Finite Group Databasebeta

← #11069507

Subgroups — #11069507

Order 768.

2624 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5617C212yesmaximal, complemented
2C3×C4×#121C211yesmaximal, characteristic, complemented
3#82403C212yesmaximal, complemented
4#82352C212yesmaximal, complemented
5D4×C4⋊Dic3C212yesmaximal, complemented
6#82076C211yesmaximal, characteristic, complemented
7C2×#4939C211yesmaximal, characteristic, complemented
8#76379C212yesmaximal, complemented
9#76131C212yesmaximal, complemented
10#75690C214yesmaximal, complemented
11#74891C214yesmaximal, complemented
12#73952C212yesmaximal, complemented
13#73692C212yesmaximal, complemented
14#73516C212yesmaximal, complemented
15#73507C212yesmaximal, complemented
16#39375—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×C4×D4C2212yes—
20C2×C3×C4×D4C2211yescharacteristic, complemented
21C22×C3×C42C2211yescharacteristic
22C2×#939C2214yescomplemented
23C2×#937C2214yes—
24C2×D4×Dic3C2214yes—
25C2×#930C2212yes—
26C2×#930C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×C4⋊Dic3C2211yescharacteristic
30C22×C4⋊Dic3C2212yescomplemented
31C2×#924C2212yes—
32#5617—216no—
33C2×#898C2214yescomplemented
34C2×#886C2214yescomplemented
35C2×#886C2214yescomplemented
36C2×#885C2214yescomplemented
37C2×#869C2211yescharacteristic, complemented
38C3×#390C2211yescharacteristic, complemented
39C3×#389C2211yescharacteristic, complemented
40C3×#388C2212yescomplemented
41C3×#386C2212yes—
42C3×#380C2211yescharacteristic
43C3×C4×C4⋊C4C2211yescharacteristic, complemented
44C3×C4×C22⋊C4C2212yescomplemented
45#5212C2212yes—
46#5212C2212yes—
47#5212C2212yescomplemented
48#4994C2214yescomplemented
49#4994C2214yescomplemented
50#4991C2214yes—
51#4984C2214yescomplemented
52#4961C2214yescomplemented
53#4961C2214yescomplemented
54#4960C2214yes—
55#4958C2214yescomplemented
56#4955C2214yes—
57#4950C2214yes—
58#4950C2214yescomplemented
59#4939C2212yes—
60#4939C2212yes—
61#4939C2212yes—
62#4939C2212yes—
63#4939C2212yes—
64#4939C2212yes—
65#4935C2211yescharacteristic, complemented
66#4935C2212yescomplemented
67C4×C4⋊Dic3C2212yescomplemented
68#4929C2212yescomplemented
69#4928C2212yescomplemented
70#4928C2212yescomplemented
71#4677C2214yescomplemented
72#4677C2214yescomplemented
73#4674C2214yescomplemented
74#4673C2214yescomplemented
75#4670C2214yescomplemented
76#4670C2214yescomplemented
77C2×#538—32no—
78#2857—31no—
79#2727—32no—
80#2710—34no—
81#2682—32no—
82#2626—32no—
83#2512—32no—
84#2501—32no—
85#2491—32no—
86#2418—34no—
87#2416—32no—
88#2408—32no—
89D4×C4⋊C4—32no—
90C4×#121D311yescharacteristic, complemented
91C2×#390—31no—
92C24×D3C2312yes—
93C22×C3×D4C2312yes—
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4C2312yes—
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67C2314yes—
100C22×#67C2314yes—
101C23×Dic3C2312yes—
102C23×Dic3C2314yes—
103C22×D12—24no—
104C22×D12—42no—
105C22×D12—42no—
106C22×D12C2312yes—
107C22×D12C2312yes—
108C22×Dic6C2312yes—
109C3×#121D418yescomplemented
110C3×C4×D4—28no—
111C3×C4×D4—42no—
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4C2312yes—
117C2×C3×C22⋊C4C2312yes—
118C2×C3×C22⋊C4C2312yes—
119C2×C3×C22⋊C4C2312yes—
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C42—42no—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2312yes—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×#217C2314yes—
128C2×#217C2314yes—
129#939—216no—
130#937—216no—
131D4×Dic3—216no—
132#930—44no—
133#930—44no—
134C2×(C2×D3)⋊C4—28no—
135C2×(C2×D3)⋊C4—44no—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
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)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×C4⋊Dic3—42no—
