Finite Group Databasebeta

← #368751

Subgroups — #368751

Order 512.

2096 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#467C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3C2×#1892C211yesmaximal, characteristic
4C2×#1892C211yesmaximal, characteristic
5C2×#1878C211yesmaximal, characteristic, complemented
6C22×#336C211yesmaximal, characteristic
7#14702C211yesmaximal, characteristic
8#11219C211yesmaximal, characteristic, complemented
9#11190C211yesmaximal, characteristic, complemented
10#11067C211yesmaximal, characteristic, complemented
11#11024C211yesmaximal, characteristic, complemented
12#10932C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#467—24no—
24C2×#467—24no—
25C2×#467C418yescomplemented
26C22×#107C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C4×C22⋊Q8—24no—
34C4×C22⋊Q8—24no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#387—21no—
40C2×#385—21no—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C4⋊C4—21no—
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4—21no—
46#1892—24no—
47#1892—24no—
48#1878—24no—
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336—24no—
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1436—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C22⋊#95—21no—
67C22⋊#95—21no—
68C23×Q8C2311yescharacteristic
69C23×Q8C2311yescharacteristic
70C24×C4D411yescharacteristic
71C24×C4D411yescharacteristic
72C24×C4C2311yescharacteristic
73C22×Q16—22no—
74C22×Q16—22no—
75C22×Q16—22no—
76C22×Q16—22no—
77C22×Q16—41no—
78C22×Q16—41no—
79C22×Q16C2×C414yescomplemented
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—22no—
85C23×C8—22no—
86C23×C8—22no—
87C23×C8—22no—
88C23×C8—22no—
89C23×C8—41no—
90C23×C8—41no—
91C23×C8—41no—
92C23×C8—41no—
93C23×C8C2×C414yes—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—22no—
101C2×C22⋊Q8—22no—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8C2×C414yes—
107C2×C22⋊Q8C2×C414yes—
108C2×C22⋊Q8D414yes—
109C2×C22⋊Q8D414yes—
110C2×C4×Q8—22no—
111C2×C4×Q8—22no—
112C2×C4×Q8—22no—
113C2×C4×Q8—22no—
114C2×C4×Q8—41no—
115C2×C4×Q8—41no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
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×C42—22no—
131C22×C42—22no—
132C22×C42—21no—
133C22×C42—21no—
134C22×C42—22no—
135C22×C42—22no—
136C22×C42—41no—
137C22×C42—41no—
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142#467—232no—
143C2×#107—22no—
144C2×#107—22no—
145C2×#107C2×C414yescomplemented
146C2×#103—22no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#103—22no—
151C2×#103—22no—
152C2×#103—22no—
153C2×#103—22no—
154C2×#103—22no—
155C2×#103—22no—
156C2×#103—22no—
157C2×#103—22no—
158C2×#103—41no—
159C2×#103—41no—
160C2×#103—41no—
161C2×#103—41no—
162C2×#103C2×C414yescomplemented
163C2×#103C2×C414yescomplemented
164#391—22no—
165#391—22no—
166#391—22no—
167#391—22no—
168#391—41no—
169#391—41no—
170#389—22no—
171#389—22no—
172#387—28no—
173#385—28no—
174#380—22no—
175#380—22no—
176#380—22no—
177#380D414yes—
178C4×C4⋊C4—28no—
179C4×C4⋊C4—22no—
180C4×C4⋊C4—22no—
181C4×C22⋊C4—28no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196#340—22no—
197#340—22no—
198#340—22no—
199#340—22no—
200#340—22no—
201#340—22no—
202#340—41no—
203#340—41no—
204#336—22no—
205#336—22no—
206#336—22no—
207#336D414yes—
208C25C2×D411yescharacteristic
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×Q8—21no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8C22×C412yes—
234C22×Q8C22×C412yes—
235C22×Q8C2×D412yes—
236C22×Q8C2×D412yes—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4Q1614yescomplemented
267C23×C4C22×C412yes—
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4#4112yes—
277C23×C4#4112yes—
278C23×C4C2411yescharacteristic
279C2×Q16—28no—
280C2×Q16—28no—
281C2×Q16—44no—
282C2×Q16—44no—
283C2×Q16—44no—
284C2×Q16—44no—
285C2×Q16—44no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—28no—
