Finite Group Databasebeta

← #368060

Subgroups — #368060

Order 512.

1940 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#427C211yesmaximal, characteristic, complemented
2C2×#2354C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic
4C2×#1854C211yesmaximal, characteristic, complemented
5C2×#1854C211yesmaximal, characteristic, complemented
6C2×#1854C211yesmaximal, characteristic, complemented
7#13871C211yesmaximal, characteristic
8#11324C211yesmaximal, characteristic, complemented
9#11323C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#427—24no—
22C2×#427—24no—
23C2×#427—24no—
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×#106C2211yescharacteristic
29C22×#106C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33#2354—24no—
34#2354—24no—
35C2×#390—21no—
36C2×#388—21no—
37C2×#388—21no—
38C2×#384C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4—21no—
45C2×C4×C4⋊C4C2211yescharacteristic
46#1869C418yescomplemented
47#1854—24no—
48#1854—24no—
49#1854—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62#1440—21no—
63#1438—21no—
64#1437—21no—
65#1436—21no—
66C4⋊#95C2211yescharacteristic
67C4⋊#95C2211yescharacteristic
68C23×D4D411yescharacteristic
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8C2×C414yes—
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4C2×C414yes—
87C2×C4×D4Q814yes—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—41no—
100C2×#117—41no—
101C2×#117—41no—
102C2×#117—41no—
103C2×#117—41no—
104C2×#117—41no—
105C2×#117D414yes—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4D411yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4D411yescharacteristic
126C22×C22⋊C4D411yescharacteristic
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42—21no—
131C22×C42C2311yescharacteristic
132#427—232no—
133C2×#107—22no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107—22no—
137C2×#107—22no—
138C2×#107—22no—
139C2×#107—22no—
140C2×#107—41no—
141C2×#107D414yescomplemented
142C2×#106—22no—
143C2×#106—22no—
144C2×#106—22no—
145C2×#106—22no—
146C2×#106—22no—
147C2×#106—22no—
148C2×#106—22no—
149C2×#106—41no—
150C2×#106D414yescomplemented
151C2×C22⋊C8—22no—
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8C2×C414yes—
158C2×C22⋊C8C2×C414yes—
159C2×C22⋊C8C2×C414yes—
160#390—28no—
161#388—28no—
162#388—28no—
163#384—22no—
164#384—22no—
165#380—22no—
166#380—22no—
167#380—22no—
168#380—22no—
169#380—22no—
170#380—22no—
171#380—22no—
172#380—41no—
173#380—41no—
174#380D414yes—
175C4×C4⋊C4—28no—
176C4×C4⋊C4—22no—
177C4×C4⋊C4—22no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188#340—22no—
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—41no—
197#340—41no—
198#336C2×C414yes—
199#336C2×C414yes—
200C25C2×D411yescharacteristic
201C25C2×D411yescharacteristic
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4C4⋊C414yes—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4C22×C412yes—
238C23×C4C22×C412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×Q812yes—
246C23×C4C2×Q812yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4C2411yescharacteristic
250C22×C8—28no—
251C22×C8—28no—
252C22×C8—28no—
253C22×C8—28no—
254C22×C8—28no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—28no—
264C22×C8—28no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C22×C412yes—
280C22×C8C22×C412yes—
281C22×C8C2×D412yes—
282C22×C8C2×D412yes—
283C22×C8#4112yes—
284C22×C8#4112yes—
285C4×D4—28no—
286C4×D4—28no—
287C4×D4—28no—
288C4×D4—28no—
289#117—28no—
290#117—28no—
291#117—44no—
292#117—44no—
293#117—44no—
294#117—44no—
295#117—44no—
296#117—44no—
297#117—44no—
298#117—44no—
299#117—44no—
300#117—44no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—81no—
348C2×C4⋊C4—81no—
349C2×C4⋊C4C4⋊C414yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4C2×D412yes—
354C2×C4⋊C4C2×D412yes—
355C2×C4⋊C4C2×D412yes—
356C2×C4⋊C4C2×D412yes—
357C2×C4⋊C4C2×D412yes—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
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—81no—
379C2×C22⋊C4—81no—
380C2×C22⋊C4—81no—
381C2×C22⋊C4—81no—
382C2×C22⋊C4—81no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4C4⋊C414yes—
387C2×C22⋊C4C4⋊C414yes—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42C22×C412yes—
405C2×C42C2×Q812yes—
406#107—28no—
407#107—28no—
408#107—44no—
409#106—28no—
410#106—28no—
411#106—44no—
412C22⋊C8—28no—
413C22⋊C8—28no—
414C22⋊C8—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—81no—
424#95—81no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24C2×C4⋊C412yes—
452C24C2×C4⋊C412yes—
453C24#12012yes—
454C24#12312yes—
455C24C22×D411yescharacteristic
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
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—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4C2×C4⋊C412yes—
