Finite Group Databasebeta

← #11633844

Subgroups — #11633844

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×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3#84068C212yesmaximal, complemented
4Q8×#217C212yesmaximal, complemented
5#83256C212yesmaximal, complemented
6#83241C212yesmaximal, complemented
7#83229C211yesmaximal, characteristic, complemented
8#82797C214yesmaximal, complemented
9#82778C212yesmaximal, complemented
10#82768C214yesmaximal, complemented
11#82754C212yesmaximal, complemented
12C4×#946C211yesmaximal, characteristic, complemented
13#82478C211yesmaximal, characteristic, complemented
14C4×#938C211yesmaximal, characteristic
15#82384C211yesmaximal, characteristic, complemented
16#82363C212yesmaximal, complemented
17#82341C212yesmaximal
18#59036—31nomaximal, Sylow
19C23×C3×Q8C2212yes—
20C3×D4×Q8—28no—
21C2×C3×C4⋊Q8C2212yes—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C22⋊Q8C2214yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2212yes—
27C2×C3×C4×D4C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C2×#946C2212yes—
30C2×Q8×Dic3C2212yes—
31C2×Q8×Dic3C2212yes—
32C2×#938C2211yescharacteristic
33C2×C4×#67C2212yes—
34#5728—28no—
35C2×#897C2212yes—
36C2×#892C2212yes—
37C2×#890C2212yes—
38C2×#887C2212yes—
39C2×C42×D3C2211yescharacteristic
40C2×#869C2211yescharacteristic
41#5231C2214yes—
42#5230C2214yes—
43#5229C2212yes—
44#5229C2214yes—
45#5229C2212yes—
46#5229C2211yescharacteristic
47#5229C2214yes—
48#5221C2212yes—
49#5221C2211yescharacteristic
50#5213C2214yes—
51#5212C2212yes—
52#5212C2212yes—
53#5212C2214yes—
54#5210C2214yes—
55C4×#217C2212yes—
56C4×#217C2214yes—
57#4994C2214yes—
58#4989C2212yes—
59#4987C2211yescharacteristic
60#4987C2211yescharacteristic
61#4984C2212yes—
62#4981C2214yes—
63#4980C2214yes—
64#4979C2214yes—
65#4978C2212yes—
66#4978C2214yes—
67#4977C2212yes—
68#4976C2214yes—
69#4975C2212yes—
70Dic3×C4⋊C4C2212yes—
71#4972C2211yescharacteristic
72#4972C2211yescharacteristic
73#4957C2214yes—
74#4956C2212yes—
75#4949C2214yes—
76#4948C2214yes—
77#4947C2214yes—
78#4944C2214yes—
79#4944C2212yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×Dic3⋊C4C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×D4×Q8D311yescharacteristic, complemented
87C2×#533—31no—
88#2692—34no—
89#2567—31no—
90#2563—31no—
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×Q8—28no—
104C22×C3×Q8—28no—
105C22×C3×Q8—44no—
106C22×C3×Q8C2314yes—
107C22×C3×Q8C2312yes—
108C22×C3×Q8C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2312yes—
111C23×C3×C4C2314yes—
112C22×#67C2312yes—
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×Dic6C2312yes—
117C3×C4⋊Q8—28no—
118C3×C4⋊Q8D418yescomplemented
119C3×C22⋊Q8—28no—
120C3×C22⋊Q8—216no—
121C3×C4×Q8—24no—
122C3×C4×D4—28no—
123C3×C4×D4—24no—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×#217C2314yes—
135C2×#217C2312yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139#946—28no—
140#946—24no—
141Q8×Dic3—28no—
142Q8×Dic3—44no—
143#938Q818yescomplemented
144C4×#67—44no—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2314yes—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2314yes—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170#897—28no—
171#892—28no—
172#890—28no—
173#887—28no—
174C42×D3—24no—
175#869—24no—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C23×Q8C2×D312yes—
191D4×Q8—28no—
192#533—68no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8C2×D312yes—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125—32no—
197C2×C22⋊Q8—31no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8C2×D312yes—
201C2×C22⋊Q8C2×D314yes—
202C2×#121—31no—
203C2×C4×Q8—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8C2×D311yescharacteristic
207C2×C4×D4—32no—
208C2×C4×D4C2×D311yescharacteristic
209C2×C4×D4C2×D312yes—