147C2×C4⋊Dic3—44no—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2314yes—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2312yes—
158#924—28no—
159C2×Dic3⋊C4C2314yes—
160C2×C4×Dic3C2314yes—
161#898—216no—
162#886—216no—
163#886—48no—
164#885—216no—
165#869—42no—
166C3×#95C2312yes—
167C3×#95C2312yes—
168C3×#95C2312yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C23×D4—31no—
174#538—616no—
175C2×C4⋊Q8—31no—
176C2×#126—34no—
177C2×#124—34no—
178C2×#123—34no—
179C2×#123—34no—
180C2×C22⋊Q8—32no—
181C2×#121—34no—
182C2×#121—32no—
183C2×#121—32no—
184C2×#121C2×D311yescharacteristic
185C2×#120—34no—
186C2×C4×D4—34no—
187C2×C4×D4C2×D312yes—
188C2×C4×D4C2×D311yescharacteristic, complemented
189C22×C4⋊C4—31no—
190C22×C4⋊C4—32no—
191C22×C22⋊C4—32no—
192C22×C22⋊C4—32no—
193C22×C42C2×D311yescharacteristic
194#399—34no—
195#399—34no—
196#397—34no—
197#396—34no—
198#396—34no—
199#394—34no—
200#394—34no—
201#394—34no—
202#393—34no—
203#392—34no—
204#391—32no—
205#390—32no—
206#390—32no—
207#390—32no—
208#390—32no—
209#390—32no—
210#390—32no—
211#390C2×D311yescharacteristic, complemented
212#389—34no—
213#389—32no—
214#389—32no—
215#389C2×D311yescharacteristic, complemented
216#388—34no—
217#388—34no—
218#388C2×D312yescomplemented
219#386—34no—
220#386C2×D312yes—
221#385—34no—
222#385—34no—
223#384—31no—
224#384—32no—
225#380—32no—
226#380—32no—
227#380—32no—
228#380C2×D311yescharacteristic
229#379—34no—
230C4×C4⋊C4—32no—
231C4×C4⋊C4C2×D311yescharacteristic, complemented
232C4×C22⋊C4C2×D312yescomplemented
233C24×C3C2412yes—
234C24×C3C2411yescharacteristic
235C23×D3—24no—
236C23×D3—24no—
237C23×D3—24no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—42no—
241C23×D3—42no—
242C23×D3C2414yes—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—41no—
246C2×C3×D4—41no—
247C2×C3×D4C2×D418yes—
248C2×C3×D4C2×D414yescomplemented
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—22no—
255C22×C3×C4—24no—
256C22×C3×C4—41no—
257C22×C3×C4—41no—
258C22×C3×C4—41no—
259C22×C3×C4C2×D414yes—
260C22×C3×C4#4114yes—
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C2×#67—28no—
271C2×#67—28no—
272C2×#67—44no—
273C2×#67—44no—
274C2×#67—44no—
275C2×#67—44no—
276C22×Dic3—28no—
277C22×Dic3—24no—
278C22×Dic3—44no—
279C22×Dic3—42no—
280C22×Dic3—44no—
281C22×Dic3—42no—
282C22×Dic3C2414yes—
283C22×Dic3C2414yes—
284C22×Dic3C2414yes—
285C2×D12—24no—
286C2×D12—24no—
287C2×D12—24no—
288C2×D12—24no—
289C2×D12—42no—
290C2×D12—42no—
291C2×D12—416no—
292C2×Dic6—24no—
293C2×Dic6—42no—
294C2×Dic6—42no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—41no—
297C3×C4⋊C4—41no—
298C3×C4⋊C4C2×D414yescomplemented
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4C2×D418yescomplemented
304C3×C42—24no—
305C3×C42—22no—
306C3×C42—22no—
307C3×C42—41no—
308C3×C42—41no—
309#217—28no—
310#217—28no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—28no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—44no—
317(C2×D3)⋊C4—44no—
318(C2×D3)⋊C4—44no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321C4⋊Dic3—24no—
322C4⋊Dic3—28no—
323C4⋊Dic3—24no—
324C4⋊Dic3—24no—
325C4⋊Dic3—24no—
326C4⋊Dic3—24no—
327C4⋊Dic3—42no—
328C4⋊Dic3—44no—
329C4⋊Dic3—42no—
330C4⋊Dic3—44no—
331Dic3⋊C4—28no—
332C4×Dic3—28no—
333C25—32no—
334C22×Q8—32no—
335C22×D4—34no—
336C22×D4—34no—
337C22×D4—32no—
338C22×D4—32no—
339C22×D4—64no—
340C22×D4—122no—
341C22×D4—122no—
342C22×D4C22×D312yes—
343C22×D4C22×D311yescharacteristic
344C23×C4—32no—
345C23×C4—34no—
346C23×C4C22×D312yes—
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C4⋊Q8—122no—
351#126—616no—
352#124—616no—
353#123—616no—
354#123—128no—
355C22⋊Q8—68no—
356#121—616no—
357#121—124no—
358#121—124no—
359#121D1218yescomplemented
