Finite Group Databasebeta

← #11069141

Subgroups — #11069141

Order 768.

2276 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5643C212yesmaximal, complemented
2C3×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#82476C211yesmaximal, characteristic, complemented
4Q8×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#82081C211yesmaximal, characteristic
6#82062C211yesmaximal, characteristic, complemented
7#76507C212yesmaximal, complemented
8#76011C212yesmaximal, complemented
9#75174C214yesmaximal, complemented
10#74629C214yesmaximal, complemented
11#74033C212yesmaximal, complemented
12#73800C212yesmaximal, complemented
13#73715C211yesmaximal, characteristic, complemented
14#73692C212yesmaximal, complemented
15#73653C211yesmaximal, characteristic, complemented
16#73585C212yesmaximal, complemented
17#73507C212yesmaximal, complemented
18#39351—31nomaximal, Sylow
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C2×#947C2212yes—
23C2×Q8×Dic3C2212yes—
24C2×#930C2212yes—
25C2×#930C2212yes—
26C2×#930C2212yes—
27C2×#926C2212yes—
28#5643—216no—
29C2×#898C2214yes—
30C2×#897C2214yes—
31C2×#897C2214yes—
32C2×#893C2212yes—
33C2×#888C2212yes—
34C2×#885C2214yes—
35C2×#883C2214yes—
36C2×#874C2211yescharacteristic
37C2×C4×D12C2212yes—
38C2×#869C2212yes—
39C3×#391C2211yescharacteristic
40C3×#389C2211yescharacteristic
41C3×#387C2212yes—
42C3×#385C2212yes—
43C3×#380C2211yescharacteristic
44C3×C4×C4⋊C4C2212yes—
45C3×C4×C4⋊C4C2211yescharacteristic
46C3×C4×C22⋊C4C2212yes—
47#5212C2211yescharacteristic
48#5212C2211yescharacteristic
49#5212C2212yes—
50#4994C2214yes—
51#4991C2214yes—
52#4988C2212yes—
53#4988C2212yes—
54#4984C2212yes—
55#4984C2214yes—
56#4984C2212yes—
57#4961C2214yes—
58#4961C2214yes—
59#4939C2212yes—
60#4939C2212yes—
61#4939C2212yes—
62#4939C2212yes—
63#4939C2212yes—
64#4939C2212yes—
65#4936C2212yes—
66#4935C2212yes—
67#4935C2211yescharacteristic
68#4935C2211yescharacteristic
69#4935C2211yescharacteristic
70C4×C4⋊Dic3C2212yes—
71C4×C4⋊Dic3C2211yescharacteristic
72C4×C4⋊Dic3C2211yescharacteristic
73C4×C4⋊Dic3C2212yes—
74#4928C2212yes—
75#4677C2214yes—
76#4677C2214yes—
77#4674C2214yes—
78#4674C2214yes—
79#4673C2214yes—
80#4670C2214yes—
81#4670C2214yes—
82#4668C2214yes—
83#4665C2214yes—
84#4656C2214yes—
85C2×#542—32no—
86#2856—31no—
87#2723—34no—
88#2672—34no—
89#2624—32no—
90#2551—31no—
91#2548—31no—
92#2542—32no—
93#2512—32no—
94#2491—32no—
95#2452—32no—
96#2448—32no—
97#2422—32no—
98#2366—31no—
99Q8×C4⋊C4—31no—
100C4×C22⋊Q8D311yescharacteristic, complemented
101#2285—31no—
102C22×C3×Q8C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C22×#67C2314yes—
107C22×D12C2312yes—
108C22×D12C2312yes—
109C22×D12C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2314yes—
112C3×C22⋊Q8D418yescomplemented
113C3×C4×Q8—24no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C22⋊C4C2312yes—
122C2×C3×C42—24no—
123C2×C3×C42C2312yes—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2312yes—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×#217C2312yes—
130C2×#217C2312yes—
131#947—28no—
132Q8×Dic3—28no—
133#930—28no—
134#930—44no—
135#930—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—
146#926—28no—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2314yes—
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165#898—216no—
166#897—216no—
167#897—48no—
168#893—28no—
169#888—28no—
170#885—216no—
171#883—216no—
172#874—24no—
173C4×D12—44no—
174#869—44no—
175C3×#95C2312yes—
176C3×#95C2312yes—
177C3×#95C2312yes—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186#542—616no—
187C2×C4⋊Q8—32no—
188C2×C4⋊Q8—32no—
189C2×#127—31no—
190C2×#126—34no—
191C2×#124—32no—
192C2×#124—34no—
193C2×#123—34no—
194C2×C22⋊Q8—34no—
195C2×C22⋊Q8—34no—
196C2×C22⋊Q8C2×D311yescharacteristic
197C2×#121—32no—
198C2×#121—32no—
199C2×#121—32no—
200C2×C4×Q8—32no—
201C2×C4×Q8C2×D311yescharacteristic
202C2×C4×D4—32no—
203C2×C4×D4—32no—
204C2×#117—32no—
205C22×C42C2×D311yescharacteristic
206#399—34no—
207#399—34no—
208#397—34no—
209#397—34no—
210#396—34no—
211#395—34no—
212#394—34no—
213#394—34no—
214#394—34no—
215#393—34no—
216#391C2×D311yescharacteristic
217#390—32no—
218#390—32no—
219#390—32no—
220#390—32no—
221#390—32no—
222#390—32no—
223#390—32no—
