Finite Group Databasebeta

← #11633857

Subgroups — #11633857

Order 768.

2374 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×#2563C211yesmaximal, characteristic, complemented
4#83243C211yesmaximal, characteristic, complemented
5C4×#938C211yesmaximal, characteristic
6#76824C214yesmaximal, complemented
7#76788C214yesmaximal, complemented
8#76325C212yesmaximal, complemented
9#76304C212yesmaximal
10#74180C212yesmaximal, complemented
11#74162C212yesmaximal, complemented
12#74017C212yesmaximal, complemented
13#73936C212yesmaximal, complemented
14#73894C212yesmaximal, complemented
15#73876C212yesmaximal, complemented
16C4×#897C211yesmaximal, characteristic, complemented
17#73650C211yesmaximal, characteristic, complemented
18#59036—31nomaximal, Sylow
19C23×Dic6C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2212yes—
23C2×Q8×Dic3C2212yes—
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2212yes—
26C2×C4×#67C2212yes—
27C2×#924C2212yes—
28#5728—28no—
29D4×Dic6—28no—
30C2×#897C2211yescharacteristic
31C2×#897C2212yes—
32C2×#892C2212yes—
33C2×#890C2212yes—
34C2×#888C2212yes—
35C2×#887C2212yes—
36C2×#887C2212yes—
37C2×#878C2214yes—
38C2×C42×D3C2211yescharacteristic
39C2×#869C2211yescharacteristic
40C2×C4×Dic6C2211yescharacteristic
41C3×#393C2214yes—
42C3×#390C2212yes—
43C3×#382C2212yes—
44C3×#380C2212yes—
45C3×#380C2212yes—
46C3×C4×C4⋊C4C2211yescharacteristic
47#5230C2214yes—
48#5221C2211yescharacteristic
49C4×#217C2212yes—
50#4987C2211yescharacteristic
51#4987C2211yescharacteristic
52#4984C2211yescharacteristic
53#4975C2212yes—
54#4973C2211yescharacteristic
55#4973C2212yes—
56#4973C2212yes—
57#4972C2212yes—
58#4972C2212yes—
59#4972C2211yescharacteristic
60#4958C2214yes—
61#4957C2214yes—
62#4956C2212yes—
63#4950C2214yes—
64#4949C2214yes—
65#4948C2214yes—
66#4945C2214yes—
67#4944C2212yes—
68#4942C2214yes—
69Dic3×C22⋊C4C2214yes—
70C4×(C2×D3)⋊C4C2212yes—
71C4×C4⋊Dic3C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74#4928C2212yes—
75#4676C2214yes—
76#4673C2214yes—
77#4668C2212yes—
78#4657C2214yes—
79#4656C2214yes—
80#4653C2214yes—
81#4653C2212yes—
82#4652C2214yes—
83#4647C2214yes—
84#4646C2214yes—
85#4646C2214yes—
86C2×D4×Q8—31no—
87C2×#533—31no—
88#2692—34no—
89#2567—31no—
90#2563D311yescharacteristic, complemented
91#2550—32no—
92#2538—32no—
93#2465—34no—
94#2454—32no—
95#2439—32no—
96#2423—32no—
97#2409—32no—
98#2365—31no—
99#2363—32no—
100Q8×C22⋊C4—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2312yes—
107C23×Dic3C2314yes—
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6—28no—
112C22×Dic6—28no—
113C22×Dic6—44no—
114C22×Dic6C2314yes—
115C22×Dic6C2312yes—
116C22×Dic6C2311yescharacteristic
117C3×C4⋊Q8—24no—
118C3×C4×D4—24no—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C42C2312yes—
128C2×C3×C42C2311yescharacteristic
129C2×#217C2314yes—
130C2×#217C2312yes—
131C2×#217C2312yes—
132C2×#217C2312yes—
133#946—28no—
134Q8×Dic3—28no—
135#938Q818yescomplemented
136D4×Dic3—28no—
137C4×#67—44no—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×C4⋊Dic3C2314yes—
143C2×C4⋊Dic3C2312yes—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2311yescharacteristic
150#924—28no—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2312yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×C4×Dic3C2314yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2314yes—
165#897—28no—
166#897—24no—
167#892—28no—
168#890—28no—
169#888—28no—
170#887—28no—
171#887—44no—
172#878—216no—
173C42×D3—24no—
174#869D418yescomplemented
175C4×Dic6—24no—
176C3×#95C2314yes—
177C3×#95C2314yes—
178C3×#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C23×Q8—32no—
191D4×Q8—68no—
192#533—68no—
193C2×C4⋊Q8—32no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—31no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—34no—
202C2×#121—31no—
203C2×C4×Q8—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8—31no—
207C2×C4×D4—32no—
208C2×C4×D4—32no—
209C2×C4×D4C2×D311yescharacteristic
210C2×#117—32no—
211C22×C42—31no—
212#399—34no—
213#398—34no—
214#396—34no—
215#396—34no—
216#395—34no—
217#395—34no—
218#393—34no—
219#393C2×D314yes—
220#391—32no—
221#391—31no—
222#391—32no—
223#391—34no—
224#391—34no—
225#390—31no—
226#390—34no—
