Finite Group Databasebeta

← #615508

Subgroups — #615508

Order 512.

4622 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×#2848C211yesmaximal, characteristic
3C22×#380C211yesmaximal, characteristic
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5#15183C212yesmaximal, complemented
6#15179C212yesmaximal, complemented
7#14997C214yesmaximal, complemented
8#14935C212yesmaximal, complemented
9#14920C212yesmaximal, complemented
10#14702C211yesmaximal, characteristic, complemented
11#14697C211yesmaximal, characteristic, complemented
12#14685C211yesmaximal, characteristic, complemented
13#14139C212yesmaximal, complemented
14#14047C214yesmaximal, complemented
15#13907C212yesmaximal, complemented
16#13877C212yesmaximal
17#13869C212yesmaximal
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25C23×C22⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2855—28no—
29#2848—28no—
30C2×#391C2212yescomplemented
31C2×#391C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#389C2212yescomplemented
34C2×#387C2214yescomplemented
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#381C2212yes—
41C2×#381C2212yes—
42C2×#380—28no—
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2214yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#379C2212yes—
53C2×C4×C22⋊C4—28no—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2212yes—
61#1445C2214yescomplemented
62#1443C2214yescomplemented
63#1442C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1436C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78C4⋊#95C2212yescomplemented
79#1434C2214yescomplemented
80C22⋊#95C2214yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—28no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2314yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—44no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—28no—
114C22×C4⋊C4—44no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—28no—
130C22×C22⋊C4—28no—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—44no—
133C22×C22⋊C4Q818yescomplemented
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—44no—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156#391—28no—
157#391—44no—
158#389—28no—
159#389—44no—
160#387—216no—
161#385—28no—
162#385—28no—
163#385—28no—
164#385—28no—
165#385—44no—
166#381—28no—
167#381—44no—
168#380—24no—
169#380—24no—
170#380—24no—
171#380—24no—
172#380—28no—
173#380—28no—
174#380—216no—
175#380—28no—
176#380D418yes—
177#379—28no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—28no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—28no—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25—22no—
210C25—24no—
211C25—22no—
212C25—24no—
213C25—22no—
214C25—22no—
215C25—42no—
216C25—42no—
217C25C2×D414yes—
218C25C2×Q814yes—
219C25#4114yes—
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—24no—
227C22×Q8—24no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—232no—
247C23×C4—232no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—28no—
265C23×C4—28no—
266C23×C4—28no—
267C23×C4—28no—
268C23×C4—416no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—432no—
277C23×C4—432no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×Q814yes—
289C23×C4C2×Q814yes—
290C23×C4#4114yes—
291C23×C4#4118yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2414yes—
297C23×C4C2414yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308C22⋊Q8—416no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4C2×D418yes—
339C2×C22⋊C4—232no—
340C2×C22⋊C4—232no—
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—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—432no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4C2×D418yes—
374C2×C22⋊C4C2×Q818yes—
375C2×C22⋊C4C2×Q818yes—
376C2×C22⋊C4#4118yes—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—416no—
390C2×C42—416no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—28no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95C2×D418yes—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—216no—
429C24—216no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24—44no—
444C24—44no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24C22⋊Q8116yes—
456C24C22×D412yes—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C22×Q812yes—
461C24C22×Q812yes—
462C24C22×Q812yes—
463C24C2×#4112yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
466C24C2×#4112yes—
467C24C2×#4114yes—
468C24C2×#4114yes—
469C24H(5,𝔽2)12yes—