360#120—616no—
361C4×D4—28no—
362C4×D4—42no—
363C4×D4—616no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—34no—
367C2×C4⋊C4—34no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—122no—
376C2×C4⋊C4—124no—
377C2×C4⋊C4C22×D312yes—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
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—68no—
394C2×C22⋊C4—124no—
395C2×C22⋊C4C22×D312yes—
396C2×C22⋊C4C22×D312yes—
397C2×C22⋊C4C22×D312yes—
398C2×C22⋊C4C22×D312yes—
399C2×C22⋊C4C22×D312yes—
400C2×C42—34no—
401C2×C42—42no—
402C2×C42C22×D312yes—
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D311yescharacteristic
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407#95—34no—
408#95—34no—
409#95—34no—
410#95—34no—
411#95C22×D312yes—
412#95C22×D312yes—
413#95C22×D312yes—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3C22×D414yes—
425C23×C3C22×D412yes—
426C23×C3C2×#4112yes—
427C23×C32−1+412yes—
428C23×C3C2511yescharacteristic
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—48no—
437C22×D3—48no—
438C22×D3—48no—
439C22×D3—84no—
440C22×D3—84no—
441C22×D3—84no—
442C22×D3—84no—
443C3×D4—216no—
444C3×D4—44no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—28no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—48no—
468C2×C3×C4C22×D414yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4H(5,𝔽2)12yes—
474C2×C3×C4H(5,𝔽2)12yes—
475C2×C3×C4H(5,𝔽2)12yes—
476#67—88no—
477#67—88no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—24no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—24no—
487C2×Dic3—84no—
488C2×Dic3—88no—
489D12—48no—
490D12—48no—
491Dic6—84no—
492C24—34no—
493C24—64no—
494C24—64no—
495C24—64no—
496C24—122no—
497C24—122no—
498C24—122no—
499C24—122no—
500C24C23×D312yes—
501C24C23×D311yescharacteristic
502C2×Q8—64no—
503C2×Q8—122no—
504C2×Q8—122no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—68no—
510C2×D4—68no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—1216no—
518C2×D4—124no—
519C2×D4—124no—
520C2×D4—124no—
521C2×D4—124no—
522C2×D4C2×D1218yes—
523C2×D4C2×D1214yescomplemented
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—34no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—64no—
538C22×C4—68no—
539C22×C4—122no—
540C22×C4—124no—
541C22×C4—122no—
542C22×C4—124no—
543C22×C4C2×D1214yes—
544C22×C4#23714yes—
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D312yes—
547C22×C4C23×D312yes—
548C22×C4C23×D312yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C4⋊C4—24no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—68no—
558C4⋊C4—68no—
559C4⋊C4—64no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—122no—
565C4⋊C4—124no—
566C4⋊C4—124no—
567C4⋊C4—122no—
568C4⋊C4C2×D1214yescomplemented
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—68no—
574C22⋊C4—68no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—68no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—124no—
581C22⋊C4—124no—
582C22⋊C4—124no—
583C22⋊C4—124no—
584C22⋊C4—124no—
585C22⋊C4C2×D1218yescomplemented
586C42—24no—
587C42—22no—
588C42—22no—
589C42—41no—
590C42—41no—
591C42—68no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3#54714yes—
606C22×C3C23×D411yescharacteristic
607C22×C3C22×#4111yescharacteristic
608C22×C3C2×H(5,𝔽2)11yescharacteristic
609C22×C3C2×H(5,𝔽2)11yescharacteristic
610C22×C3C2×H(5,𝔽2)11yescharacteristic
611C22×C3C2×2−1+411yescharacteristic
612C22×C3#58511yescharacteristic
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—44no—
620C2×D3—816no—
621C3×C4—22no—
622C3×C4—24no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—41no—
629C3×C4#53814yescomplemented
630Dic3—44no—
631Dic3—44no—
632Dic3—44no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—64no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—128no—
