Finite Group Databasebeta

← #2738884

Subgroups — #2738884

Order 512.

2646 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2488C212yesmaximal, complemented
2#17222C211yesmaximal, characteristic, complemented
3#17222C211yesmaximal, characteristic, complemented
4#17159C211yesmaximal, characteristic, complemented
5#17158C212yesmaximal, complemented
6#17153C212yesmaximal, complemented
7#17137C211yesmaximal, characteristic, complemented
8#17049C212yesmaximal, complemented
9#17029C212yesmaximal, complemented
10#16694C212yesmaximal, complemented
11#15069C212yesmaximal, complemented
12#14934C212yesmaximal, complemented
13#14927C212yesmaximal, complemented
14#14926C212yesmaximal
15#14913C211yesmaximal, characteristic
16#14759C212yesmaximal, complemented
17#14625C212yesmaximal, complemented
18#13966C211yesmaximal, characteristic, complemented
19C2×#1442C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#123C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×#121C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2488—216no—
26C2×#400C2212yes—
27C2×#400C2212yes—
28C2×#397C2212yes—
29C2×#393C2212yes—
30C2×#393C2212yes—
31C2×#391C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#382C2212yes—
39C2×#381C2212yes—
40C2×#381C2212yes—
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2212yes—
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2212yes—
47#1446C2212yes—
48#1446C2212yes—
49#1446C2212yes—
50#1444C2212yes—
51#1444C2212yes—
52#1444C2212yes—
53#1444C2212yes—
54#1444C2212yes—
55#1444C2212yes—
56#1442C2211yescharacteristic
57#1442C2212yes—
58#1442C2212yes—
59#1442C2211yescharacteristic
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2211yescharacteristic
64#1442C2212yes—
65#1442C2211yescharacteristic
66#1442C2211yescharacteristic
67#1442C2212yes—
68#1442C2211yescharacteristic
69#1442C2211yescharacteristic
70#1442C2212yes—
71#1442C2212yes—
72#1442C2211yescharacteristic
73#1442C2212yes—
74#1442C2211yescharacteristic
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2211yescharacteristic
79#1441C2212yes—
80#1441C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1440C2212yes—
84#1440C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2211yescharacteristic
99#1438C2212yes—
100#1438C2211yescharacteristic
101#1438C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C23×Q8C2312yes—
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C2×#123—28no—
117C2×#123—44no—
118C2×#123—44no—
119C2×#123—44no—
120C2×#123—44no—
121C2×#123—44no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—44no—
124C2×C22⋊Q8—44no—
125C2×#121—42no—
126C2×#121—44no—
127C22×C4⋊C4—42no—
128C22×C4⋊C4—44no—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2312yes—
159#400—28no—
160#400—28no—
161#397—28no—
162#393—28no—
163#393—28no—
164#391—28no—
165#388—28no—
166#388—28no—
167#386—28no—
168#386—28no—
169#386—44no—
170#386—44no—
171#382—28no—
172#381—28no—
173#381—44no—
174#380—42no—
175C4×C22⋊C4D418yescomplemented
176C2×#95—28no—
177C2×#95—24no—
178C2×#95—42no—
179C2×#95—44no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C25C2412yes—
230C25C2411yescharacteristic
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4—41no—
248C22×D4—41no—
249C22×D4—42no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—42no—
271C23×C4—41no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4C2×D414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296#123—432no—
297#123—432no—
298C22⋊Q8—432no—
299#121—416no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
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—42no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—41no—
335C2×C22⋊C4—24no—
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—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
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×C22⋊C4—42no—
382C2×C22⋊C4C2×D418yes—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42C2×D418yes—
386#95—24no—
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—24no—
398#95—24no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—41no—
406#95—41no—
407#95—41no—
408#95—41no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—42no—
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#95C2×D414yes—
433#95C2×D414yes—
434#95#4114yes—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C22×D412yes—
457C24H(5,𝔽2)14yes—
458C24H(5,𝔽2)14yes—
459C24H(5,𝔽2)12yes—
460C242−1+412yes—
461C24C2511yescharacteristic
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—84no—
465C2×Q8—84no—
466C2×Q8—84no—
467C2×Q8—84no—
468C2×Q8—84no—
469C2×D4—44no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—84no—
478C2×D4—82no—
479C2×D4—84no—
480C2×D4—82no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
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—22no—
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—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
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—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—84no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—84no—
605C22×C4—82no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D414yes—
612C22×C4C22×D414yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4114yes—
615C22×C42−1+412yes—
616C22×C42−1+412yes—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C22⋊C4—216no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C42—48no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
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—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
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#53518yes—
701C23#53714yes—
702C23H(3,𝔽4)14yes—
703C23H(3,𝔽4)14yes—
704C23#56218yes—
705C23C23×D411yescharacteristic
706C23C22×#4111yescharacteristic
707C23C2×H(5,𝔽2)12yes—
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×2−1+411yescharacteristic
711C23C2×2−1+411yescharacteristic
712C23C2×2−1+411yescharacteristic
713C23#58511yescharacteristic
714C23#58512yes—
715C23#58512yes—
716Q8—816no—
717D4—88no—
718D4—816no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
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—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
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—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
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—88no—
828C2×C4—88no—
829C2×C4—816no—
830C2×C4—816no—
831C22—28no—
832C22—24no—
833C22—24no—
834C22—28no—
835C22—28no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—28no—
840C22—24no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22#281918yes—
857C22C2×#53512yes—
858C22C2×#53711yescharacteristic
859C22D4×#4111yescharacteristic
860C22#348512yes—
861C22#349211yescharacteristic
862C22#349412yes—
863C22#349911yescharacteristic
864C22#351312yes—
865C22#352311yescharacteristic
866C22C2×H(3,𝔽4)11yescharacteristic
867C22C2×H(3,𝔽4)11yescharacteristic
868C22C2×#56212yes—
869C22#353311yescharacteristic
870C22#353512yes—
871C22#353511yescharacteristic
872C22#353512yes—
873C22#354512yes—
874C22#354511yescharacteristic
875C22#355912yes—
876C22#355912yes—
877C22#356012yes—
878C22#356311yescharacteristic
879C22#356412yes—
880C4—44no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—82no—
896C4—82no—
897C2—28no—
898C2—162no—
899C2C2×#281911yescharacteristic
900C2#3836212yes—
901C2#3842711yescharacteristic
902C2#4137512yes—
903C2#4140511yescharacteristic
904C2#4553911yescharacteristic
905C2#4558112yes—
906C2#4599111yescharacteristic
907C2#5275311yescharacteristic
908C2#5280012yes—
909C2#5292511yescharacteristic
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. C2×#2488C2semidirect
2. #17222C2semidirect
3. #17222C2semidirect
4. #17159C2semidirect
5. #17158C2semidirect
6. #17153C2semidirect
7. #17137C2semidirect
8. #17049C2semidirect
9. #17029C2semidirect
10. #16694C2semidirect
11. #15069C2semidirect
12. #14934C2semidirect
13. #14927C2semidirect
16. #14759C2semidirect
17. #14625C2semidirect
18. #13966C2semidirect
19. C2×#1442C2semidirect
175. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24882
#172222
#171592
#171582
#171532
#171372
#170492
#170292
#166942
#150692
#149342
#149272
#149262
#149132
#147592
#146252
#139662
C2×#14422