Finite Group Databasebeta

← #641847

Subgroups — #641847

Order 512.

3310 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2627C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic
3C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic
5#16901C212yesmaximal, complemented
6#16899C212yesmaximal, complemented
7#16515C214yesmaximal, complemented
8#15103C212yesmaximal, complemented
9#15093C214yesmaximal, complemented
10#14935C212yesmaximal, complemented
11#14877C212yesmaximal, complemented
12#14726C212yesmaximal
13#14686C211yesmaximal, characteristic, complemented
14#14339C211yesmaximal, characteristic, complemented
15#14338C211yesmaximal, characteristic
16#14149C212yesmaximal, complemented
17#13903C212yesmaximal
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic, complemented
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2627—28no—
26#2626—28no—
27C2×#400C2212yescomplemented
28C2×#399C2212yes—
29C2×#398C2214yescomplemented
30C2×#396C2214yes—
31C2×#396C2214yes—
32C2×#395C2212yescomplemented
33C2×#393C2212yes—
34C4×C22⋊Q8—28no—
35C2×#391C2211yescharacteristic, complemented
36C2×#389C2211yescharacteristic, complemented
37C2×#388—28no—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yescomplemented
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#384C2212yescomplemented
47C2×#381C2212yes—
48C2×#381C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×C4×C4⋊C4C2212yescomplemented
57C2×C4×C4⋊C4C2211yescharacteristic, complemented
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1443C2214yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1441C2214yescomplemented
70#1439C2212yes—
71#1439C2212yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1437C2214yes—
79#1437C2214yes—
80#1436C2214yescomplemented
81#1436C2214yescomplemented
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C4⋊#95C2212yescomplemented
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8D418yes—
98C2×C4×Q8—24no—
99C2×C4×Q8—44no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—44no—
124C22×C22⋊C4Q818yescomplemented
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C42—44no—
140C22×C42D418yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#400—28no—
148#399—28no—
149#398—216no—
150#396—216no—
151#396—48no—
152#395—28no—
153#393—28no—
154#391—24no—
155#389—24no—
156#388—28no—
157#388—28no—
158#388—28no—
159#388—28no—
160#387—28no—
161#385—28no—
162#385—28no—
163#385—28no—
164#384—44no—
165#381—28no—
166#381—44no—
167#380—24no—
168#380—24no—
169#380—24no—
170#380—28no—
171#380—44no—
172#379—28no—
173#379—44no—
174C4×C4⋊C4—28no—
175C4×C4⋊C4—24no—
176C4×C22⋊C4—28no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—42no—
209C25—42no—
210C25—42no—
211C25—42no—
212C25C2×Q814yes—
213C25C2412yes—
214C25C2411yescharacteristic
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—42no—
218C22×Q8—42no—
219C22×Q8C2×D414yes—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4C2×D414yes—
245C23×C4C2×D414yes—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×Q814yes—
249C23×C4C2×Q814yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4C2414yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C22⋊Q8—232no—
268C4×Q8—416no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—416no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4C2×D418yes—
307C2×C4⋊C4C2×D414yes—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—232no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—416no—
337C2×C22⋊C4—416no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D418yes—
349C2×C22⋊C4C2×Q818yes—
350C2×C22⋊C4C2×Q818yes—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—416no—
356C2×C42—44no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—44no—
360C2×C42C2×D414yes—
361C2×C42C2×D414yes—
362C2×C42C2×D414yes—
363C2×C42C2×D414yes—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—28no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—28no—
403C24—28no—
404C24—48no—
405C24—48no—
406C24—44no—
407C24—44no—
408C24—44no—
409C24—44no—
410C24—48no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—44no—
416C24—84no—
417C24—84no—
418C24—84no—
419C24—84no—
420C24—84no—
421C24—84no—
422C24—84no—
423C24—84no—
424C24C22×D412yes—
425C24C22×D412yes—
426C24C22×Q814yes—
