Finite Group Databasebeta

← #3169990

Subgroups — #3169990

Order 512.

2478 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17223C212yesmaximal, complemented
2#16955C212yesmaximal, complemented
3#16660C211yesmaximal, characteristic, complemented
4#16299C212yesmaximal, complemented
5#16254C211yesmaximal, characteristic, complemented
6#16141C212yesmaximal, complemented
7#15538C212yesmaximal, complemented
8#15476C212yesmaximal, complemented
9#15476C212yesmaximal, complemented
10#15453C212yesmaximal, complemented
11#15368C212yesmaximal, complemented
12#15299C212yesmaximal, complemented
13#14811C211yesmaximal, characteristic
14#14759C212yesmaximal, complemented
15#14572C211yesmaximal, characteristic, complemented
16#14508C211yesmaximal, characteristic, complemented
17#14375C212yesmaximal, complemented
18#14344C211yesmaximal, characteristic, complemented
19#13968C211yesmaximal, characteristic, complemented
20C22×#123C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C4×D4C2211yescharacteristic
23C2×#395C2212yes—
24C2×#395C2212yes—
25C2×#394C2212yes—
26C2×#393C2212yes—
27C2×#393C2212yes—
28C2×#393C2212yes—
29C2×#392C2211yescharacteristic
30C2×#392C2212yes—
31C2×#392C2211yescharacteristic
32C2×#390C2212yes—
33C2×#390C2211yescharacteristic
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2211yescharacteristic
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#381C2211yescharacteristic
43C2×#381C2211yescharacteristic
44C2×#381C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2212yes—
47C22×#95C2211yescharacteristic
48#1446C2212yes—
49#1445C2212yes—
50#1445C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1443C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1441C2211yescharacteristic
63#1441C2211yescharacteristic
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1439C2211yescharacteristic
72#1439C2211yescharacteristic
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2211yescharacteristic
83#1439C2212yes—
84#1439C2212yes—
85#1439C2211yescharacteristic
86#1439C2212yes—
87#1438C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1434C2212yes—
97#1434C2211yescharacteristic
98#1434C2212yes—
99#1434C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C23×Q8C2312yes—
108C23×D4C2311yescharacteristic
109C23×D4C2312yes—
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C2×#123—24no—
118C2×#123—42no—
119C2×#123—42no—
120C2×C22⋊Q8—44no—
121C2×C22⋊Q8—44no—
122C2×C22⋊Q8—44no—
123C2×C4×D4—24no—
124C2×C4×D4—42no—
125C2×C4×D4—42no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊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⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160#395—44no—
161#395—44no—
162#394—44no—
163#393—44no—
164#393—44no—
165#393—44no—
166#392—24no—
167#392—42no—
168#392—44no—
169#390—42no—
170#390—44no—
171#386—28no—
172#386—44no—
173#386—42no—
174#386—44no—
175#386—44no—
176#386—44no—
177#386—44no—
178#386—44no—
179#381—24no—
180#381—44no—
181#381—42no—
182#380—42no—
183#380—44no—
184C2×#95—42no—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C25C2411yescharacteristic
229C25C2412yes—
230C25C2411yescharacteristic
231C22×Q8—24no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4—41no—
253C22×D4—41no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—41no—
261C22×D4—42no—
262C22×D4—41no—
263C22×D4—42no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—41no—
277C23×C4—42no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—41no—
292C23×C4—42no—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309#123—416no—
310C22⋊Q8—432no—
311C4×D4—416no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
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—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
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—41no—
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×C22⋊C4—41no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4#4114yes—
404C2×C22⋊C4#4114yes—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—41no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—22no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
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—41no—
436#95—41no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—41no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—21no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—22no—