227#390C2×D312yes—
228#389—32no—
229#389—32no—
230#389—31no—
231#389—31no—
232#389—32no—
233#389—34no—
234#388—34no—
235#388—32no—
236#387—34no—
237#387—34no—
238#387—32no—
239#386—34no—
240#386—32no—
241#385—34no—
242#385—32no—
243#384—32no—
244#382C2×D312yes—
245#380—31no—
246#380—31no—
247#380—34no—
248#380C2×D312yes—
249#380C2×D312yes—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4—32no—
257C24×C3C2412yes—
258C23×D3C2411yescharacteristic
259C2×C3×Q8—24no—
260C2×C3×Q8—42no—
261C2×C3×Q8—42no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4C2×Q814yes—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—24no—
268C22×C3×C4C2412yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2414yes—
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C2×#67—42no—
276C2×#67—42no—
277C2×#67C2×Q818yescomplemented
278C22×Dic3—28no—
279C22×Dic3—28no—
280C22×Dic3—44no—
281C22×Dic3C2412yes—
282C22×Dic3C2411yescharacteristic
283C22×Dic3C2411yescharacteristic
284C22×Dic3C2412yes—
285C22×Dic3C2414yes—
286C22×Dic3C2411yescharacteristic
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—41no—
296C2×C4×D3—41no—
297C2×C4×D3C2×Q814yescomplemented
298C2×Dic6—22no—
299C2×Dic6—24no—
300C2×Dic6—24no—
301C2×Dic6—22no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—432no—
305C2×Dic6—44no—
306C2×Dic6C2×D418yes—
307C2×Dic6#4114yes—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—22no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—44no—
315C3×C22⋊C4—44no—
316C3×C42—24no—
317C3×C42C2×D414yes—
318#217—28no—
319#217—42no—
320#217—42no—
321#217C2×Q818yescomplemented
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—28no—
329C4⋊Dic3—24no—
330C4⋊Dic3—42no—
331C4⋊Dic3C2×D418yes—
332C4⋊Dic3C2×D418yes—
333C4⋊Dic3C2×Q814yescomplemented
334Dic3⋊C4—24no—
335Dic3⋊C4—28no—
336Dic3⋊C4—28no—
337Dic3⋊C4—44no—
338Dic3⋊C4—44no—
339Dic3⋊C4—44no—
340Dic3⋊C4—42no—
341C4×Dic3—24no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—24no—
346C4×Dic3—28no—
347C4×Dic3—44no—
348C22×Q8—32no—
349C22×Q8—31no—
350C22×Q8—34no—
351C22×Q8—68no—
352C22×Q8—68no—
353C22×Q8—124no—
354C22×Q8C22×D312yes—
355C22×D4—32no—
356C22×D4C22×D311yescharacteristic
357C23×C4—31no—
358C23×C4—34no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4C22×D312yes—
362C4⋊Q8—24no—
363C4⋊Q8—38no—
364C4⋊Q8—68no—
365#125—68no—
366C22⋊Q8—616no—
367C22⋊Q8—68no—
368C22⋊Q8—64no—
369C22⋊Q8—68no—
370C22⋊Q8—68no—
371#121—38no—
372C4×Q8—68no—
373C4×Q8—68no—
374C4×Q8—64no—
375C4×Q8—124no—
376C4×D4—24no—
377C4×D4—68no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4C22×D312yes—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4C22×D312yes—
409C2×C22⋊C4C22×D314yes—
410C2×C22⋊C4C22×D314yes—
411C2×C42—34no—
412C2×C42—32no—
413C2×C42—32no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—34no—
418C2×C42—64no—
419C2×C42C22×D312yes—
420C2×C42C22×D311yescharacteristic
421#95—32no—
422#95—32no—
423#95—34no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—32no—
428#95—32no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95C22×D312yes—
433#95C22×D314yes—
434#95C22×D314yes—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3C22×Q814yes—
442C23×C3C2511yescharacteristic
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3C22×Q812yes—
450C3×Q8—48no—
451C3×D4—28no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—48no—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×Q812yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4H(5,𝔽2)12yes—
473C2×C3×C42−1+412yes—
474#67—48no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—22no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—416no—
496C2×Dic3C22×D418yes—
497C2×Dic3C22×Q814yes—
498C2×Dic3C22×Q812yes—
499C2×Dic3C2×#4114yes—
500C4×D3—28no—
501C4×D3—44no—
502C4×D3—44no—
503Dic6—28no—
504Dic6—216no—
505Dic6—416no—
506C24—31no—
507C24C23×D312yes—
508C2×Q8—24no—
509C2×Q8—38no—
510C2×Q8—34no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—68no—
514C2×Q8—68no—
515C2×Q8—62no—
516C2×Q8—64no—
517C2×Q8—64no—
518C2×Q8—62no—
519C2×Q8—124no—
520C2×Q8—1232no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—38no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4D3×Q814yes—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—31no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—34no—
