Finite Group Databasebeta

← #544439

Subgroups — #544439

Order 512.

3304 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#2314C211yesmaximal, characteristic, complemented
4#14630C212yesmaximal, complemented
5#14549C214yesmaximal, complemented
6#14518C214yesmaximal, complemented
7#14340C211yesmaximal, characteristic, complemented
8#14328C212yesmaximal, complemented
9#14300C212yesmaximal, complemented
10#14189C212yesmaximal
11#13910C211yesmaximal, characteristic, complemented
12#13906C212yesmaximal, complemented
13#13905C211yesmaximal, characteristic, complemented
14#13880C212yesmaximal, complemented
15#13875C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17#13804C211yesmaximal, characteristic, complemented
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2212yes—
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#2392C4116yescomplemented
24C2×#398C2211yescharacteristic
25C2×#397C2211yescharacteristic
26C2×#396C2212yes—
27C2×#394C2211yescharacteristic
28C2×#394C2212yes—
29C2×#392C2211yescharacteristic
30D4×C4⋊C4—28no—
31#2314—28no—
32C2×#390C2214yes—
33C2×#389C2212yes—
34C2×#389C2214yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#386C2214yes—
40C2×#385C2214yes—
41C2×#385C2214yes—
42C2×#385C2214yes—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#384C2212yes—
46C2×#382C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59#1445C2212yes—
60#1444C2214yes—
61#1444C2212yes—
62#1444C2214yes—
63#1444C2212yes—
64#1443C2214yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2212yes—
75#1437C2214yes—
76#1437C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2214yes—
82#1434C2212yes—
83#1434C2214yes—
84C22⋊#95C2214yes—
85C4×#95C2212yes—
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2314yes—
91C2×C4×D4—24no—
92C2×C4×D4—28no—
93C2×C4×D4—24no—
94C2×C4×D4—44no—
95C2×C4×D4—44no—
96C2×C4×D4—48no—
97C2×C4×D4C2×C418yes—
98C2×C4×D4C2×C4116yescomplemented
99C2×#117—24no—
100C2×#117—24no—
101C2×#117C2×C418yescomplemented
102C22×C4⋊C4—28no—
103C22×C4⋊C4—44no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2314yes—
139C22×C42C2312yes—
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142#398C2×C418yescomplemented
143#397C2×C418yescomplemented
144#396C2×C4116yescomplemented
145#394C2×C418yes—
146#394C2×C4116yescomplemented
147#392C2×C418yes—
148#390—48no—
149#389—28no—
150#389—48no—
151#388—28no—
152#388—28no—
153#387—28no—
154#387—28no—
155#386—48no—
156#385—216no—
157#385—48no—
158#385—48no—
159#384—24no—
160#384—24no—
161#384—44no—
162#382—24no—
163#382—24no—
164#380—24no—
165#380—24no—
166#380—28no—
167#380—44no—
168#380—44no—
169#380—44no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—44no—
172C4×C4⋊C4C2×C418yescomplemented
173C4×C4⋊C4D418yescomplemented
174C4×C22⋊C4C2×C4116yescomplemented
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C25C2411yescharacteristic
199C25C2412yes—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—42no—
209C22×D4—42no—
210C22×D4C22×C414yes—
211C22×D4C22×C418yes—
212C23×C4—24no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—28no—
225C23×C4—28no—
226C23×C4—44no—
227C23×C4—44no—
228C23×C4—44no—
229C23×C4—44no—
230C23×C4—44no—
231C23×C4C22×C414yes—
232C23×C4C22×C418yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2414yes—
236C23×C4C2414yes—
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2412yes—
240C23×C4C2411yescharacteristic
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C4×D4—232no—
249C4×D4—432no—
250C4×D4—432no—
251#117—232no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—432no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4C22×C414yes—
297C2×C4⋊C4C22×C414yes—
298C2×C4⋊C4C22×C414yes—
299C2×C4⋊C4C22×C418yes—
300C2×C4⋊C4C22×C418yes—
301C2×C4⋊C4C2×D414yes—
302C2×C4⋊C4C2×D414yes—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4C22×C414yes—
334C2×C22⋊C4C22×C414yes—
335C2×C22⋊C4C22×C418yes—
336C2×C22⋊C4C22×C418yes—
337C2×C22⋊C4C22×C418yes—
338C2×C22⋊C4C22×C418yes—
339C2×C22⋊C4C22×C418yes—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—28no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349C2×C42—44no—
350C2×C42C22×C414yes—
351C2×C42C22×C418yes—
352C2×C42C22×C414yes—
353C2×C42C2×D418yes—
354C2×C42C2×D414yes—
355C2×C42#4114yes—
356#95—24no—
357#95—28no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—28no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95C22×C418yes—
375#95C22×C418yes—