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#393—34no—
220#391—32no—
221#391—31no—
222#391—34no—
223#391—34no—
224#391—32no—
225#390—32no—
226#390—31no—
227#390—34no—
228#389—32no—
229#389—31no—
230#389—31no—
231#389—34no—
232#389—32no—
233#389—32no—
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#382—32no—
245#380—32no—
246#380—32no—
247#380—34no—
248#380—31no—
249#380—31no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—32no—
254C4×C22⋊C4—34no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C24×C3C2412yes—
258C23×D3C2411yescharacteristic
259C2×C3×Q8—22no—
260C2×C3×Q8—28no—
261C2×C3×Q8—24no—
262C2×C3×Q8—28no—
263C2×C3×Q8—24no—
264C2×C3×Q8—22no—
265C2×C3×Q8—44no—
266C2×C3×Q8—432no—
267C2×C3×Q8C2×D418yes—
268C2×C3×Q8#4114yes—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4C2×Q814yes—
272C22×C3×C4—28no—
273C22×C3×C4—24no—
274C22×C3×C4—28no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—44no—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2414yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C2×#67—42no—
286C2×#67—42no—
287C2×#67C2×Q818yescomplemented
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2411yescharacteristic
292C22×Dic3C2414yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2412yes—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—41no—
303C2×C4×D3—41no—
304C2×C4×D3C2×Q814yescomplemented
305C2×Dic6—24no—
306C2×Dic6—42no—
307C2×Dic6—42no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—28no—
312C3×C4⋊C4C2×D418yes—
313C3×C4⋊C4C2×D418yes—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—24no—
316C3×C42—24no—
317C3×C42C2×D414yes—
318#217—42no—
319#217—42no—
320#217—44no—
321#217—44no—
322#217C2×Q818yescomplemented
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—28no—
330C4⋊Dic3—22no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—44no—
334C4⋊Dic3C2×Q814yescomplemented
335Dic3⋊C4—28no—
336Dic3⋊C4—24no—
337Dic3⋊C4—44no—
338Dic3⋊C4—44no—
339Dic3⋊C4—42no—
340Dic3⋊C4—42no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—28no—
345C4×Dic3—24no—
346C4×Dic3—24no—
347C4×Dic3—44no—
348C22×Q8—28no—
349C22×Q8—28no—
350C22×Q8—32no—
351C22×Q8—44no—
352C22×Q8C22×D314yes—
353C22×Q8C22×D311yescharacteristic
354C22×Q8C22×D312yes—
355C22×D4—32no—
356C22×D4C22×D311yescharacteristic
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4C22×D312yes—
361C23×C4C22×D314yes—
362C4⋊Q8—28no—
363C4⋊Q8—64no—
364C4⋊Q8#6718yescomplemented
365#125—68no—
366C22⋊Q8—28no—
367C22⋊Q8—216no—
368C22⋊Q8—64no—
369C22⋊Q8—68no—
370C22⋊Q8—68no—
371#121—38no—
372C4×Q8—24no—
373C4×Q8—68no—
374C4×Q8—68no—
375C4×Q8—124no—
376C4×D4—28no—
377C4×D4—24no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D314yes—
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D312yes—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4C22×D312yes—
410C2×C22⋊C4C22×D314yes—
411C2×C42—34no—
412C2×C42—32no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—32no—
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—32no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—34no—
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—28no—
451C3×Q8—216no—
452C3×Q8—416no—
453C3×D4—28no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—416no—
467C2×C3×C4—48no—
468C2×C3×C4C22×D418yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×D412yes—
472C2×C3×C4C22×Q812yes—
473C2×C3×C4C2×#4114yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4H(5,𝔽2)12yes—
476C2×C3×C42−1+412yes—
477#67—48no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—24no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3C22×Q814yes—
501C2×Dic3C22×Q812yes—
502C4×D3—28no—
503C4×D3—44no—
504C4×D3—44no—
505Dic6—48no—
506C24—31no—
507C24C23×D312yes—
508C2×Q8—24no—
509C2×Q8—28no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—28no—
