Finite Group Databasebeta

← #636496

Subgroups — #636496

Order 512.

3340 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic
3C2×C4×#123C211yesmaximal, characteristic
4C22×#384C211yesmaximal, characteristic, complemented
5#16563C214yesmaximal, complemented
6#16515C214yesmaximal, complemented
7#15184C212yesmaximal, complemented
8#15182C212yesmaximal, complemented
9#15133C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#14821C212yesmaximal, complemented
12#14729C212yesmaximal
13#14339C212yesmaximal, complemented
14#14256C212yesmaximal
15#14139C211yesmaximal, characteristic, complemented
16#13907C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic
18C22×#123C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2855—28no—
28#2417—28no—
29C2×#398C2212yes—
30C2×#398C2214yes—
31C2×#396C2212yes—
32C2×#396C2214yes—
33C4×#123—28no—
34C2×#391C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2212yes—
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2212yes—
40C2×#388C2212yes—
41C2×#387C2214yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2211yescharacteristic
45C2×#386C2212yes—
46C2×#385C2212yes—
47C2×#385C2211yescharacteristic
48C2×#384—28no—
49C2×#384C2212yes—
50C2×#384C2212yes—
51C2×#384C2214yes—
52C2×#381C2211yescharacteristic
53C2×#381C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2211yescharacteristic
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2312yes—
95C2×#123—24no—
96C2×#123—24no—
97C2×#123Q818yescomplemented
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—44no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—28no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—28no—
110C22×C4⋊C4—44no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4—48no—
113C22×C4⋊C4—44no—
114C22×C4⋊C4D418yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42D418yes—
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152#398—28no—
153#398—48no—
154#396—28no—
155#396—48no—
156#391—24no—
157#391—28no—
158#391—44no—
159#389—24no—
160#389—28no—
161#389—44no—
162#388—28no—
163#387—216no—
164#387—28no—
165#386—28no—
166#386—24no—
167#386—44no—
168#385—28no—
169#385—24no—
170#384—28no—
171#384—28no—
172#384—216no—
173#381—28no—
174#381—24no—
175#380—24no—
176#380—28no—
177#380—24no—
178#380—44no—
179#380—44no—
180C4×C4⋊C4—28no—
181C4×C22⋊C4—24no—
182C4×C22⋊C4—28no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4C2×Q814yes—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×D414yes—
245C23×C4C2×D414yes—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×D418yes—
249C23×C4C2×Q814yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2414yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2414yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267#123—232no—
268C22⋊Q8—416no—
269C22⋊Q8—416no—
270C4×D4—416no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—432no—
316C2×C4⋊C4—432no—
317C2×C4⋊C4—416no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D418yes—
325C2×C4⋊C4C2×Q818yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4C2×Q814yes—
356C2×C22⋊C4C2×Q818yes—
357C2×C42—232no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42C2×D418yes—
369C2×C42C2×D418yes—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—24no—
382#95—24no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24C22×D412yes—
408C24C22×D412yes—
409C24C22×Q812yes—
410C24C22×Q812yes—
411C24C2×#4112yes—
412C24C2×#4112yes—
413C24H(5,𝔽2)12yes—
414C242−1+412yes—
415C24C2511yescharacteristic
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—48no—
420C2×Q8—48no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—44no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—216no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—216no—
451C22×C4—216no—
452C22×C4—216no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—216no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—88no—