427C24C22×Q812yes—
428C24C2×#4112yes—
429C24C2×#4112yes—
430C24H(5,𝔽2)12yes—
431C242−1+412yes—
432C24C2511yescharacteristic
433C2×Q8—28no—
434C2×Q8—48no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—48no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4#121116yes—
532C22×C4C22⋊Q8116yes—
533C22×C4C22×D412yes—
534C22×C4C22×D414yes—
535C22×C4C22×D414yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×Q814yes—
544C22×C4C22×Q812yes—
545C22×C4C22×Q812yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4C2×#4112yes—
550C22×C4H(5,𝔽2)14yes—
551C4⋊C4—28no—
552C4⋊C4—216no—
553C4⋊C4—44no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—84no—
560C4⋊C4—84no—
561C4⋊C4—88no—
562C4⋊C4—88no—
563C4⋊C4—88no—
564C4⋊C4—88no—
565C22⋊C4—216no—
566C22⋊C4—216no—
567C22⋊C4—216no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C42—28no—
580C42—28no—
581C42—44no—
582C42—44no—
583C42—48no—
584C42—48no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—28no—
603C23—24no—
604C23—24no—
605C23—28no—
606C23—416no—
607C23—416no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—416no—
626C23—44no—
627C23—816no—
628C23—816no—
629C23—88no—
630C23—816no—
631C23—88no—
632C23—88no—
633C23—816no—
634C23—88no—
635C23C2×#12114yes—
636C23C2×C22⋊Q814yes—
637C23#53714yes—
638C23D4×Q814yes—
639C23#55014yes—
640C23#55414yes—
641C23#55614yes—
642C23C23×D411yescharacteristic
643C23C23×D411yescharacteristic
644C23C23×Q811yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C2×H(5,𝔽2)12yes—
648C23C2×H(5,𝔽2)11yescharacteristic
649C23C2×2−1+411yescharacteristic
650C23#58512yes—
651C23#58512yes—
652C23#58512yes—
653Q8—416no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—416no—
685C2×C4—416no—
686C2×C4—416no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—88no—
735C2×C4—88no—
736C2×C4C2×#12114yes—
737C2×C4C2×#12114yes—
738C2×C4C2×C22⋊Q814yes—
739C2×C4C2×C22⋊Q814yes—
740C2×C4#53414yes—
741C22—28no—
742C22—24no—
743C22—24no—
744C22—28no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—28no—
749C22—28no—
750C22—24no—
751C22—48no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—48no—
756C22—832no—
757C22—82no—
758C22—84no—
759C22—82no—
760C22—82no—
761C22—84no—
762C22—82no—
763C22#253818yes—
764C22C22×#12111yescharacteristic
765C22C22×C22⋊Q811yescharacteristic
766C22C2×#53411yescharacteristic
767C22C2×#53711yescharacteristic
768C22#344911yescharacteristic
769C22#344911yescharacteristic
770C22#344911yescharacteristic
771C22#345512yes—
772C22#345812yes—
773C22C2×D4×Q811yescharacteristic
774C22C2×#55011yescharacteristic
775C22C2×#55411yescharacteristic
776C22C2×#55611yescharacteristic
777C22#349612yes—
778C22#350012yes—
779C22#350112yes—
780C22#350512yes—
781C22#350512yes—
782C22#351012yes—
783C22#353412yes—
784C22#353512yes—
785C22#356012yes—
786C22#356412yes—
787C4—24no—
788C4—24no—
789C4—24no—
790C4—24no—
791C4—24no—
792C4—42no—
793C4—44no—
794C4—44no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—84no—
800C4—84no—
801C4—82no—
802C2—28no—
803C2—84no—
804C2#3463411yescharacteristic
805C2C2×#253811yescharacteristic
806C2#3500011yescharacteristic
807C2#3501011yescharacteristic
808C2#3532711yescharacteristic
809C2#3745211yescharacteristic
810C2#3753811yescharacteristic
811C2#3936412yes—
812C2#3938012yes—
813C2#3949212yes—
814C2#3950812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2627C2semidirect
3. C2×C4×C22⋊Q8C2semidirect
5. #16901C2semidirect
6. #16899C2semidirect
7. #16515C2semidirect
8. #15103C2semidirect
9. #15093C2semidirect
10. #14935C2semidirect
11. #14877C2semidirect
13. #14686C2semidirect
14. #14339C2semidirect
16. #14149C2semidirect
19. C22×C4×Q8C22semidirect
27. C2×#400C22semidirect
29. C2×#398C22semidirect
32. C2×#395C22semidirect
35. C2×#391C22semidirect
36. C2×#389C22semidirect
42. C2×#387C22semidirect
46. C2×#384C22semidirect
56. C2×C4×C4⋊C4C22semidirect
57. C2×C4×C4⋊C4C22semidirect
61. #1443C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
80. #1436C22semidirect
81. #1436C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
84. C4⋊#95C22semidirect
124. C22×C22⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#26272
C2×#26262
C2×C4×C22⋊Q82
C22×#3882
#169012
#168992
#165152
#151032
#150932
#149352
#148772
#147262
#146862
#143392
#143382
#141492
#139032