224#390—32no—
225#389—32no—
226#389—34no—
227#389—32no—
228#389—32no—
229#389C2×D311yescharacteristic
230#388—34no—
231#388—34no—
232#387C2×D312yes—
233#386—34no—
234#385—34no—
235#385C2×D312yes—
236#384—31no—
237#384—32no—
238#384—31no—
239#384—31no—
240#382—32no—
241#380—32no—
242#380—31no—
243#380—31no—
244#380C2×D311yescharacteristic
245C4×C4⋊C4—31no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4—31no—
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D312yes—
251C4×C22⋊C4C2×D312yes—
252C24×C3C2411yescharacteristic
253C23×D3C2414yes—
254C2×C3×Q8—22no—
255C2×C3×Q8—22no—
256C2×C3×Q8C2×D414yes—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—41no—
265C22×C3×C4C2×D414yes—
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2412yes—
268C22×C3×C4C2412yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C2×#67—28no—
277C2×#67—44no—
278C2×#67—44no—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2414yes—
282C22×Dic3C2412yes—
283C22×Dic3C2412yes—
284C2×D12—24no—
285C2×D12—24no—
286C2×D12—24no—
287C2×D12—24no—
288C2×D12—24no—
289C2×D12—24no—
290C2×D12—24no—
291C2×D12—42no—
292C2×D12—42no—
293C2×C4×D3—28no—
294C2×C4×D3—44no—
295C2×C4×D3—44no—
296C2×Dic6—28no—
297C2×Dic6—44no—
298C2×Dic6—44no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4C2×D414yes—
304C3×C4⋊C4C2×D418yes—
305C3×C22⋊C4—42no—
306C3×C22⋊C4C2×D418yes—
307C3×C42—22no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—24no—
311C3×C42—24no—
312C3×C42#4114yes—
313#217—24no—
314#217—24no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325C4⋊Dic3—28no—
326C4⋊Dic3—24no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—22no—
330C4⋊Dic3—24no—
331C4⋊Dic3—22no—
332C4⋊Dic3—24no—
333C4⋊Dic3—22no—
334C4⋊Dic3—22no—
335C4⋊Dic3—44no—
336C4⋊Dic3—44no—
337C4⋊Dic3—42no—
338C4⋊Dic3—42no—
339Dic3⋊C4—28no—
340C4×Dic3—28no—
341C4×Dic3—24no—
342C4×Dic3—24no—
343C22×Q8—34no—
344C22×Q8C22×D311yescharacteristic
345C22×D4—34no—
346C22×D4—32no—
347C22×D4—32no—
348C22×D4—32no—
349C23×C4—34no—
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C4⋊Q8—68no—
354C4⋊Q8—124no—
355#127—64no—
356#126—616no—
357#124—68no—
358#124—616no—
359#123—616no—
360C22⋊Q8—616no—
361C22⋊Q8—128no—
362C22⋊Q8D1218yescomplemented
363#121—68no—
364#121—124no—
365#121—124no—
366C4×Q8—24no—
367C4×Q8—68no—
368C4×D4—68no—
369C4×D4—124no—
370#117—68no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D312yes—
388C2×C4⋊C4C22×D312yes—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D312yes—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4C22×D312yes—
405C2×C22⋊C4C22×D312yes—
406C2×C42—24no—
407C2×C42—32no—
408C2×C42—32no—
409C2×C42—34no—
410C2×C42C22×D312yes—
411C2×C42C22×D312yes—
412C2×C42C22×D311yescharacteristic
413C2×C42C22×D311yescharacteristic
414C2×C42C22×D311yescharacteristic
415C2×C42C22×D311yescharacteristic
416#95—32no—
417#95—32no—
418#95—32no—
419#95—32no—
420#95—34no—
421#95—34no—
422#95C22×D312yes—
423#95C22×D312yes—
424#95C22×D312yes—
425#95C22×D312yes—
426#95C22×D312yes—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3C22×D412yes—
434C23×C3C2511yescharacteristic
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C3×Q8—28no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—28no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4C22×D414yes—
466C2×C3×C4C22×D414yes—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C2×#4112yes—
470C2×C3×C4C2×#4112yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4H(5,𝔽2)12yes—
473C2×C3×C4H(5,𝔽2)12yes—
474C2×C3×C42−1+412yes—
475C2×C3×C42−1+412yes—
476#67—88no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492D12—48no—
493D12—48no—
494D12—84no—
495C4×D3—88no—
496Dic6—88no—
497C24—34no—
498C24C23×D311yescharacteristic
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—68no—
502C2×Q8—124no—
503C2×Q8—124no—
504C2×Q8C2×D1214yes—
505C2×D4—68no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4—124no—
516C2×D4—124no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—34no—
529C22×C4—41no—
530C22×C4—68no—
531C22×C4—124no—
532C22×C4—124no—
533C22×C4C2×D1214yes—
534C22×C4C23×D311yescharacteristic
535C22×C4C23×D312yes—
536C22×C4C23×D312yes—
537C22×C4C23×D312yes—
538C22×C4C23×D311yescharacteristic
539C22×C4C23×D312yes—