376#95C22×C414yes—
377#95C22×C414yes—
378#95C2×D418yes—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24C23×C412yes—
402C24C23×C414yes—
403C24H(5,𝔽2)14yes—
404C242−1+414yes—
405C24C2511yescharacteristic
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—216no—
409C2×D4—216no—
410C2×D4—216no—
411C2×D4—28no—
412C2×D4—216no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—216no—
462C22×C4—28no—
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—416no—
491C22×C4—416no—
492C22×C4—48no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—44no—
496C22×C4—48no—
497C22×C4—44no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—88no—
501C22×C4—88no—
502C22×C4—88no—
503C22×C4—88no—
504C22×C4—88no—
505C22×C4C23×C412yes—
506C22×C4C23×C412yes—
507C22×C4C23×C414yes—
508C22×C4C23×C414yes—
509C22×C4C23×C412yes—
510C22×C4C23×C412yes—
511C22×C4C23×C412yes—
512C22×C4C23×C414yes—
513C22×C4C23×C412yes—
514C22×C4C22×D414yes—
515C22×C4C22×D414yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4H(5,𝔽2)14yes—
523C22×C4H(5,𝔽2)12yes—
524C22×C4H(5,𝔽2)12yes—
525C22×C4H(5,𝔽2)12yes—
526C22×C42−1+414yes—
527C22×C42−1+412yes—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—28no—
531C4⋊C4—216no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—48no—
535C4⋊C4—416no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—48no—
539C4⋊C4—44no—
540C4⋊C4—48no—
541C4⋊C4—84no—
542C4⋊C4—88no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—88no—
546C22⋊C4—216no—
547C22⋊C4—28no—
548C22⋊C4—28no—
549C22⋊C4—216no—
550C22⋊C4—216no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—416no—
554C22⋊C4—84no—
555C22⋊C4—84no—
556C22⋊C4—88no—
557C22⋊C4—88no—
558C22⋊C4—88no—
559C42—28no—
560C42—216no—
561C42—48no—
562C42—84no—
563C42—88no—
564C42C4×D4116yes—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23#52018yes—
623C23C24×C411yescharacteristic
624C23C23×D411yescharacteristic
625C23C22×#4111yescharacteristic
626C23C2×H(5,𝔽2)11yescharacteristic
627C23C2×H(5,𝔽2)11yescharacteristic
628C23C2×H(5,𝔽2)11yescharacteristic
629C23C2×H(5,𝔽2)12yes—
630C23C2×H(5,𝔽2)12yes—
631C23C2×2−1+411yescharacteristic
632C23C2×2−1+412yes—
633C23C2×2−1+412yes—
634D4—232no—
635D4—432no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—432no—
692C2×C4—416no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—832no—
718C2×C4C2×C4×D414yes—
719C2×C4C2×C4×D414yes—
720C2×C4C2×C4×D414yes—
721C2×C4#51814yes—
722C2×C4#52018yes—
723C2×C4#52014yes—
724C2×C4#53514yes—
725C2×C4#53714yes—
726C2×C4#54014yes—
727C2×C4#54214yes—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—82no—
753C22—82no—
754C22C22×C4×D411yescharacteristic
755C22C2×#51811yescharacteristic
756C22C2×#52011yescharacteristic
757C22C2×#52012yes—
758C22C2×#52012yes—
759C22C2×#53511yescharacteristic
760C22C2×#53711yescharacteristic
761C22C2×#54011yescharacteristic
762C22C2×#54211yescharacteristic
763C22#348411yescharacteristic
764C22#348611yescharacteristic
765C22#349212yes—
766C22#349811yescharacteristic
767C22#349911yescharacteristic
768C22#351112yes—
769C22#353612yes—
770C22#353612yes—
771C22#353712yes—
772C22#353812yes—
773C22#354312yes—
774C22#354412yes—
775C22#355212yes—
776C22#355212yes—
777C4—28no—
778C4—24no—
779C4—24no—
780C4—44no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—84no—
790C4—84no—
791C4#232418yes—
792C2—48no—
793C2—82no—
794C2C2×#232411yescharacteristic
795C2#3420011yescharacteristic
796C2#3420711yescharacteristic
797C2#3436012yes—
798C2#3438412yes—
799C2#4242811yescharacteristic
800C2#4243011yescharacteristic
801C2#4245812yes—
802C2#4246012yes—
803C2#4279211yescharacteristic
804C2#4279411yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
3. C2×#2314C2semidirect
4. #14630C2semidirect
5. #14549C2semidirect
6. #14518C2semidirect
7. #14340C2semidirect
8. #14328C2semidirect
9. #14300C2semidirect
11. #13910C2semidirect
12. #13906C2semidirect
13. #13905C2semidirect
14. #13880C2semidirect
15. #13875C2semidirect
16. #13872C2semidirect
17. #13804C2semidirect
23. #2392C4semidirect
98. C2×C4×D4C2×C4semidirect
101. C2×#117C2×C4semidirect
142. #398C2×C4semidirect
143. #397C2×C4semidirect
144. #396C2×C4semidirect
146. #394C2×C4semidirect
172. C4×C4⋊C4C2×C4semidirect
173. C4×C4⋊C4D4semidirect
174. C4×C22⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23922
C2×D4×C4⋊C42
C2×#23142
#146302
#145492
#145182
#143402
#143282
#143002
#141892
#139102
#139062
#139052
#138802
#138752
#138722
#138042