514C2×Q8—44no—
515C2×Q8—432no—
516C2×Q8—64no—
517C2×Q8—122no—
518C2×Q8—122no—
519C2×Q8#23714yes—
520C2×Q8C2×#6718yes—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—38no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4D3×Q814yes—
527C22×C4—28no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—24no—
532C22×C4—31no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—31no—
539C22×C4—34no—
540C22×C4—31no—
541C22×C4—44no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—121no—
549C22×C4—121no—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D312yes—
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D314yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—28no—
561C4⋊C4—34no—
562C4⋊C4—64no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—64no—
567C4⋊C4—68no—
568C4⋊C4—68no—
569C4⋊C4—64no—
570C4⋊C4—122no—
571C4⋊C4—124no—
572C4⋊C4—124no—
573C4⋊C4—124no—
574C4⋊C4—122no—
575C4⋊C4C2×#6718yes—
576C4⋊C4C2×#6718yes—
577C22⋊C4—28no—
578C22⋊C4—24no—
579C22⋊C4—38no—
580C22⋊C4—64no—
581C22⋊C4—68no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—124no—
586C22⋊C4—124no—
587C22⋊C4—122no—
588C42—24no—
589C42—64no—
590C42—64no—
591C42—62no—
592C42—62no—
593C42—62no—
594C42—68no—
595C42—124no—
596C42C2×#6714yes—
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—24no—
619C3×C4—28no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4#54614yes—
624C3×C4D4×Q814yes—
625Dic3—22no—
626Dic3—24no—
627Dic3—41no—
628Dic3—44no—
629Dic3—41no—
630Dic3—42no—
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—28no—
649Q8—216no—
650Q8—416no—
651Q8—128no—
652D4—28no—
653D4—128no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—32no—
667C2×C4—34no—
668C2×C4—416no—
669C2×C4—48no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—68no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—64no—
693C2×C4—124no—
694C2×C4—124no—
695C2×C4C2×#23714yes—
696C2×C4C2×#23712yes—
697C2×C4#100412yes—
698C2×C4C2×D3×Q812yes—
699C2×C4#100712yes—
700C2×C4C22×#6712yes—
701C2×C4C22×#6718yes—
702C2×C4C22×#6712yes—
703C2×C4C22×#6712yes—
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×#23711yescharacteristic
728C22C2×#100411yescharacteristic
729C22C22×D3×Q811yescharacteristic
730C22C2×#100711yescharacteristic
731C22#596811yescharacteristic
732C22#596811yescharacteristic
733C22C23×#6711yescharacteristic
734C4—24no—
735C4—28no—
736C4—22no—
737C4—42no—
738C4—42no—
739C4—62no—
740C4—64no—
741C4—121no—
742C4—122no—
743C4—122no—
744C4—122no—
745C4—121no—
746C4—124no—
747C4#580614yes—
748C4Q8×#6714yes—
749C3#5903611yescharacteristic, complemented, Sylow
750C2—44no—
751C2—122no—
752C2Q8×#23711yescharacteristic
753C2#8675011yescharacteristic
754C2#8676111yescharacteristic
755C2#8676311yescharacteristic
756C2C2×#580611yescharacteristic
757C2C2×Q8×#6711yescharacteristic
758C2#8729011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×D4×Q8C2
prime radicalC2×#938C22
hypercenterC2×D4×Q8D3
hypocenterC3#59036
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Q8C2semidirect
2. C2×#5728C2semidirect
3. #84068C2semidirect
4. Q8×#217C2semidirect
5. #83256C2semidirect
6. #83241C2semidirect
7. #83229C2semidirect
8. #82797C2semidirect
9. #82778C2semidirect
10. #82768C2semidirect
11. #82754C2semidirect
12. C4×#946C2semidirect
13. #82478C2semidirect
15. #82384C2semidirect
16. #82363C2semidirect
86. C2×D4×Q8D3semidirect
118. C3×C4⋊Q8D4semidirect
143. #938Q8semidirect
287. C2×#67C2×Q8semidirect
304. C2×C4×D3C2×Q8semidirect
322. #217C2×Q8semidirect
334. C4⋊Dic3C2×Q8semidirect
364. C4⋊Q8#67semidirect
749. C3#59036semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Q82
C2×#57282
#840682
Q8×#2172
#832562
#832412
#832292
#827972
#827782
#827682
#827542
C4×#9462
#824782
C4×#9382
#823842
#823632
#823412
#590363