescharacteristic, complemented, Sylow
759C2—42no—
760C2—64no—
761C2—242no—
762C2#7460011yescharacteristic
763C2#7912411yescharacteristic
764C2#7922511yescharacteristic
765C2#8004111yescharacteristic
766C2D3×#45011yescharacteristic
767C2#8133511yescharacteristic
768C2#8143511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1853C2
socleC23×C3C22×D4
prime radicalC2×#5507C2
hypercenter#1853D3
hypocenterC3#24089
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#4863C2semidirect
3. C2×D3×#106C2semidirect
4. #73912C2semidirect
5. C3×#1853C2semidirect
6. #71556C2semidirect
7. #70584C2semidirect
8. #70565C2semidirect
9. #69957C2semidirect
10. #69935C2semidirect
11. #69524C2semidirect
12. #68895C2semidirect
13. #68883C2semidirect
14. #68871C2semidirect
15. #68827C2semidirect
77. #1853D3semidirect
270. C2×C3×C8#41semidirect
307. C2×C3⋊C8#41semidirect
545. C2×C8#235semidirect
758. C3#24089semidirect

Maximal subgroups

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

subgroupindex
C2×#55072
C2×#48632
C2×D3×#1062
#739122
C3×#18532
#715562
#705842
#705652
#699572
#699352
#695242
#688952
#688832
#688712
#688272
#240893