Finite Group Databasebeta

← #10968114

Subgroups — #10968114

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×#5644C212yesmaximal, complemented
2C3×#2857C211yesmaximal, characteristic, complemented
3#83257C212yesmaximal, complemented
4#82824C212yesmaximal, complemented
5#82081C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#76539C214yesmaximal, complemented
8#76238C212yesmaximal, complemented
9#76220C212yesmaximal, complemented
10#76070C214yesmaximal, complemented
11#74362C212yesmaximal, complemented
12#74048C212yesmaximal, complemented
13#74031C212yesmaximal, complemented
14#73873C212yesmaximal, complemented
15#73865C212yesmaximal, complemented
16#35005—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic, complemented
19C2×C3×C22⋊Q8C2212yes—
20C22×C3×C42C2211yescharacteristic
21C2×#947C2214yes—
22C2×#930C2212yes—
23C2×#930C2212yes—
24C2×#930C2212yes—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28#5644—216no—
29C2×#898C2214yes—
30C2×#895C2214yes—
31C2×#895C2212yes—
32C2×#895C2212yes—
33C2×#894C2214yes—
34C2×#893C2212yescomplemented
35C2×#882C2214yes—
36C2×#67⋊C4C2214yes—
37C2×#874C2211yescharacteristic, complemented
38C3×#391C2212yescomplemented
39C3×#389C2212yescomplemented
40C3×#389C2212yescomplemented
41C3×#384C2211yescharacteristic, complemented
42C3×#380C2212yes—
43C3×#380C2212yes—
44#5231C2214yescomplemented
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47#4992C2214yescomplemented
48#4991C2214yes—
49#4991C2214yes—
50#4991C2214yescomplemented
51#4990C2214yescomplemented
52#4989C2214yescomplemented
53#4988C2212yescomplemented
54#4987C2212yes—
55#4987C2212yes—
56#4986C2214yescomplemented
57Dic3×C4⋊C4C2212yescomplemented
58#4972C2212yescomplemented
59#4958C2214yes—
60#4958C2214yes—
61#4939C2212yescomplemented
62#4939C2212yescomplemented
63#4939C2212yescomplemented
64C4×(C2×D3)⋊C4C2212yes—
65C4×(C2×D3)⋊C4C2212yes—
66C4×(C2×D3)⋊C4C2212yes—
67C4×(C2×D3)⋊C4C2212yes—
68#4935C2211yescharacteristic, complemented
69#4674C2214yes—
70#4671C2214yes—
71#4669C2214yescomplemented
72#4666C2214yescomplemented
73#4665C2214yes—
74#4665C2214yes—
75#4665C2214yescomplemented
76#4654C2214yescomplemented
77C2×#538—32no—
78#2857D311yescharacteristic, complemented
79#2856—31no—
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×Q8C2312yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67C2314yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×D12C2312yes—
102C22×D12C2314yes—
103C22×D12C2314yes—
104C22×D12C2312yes—
105C22×D12C2312yes—
106C22×C4×D3—24no—
107C22×C4×D3—42no—
108C22×C4×D3—42no—
109C22×C4×D3C2312yes—
110C22×C4×D3C2312yes—
111C22×C4×D3C2314yes—
112C3×C4⋊Q8—42no—
113C3×C22⋊Q8—28no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C22⋊C4C2314yes—
121C2×C3×C42—42no—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126#947—216no—
127#930—28no—
128#930—28no—
129#930—28no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4D418yescomplemented
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×Dic3⋊C4C2314yes—
150C2×C4×Dic3—42no—
151C2×C4×Dic3C2314yes—
152C2×C4×Dic3C2312yes—
153C2×C4×Dic3C2312yes—
154#898—216no—
155#895—216no—
156#895—44no—
157#895—44no—
158#894—216no—
159#893—44no—
160#882—216no—
161#67⋊C4—216no—
162#874—42no—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3⋊#95C2312yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2312yes—
171C3⋊#95C2312yes—
172C3⋊#95C2312yes—
173C24×C4—31no—
174#538—616no—
175C2×C4⋊Q8C2×D311yescharacteristic, complemented
176C2×#127—31no—
177C2×#126—34no—
178C2×#124—34no—
179C2×#123—34no—
180C2×C22⋊Q8C2×D312yes—
181C2×#121—32no—
182C2×#121—32no—
183C2×#121—32no—
184C2×#121—34no—
185C2×#121—32no—
186C2×#121—32no—
187C2×#120—34no—
188C2×C4×D4—32no—
189C2×C4×D4—34no—
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#391C2×D312yescomplemented
203#390—32no—
204#390—32no—
205#390—32no—
206#390—32no—
207#389—32no—
208#389C2×D312yescomplemented
209#389C2×D312yescomplemented
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#380C2×D312yes—
224#380C2×D312yes—
225C4×C4⋊C4—32no—
226C4×C22⋊C4—32no—
227C4×C22⋊C4—32no—
228C4×C22⋊C4—32no—
229C4×C22⋊C4—32no—
230C4×C22⋊C4—34no—
231C2×#95—31no—
232C2×#95—31no—
233C24×C3C2411yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—41no—
237C23×D3—41no—
