Finite Group Databasebeta

← #1016674

Subgroups — #1016674

Order 512.

3032 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17295C211yesmaximal, characteristic, complemented
2#17224C211yesmaximal, characteristic, complemented
3#16741C212yesmaximal, complemented
4#16741C212yesmaximal, complemented
5#16666C212yesmaximal, complemented
6#16217C211yesmaximal, characteristic, complemented
7#16217C212yesmaximal, complemented
8#15506C211yesmaximal, characteristic, complemented
9#15468C212yesmaximal, complemented
10#14926C211yesmaximal, characteristic
11#14873C212yesmaximal, complemented
12C22⋊#401C212yesmaximal, complemented
13#14596C212yesmaximal, complemented
14#14135C212yesmaximal, complemented
15#14023C212yesmaximal
16#13968C212yesmaximal, complemented
17#13958C211yesmaximal, characteristic, complemented
18#13894C212yesmaximal, complemented
19C2×#1446C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×#123C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2211yescharacteristic
25C2×#401C2212yes—
26C2×#393C2212yes—
27C2×#393C2212yes—
28C2×#393C2212yes—
29C2×#393C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#381C2212yes—
36C2×#381C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2212yes—
41#1446C2211yescharacteristic
42#1446C2212yes—
43#1446C2212yes—
44#1446C2211yescharacteristic
45#1446C2212yes—
46#1446C2211yescharacteristic
47#1446C2211yescharacteristic
48#1446C2212yes—
49#1446C2212yes—
50#1446C2212yes—
51#1445C2211yescharacteristic
52#1445C2212yes—
53#1445C2212yes—
54#1445C2211yescharacteristic
55#1445C2211yescharacteristic
56#1445C2211yescharacteristic
57#1444C2211yescharacteristic
58#1444C2211yescharacteristic
59#1443C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1438C2211yescharacteristic
82#1438C2212yes—
83#1438C2211yescharacteristic
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C23×Q8—24no—
108C23×Q8—42no—
109C23×Q8—44no—
110C23×Q8—44no—
111C23×Q8—42no—
112C23×Q8C2312yes—
113C23×Q8C2311yescharacteristic
114C23×Q8C2311yescharacteristic
115C23×D4C2312yes—
116C23×D4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2312yes—
119C24×C4C2311yescharacteristic
120C24×C4C2312yes—
121C24×C4C2311yescharacteristic
122C24×C4C2312yes—
123C2×#123—28no—
124C2×#123—28no—
125C2×#123—44no—
126C2×#121—28no—
127C2×#121—42no—
128C2×C4×D4—28no—
129C2×C4×D4—44no—
130C2×C4×D4—44no—
131C2×#117—24no—
132C2×#117—42no—
133C2×#117—42no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157#401—44no—
158#393—28no—
159#393—44no—
160#393—44no—
161#393—44no—
162#386—44no—
163#386—44no—
164#386—44no—
165#386—44no—
166#386—44no—
167#381—44no—
168#381—42no—
169C2×#95—42no—
170C2×#95—44no—
171C2×#95—42no—
172C2×#95—44no—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C25C2412yes—
227C25C2411yescharacteristic
228C22×Q8—24no—
229C22×Q8—22no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—41no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—41no—
237C22×Q8—42no—
238C22×Q8—42no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8—41no—
242C22×Q8—42no—
243C22×Q8—41no—
244C22×Q8—416no—
245C22×Q8—432no—
246C22×Q8—416no—
247C22×Q8—432no—
248C22×Q8—416no—
249C22×Q8#4114yes—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—41no—
259C22×D4—42no—
260C22×D4—41no—
261C22×D4#4118yes—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—41no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4#4114yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315#123—432no—
316#121—416no—
317C4×D4—432no—
318#117—416no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
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—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—22no—
398#95—24no—
399#95—24no—
400#95—41no—
401#95—42no—
402#95—42no—
403#95—41no—
404#95—41no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—41no—
410#95—41no—
411#95—41no—
412#95—42no—
413#95—41no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—41no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×#4114yes—
461C24C2×#4112yes—
462C24C2×#4114yes—
463C24H(5,𝔽2)12yes—
464C24H(5,𝔽2)12yes—
465C24H(5,𝔽2)14yes—
466C24C2511yescharacteristic
467C2×Q8—44no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—48no—
471C2×Q8—48no—
472C2×Q8—44no—
473C2×Q8—48no—
474C2×Q8—44no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—4128no—
480C2×Q8—44no—
481C2×Q8—48no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—48no—
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—216no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—82no—
495C2×D4—84no—
496C2×D4—82no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—82no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4C2×#4114yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4112yes—
636C22×C4H(5,𝔽2)14yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C42−1+412yes—
639C22×C42−1+414yes—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C42—48no—
662C42—48no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23#53814yes—
717C23#53818yes—
718C23#55118yes—
719C23#55114yes—
720C23#56014yes—
721C23C22×#4111yescharacteristic
722C23C22×#4112yes—
723C23C22×#4111yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)12yes—
727C23C2×H(5,𝔽2)12yes—
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×2−1+412yes—
730C23C2×2−1+411yescharacteristic
731C23#58511yescharacteristic
732Q8—416no—
733Q8—432no—
734Q8—416no—
735D4—432no—
736D4—88no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—432no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—416no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—88no—
848C2×C4—816no—
849C2×C4—816no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—28no—
857C22—28no—
858C22—28no—
859C22—28no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22#276018yes—
876C22C2×#53811yescharacteristic
877C22C2×#53812yes—
878C22C2×#55111yescharacteristic
879C22C2×#55112yes—
880C22#348011yescharacteristic
881C22#348212yes—
882C22#349011yescharacteristic
883C22#349012yes—
884C22#351112yes—
885C22#351111yescharacteristic
886C22#351412yes—
887C22#352012yes—
888C22#352012yes—
889C22#352211yescharacteristic
890C22C2×#56011yescharacteristic
891C22#353211yescharacteristic
892C22#353212yes—
893C22#353511yescharacteristic
894C22#353512yes—
895C22#353612yes—
896C22#354411yescharacteristic
897C22#354412yes—
898C22#355811yescharacteristic
899C4—44no—
900C4—42no—
901C4—42no—
902C4—44no—
903C4—42no—
904C4—44no—
905C4—42no—
906C4—42no—
907C4—44no—
908C4—82no—
909C4—82no—
910C4—81no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C2—28no—
917C2—84no—
918C2#3848611yescharacteristic
919C2#3859612yes—
920C2#4089312yes—
921C2#4202311yescharacteristic
922C2#4366711yescharacteristic
923C2#4397812yes—
924C2#4545711yescharacteristic
925C2C2×#276011yescharacteristic
926C2#5291311yescharacteristic
927C2#5988212yes—
928C2#5994111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17295C2semidirect
2. #17224C2semidirect
3. #16741C2semidirect
4. #16741C2semidirect
5. #16666C2semidirect
6. #16217C2semidirect
7. #16217C2semidirect
8. #15506C2semidirect
9. #15468C2semidirect
11. #14873C2semidirect
12. C22⋊#401C2semidirect
13. #14596C2semidirect
14. #14135C2semidirect
16. #13968C2semidirect
17. #13958C2semidirect
18. #13894C2semidirect
19. C2×#1446C2semidirect

Maximal subgroups

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

subgroupindex
#172952
#172242
#167412
#166662
#162172
#155062
#154682
#149262
#148732
C22⋊#4012
#145962
#141352
#140232
#139682
#139582
#138942
C2×#14462