535C22×C4—32no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—32no—
539C22×C4—68no—
540C22×C4—68no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—121no—
548C22×C4—121no—
549C22×C4—124no—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D312yes—
553C22×C4C23×D314yes—
554C22×C4C23×D311yescharacteristic
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—38no—
563C4⋊C4—38no—
564C4⋊C4—34no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—122no—
573C4⋊C4—124no—
574C4⋊C4—124no—
575C4⋊C4—124no—
576C4⋊C4—122no—
577C22⋊C4—24no—
578C22⋊C4—38no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—68no—
582C22⋊C4—64no—
583C22⋊C4—68no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—24no—
589C42—68no—
590C42—62no—
591C42—62no—
592C42—62no—
593C42—64no—
594C42—64no—
595C42—124no—
596C42D3×D414yes—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3C23×D411yescharacteristic
605C22×C3C23×Q811yescharacteristic
606C22×C3C22×#4111yescharacteristic
607C22×C3C2×H(5,𝔽2)11yescharacteristic
608C22×C3C2×2−1+411yescharacteristic
609C22×C3#58511yescharacteristic
610C22×C3#58511yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C3×C4—22no—
619C3×C4—42no—
620C3×C4—44no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4#54614yes—
624C3×C4D4×Q814yes—
625Dic3—24no—
626Dic3—28no—
627Dic3—22no—
628Dic3—24no—
629Dic3—41no—
630Dic3—41no—
631Dic3—42no—
632Dic3—42no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—32no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23C2×D3×Q814yes—
647C23C24×D311yescharacteristic
648Q8—48no—
649Q8—68no—
650Q8—616no—
651Q8—1216no—
652D4—28no—
653D4—128no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—38no—
669C2×C4—32no—
670C2×C4—34no—
671C2×C4—34no—
672C2×C4—48no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—64no—
676C2×C4—62no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—68no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—61no—
694C2×C4—124no—
695C2×C4—1216no—
696C2×C4—124no—
697C2×C4C2×D3×D412yes—
698C2×C4C2×D3×D412yes—
699C2×C4C2×D3×D412yes—
700C2×C4C2×D3×Q812yes—
701C2×C4D3×#4112yes—
702C2×C4#100912yes—
703C2×C4#101012yes—
704C2×C3—44no—
705C2×C3C2×#54611yescharacteristic
706C2×C3C2×D4×Q811yescharacteristic
707C2×C3Q8×#4111yescharacteristic
708C2×C3#348711yescharacteristic
709C2×C3#350111yescharacteristic
710C2×C3#351811yescharacteristic
711C2×C3#354711yescharacteristic
712D3—42no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—62no—
721C22—62no—
722C22—62no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22C22×D3×D411yescharacteristic
728C22C22×D3×Q811yescharacteristic
729C22C2×D3×#4111yescharacteristic
730C22C2×#100911yescharacteristic
731C22C2×#101011yescharacteristic
732C22#596611yescharacteristic
733C22#596611yescharacteristic
734C4—22no—
735C4—44no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—64no—
740C4—68no—
741C4—64no—
742C4—62no—
743C4—121no—
744C4—122no—
745C4—121no—
746C4—122no—
747C4#563214yes—
748C4#567614yes—
749C3#5903611yescharacteristic, complemented, Sylow
750C2—44no—
751C2—122no—
752C2C2×#563211yescharacteristic
753C2C2×#567611yescharacteristic
754C2#8631511yescharacteristic
755C2#8692311yescharacteristic
756C2#8694811yescharacteristic
757C2#8696311yescharacteristic
758C2#8697711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2563C2
prime radicalC2×#938C22
hypercenter#2563D3
hypocenterC3#59036
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×D4×Dic6C2semidirect
3. C3×#2563C2semidirect
4. #83243C2semidirect
6. #76824C2semidirect
7. #76788C2semidirect
8. #76325C2semidirect
10. #74180C2semidirect
11. #74162C2semidirect
12. #74017C2semidirect
13. #73936C2semidirect
14. #73894C2semidirect
15. #73876C2semidirect
16. C4×#897C2semidirect
17. #73650C2semidirect
90. #2563D3semidirect
135. #938Q8semidirect
174. #869D4semidirect
277. C2×#67C2×Q8semidirect
297. C2×C4×D3C2×Q8semidirect
321. #217C2×Q8semidirect
333. C4⋊Dic3C2×Q8semidirect
749. C3#59036semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×D4×Dic62
C3×#25632
#832432
C4×#9382
#768242
#767882
#763252
#763042
#741802
#741622
#740172
#739362
#738942
#738762
C4×#8972
#736502
#590363