Finite Group Databasebeta

← #360565

Subgroups — #360565

Order 512.

2580 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#416C211yesmaximal, characteristic
2C2×#2339C211yesmaximal, characteristic
3C2×#1850C211yesmaximal, characteristic, complemented
4C2×#1804C211yesmaximal, characteristic, complemented
5C2×#1802C211yesmaximal, characteristic, complemented
6C2×#1788C211yesmaximal, characteristic
7#13879C211yesmaximal, characteristic, complemented
8#11077C211yesmaximal, characteristic, complemented
9#11077C211yesmaximal, characteristic, complemented
10#11052C211yesmaximal, characteristic, complemented
11#11050C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C2×#416—24no—
24C2×#416—24no—
25C2×#416—24no—
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35#2339—24no—
36#2339C418yescomplemented
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#386—21no—
40C2×#386—21no—
41C2×#384C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#381—21no—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47C22×#95—21no—
48#1850—24no—
49#1804—24no—
50#1802—24no—
51#1788—24no—
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1439—21no—
63#1439—21no—
64#1436—21no—
65#1436—21no—
66C4⋊#95C2211yescharacteristic
67C4⋊#95C2211yescharacteristic
68C22×#41—22no—
69C22×#41—22no—
70C22×#41—22no—
71C22×#41—22no—
72C22×#41—22no—
73C22×#41—22no—
74C22×#41—22no—
75C22×#41—41no—
76C22×#41—41no—
77C22×#41—41no—
78C22×#41—41no—
79C22×#41C2×C414yes—
80C22×#41D414yes—
81C22×#41Q814yes—
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4—21no—
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C23×C8—22no—
90C23×C8—22no—
91C23×C8—22no—
92C23×C8—22no—
93C23×C8—22no—
94C23×C8—41no—
95C23×C8—41no—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C2×C4×D4—22no—
101C2×C4×D4—22no—
102C2×C4×D4—22no—
103C2×C4×D4—22no—
104C2×C4×D4—22no—
105C2×C4×D4—22no—
106C2×C4×D4—41no—
107C2×C4×D4—41no—
108C2×C4×D4—41no—
109C2×C4×D4—41no—
110C2×C4×D4C2×C414yes—
111C2×C4×D4C2×C414yes—
112C2×#117—22no—
113C2×#117—22no—
114C2×#117—22no—
115C2×#117—22no—
116C2×#117—41no—
117C2×#117—41no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4D411yescharacteristic
132C22×C22⋊C4D411yescharacteristic
133C22×C42—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C2×C4⋊C8—22no—
137C2×C4⋊C8—22no—
138C2×C4⋊C8—22no—
139C2×C4⋊C8—22no—
140C2×C4⋊C8—41no—
141C2×C4⋊C8—41no—
142#416—232no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#103—22no—
151C2×#103—41no—
152C2×#103—41no—
153C2×#103—41no—
154C2×#103—41no—
155C2×#102—22no—
156C2×#102—22no—
157C2×#102—22no—
158C2×#102—22no—
159C2×#102—22no—
160C2×#102—22no—
161C2×#102—22no—
162C2×#102—22no—
163C2×#102—22no—
164C2×#102—22no—
165C2×#102D414yes—
166C2×#102D414yes—
167C2×C22⋊C8—22no—
168C2×C22⋊C8—22no—
169C2×C22⋊C8—22no—
170#391—22no—
171#391—22no—
172#391C2×C414yes—
173#391C2×C414yes—
174#386—28no—
175#386—28no—
176#384—22no—
177#384—41no—
178#382—22no—
179#382—41no—
180#381—28no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380C2×C414yes—
185C4×C22⋊C4C2×C414yes—
186C4×C22⋊C4D414yes—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—28no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95D411yescharacteristic
201C2×#95D411yescharacteristic
202#340—22no—
203#340—22no—
204#340—22no—
205#340—22no—
206#340—41no—
207#340—41no—
208#340—41no—
209#340—41no—
210#336—22no—
211#336—22no—
212C25—21no—
213C25C2×D411yescharacteristic
214C2×#41—28no—
215C2×#41—28no—
216C2×#41—28no—
217C2×#41—28no—
218C2×#41—28no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—28no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—44no—