470C242−1+412yes—
471C24C2511yescharacteristic
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—48no—
476C2×Q8—48no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
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—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—4128no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—416no—
598C22×C4—88no—
599C22×C4—88no—
600C22×C4—88no—
601C22×C4#121116yes—
602C22×C4#123116yes—
603C22×C4C22×D412yes—
604C22×C4C22×D418yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×Q814yes—
611C22×C4C22×Q814yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4114yes—
618C22×C4H(5,𝔽2)14yes—
619C4⋊C4—216no—
620C4⋊C4—416no—
621C4⋊C4—416no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—88no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C42—48no—
644C42—48no—
645C42—48no—
646C42—48no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—232no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—232no—
687C23—24no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—416no—
698C23—416no—
699C23—416no—
700C23—432no—
701C23—432no—
702C23—432no—
703C23—432no—
704C23—416no—
705C23—416no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#12114yes—
715C23C2×C22⋊Q814yes—
716C23C2×C22⋊Q814yes—
717C23C2×C22⋊Q814yes—
718C23C2×#12314yes—
719C23#52514yes—
720C23#52918yes—
721C23#53318yes—
722C23#53714yes—
723C23#54614yes—
724C23D4×Q814yes—
725C23#55214yes—
726C23#55414yes—
727C23C23×D411yescharacteristic
728C23C23×D411yescharacteristic
729C23C23×Q811yescharacteristic
730C23C22×#4111yescharacteristic
731C23C22×#4111yescharacteristic
732C23C22×#4112yes—
733C23C22×#4112yes—
734C23C2×H(5,𝔽2)12yes—
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×2−1+411yescharacteristic
737C23#58512yes—
738Q8—88no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—232no—
748C2×C4—232no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—416no—
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—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—416no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—832no—
825C2×C4C2×#12114yes—
826C2×C4C2×#12114yes—
827C2×C4C2×#12314yes—
828C2×C4C2×#12314yes—
829C2×C4#53414yes—
830C2×C4#54618yes—
831C2×C4#55118yes—
832C22—24no—
833C22—24no—
834C22—28no—
835C22—28no—
836C22—24no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—28no—
842C22—28no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—464no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22#241718yes—
865C22#285518yescomplemented
866C22C22×#12111yescharacteristic
867C22C22×C22⋊Q811yescharacteristic
868C22C22×#12311yescharacteristic
869C22C2×#52511yescharacteristic
870C22C2×#52912yes—
871C22C2×#53312yes—
872C22C2×#53411yescharacteristic
873C22C2×#53711yescharacteristic
874C22#344911yescharacteristic
875C22C2×#54611yescharacteristic
876C22C2×#54612yes—
877C22C2×D4×Q811yescharacteristic
878C22D4×#4112yes—
879C22C2×#55112yes—
880C22C2×#55211yescharacteristic
881C22C2×#55411yescharacteristic
882C22#347512yes—
883C22#349412yes—
884C22#349512yes—
885C22#350112yes—
886C22#350512yes—
887C22#351912yes—
888C22#352012yes—
889C4—24no—
890C4—24no—
891C4—44no—
892C4—48no—
893C4—42no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—82no—
898C4—84no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4#241218yes—
903C2—28no—
904C2—28no—
905C2—44no—
906C2C2×#241211yescharacteristic
907C2C2×#241711yescharacteristic
908C2#3473711yescharacteristic
909C2#3501011yescharacteristic
910C2#3507711yescharacteristic
911C2#3526311yescharacteristic
912C2#3610712yes—
913C2#3613012yes—
914C2#3616712yes—
915C2#3619012yes—
916C2C2×#285511yescharacteristic
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×#2855C2semidirect
5. #15183C2semidirect
6. #15179C2semidirect
7. #14997C2semidirect
8. #14935C2semidirect
9. #14920C2semidirect
10. #14702C2semidirect
11. #14697C2semidirect
12. #14685C2semidirect
13. #14139C2semidirect
14. #14047C2semidirect
15. #13907C2semidirect
30. C2×#391C22semidirect
31. C2×#391C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
34. C2×#387C22semidirect
61. #1445C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. C4⋊#95C22semidirect
79. #1434C22semidirect
133. C22×C22⋊C4Q8semidirect
865. C22#2855semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×#28482
C22×#3802
C22×C4×C22⋊C42
#151832
#151792
#149972
#149352
#149202
#147022
#146972
#146852
#141392
#140472
#139072
#138772
#138692