474C24—21no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24C2×#4112yes—
487C24C2×#4112yes—
488C24H(5,𝔽2)12yes—
489C24H(5,𝔽2)12yes—
490C242−1+414yes—
491C24C2511yescharacteristic
492C2×Q8—48no—
493C2×Q8—84no—
494C2×Q8—84no—
495C2×Q8—84no—
496C2×Q8—84no—
497C2×Q8—84no—
498C2×Q8—84no—
499C2×D4—28no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—82no—
516C2×D4—84no—
517C2×D4—84no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4—84no—
521C2×D4—84no—
522C2×D4—84no—
523C2×D4—82no—
524C2×D4—84no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
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—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—48no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—82no—
636C22×C4—82no—
637C22×C4—82no—
638C22×C4—84no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—84no—
642C22×C4—82no—
643C22×C4—82no—
644C22×C4—82no—
645C22×C4—82no—
646C22×C4—82no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4—84no—
650C22×C4—82no—
651C22×C4C2×#4112yes—
652C22×C4C2×#4114yes—
653C22×C4C2×#4112yes—
654C22×C4H(5,𝔽2)12yes—
655C22×C4H(5,𝔽2)12yes—
656C22×C4H(5,𝔽2)14yes—
657C22×C4H(5,𝔽2)14yes—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—84no—
666C4⋊C4—82no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—84no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—82no—
682C22⋊C4—84no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C22⋊C4—84no—
688C22⋊C4—84no—
689C22⋊C4—84no—
690C42—44no—
691C42—84no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—41no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23#55514yes—
773C23C22×#4111yescharacteristic
774C23C22×#4111yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)11yescharacteristic
779C23C2×H(5,𝔽2)12yes—
780C23C2×H(5,𝔽2)12yes—
781C23C2×2−1+412yes—
782C23#58511yescharacteristic
783C23#58512yes—
784Q8—816no—
785D4—416no—
786D4—816no—
787D4—88no—
788D4—816no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
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—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—88no—
894C2×C4—88no—
895C2×C4—816no—
896C2×C4—88no—
897C2×C4—88no—
898C22—24no—
899C22—28no—
900C22—44no—
901C22—44no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—44no—
908C22—42no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—44no—
920C22—44no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—81no—
928C22—82no—
929C22—81no—
930C22—81no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—81no—
935C22#346011yescharacteristic
936C22C2×#55511yescharacteristic
937C22#349011yescharacteristic
938C22#349011yescharacteristic
939C22#349411yescharacteristic
940C22#351412yes—
941C22#351412yes—
942C22#352012yes—
943C22#352012yes—
944C22#353212yes—
945C22#353311yescharacteristic
946C22#353412yes—
947C22#353411yescharacteristic
948C22#353512yes—
949C22#353512yes—
950C22#353612yes—
951C22#353711yescharacteristic
952C22#353711yescharacteristic
953C22#353811yescharacteristic
954C22#354112yes—
955C22#354312yes—
956C22#354311yescharacteristic
957C22#355112yes—
958C4—44no—
959C4—44no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—44no—
964C4—42no—
965C4—82no—
966C4—82no—
967C4—82no—
968C4—81no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—82no—
974C2—44no—
975C2—84no—
976C2—82no—
977C2#3703511yescharacteristic
978C2#3794911yescharacteristic
979C2#4136511yescharacteristic
980C2#4364512yes—
981C2#4758912yes—
982C2#4866112yes—
983C2#4897111yescharacteristic
984C2#5162911yescharacteristic
985C2#5721311yescharacteristic
986C2#5759711yescharacteristic
987C2#5816612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14811C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17223C2semidirect
2. #16955C2semidirect
3. #16660C2semidirect
4. #16299C2semidirect
5. #16254C2semidirect
6. #16141C2semidirect
7. #15538C2semidirect
8. #15476C2semidirect
9. #15476C2semidirect
10. #15453C2semidirect
11. #15368C2semidirect
12. #15299C2semidirect
14. #14759C2semidirect
15. #14572C2semidirect
16. #14508C2semidirect
17. #14375C2semidirect
18. #14344C2semidirect
19. #13968C2semidirect

Maximal subgroups

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

subgroupindex
#172232
#169552
#166602
#162992
#162542
#161412
#155382
#154762
#154532
#153682
#152992
#148112
#147592
#145722
#145082
#143752
#143442
#139682