Finite Group Databasebeta

← #627982

Subgroups — #627982

Order 512.

4626 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic
4C22×#388C211yesmaximal, characteristic, complemented
5#15939C214yesmaximal, complemented
6#15880C214yesmaximal, complemented
7#15275C214yesmaximal, complemented
8#15272C214yesmaximal, complemented
9#14912C212yesmaximal, complemented
10#14911C212yesmaximal, complemented
11#14702C211yesmaximal, characteristic, complemented
12#14698C211yesmaximal, characteristic, complemented
13#14339C211yesmaximal, characteristic, complemented
14#14016C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16C2×#539—28no—
17C2×#539—28no—
18C2×#539—28no—
19C22×#126C2212yescomplemented
20C22×#125C2212yescomplemented
21C22×#123C2212yes—
22C22×#123C2212yescomplemented
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yescomplemented
25C22×#121C2211yescharacteristic
26C22×#120C2212yes—
27C22×C4×D4C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2626—28no—
34#2617—28no—
35C2×#399C2212yes—
36C2×#397C2212yes—
37C2×#396C2214yes—
38C2×#394C2214yes—
39C2×#393C2212yes—
40C2×#392C2212yes—
41C2×#391C2212yescomplemented
42C2×#390C2212yescomplemented
43C2×#388—28no—
44C2×#388C2214yes—
45C2×#388C2214yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2212yes—
51C2×#381C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#379C2212yes—
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57#1442C2214yescomplemented
58#1442C2214yescomplemented
59#1441C2214yescomplemented
60#1441C2214yescomplemented
61#1441C2214yescomplemented
62#1440C2214yescomplemented
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1438C2214yes—
69#1438C2214yes—
70#1438C2214yes—
71#1437C2214yes—
72#1437C2214yescomplemented
73#1436C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2214yescomplemented
81C26C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2314yes—
85C23×D4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93#539—2128no—
94C2×#126—28no—
95C2×#126—28no—
96C2×#126—28no—
97C2×#125—28no—
98C2×#125—28no—
99C2×#125—28no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—28no—
105C2×#123—28no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8D418yescomplemented
112C2×#121—24no—
113C2×#121—24no—
114C2×#121D418yes—
115C2×#120—28no—
116C2×#120—28no—
117C2×#120—44no—
118C2×C4×D4—28no—
119C2×C4×D4—28no—
120C2×C4×D4—28no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4D418yescomplemented
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—44no—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C42—24no—
161C22×C42—44no—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165#399—28no—
166#397—28no—
167#396—216no—
168#394—216no—
169#393—28no—
170#392—28no—
171#391—44no—
172#390—44no—
173#388—216no—
174#388—216no—
175#386—28no—
176#386—28no—
177#386—48no—
178#386—44no—
179#385—28no—
180#381—44no—
181#380—24no—
182#380—24no—
183#379—28no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
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—
212C25#4114yes—
213C25C2412yes—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8C2×D414yes—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—44no—
232C22×D4—42no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—42no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4C2×D418yes—
239C22×D4C2×D414yes—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4#4114yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289#126—264no—
290#125—264no—
291#123—264no—
292#123—264no—
293C22⋊Q8—264no—
294C22⋊Q8—232no—
295#121—232no—
296#120—432no—
297C4×D4—264no—
298C2×C4⋊C4—232no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4C2×D418yes—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C22⋊C4—232no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—416no—
373C2×C22⋊C4—416no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4C2×D418yes—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—416no—
396#95—28no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—28no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—24no—
426C24—24no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—28no—
438C24—28no—
439C24—48no—
440C24—48no—
441C24—44no—
442C24—48no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—48no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—84no—
452C24—84no—
453C24—84no—