291C22×C8—28no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—28no—
311C22×C8—44no—
312C22×C8—44no—
313C22×C8—44no—
314C22×C8—44no—
315C22×C8—44no—
316C22×C8—44no—
317C22×C8—44no—
318C22×C8—44no—
319C22×C8—44no—
320C22×C8—44no—
321C22×C8—44no—
322C22×C8C22×C412yes—
323C22×C8C22×C412yes—
324C22×C8C2×D412yes—
325C22×C8C2×D412yes—
326C22×C8#4112yes—
327C22×C8#4112yes—
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8C22⋊C4116yes—
336C4×Q8—44no—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—44no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D412yes—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
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×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—44no—
417C2×C42—44no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42C2×D412yes—
427C2×C42#4112yes—
428#107—28no—
429#103—28no—
430#103—28no—
431#103—44no—
432#103—44no—
433#103—44no—
434#103—44no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24C4×D412yes—
458C24#12012yes—
459C24#12112yes—
460C24C2×Q1612yes—
461C24#13512yes—
462C24#13712yes—
463C24#13712yes—
464C24C22×D411yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8—41no—
511C2×Q8—41no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8—41no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—41no—
519C2×Q8—41no—
520C2×Q8C2×C22⋊C414yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
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—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—28no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—44no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4C2×C22⋊C414yes—
642C22×C4C4×D414yes—
643C22×C4C4×D412yes—
644C22×C4#12012yes—
645C22×C4#12112yes—
646C22×C4#12114yes—
647C22×C4#12112yes—
648C22×C4#12112yes—
649C22×C4#12314yes—
650C22×C4C2×Q1612yes—
651C22×C4C2×Q1612yes—
652C22×C4#13512yes—
653C22×C4#13512yes—
654C22×C4C23×C411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C2×#4111yescharacteristic
660C22×C4C2×#4111yescharacteristic
661C22×C4C2×#4111yescharacteristic
662C22×C4C2×#4111yescharacteristic
663C22×C4C2×#4111yescharacteristic
664C22×C4H(5,𝔽2)11yescharacteristic
665C22×C4H(5,𝔽2)11yescharacteristic
666C22×C4H(5,𝔽2)11yescharacteristic
667C22×C42−1+411yescharacteristic
668Q16—416no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—416no—
685C2×C8—416no—
686C2×C8—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8C4×D414yes—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—216no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—41no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—41no—
716C4⋊C4—41no—
717C4⋊C4—48no—
718C4⋊C4—41no—
719C4⋊C4—41no—
720C4⋊C4—41no—
721C4⋊C4—41no—
722C4⋊C4—41no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4C2×C22⋊C414yes—
727C22⋊C4—216no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—84no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—44no—
736C42—44no—
737C42—48no—
738C42—48no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—41no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23#38614yes—
772C23C4×Q1614yes—
773C23#44114yes—
774C23#45114yes—
775C23#45214yes—
776C23#46214yes—
777C23#46414yes—
778C23C2×C4×D411yescharacteristic
779C23C2×#12011yescharacteristic
780C23C2×#12111yescharacteristic
781C23C2×#12111yescharacteristic
782C23#53211yescharacteristic
783C23#53411yescharacteristic
784C23#53711yescharacteristic
785C23C22×Q1611yescharacteristic
786C23C2×#13511yescharacteristic
787C23C2×#13511yescharacteristic
788C23C2×#13511yescharacteristic
789C23C2×#13711yescharacteristic
790C23C2×#13711yescharacteristic
791C23#57511yescharacteristic
792C23#57511yescharacteristic
793Q8—24no—
794Q8—24no—
795Q8—42no—
796Q8—42no—
797Q8—42no—
798Q8—42no—
799Q8—42no—
800Q8—42no—
801Q8—42no—
802Q8—42no—
803Q8—42no—
804Q8—42no—
805Q8—81no—
806Q8—81no—
807Q8—81no—
808Q8—81no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—416no—
841C2×C4—416no—