238C23×D3—41no—
239C23×D3—41no—
240C23×D3C2×D414yes—
241C23×D3C2414yes—
242C23×D3C2412yes—
243C2×C3×Q8—24no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4C2×D414yes—
253C22×C3×C4#4114yes—
254C22×C3×C4#4114yes—
255C22×C3×C4C2414yes—
256C22×C3×C4C2414yes—
257C22×C3×C4C2411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C2×#67—28no—
264C2×#67—28no—
265C2×#67—28no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—41no—
269C22×Dic3—41no—
270C22×Dic3—41no—
271C22×Dic3—41no—
272C22×Dic3—41no—
273C22×Dic3—41no—
274C22×Dic3C2×D414yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2414yes—
278C22×Dic3C2412yes—
279C2×D12—24no—
280C2×D12—24no—
281C2×D12—24no—
282C2×D12—28no—
283C2×D12—28no—
284C2×D12—24no—
285C2×D12—24no—
286C2×D12—42no—
287C2×D12—42no—
288C2×D12—44no—
289C2×D12—44no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—44no—
293C2×D12—44no—
294C2×C4×D3—24no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3—28no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—416no—
302C2×C4×D3—44no—
303C2×C4×D3—44no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—28no—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4—42no—
310C3×C22⋊C4—28no—
311C3×C42—22no—
312C3×C42—22no—
313C3×C42—41no—
314C3×C42—41no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4C2×D418yes—
328(C2×D3)⋊C4C2×D418yes—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3—24no—
332Dic3⋊C4—28no—
333C4×Dic3—24no—
334C4×Dic3—28no—
335C4×Dic3—42no—
336C25—31no—
337C22×Q8C22×D312yes—
338C22×D4—34no—
339C22×D4—32no—
340C22×D4—34no—
341C22×D4—34no—
342C22×D4—32no—
343C22×D4—32no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—32no—
348C23×C4—34no—
349C23×C4—32no—
350C23×C4—64no—
351C23×C4—122no—
352C23×C4—122no—
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C4⋊Q8—42no—
357#127—122no—
358#126—616no—
359#124—616no—
360#123—616no—
361C22⋊Q8—28no—
362#121—616no—
363#121—68no—
364#121—68no—
365#121—68no—
366#121—124no—
367#121—124no—
368#120—616no—
369C4×D4—616no—
370C4×D4—124no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4C22×D312yes—
376C2×C4⋊C4C22×D314yes—
377C2×C4⋊C4C22×D312yes—
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—32no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—34no—
387C2×C22⋊C4—34no—
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—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—64no—
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#95C22×D314yes—
416#95C22×D314yes—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3C22×D412yes—
422C23×C3C2×#4112yes—
423C23×C3C2×#4112yes—
424C23×C3C2511yescharacteristic
425C22×D3—28no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C22×D3—44no—
444C22×D3—44no—
445C22×D3C22×D414yes—
446C3×Q8—84no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
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—28no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
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—416no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—44no—
487C2×Dic3—44no—
488C2×Dic3—44no—
489C2×Dic3C22×D414yes—
490D12—48no—
491D12—84no—
492D12—84no—
493D12—88no—
494D12—88no—
495C4×D3—48no—
496C4×D3—48no—
497C4×D3—88no—
498C24—32no—
499C24—34no—
500C24—34no—
501C24—62no—
502C24—62no—
503C24—121no—
504C24—121no—
505C24—121no—
506C24—121no—
507C24C23×D311yescharacteristic
508C2×Q8—24no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×D4—68no—
512C2×D4—68no—
513C2×D4—68no—
514C2×D4—68no—
515C2×D4—68no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—64no—
521C2×D4—124no—
522C2×D4—124no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4—122no—
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—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—68no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4—1216no—
552C22×C4—121no—
553C22×C4—121no—
554C22×C4—121no—
555C22×C4—121no—
556C22×C4—121no—
557C22×C4—121no—
558C22×C4D3×D414yes—
559C22×C4#23914yes—
560C22×C4#23914yes—
561C22×C4C23×D314yes—
562C22×C4C23×D314yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D311yescharacteristic
569C4⋊C4—28no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—68no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C22⋊C4—28no—
580C22⋊C4—38no—
581C22⋊C4—38no—