651C23—128no—
652C23—128no—
653C23—244no—
654C23—244no—
655C23—244no—
656C23—244no—
657C23C22×D1214yes—
658C23C22×D1212yes—
659C23C2×#23712yes—
660C23#101012yes—
661C23C24×D311yescharacteristic
662Q8—244no—
663D4—216no—
664D4—44no—
665D4—128no—
666D4—128no—
667D4—248no—
668D4—248no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—244no—
702C2×C4—248no—
703C2×C4C22×D1214yes—
704C2×C4C22×D1212yes—
705C2×C4C22×D1212yes—
706C2×C4C2×#23712yes—
707C2×C4C2×#23712yes—
708C2×C4#100412yes—
709C2×C4#100912yes—
710C2×C4#100912yes—
711C2×C3—24no—
712C2×C3—44no—
713C2×C3C2×#53811yescharacteristic
714C2×C3C2×#54711yescharacteristic
715C2×C3#349611yescharacteristic
716C2×C3#349811yescharacteristic
717C2×C3#350611yescharacteristic
718C2×C3#353611yescharacteristic
719C2×C3#356111yescharacteristic
720D3—84no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—124no—
735C22—124no—
736C22—124no—
737C22—124no—
738C22—124no—
739C22—124no—
740C22—124no—
741C22—2416no—
742C22#555514yes—
743C22C23×D1211yescharacteristic
744C22C22×#23711yescharacteristic
745C22C2×#100411yescharacteristic
746C22C2×#100911yescharacteristic
747C22C2×#100911yescharacteristic
748C22C2×#101011yescharacteristic
749C22#596411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—24no—
755C4—41no—
756C4—42no—
757C4—42no—
758C4—124no—
759C4—124no—
760C4—124no—
761C4#561714yescomplemented
762C3#3937511yescharacteristic, complemented, Sylow
763C2—24no—
764C2—44no—
765C2—244no—
766C2C2×#555511yescharacteristic
767C2#8578611yescharacteristic
768C2#8584611yescharacteristic
769C2C2×#561711yescharacteristic
770C2#8605111yescharacteristic
771C2#8614111yescharacteristic
772C2#8622311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#39375
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5617C2semidirect
2. C3×C4×#121C2semidirect
3. #82403C2semidirect
4. #82352C2semidirect
5. D4×C4⋊Dic3C2semidirect
6. #82076C2semidirect
7. C2×#4939C2semidirect
8. #76379C2semidirect
9. #76131C2semidirect
10. #75690C2semidirect
11. #74891C2semidirect
12. #73952C2semidirect
13. #73692C2semidirect
14. #73516C2semidirect
15. #73507C2semidirect
20. C2×C3×C4×D4C22semidirect
22. C2×#939C22semidirect
30. C22×C4⋊Dic3C22semidirect
33. C2×#898C22semidirect
34. C2×#886C22semidirect
35. C2×#886C22semidirect
36. C2×#885C22semidirect
37. C2×#869C22semidirect
38. C3×#390C22semidirect
39. C3×#389C22semidirect
40. C3×#388C22semidirect
43. C3×C4×C4⋊C4C22semidirect
44. C3×C4×C22⋊C4C22semidirect
47. #5212C22semidirect
48. #4994C22semidirect
49. #4994C22semidirect
51. #4984C22semidirect
52. #4961C22semidirect
53. #4961C22semidirect
55. #4958C22semidirect
58. #4950C22semidirect
65. #4935C22semidirect
66. #4935C22semidirect
67. C4×C4⋊Dic3C22semidirect
68. #4929C22semidirect
69. #4928C22semidirect
70. #4928C22semidirect
71. #4677C22semidirect
72. #4677C22semidirect
73. #4674C22semidirect
74. #4673C22semidirect
75. #4670C22semidirect
76. #4670C22semidirect
90. C4×#121D3semidirect
109. C3×#121D4semidirect
188. C2×C4×D4C2×D3semidirect
211. #390C2×D3semidirect
215. #389C2×D3semidirect
218. #388C2×D3semidirect
231. C4×C4⋊C4C2×D3semidirect
232. C4×C22⋊C4C2×D3semidirect
248. C2×C3×D4C2×D4semidirect
298. C3×C4⋊C4C2×D4semidirect
303. C3×C22⋊C4C2×D4semidirect
359. #121D12semidirect
523. C2×D4C2×D12semidirect
568. C4⋊C4C2×D12semidirect
585. C22⋊C4C2×D12semidirect
629. C3×C4#538semidirect
761. C4#5617semidirect
762. C3#39375semidirect

Maximal subgroups

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

subgroupindex
C2×#56172
C3×C4×#1212
#824032
#823522
D4×C4⋊Dic32
#820762
C2×#49392
#763792
#761312
#756902
#748912
#739522
#736922
#735162
#735072
#393753