Finite Group Databasebeta

← #10968110

Subgroups — #10968110

Order 768.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5617C212yesmaximal, complemented
2C3×#2856C211yesmaximal, characteristic, complemented
3#83186C212yesmaximal, complemented
4#82723C212yesmaximal, complemented
5#82710C212yesmaximal, complemented
6#82679C212yesmaximal, complemented
7#82634C212yesmaximal, complemented
8Dic3×#121C212yesmaximal, complemented
9#82076C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#76452C212yesmaximal, complemented
12#76441C212yesmaximal, complemented
13#76359C214yesmaximal, complemented
14#76357C214yesmaximal, complemented
15#74364C212yesmaximal, complemented
16#35005—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C2×C3×#127C2211yescharacteristic, complemented
19C2×C3×#121C2212yes—
20C2×C3×#121C2212yes—
21C2×C3×#121C2212yes—
22C22×C3×C42C2211yescharacteristic
23C2×#939C2214yes—
24C2×#938C2212yes—
25C2×#938C2212yes—
26C2×#937C2214yes—
27C2×D4×Dic3C2214yes—
28C2×D4×Dic3C2212yescomplemented
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C2×#924C2212yes—
32C22×C4×Dic3C2211yescharacteristic
33#5617—216no—
34C2×#898C2214yes—
35C2×#886C2214yes—
36C2×#885C2214yes—
37C2×#869C2211yescharacteristic, complemented
38C3×#390C2212yescomplemented
39C3×#390C2212yescomplemented
40C3×#390C2212yescomplemented
41C3×#384C2211yescharacteristic, complemented
42#5223C2214yes—
43#5222C2214yescomplemented
44#5221C2212yescomplemented
45#5220C2214yes—
46#5220C2214yes—
47#5220C2214yescomplemented
48#5212C2212yes—
49#5212C2212yes—
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4992C2214yes—
53#4987C2212yes—
54#4987C2212yes—
55#4985C2214yescomplemented
56#4984C2212yescomplemented
57#4980C2214yescomplemented
58Dic3×C4⋊C4C2212yescomplemented
59#4961C2214yes—
60#4961C2214yes—
61#4956C2214yes—
62#4956C2214yes—
63#4953C2214yescomplemented
64#4951C2214yescomplemented
65#4951C2214yescomplemented
66#4950C2214yescomplemented
67#4947C2214yescomplemented
68Dic3×C22⋊C4C2214yescomplemented
69C4×(C2×D3)⋊C4C2212yes—
70C4×(C2×D3)⋊C4C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72C4×(C2×D3)⋊C4C2212yes—
73#4935C2211yescharacteristic, complemented
74#4929C2212yescomplemented
75#4928C2212yescomplemented
76#4928C2212yescomplemented
77C2×#538—32no—
78#2857—31no—
79#2856D311yescharacteristic, complemented
80#2847—32no—
81#2639—32no—
82#2617—32no—
83#2559—34no—
84#2557—34no—
85#2496—32no—
86#2491—32no—
87#2428—32no—
88#2422—32no—
89#2325—32no—
90C4×#121—32no—
91C2×C4×C22⋊C4—31no—
92C24×D3C2311yescharacteristic
93C22×C3×D4C2314yes—
94C22×C3×D4C2312yes—
95C22×C3×D4C2312yes—
96C22×C3×D4C2312yes—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C22×#67C2314yes—
101C22×#67C2314yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2314yes—
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×C4×D3—24no—
107C22×C4×D3—42no—
108C22×C4×D3—42no—
109C22×C4×D3C2312yes—
110C22×C4×D3C2312yes—
111C22×Dic6C2312yes—
112C3×#127—42no—
113C3×#121—28no—
114C3×#121—28no—
115C3×#121—28no—
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C22⋊C4C2314yes—
120C2×C3×C22⋊C4C2314yes—
121C2×C3×C22⋊C4C2314yes—
122C2×C3×C42—42no—
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×#217C2314yes—
132C2×#217C2314yes—
133#939—216no—
134#938—44no—
135#938—44no—
136#937—216no—
137D4×Dic3—216no—
138D4×Dic3—44no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4D418yescomplemented
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153#924—28no—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3—42no—