230C2×#41—44no—
231C2×#41—44no—
232C2×#41—44no—
233C2×#41—44no—
234C2×#41—44no—
235C2×#41—44no—
236C2×#41—44no—
237C2×#41—44no—
238C2×#41—44no—
239C2×#41—44no—
240C2×#41—44no—
241C2×#41C4⋊C4116yescomplemented
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8C22×C412yes—
254C22×Q8C2×D412yes—
255C22×Q8C2×Q812yes—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4C22×C412yes—
271C22×D4C2×D412yes—
272C22×D4C2×D412yes—
273C22×D4C2×D412yes—
274C22×D4C2×Q812yes—
275C22×D4#4112yes—
276C22×D4#4112yes—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—81no—
310C23×C4—81no—
311C23×C4—81no—
312C23×C4—81no—
313C23×C4C22×C412yes—
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D412yes—
320C23×C4C2×D412yes—
321C23×C4C2×Q812yes—
322C23×C4#4112yes—
323C23×C4#4112yes—
324C23×C4C2411yescharacteristic
325C22×C8—28no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—44no—
353C22×C8—44no—
354C22×C8—44no—
355C22×C8—44no—
356C22×C8—44no—
357C22×C8—44no—
358C22×C8C2×D412yes—
359C22×C8C2×D412yes—
360C4×D4—28no—
361C4×D4—28no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—44no—
368#117—28no—
369#117—44no—
370#117—44no—
371#117—44no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—81no—
409C2×C4⋊C4—81no—
410C2×C4⋊C4C22×C412yes—
411C2×C4⋊C4C22×C412yes—
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D412yes—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—81no—
430C2×C22⋊C4—81no—
431C2×C22⋊C4—81no—
432C2×C22⋊C4—81no—
433C2×C22⋊C4C22⋊C414yes—
434C2×C22⋊C4C22⋊C414yes—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42—42no—
446C2×C42C22×C412yes—
447C2×C42C22×C412yes—
448C2×C42C2×D412yes—
449C2×C42C2×D412yes—
450C4⋊C8—44no—
451C4⋊C8—44no—
452#103—28no—
453#103—28no—
454#103—44no—
455#103—44no—
456#102—28no—
457#102—28no—
458#102—44no—
459#102—44no—
460C22⋊C8—44no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—81no—
472#95—81no—
473#95C22⋊C414yes—
474#95C22⋊C414yes—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—41no—
495C24—41no—
496C24—41no—
497C24—41no—
498C24—41no—
499C24—41no—
500C24—41no—
501C24—41no—
502C24C2×C22⋊C412yes—
503C24#12112yes—
504C24C22⋊Q812yes—
505C24C22×D411yescharacteristic
506#41—232no—
507#41—416no—
508#41—416no—
509#41—416no—
510#41—416no—
511#41—416no—
512#41—416no—
513#41—416no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8C2×C4⋊C414yes—
542C2×D4—216no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4C2×C4⋊C414yes—
571C2×D4C4×D414yes—
572C2×D4C4×D414yes—
573C2×D4#12014yes—
574C2×D4C22⋊Q814yes—
575C2×D4C22⋊Q814yes—
576C2×D4#12314yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
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—22no—
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—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—216no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—48no—
643C22×C4—48no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—48no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—84no—
688C22×C4—84no—
689C22×C4—84no—
690C22×C4—84no—
691C22×C4—84no—
692C22×C4—84no—
693C22×C4—84no—
694C22×C4—84no—
695C22×C4—84no—
696C22×C4—84no—
697C22×C4C2×C22⋊C412yes—
698C22×C4C2×C22⋊C412yes—
699C22×C4C2×C22⋊C412yes—
700C22×C4C2×C22⋊C412yes—
701C22×C4C2×C22⋊C412yes—
702C22×C4C2×C4⋊C414yes—
703C22×C4#11714yes—
704C22×C4#12114yes—
705C22×C4#12112yes—
706C22×C4C22⋊Q814yes—
707C22×C4C22⋊Q812yes—
708C22×C4#13512yes—
709C22×C4#13512yes—
710C22×C4C23×C411yescharacteristic
711C22×C4C22×D411yescharacteristic
712C22×C4C22×D411yescharacteristic