582C22⋊C4—68no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—68no—
589C22⋊C4—68no—
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#53214yes—
608C22×C3C23×D411yescharacteristic
609C22×C3C22×#4111yescharacteristic
610C22×C3C22×#4111yescharacteristic
611C22×C3C2×H(5,𝔽2)11yescharacteristic
612C22×C3C2×H(5,𝔽2)11yescharacteristic
613C22×C3#58511yescharacteristic
614C22×C3#58511yescharacteristic
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—416no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—44no—
636C3×C4—44no—
637C3×C4#53814yescomplemented
638Dic3—24no—
639Dic3—44no—
640Dic3—42no—
641Dic3—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—34no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—68no—
654C23—64no—
655C23—64no—
656C23—64no—
657C23—64no—
658C23—64no—
659C23—64no—
660C23—64no—
661C23—124no—
662C23—124no—
663C23—124no—
664C23—124no—
665C23—124no—
666C23—124no—
667C23C2×D3×D412yes—
668C23C2×#23912yes—
669C23C2×#23912yes—
670C23C24×D311yescharacteristic
671Q8—84no—
672D4—1216no—
673D4—128no—
674D4—244no—
675D4—244no—
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—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—34no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—64no—
704C2×C4—64no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
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×C4#100412yes—
718C2×C4C2×#23912yes—
719C2×C4C2×#23912yes—
720C2×C4C2×#23912yes—
721C2×C4C2×#23912yes—
722C2×C4#100912yes—
723C2×C3—24no—
724C2×C3C2×#53211yescharacteristic
725C2×C3C2×#53811yescharacteristic
726C2×C3#345511yescharacteristic
727C2×C3#349611yescharacteristic
728C2×C3#349611yescharacteristic
729C2×C3#350511yescharacteristic
730C2×C3#350611yescharacteristic
731D3—44no—
732D3—84no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—64no—
740C22—64no—
741C22—64no—
742C22—1216no—
743C22—122no—
744C22—122no—
745C22—122no—
746C22—122no—
747C22—124no—
748C22—124no—
749C22—124no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22—124no—
754C22#572514yes—
755C22C22×D3×D411yescharacteristic
756C22C2×#100411yescharacteristic
757C22C22×#23911yescharacteristic
758C22C22×#23911yescharacteristic
759C22C2×#100911yescharacteristic
760C22#596411yescharacteristic
761C22#596411yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—44no—
768C4—44no—
769C4—64no—
770C4—124no—
771C4—122no—
772C4—122no—
773C4#564414yescomplemented
774C3#3500511yescharacteristic, complemented, Sylow
775C2—24no—
776C2—124no—
777C2—244no—
778C2#8595011yescharacteristic
779C2#8597111yescharacteristic
780C2C2×#564411yescharacteristic
781C2C2×#572511yescharacteristic
782C2#8624111yescharacteristic
783C2#8625911yescharacteristic
784C2#8627311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2857C2
hypercenter#2857D3
hypocenterC3#35005
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#5644C2semidirect
2. C3×#2857C2semidirect
3. #83257C2semidirect
4. #82824C2semidirect
5. #82081C2semidirect
6. C2×C4×(C2×D3)⋊C4C2semidirect
7. #76539C2semidirect
8. #76238C2semidirect
9. #76220C2semidirect
10. #76070C2semidirect
11. #74362C2semidirect
12. #74048C2semidirect
13. #74031C2semidirect
14. #73873C2semidirect
15. #73865C2semidirect
18. C2×C3×C4⋊Q8C22semidirect
34. C2×#893C22semidirect
37. C2×#874C22semidirect
38. C3×#391C22semidirect
39. C3×#389C22semidirect
40. C3×#389C22semidirect
41. C3×#384C22semidirect
44. #5231C22semidirect
47. #4992C22semidirect
50. #4991C22semidirect
51. #4990C22semidirect
52. #4989C22semidirect
53. #4988C22semidirect
56. #4986C22semidirect
57. Dic3×C4⋊C4C22semidirect
58. #4972C22semidirect
61. #4939C22semidirect
62. #4939C22semidirect
63. #4939C22semidirect
68. #4935C22semidirect
71. #4669C22semidirect
72. #4666C22semidirect
75. #4665C22semidirect
76. #4654C22semidirect
78. #2857D3semidirect
131. C2×(C2×D3)⋊C4D4semidirect
175. C2×C4⋊Q8C2×D3semidirect
202. #391C2×D3semidirect
208. #389C2×D3semidirect
209. #389C2×D3semidirect
220. #384C2×D3semidirect
637. C3×C4#538semidirect
773. C4#5644semidirect
774. C3#35005semidirect

Maximal subgroups

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

subgroupindex
C2×#56442
C3×#28572
#832572
#828242
#820812
C2×C4×(C2×D3)⋊C42
#765392
#762382
#762202
#760702
#743622
#740482
#740312
#738732
#738652
#350053