156C2×C4×Dic3C2312yes—
157C2×C4×Dic3C2314yes—
158C2×C4×Dic3C2312yes—
159#898—216no—
160#886—216no—
161#885—216no—
162#869—42no—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2312yes—
166C3⋊#95C2312yes—
167C3⋊#95C2312yes—
168C3⋊#95C2312yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C24×C4—31no—
174#538—616no—
175C2×C4⋊Q8—31no—
176C2×#127C2×D311yescharacteristic, complemented
177C2×#126—34no—
178C2×#124—34no—
179C2×#123—34no—
180C2×C22⋊Q8—32no—
181C2×#121—34no—
182C2×#121—32no—
183C2×#121—32no—
184C2×#121C2×D312yes—
185C2×#121C2×D312yes—
186C2×#121C2×D312yes—
187C2×#120—34no—
188C2×C4×D4—34no—
189C2×C4×D4—32no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C42—31no—
193C22×C42C2×D311yescharacteristic
194#400—34no—
195#397—34no—
196#397—34no—
197#394—34no—
198#394—34no—
199#394—34no—
200#393—34no—
201#392—34no—
202#391—32no—
203#390—32no—
204#390C2×D312yescomplemented
205#390C2×D312yescomplemented
206#390C2×D312yescomplemented
207#389—32no—
208#389—32no—
209#389—32no—
210#388—34no—
211#388—34no—
212#387—34no—
213#386—34no—
214#386—34no—
215#386—34no—
216#386—34no—
217#386—34no—
218#385—34no—
219#384—31no—
220#384C2×D311yescharacteristic, complemented
221#380—32no—
222#380—32no—
223#380—32no—
224#380—32no—
225C4×C4⋊C4—32no—
226C4×C22⋊C4—34no—
227C4×C22⋊C4—32no—
228C4×C22⋊C4—32no—
229C4×C22⋊C4—32no—
230C4×C22⋊C4—32no—
231C2×#95—31no—
232C2×#95—31no—
233C24×C3C2414yes—
234C24×C3C2411yescharacteristic
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—41no—
238C23×D3—41no—
239C23×D3—41no—
240C23×D3—41no—
241C23×D3C2×D414yes—
242C23×D3C2412yes—
243C2×C3×D4—28no—
244C2×C3×D4—28no—
245C2×C3×D4—28no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—24no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—41no—
258C22×C3×C4—41no—
259C22×C3×C4—41no—
260C22×C3×C4—41no—
261C22×C3×C4C2×D414yes—
262C22×C3×C4#4114yes—
263C22×C3×C4#4114yes—
264C22×C3×C4C2414yes—
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2411yescharacteristic
271C2×#67—28no—
272C2×#67—28no—
273C2×#67—44no—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—28no—
280C22×Dic3—41no—
281C22×Dic3—41no—
282C22×Dic3—41no—
283C22×Dic3—41no—
284C22×Dic3—41no—
285C22×Dic3—41no—
286C22×Dic3—44no—
287C22×Dic3—44no—
288C22×Dic3C2×D414yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2414yes—
292C22×Dic3C2414yes—
293C22×Dic3C2412yes—
294C2×C4×D3—24no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—416no—
301C2×Dic6—24no—
302C2×Dic6—42no—
303C2×Dic6—42no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—24no—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—28no—
310C3×C42—22no—
311C3×C42—22no—
312C3×C42—41no—
313C3×C42—41no—
314#217—28no—
315#217—28no—
316#217—44no—
317#217—44no—
318#217—44no—
319#217—44no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4C2×D418yes—
325(C2×D3)⋊C4C2×D418yes—
326C4⋊Dic3—24no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—28no—
330C4⋊Dic3—42no—
331C4⋊Dic3—42no—
332Dic3⋊C4—28no—
333C4×Dic3—24no—
334C4×Dic3—28no—
335C4×Dic3—42no—
336C25—31no—
337C22×Q8—32no—
338C22×D4—34no—
339C22×D4—34no—
340C22×D4C22×D314yes—
341C22×D4C22×D312yes—
342C22×D4C22×D312yes—
343C22×D4C22×D312yes—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—34no—
347C23×C4—31no—
348C23×C4—32no—
349C23×C4—32no—
350C23×C4—64no—
351C23×C4—122no—
352C23×C4—122no—
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C4⋊Q8—122no—
357#127—42no—
358#126—616no—
359#124—616no—
360#123—616no—
361C22⋊Q8—68no—