526C22×C4—88no—
527C22×C4—88no—
528C22×C4—88no—
529C22×C4#121116yes—
530C22×C4C22⋊Q8116yescomplemented
531C22×C4C22×D414yes—
532C22×C4C22×D414yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D414yes—
536C22×C4C22×D414yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×Q814yes—
540C22×C4C22×Q812yes—
541C22×C4C22×Q814yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4114yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)14yes—
546C22×C4H(5,𝔽2)14yes—
547C22×C42−1+414yes—
548C22×C42−1+414yes—
549C4⋊C4—216no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—48no—
553C4⋊C4—416no—
554C4⋊C4—416no—
555C4⋊C4—416no—
556C4⋊C4—416no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—416no—
565C4⋊C4—48no—
566C4⋊C4—84no—
567C4⋊C4—88no—
568C22⋊C4—28no—
569C22⋊C4—216no—
570C22⋊C4—48no—
571C22⋊C4—44no—
572C22⋊C4—48no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—44no—
576C22⋊C4—48no—
577C22⋊C4—84no—
578C22⋊C4—88no—
579C42—216no—
580C42—216no—
581C42—44no—
582C42—48no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23C2×#12114yes—
623C23C2×C22⋊Q814yes—
624C23#53714yes—
625C23#54614yes—
626C23D4×Q814yes—
627C23#55214yes—
628C23#55414yes—
629C23C23×D411yescharacteristic
630C23C23×D411yescharacteristic
631C23C23×Q811yescharacteristic
632C23C22×#4111yescharacteristic
633C23C22×#4111yescharacteristic
634C23C2×H(5,𝔽2)12yes—
635C23C2×H(5,𝔽2)11yescharacteristic
636C23C2×H(5,𝔽2)12yes—
637C23C2×2−1+412yes—
638C23C2×2−1+411yescharacteristic
639C23C2×2−1+412yes—
640Q8—88no—
641D4—416no—
642C2×C4—232no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—232no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—232no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—816no—
727C2×C4—816no—
728C2×C4—88no—
729C2×C4C2×#12114yes—
730C2×C4C2×#12114yes—
731C2×C4C2×C22⋊Q818yes—
732C2×C4#53414yes—
733C2×C4#53614yes—
734C2×C4#53718yes—
735C2×C4#53718yes—
736C2×C4#53918yes—
737C22—24no—
738C22—24no—
739C22—28no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—24no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—81no—
753C22—81no—
754C22—82no—
755C22—81no—
756C22—82no—
757C22—81no—
758C22#241718yes—
759C22C22×#12111yescharacteristic
760C22C22×C22⋊Q811yescharacteristic
761C22C2×#53411yescharacteristic
762C22C2×#53611yescharacteristic
763C22C2×#53711yescharacteristic
764C22C2×#53712yes—
765C22C2×#53712yes—
766C22C2×#53912yes—
767C22C2×#54611yescharacteristic
768C22C2×D4×Q811yescharacteristic
769C22C2×#55211yescharacteristic
770C22C2×#55411yescharacteristic
771C22#348411yescharacteristic
772C22#348611yescharacteristic
773C22#349212yes—
774C22#350312yes—
775C22#350312yes—
776C22#350812yes—
777C22#350912yes—
778C22#354312yes—
779C22#354412yes—
780C22#355212yes—
781C22#355212yes—
782C4—28no—
783C4—28no—
784C4—24no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—44no—
789C4—84no—
790C4—81no—
791C4—82no—
792C4—82no—
793C4—84no—
794C4—81no—
795C4—82no—
796C4#261818yes—
797C2—28no—
798C2—82no—
799C2C2×#261811yescharacteristic
800C2C2×#241711yescharacteristic
801C2#3522311yescharacteristic
802C2#3528012yes—
803C2#3762012yes—
804C2#3946411yescharacteristic
805C2#3946511yescharacteristic
806C2#3947612yes—
807C2#3959211yescharacteristic
808C2#3959311yescharacteristic
809C2#3960412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2855C2semidirect
4. C22×#384C2semidirect
5. #16563C2semidirect
6. #16515C2semidirect
7. #15184C2semidirect
8. #15182C2semidirect
9. #15133C2semidirect
10. #15131C2semidirect
11. #14821C2semidirect
13. #14339C2semidirect
15. #14139C2semidirect
16. #13907C2semidirect
97. C2×#123Q8semidirect
530. C22×C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×#24172
C2×C4×#1232
C22×#3842
#165632
#165152
#151842
#151822
#151332
#151312
#148212
#147292
#143392
#142562
#141392
#139072
#138722