713C22×C4C22×D411yescharacteristic
714C22×C4C22×D411yescharacteristic
715C22×C4C22×Q811yescharacteristic
716C22×C4C2×#4111yescharacteristic
717C22×C4C2×#4111yescharacteristic
718C22×C4C2×#4111yescharacteristic
719C22×C4C2×#4111yescharacteristic
720C22×C4H(5,𝔽2)11yescharacteristic
721C22×C4H(5,𝔽2)11yescharacteristic
722C22×C4H(5,𝔽2)11yescharacteristic
723C22×C4H(5,𝔽2)11yescharacteristic
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—22no—
730C2×C8—416no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—41no—
734C2×C8—41no—
735C2×C8—41no—
736C2×C8—41no—
737C2×C8—41no—
738C2×C8—41no—
739C2×C8—41no—
740C2×C8—41no—
741C2×C8—41no—
742C2×C8—41no—
743C2×C8—41no—
744C2×C8—41no—
745C2×C8—41no—
746C2×C8—41no—
747C2×C8—41no—
748C2×C8—41no—
749C2×C8—41no—
750C2×C8—41no—
751C2×C8—41no—
752C2×C8—41no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—41no—
762C4⋊C4—41no—
763C4⋊C4—41no—
764C4⋊C4—41no—
765C4⋊C4—41no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4—41no—
770C4⋊C4—41no—
771C4⋊C4—41no—
772C4⋊C4—41no—
773C4⋊C4—41no—
774C4⋊C4—41no—
775C4⋊C4—41no—
776C4⋊C4—41no—
777C4⋊C4—84no—
778C4⋊C4—84no—
779C22⋊C4—28no—
780C22⋊C4—44no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—84no—
785C22⋊C4—84no—
786C42—22no—
787C42—22no—
788C42—22no—
789C42—22no—
790C42—22no—
791C42—22no—
792C42—22no—
793C42—22no—
794C42—48no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—22no—
810C23—24no—
811C23—22no—
812C23—22no—
813C23—24no—
814C23—24no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—22no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—42no—
832C23—42no—
833C23—41no—
834C23—41no—
835C23—42no—
836C23—42no—
837C23—41no—
838C23—42no—
839C23—41no—
840C23—41no—
841C23—42no—
842C23—41no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—41no—
848C23—42no—
849C23—41no—
850C23—42no—
851C23—42no—
852C23—41no—
853C23—42no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—41no—
860C23—41no—
861C23—42no—
862C23—42no—
863C23—41no—
864C23#38014yes—
865C23C22×C22⋊C411yescharacteristic
866C23C2×#12111yescharacteristic
867C23C2×C22⋊Q811yescharacteristic
868C23D4211yescharacteristic
869C23D4211yescharacteristic
870C23#54611yescharacteristic
871C23#54611yescharacteristic
872C23C2×#13511yescharacteristic
873C23C2×#13511yescharacteristic
874C23#57511yescharacteristic
875C23#57511yescharacteristic
876C23#57611yescharacteristic
877C23#57711yescharacteristic
878C23#57711yescharacteristic
879C23#57811yescharacteristic
880Q8—24no—
881Q8—24no—
882Q8—42no—
883Q8—42no—
884Q8—42no—
885Q8—42no—
886Q8—42no—
887Q8—42no—
888D4—24no—
889D4—24no—
890D4—24no—
891D4—24no—
892D4—24no—
893D4—24no—
894D4—24no—
895D4—432no—
896D4#38518yes—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—432no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—816no—
959C2×C4—816no—
960C2×C4—81no—
961C2×C4—81no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4—81no—
973C2×C4—81no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—81no—
982C2×C4—81no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4#38014yes—
991C2×C4#41614yescomplemented
992C2×C4C22×C4⋊C411yescharacteristic
993C2×C4C2×#11711yescharacteristic
994C2×C4C2×C4×D411yescharacteristic
995C2×C4C2×C4×D411yescharacteristic
996C2×C4#51811yescharacteristic
997C2×C4#51811yescharacteristic
998C2×C4C2×#12011yescharacteristic
999C2×C4C2×#12111yescharacteristic
1000C2×C4C2×C22⋊Q811yescharacteristic
1001C2×C4C2×C22⋊Q811yescharacteristic
1002C2×C4C2×C22⋊Q811yescharacteristic
1003C2×C4C2×#12311yescharacteristic
1004C2×C4#53411yescharacteristic
1005C2×C4#53411yescharacteristic