540C22×C4C23×D311yescharacteristic
541C22×C4C23×D311yescharacteristic
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D311yescharacteristic
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—64no—
551C4⋊C4—68no—
552C4⋊C4—68no—
553C4⋊C4—62no—
554C4⋊C4—62no—
555C4⋊C4—62no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—62no—
559C4⋊C4—122no—
560C4⋊C4—124no—
561C4⋊C4—124no—
562C4⋊C4—122no—
563C4⋊C4C2×D1214yes—
564C4⋊C4C2×D1218yes—
565C22⋊C4—42no—
566C22⋊C4—64no—
567C22⋊C4—64no—
568C22⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—124no—
574C22⋊C4—124no—
575C22⋊C4—124no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C22⋊C4C2×D1218yes—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—24no—
583C42—24no—
584C42—64no—
585C42—64no—
586C42—68no—
587C42#23714yes—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3C23×D411yescharacteristic
596C22×C3C22×#4111yescharacteristic
597C22×C3C2×H(5,𝔽2)11yescharacteristic
598C22×C3C2×H(5,𝔽2)11yescharacteristic
599C22×C3C2×2−1+411yescharacteristic
600C22×C3C2×2−1+411yescharacteristic
601C22×C3#58511yescharacteristic
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C3×C4—22no—
610C3×C4—24no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—24no—
614C3×C4—41no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4#54214yescomplemented
618C3×C4#54714yes—
619Dic3—42no—
620Dic3—42no—
621Dic3—42no—
622Dic3—44no—
623Dic3—42no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—64no—
631C23—64no—
632C23—64no—
633C23—64no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23C22×D1212yes—
638C23C24×D311yescharacteristic
639Q8—28no—
640Q8—248no—
641D4—128no—
642D4—128no—
643D4—244no—
644D4—248no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—28no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—64no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—64no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—248no—
683C2×C4C22×D1214yes—
684C2×C4C22×D1212yes—
685C2×C4C22×D1214yes—
686C2×C4C22×D1212yes—
687C2×C4C2×#23712yes—
688C2×C4C2×#23712yes—
689C2×C4C2×#23712yes—
690C2×C4#100712yes—
691C2×C4#100912yes—
692C2×C4#100912yes—
693C2×C4#101012yes—
694C2×C3—42no—
695C2×C3C2×#54211yescharacteristic
696C2×C3C2×#54711yescharacteristic
697C2×C3#349411yescharacteristic
698C2×C3#349711yescharacteristic
699C2×C3#349811yescharacteristic
700C2×C3#355011yescharacteristic
701C2×C3#355411yescharacteristic
702D3—84no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—124no—
711C22—124no—
712C22—124no—
713C22—124no—
714C22—124no—
715C22—124no—
716C22—124no—
717C22C23×D1211yescharacteristic
718C22C22×#23711yescharacteristic
719C22C2×#100711yescharacteristic
720C22C2×#100911yescharacteristic
721C22C2×#100911yescharacteristic
722C22C2×#101011yescharacteristic
723C22#596411yescharacteristic
724C4—22no—
725C4—22no—
726C4—24no—
727C4—22no—
728C4—24no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—122no—
733C4—122no—
734C4—122no—
735C4—124no—
736C4—122no—
737C4#555514yes—
738C4#564314yescomplemented
739C3#3935111yescharacteristic, complemented, Sylow
740C2—42no—
741C2—244no—
742C2C2×#555511yescharacteristic
743C2#8581811yescharacteristic
744C2#8584611yescharacteristic
745C2C2×#564311yescharacteristic
746C2#8602711yescharacteristic
747C2#8613711yescharacteristic
748C2#8626711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×C22⋊Q8C2
prime radical#82081C2
hypercenterC4×C22⋊Q8D3
hypocenterC3#39351
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#5643C2semidirect
2. C3×C4×C22⋊Q8C2semidirect
3. #82476C2semidirect
4. Q8×C4⋊Dic3C2semidirect
6. #82062C2semidirect
7. #76507C2semidirect
8. #76011C2semidirect
9. #75174C2semidirect
10. #74629C2semidirect
11. #74033C2semidirect
12. #73800C2semidirect
13. #73715C2semidirect
14. #73692C2semidirect
15. #73653C2semidirect
16. #73585C2semidirect
17. #73507C2semidirect
100. C4×C22⋊Q8D3semidirect
112. C3×C22⋊Q8D4semidirect
362. C22⋊Q8D12semidirect
617. C3×C4#542semidirect
738. C4#5643semidirect
739. C3#39351semidirect

Maximal subgroups

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

subgroupindex
C2×#56432
C3×C4×C22⋊Q82
#824762
Q8×C4⋊Dic32
#820812
#820622
#765072
#760112
#751742
#746292
#740332
#738002
#737152
#736922
#736532
#735852
#735072
#393513