362#121—28no—
363#121—28no—
364#121—28no—
365#121—616no—
366#121—124no—
367#121—124no—
368#120—616no—
369C4×D4—616no—
370C4×D4—124no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4C22×D312yes—
379C2×C4⋊C4C22×D312yes—
380C2×C4⋊C4C22×D312yes—
381C2×C22⋊C4—38no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4C22×D314yes—
396C2×C22⋊C4C22×D314yes—
397C2×C22⋊C4C22×D314yes—
398C2×C42—34no—
399C2×C42—32no—
400C2×C42—32no—
401C2×C42—42no—
402C2×C42—122no—
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D311yescharacteristic
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407#95—32no—
408#95—32no—
409#95—32no—
410#95—32no—
411#95—34no—
412#95—34no—
413#95—34no—
414#95—34no—
415#95—34no—
416#95—34no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3C22×D412yes—
429C23×C3C2×#4112yes—
430C23×C3C2×#4112yes—
431C23×C3C2511yescharacteristic
432C22×D3—28no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C22×D3—44no—
444C22×D3—44no—
445C22×D3C22×D414yes—
446C3×D4—416no—
447C3×D4—48no—
448C3×D4—84no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—28no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—44no—
465C2×C3×C4—44no—
466C2×C3×C4C22×D412yes—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C2×#4112yes—
469C2×C3×C4C2×#4112yes—
470C2×C3×C4C2×#4112yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4H(5,𝔽2)12yes—
473C2×C3×C4H(5,𝔽2)12yes—
474#67—88no—
475#67—88no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—24no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—44no—
491C2×Dic3—44no—
492C2×Dic3—44no—
493C2×Dic3—88no—
494C2×Dic3C22×D414yes—
495C4×D3—48no—
496C4×D3—48no—
497Dic6—84no—
498C24—32no—
499C24—34no—
500C24—62no—
501C24—62no—
502C24—121no—
503C24—121no—
504C24—121no—
505C24—121no—
506C24C23×D314yes—
507C24C23×D311yescharacteristic
508C2×Q8—64no—
509C2×Q8—122no—
510C2×Q8—122no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—68no—
524C2×D4—68no—
525C2×D4—124no—
526C2×D4—124no—
527C2×D4—124no—
528C2×D4—124no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—32no—
532C22×C4—34no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—34no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—68no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—1216no—
551C22×C4—121no—
552C22×C4—121no—
553C22×C4—121no—
554C22×C4—121no—
555C22×C4—121no—
556C22×C4—121no—
557C22×C4—124no—
558C22×C4—124no—
559C22×C4D3×D414yes—
560C22×C4#23714yes—
561C22×C4#23714yes—
562C22×C4C23×D314yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D311yescharacteristic
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—68no—
573C4⋊C4—68no—
574C4⋊C4—64no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—38no—
583C22⋊C4—38no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—124no—
591C22⋊C4—124no—
592C22⋊C4—124no—
593C22⋊C4—124no—
594C42—22no—
595C42—22no—
596C42—41no—
597C42—41no—
598C42—68no—
599C42—64no—
600C42—122no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—44no—
613C22×C3—44no—
614C22×C3#53214yes—
615C22×C3C23×D411yescharacteristic
616C22×C3C22×#4111yescharacteristic
617C22×C3C22×#4111yescharacteristic
618C22×C3C2×H(5,𝔽2)11yescharacteristic
619C22×C3C2×H(5,𝔽2)11yescharacteristic
620C22×C3#58511yescharacteristic
621C22×C3#58511yescharacteristic
622C2×D3—24no—
623C2×D3—24no—
624C2×D3—24no—
625C2×D3—416no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—44no—
636C3×C4#53814yescomplemented
637Dic3—24no—
638Dic3—42no—
639Dic3—44no—
640Dic3—44no—