842C2×C4—42no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
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—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4#38614yes—
909C2×C4#46714yescomplemented
910C2×C4C22×C22⋊C411yescharacteristic
911C2×C4C2×C4×D411yescharacteristic
912C2×C4C2×C4×D411yescharacteristic
913C2×C4C4×#4111yescharacteristic
914C2×C4#51811yescharacteristic
915C2×C4#52011yescharacteristic
916C2×C4C2×#12111yescharacteristic
917C2×C4C2×#12311yescharacteristic
918C2×C4#52511yescharacteristic
919C2×C4#52911yescharacteristic
920C2×C4#53811yescharacteristic
921C2×C4#53911yescharacteristic
922C2×C4D4211yescharacteristic
923C2×C4D4211yescharacteristic
924C2×C4D4211yescharacteristic
925C2×C4#54611yescharacteristic
926C2×C4#54611yescharacteristic
927C2×C4#54611yescharacteristic
928C2×C4#54611yescharacteristic
929C2×C4#54611yescharacteristic
930C2×C4#54611yescharacteristic
931C2×C4#54711yescharacteristic
932C2×C4#54711yescharacteristic
933C2×C4#54711yescharacteristic
934C2×C4#54811yescharacteristic
935C2×C4#55311yescharacteristic
936C2×C4#55311yescharacteristic
937C2×C4#55311yescharacteristic
938C8—24no—
939C8—42no—
940C8—42no—
941C8—42no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22#187818yescomplemented
957C22C2×#38611yescharacteristic
958C22C4×#12111yescharacteristic
959C22#232511yescharacteristic
960C22#241011yescharacteristic
961C22#241611yescharacteristic
962C22#243011yescharacteristic
963C22#254311yescharacteristic
964C22C2×C4×Q1611yescharacteristic
965C22C4×#13511yescharacteristic
966C22C2×#44111yescharacteristic
967C22#294311yescharacteristic
968C22C2×#45111yescharacteristic
969C22C2×#45211yescharacteristic
970C22#300211yescharacteristic
971C22#300211yescharacteristic
972C22C2×#46211yescharacteristic
973C22C2×#46411yescharacteristic
974C22#303511yescharacteristic
975C22#303511yescharacteristic
976C22C2×#46711yescharacteristic
977C22#305011yescharacteristic
978C22#305611yescharacteristic
979C22#305611yescharacteristic
980C22#316811yescharacteristic
981C22#317011yescharacteristic
982C22#318111yescharacteristic
983C22#318111yescharacteristic
984C22#318911yescharacteristic
985C22#319011yescharacteristic
986C22#319011yescharacteristic
987C22#319111yescharacteristic
988C22#324811yescharacteristic
989C22#324811yescharacteristic
990C22#324911yescharacteristic
991C22#325011yescharacteristic
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—44no—
998C4—44no—
999C4—82no—
1000C4—82no—
1001C4—82no—
1002C4—82no—
1003C4—161no—
1004C4—161no—
1005C4D4×C22⋊C411yescharacteristic
1006C4#233911yescharacteristic
1007C4#236111yescharacteristic
1008C4#236411yescharacteristic
1009C4#242411yescharacteristic
1010C4#242511yescharacteristic
1011C4#244311yescharacteristic
1012C4#244411yescharacteristic
1013C2—28no—
1014C2#1402311yescharacteristic
1015C2C2×#187811yescharacteristic
1016C2#2092411yescharacteristic
1017C2C4×#46711yescharacteristic
1018C2#2152711yescharacteristic
1019C2#2218211yescharacteristic
1020C2#2218311yescharacteristic
1021C2#2438011yescharacteristic
1022C2#2438311yescharacteristic
1023C2#2475211yescharacteristic
1024C2#2475511yescharacteristic
1025C2#2549811yescharacteristic
1026C2#2549911yescharacteristic
1027C2#2857511yescharacteristic
1028C2#2857611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. C2×#1878C2semidirect
8. #11219C2semidirect
9. #11190C2semidirect
10. #11067C2semidirect
11. #11024C2semidirect
12. #10932C2semidirect
13. #10907C2semidirect
14. #10789C2semidirect
25. C2×#467C4semidirect
79. C22×Q16C2×C4semidirect
145. C2×#107C2×C4semidirect
162. C2×#103C2×C4semidirect
163. C2×#103C2×C4semidirect
266. C23×C4Q16semidirect
909. C2×C4#467semidirect
956. C22#1878semidirect

Maximal subgroups

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

subgroupindex
C22×#4672
C2×C4×C22⋊Q82
C2×#18922
C2×#18782
C22×#3362
#147022
#112192
#111902
#110672
#110242
#109322
#109072
#107892
#107212