1006C2×C4#54311yescharacteristic
1007C2×C4#54311yescharacteristic
1008C2×C4D4211yescharacteristic
1009C2×C4D4211yescharacteristic
1010C2×C4#54611yescharacteristic
1011C2×C4#54611yescharacteristic
1012C2×C4#54611yescharacteristic
1013C2×C4#54611yescharacteristic
1014C2×C4#54611yescharacteristic
1015C2×C4#54611yescharacteristic
1016C2×C4#55111yescharacteristic
1017C2×C4#55111yescharacteristic
1018C2×C4#55111yescharacteristic
1019C2×C4#55111yescharacteristic
1020C8—42no—
1021C8—42no—
1022C8—81no—
1023C8—81no—
1024C22—24no—
1025C22—28no—
1026C22—24no—
1027C22—24no—
1028C22—42no—
1029C22—44no—
1030C22—42no—
1031C22—44no—
1032C22—42no—
1033C22—44no—
1034C22—42no—
1035C22—44no—
1036C22—42no—
1037C22—44no—
1038C22—42no—
1039C22—44no—
1040C22—44no—
1041C22—42no—
1042C22—42no—
1043C22—44no—
1044C22—42no—
1045C22—44no—
1046C22—44no—
1047C22—42no—
1048C22—44no—
1049C22—44no—
1050C22—42no—
1051C22—44no—
1052C22—42no—
1053C22—44no—
1054C22C2×#38011yescharacteristic
1055C22D4×C22⋊C411yescharacteristic
1056C22D4×C22⋊C411yescharacteristic
1057C22#241011yescharacteristic
1058C22#241211yescharacteristic
1059C22#243711yescharacteristic
1060C22#243711yescharacteristic
1061C22C2×#41611yescharacteristic
1062C22#289611yescharacteristic
1063C22#289711yescharacteristic
1064C22#289811yescharacteristic
1065C22#303511yescharacteristic
1066C22#303511yescharacteristic
1067C22#304511yescharacteristic
1068C22#304611yescharacteristic
1069C22#307611yescharacteristic
1070C22#307611yescharacteristic
1071C22#308311yescharacteristic
1072C22#308411yescharacteristic
1073C22#326711yescharacteristic
1074C22#326711yescharacteristic
1075C22#326811yescharacteristic
1076C22#326911yescharacteristic
1077C22#328011yescharacteristic
1078C22#328211yescharacteristic
1079C22#328311yescharacteristic
1080C22#328411yescharacteristic
1081C22#329611yescharacteristic
1082C22#329711yescharacteristic
1083C22#330211yescharacteristic
1084C22#330311yescharacteristic
1085C22#330711yescharacteristic
1086C22#331111yescharacteristic
1087C22#331511yescharacteristic
1088C22#331911yescharacteristic
1089C4—24no—
1090C4—24no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—82no—
1096C4—82no—
1097C4—82no—
1098C4—82no—
1099C4—161no—
1100C4—161no—
1101C4C2×#38511yescharacteristic
1102C4#231511yescharacteristic
1103C4#234211yescharacteristic
1104C4#234211yescharacteristic
1105C4#241011yescharacteristic
1106C4#241211yescharacteristic
1107C4#243711yescharacteristic
1108C4#243711yescharacteristic
1109C2—44no—
1110C2—48no—
1111C2#1387711yescharacteristic
1112C2#2064511yescharacteristic
1113C2#2065211yescharacteristic
1114C2#2241411yescharacteristic
1115C2#2241711yescharacteristic
1116C2#2242011yescharacteristic
1117C2#2242411yescharacteristic
1118C2#2436411yescharacteristic
1119C2#2436511yescharacteristic
1120C2#2453611yescharacteristic
1121C2#2453711yescharacteristic
1122C2#2595411yescharacteristic
1123C2#2595611yescharacteristic
1124C2#2596211yescharacteristic
1125C2#2596411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1850C2semidirect
4. C2×#1804C2semidirect
5. C2×#1802C2semidirect
7. #13879C2semidirect
8. #11077C2semidirect
9. #11077C2semidirect
10. #11052C2semidirect
11. #11050C2semidirect
12. #10788C2semidirect
13. #10788C2semidirect
14. #10731C2semidirect
15. #10721C2semidirect
36. #2339C4semidirect
241. C2×#41C4⋊C4semidirect
991. C2×C4#416semidirect

Maximal subgroups

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

subgroupindex
C22×#4162
C2×#23392
C2×#18502
C2×#18042
C2×#18022
C2×#17882
#138792
#110772
#110522
#110502
#107882
#107312
#107212