454C24—84no—
455C24—84no—
456C24—84no—
457C24—84no—
458C24—84no—
459C24C22×D414yes—
460C24C22×D412yes—
461C24C22×D412yes—
462C24C22×D412yes—
463C24C2×#4114yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
466C24H(5,𝔽2)12yes—
467C242−1+412yes—
468C24C2511yescharacteristic
469C2×Q8—28no—
470C2×Q8—48no—
471C2×Q8—82no—
472C2×Q8—82no—
473C2×Q8—84no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—216no—
477C2×D4—28no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—82no—
486C2×D4—82no—
487C2×D4—84no—
488C2×D4—88no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—216no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—88no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—88no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4#120116yes—
589C22×C4C22×D414yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4114yes—
601C22×C4H(5,𝔽2)14yes—
602C4⋊C4—216no—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—28no—
608C4⋊C4—216no—
609C4⋊C4—28no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—88no—
613C22⋊C4—232no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—216no—
619C22⋊C4—416no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C42—216no—
631C42—48no—
632C42—48no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—28no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—416no—
660C23—416no—
661C23—416no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—816no—
699C23—816no—
700C23—88no—
701C23—88no—
702C23—88no—
703C23—88no—
704C23—816no—
705C23—816no—
706C23C2×#12014yes—
707C23#52514yes—
708C23#53714yes—
709C23#54614yes—
710C23#54714yes—
711C23#54814yes—
712C23#55014yes—
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C23×D411yescharacteristic
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+411yescharacteristic
721C23#58512yes—
722C23#58512yes—
723C23#58512yes—
724Q8—88no—
725D4—432no—
726D4—88no—
727D4—832no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—416no—
758C2×C4—416no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—88no—
803C2×C4—816no—
804C2×C4—88no—
805C2×C4C2×#12014yes—
806C2×C4C2×#12014yes—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—28no—
814C22—28no—
815C22—28no—
816C22—28no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—48no—
827C22—832no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—84no—
837C22—84no—
838C22—84no—
839C22—84no—
840C22#240718yes—
841C22C22×#12011yescharacteristic
842C22C2×#52511yescharacteristic
843C22C2×#53711yescharacteristic
844C22#345512yes—
845C22#345912yes—
846C22C2×#54611yescharacteristic
847C22C2×#54711yescharacteristic
848C22C2×#54811yescharacteristic
849C22C2×#55011yescharacteristic
850C22#348411yescharacteristic
851C22#348511yescharacteristic
852C22#348711yescharacteristic
853C22#348711yescharacteristic
854C22#349112yes—
855C22#349612yes—
856C22#349612yes—
857C22#350012yes—
858C22#350012yes—
859C22#350512yes—
860C22#353412yes—
861C22#353512yes—
862C22#356012yes—
863C22#356412yes—
864C4—24no—
865C4—24no—
866C4—44no—
867C4—44no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—44no—
873C4—82no—
874C4—84no—
875C4—84no—
876C2—28no—
877C2—84no—
878C2—84no—
879C2C2×#240711yescharacteristic
880C2#3498711yescharacteristic
881C2#3509411yescharacteristic
882C2#3534711yescharacteristic
883C2#3567611yescharacteristic
884C2#3672211yescharacteristic
885C2#3697111yescharacteristic
886C2#3937112yes—
887C2#3938012yes—
888C2#3941412yes—
889C2#3942212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2617C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#539C2semidirect
2. C2×#2626C2semidirect
4. C22×#388C2semidirect
5. #15939C2semidirect
6. #15880C2semidirect
7. #15275C2semidirect
8. #15272C2semidirect
9. #14912C2semidirect
10. #14911C2semidirect
11. #14702C2semidirect
12. #14698C2semidirect
13. #14339C2semidirect
14. #14016C2semidirect
15. #13967C2semidirect
19. C22×#126C22semidirect
20. C22×#125C22semidirect
22. C22×#123C22semidirect
24. C22×C22⋊Q8C22semidirect
41. C2×#391C22semidirect
42. C2×#390C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
72. #1437C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
80. C22⋊#95C22semidirect
111. C2×C22⋊Q8D4semidirect
123. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#26262
C2×#26172
C22×#3882
#159392
#158802
#152752
#152722
#149122
#149112
#147022
#146982
#143392
#140162
#139672