641Dic3—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—34no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—68no—
661C23—124no—
662C23—124no—
663C23—124no—
664C23—124no—
665C23—124no—
666C23—124no—
667C23C2×D3×D412yes—
668C23C2×#23712yes—
669C23C2×#23712yes—
670C23C24×D311yescharacteristic
671Q8—244no—
672D4—416no—
673D4—48no—
674D4—84no—
675D4—84no—
676D4—248no—
677D4—248no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—28no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—34no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—64no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—128no—
710C2×C4—124no—
711C2×C4—124no—
712C2×C4—124no—
713C2×C4—128no—
714C2×C4—248no—
715C2×C4C2×D3×D412yes—
716C2×C4C2×D3×D412yes—
717C2×C4C2×#23712yes—
718C2×C4C2×#23712yes—
719C2×C4C2×#23712yes—
720C2×C4C2×#23712yes—
721C2×C4#100412yes—
722C2×C4#100912yes—
723C2×C3—24no—
724C2×C3—84no—
725C2×C3C2×#53211yescharacteristic
726C2×C3C2×#53811yescharacteristic
727C2×C3#345511yescharacteristic
728C2×C3#349611yescharacteristic
729C2×C3#349611yescharacteristic
730C2×C3#350511yescharacteristic
731C2×C3#350611yescharacteristic
732D3—44no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—64no—
747C22—64no—
748C22—64no—
749C22—1216no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22#571614yes—
755C22C22×D3×D411yescharacteristic
756C22C22×#23711yescharacteristic
757C22C22×#23711yescharacteristic
758C22C2×#100411yescharacteristic
759C22C2×#100911yescharacteristic
760C22#596411yescharacteristic
761C22#596411yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—44no—
768C4—64no—
769C4—122no—
770C4—124no—
771C4—122no—
772C4—124no—
773C4#561714yescomplemented
774C3#3500511yescharacteristic, complemented, Sylow
775C2—24no—
776C2—84no—
777C2—124no—
778C2#8593711yescharacteristic
779C2C2×#561711yescharacteristic
780C2#8595011yescharacteristic
781C2C2×#571611yescharacteristic
782C2#8622311yescharacteristic
783C2#8623611yescharacteristic
784C2#8624111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2856C2
hypercenter#2856D3
hypocenterC3#35005
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#5617C2semidirect
2. C3×#2856C2semidirect
3. #83186C2semidirect
4. #82723C2semidirect
5. #82710C2semidirect
6. #82679C2semidirect
7. #82634C2semidirect
8. Dic3×#121C2semidirect
9. #82076C2semidirect
10. C2×C4×(C2×D3)⋊C4C2semidirect
11. #76452C2semidirect
12. #76441C2semidirect
13. #76359C2semidirect
14. #76357C2semidirect
15. #74364C2semidirect
18. C2×C3×#127C22semidirect
28. C2×D4×Dic3C22semidirect
37. C2×#869C22semidirect
38. C3×#390C22semidirect
39. C3×#390C22semidirect
40. C3×#390C22semidirect
41. C3×#384C22semidirect
43. #5222C22semidirect
44. #5221C22semidirect
47. #5220C22semidirect
55. #4985C22semidirect
56. #4984C22semidirect
57. #4980C22semidirect
58. Dic3×C4⋊C4C22semidirect
63. #4953C22semidirect
64. #4951C22semidirect
65. #4951C22semidirect
66. #4950C22semidirect
67. #4947C22semidirect
68. Dic3×C22⋊C4C22semidirect
73. #4935C22semidirect
74. #4929C22semidirect
75. #4928C22semidirect
76. #4928C22semidirect
79. #2856D3semidirect
140. C2×(C2×D3)⋊C4D4semidirect
176. C2×#127C2×D3semidirect
204. #390C2×D3semidirect
205. #390C2×D3semidirect
206. #390C2×D3semidirect
220. #384C2×D3semidirect
636. C3×C4#538semidirect
773. C4#5617semidirect
774. C3#35005semidirect

Maximal subgroups

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

subgroupindex
C2×#56172
C3×#28562
#831862
#827232
#827102
#826792
#826342
Dic3×#1212
#820762
C2×C4×(C2×D3)⋊C42
#764522
#764412
#763592
#763572
#743642
#350053