592C22×C4C2×C4⋊C412yes—
593C22×C4C2×C4⋊C412yes—
594C22×C4C2×C4⋊C412yes—
595C22×C4C4×D414yes—
596C22×C4C4×D414yes—
597C22×C4#12012yes—
598C22×C4C22⋊Q814yes—
599C22×C4C22⋊Q814yes—
600C22×C4#12312yes—
601C22×C4#13512yes—
602C22×C4#13512yes—
603C22×C4C23×C411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×Q811yescharacteristic
609C22×C4C2×#4111yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4H(5,𝔽2)11yescharacteristic
614C22×C4H(5,𝔽2)11yescharacteristic
615C22×C42−1+411yescharacteristic
616C22×C42−1+411yescharacteristic
617C2×C8—232no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8C4×D414yes—
645C2×C8C4×D414yes—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—28no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—48no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—84no—
680C4⋊C4#12014yes—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—84no—
687C22⋊C4—84no—
688C22⋊C4—84no—
689C22⋊C4—84no—
690C22⋊C4—84no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—48no—
696C42—48no—
697C42—48no—
698C42—48no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23#38514yes—
769C23C22×C4⋊C411yescharacteristic
770C23C2×#12011yescharacteristic
771C23C2×#12311yescharacteristic
772C23D4211yescharacteristic
773C23D4211yescharacteristic
774C23#54711yescharacteristic
775C23#54711yescharacteristic
776C23C2×#13511yescharacteristic
777C23C2×#13511yescharacteristic
778C23#57511yescharacteristic
779C23#57511yescharacteristic
780C23#57611yescharacteristic
781C23#57711yescharacteristic
782C23#57711yescharacteristic
783C23#57811yescharacteristic
784D4—416no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
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—42no—
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—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4#38514yes—
884C2×C4#42714yescomplemented
885C2×C4C2×C4×D411yescharacteristic
886C2×C4C2×C4×D411yescharacteristic
887C2×C4C2×C4×D411yescharacteristic
888C2×C4C2×C4×D411yescharacteristic
889C2×C4#52011yescharacteristic
890C2×C4#52011yescharacteristic
891C2×C4C2×#12011yescharacteristic
892C2×C4C2×C22⋊Q811yescharacteristic
893C2×C4C2×C22⋊Q811yescharacteristic
894C2×C4#52511yescharacteristic
895C2×C4#52511yescharacteristic
896C2×C4#52511yescharacteristic
897C2×C4#53411yescharacteristic
898C2×C4#53611yescharacteristic
899C2×C4#53911yescharacteristic
900C2×C4#53911yescharacteristic
901C2×C4D4211yescharacteristic
902C2×C4D4211yescharacteristic
903C2×C4#54711yescharacteristic
904C2×C4#54711yescharacteristic
905C2×C4#54811yescharacteristic
906C2×C4#54811yescharacteristic
907C2×C4D4×Q811yescharacteristic
908C2×C4D4×Q811yescharacteristic
909C2×C4#55311yescharacteristic
910C2×C4#55311yescharacteristic
911C2×C4#55411yescharacteristic
912C2×C4#55411yescharacteristic
913C8—24no—
914C8—24no—
915C8—42no—
916C8—42no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22C2×#38511yescharacteristic
948C22D4×C4⋊C411yescharacteristic
949C22D4×C4⋊C411yescharacteristic
950C22#240311yescharacteristic
951C22#240611yescharacteristic
952C22#244311yescharacteristic
953C22#244311yescharacteristic
954C22C2×#42711yescharacteristic
955C22#291111yescharacteristic
956C22#291211yescharacteristic
957C22#291311yescharacteristic
958C22#300211yescharacteristic
959C22#300211yescharacteristic
960C22#301211yescharacteristic
961C22#301311yescharacteristic
962C22#309111yescharacteristic
963C22#309111yescharacteristic
964C22#309611yescharacteristic
965C22#309711yescharacteristic
966C22#326711yescharacteristic
967C22#326811yescharacteristic
968C22#326911yescharacteristic
969C22#327111yescharacteristic
970C22#328311yescharacteristic
971C22#328411yescharacteristic
972C22#328411yescharacteristic
973C22#328711yescharacteristic
974C22#334011yescharacteristic
975C22#334011yescharacteristic
976C22#334111yescharacteristic
977C22#334211yescharacteristic
978C22#334711yescharacteristic
979C22#334811yescharacteristic
980C22#334911yescharacteristic
981C22#335011yescharacteristic
982C4—24no—
983C4—24no—
984C4—44no—
985C4—42no—
986C4—42no—
987C4—82no—
988C4—82no—
989C4—82no—
990C4—82no—
991C4—82no—
992C4—161no—
993C4—161no—
994C4C4×#12011yescharacteristic
995C4#232211yescharacteristic
996C4#236111yescharacteristic
997C4#236111yescharacteristic
998C4#240911yescharacteristic
999C4#244911yescharacteristic
1000C4#244911yescharacteristic
1001C4#257911yescharacteristic
1002C2—44no—
1003C2—82no—
1004C2#1401511yescharacteristic
1005C2#2084311yescharacteristic
1006C2#2084911yescharacteristic
1007C2#2265711yescharacteristic
1008C2#2265811yescharacteristic
1009C2#2266011yescharacteristic
1010C2#2266211yescharacteristic
1011C2#2385311yescharacteristic
1012C2#2385711yescharacteristic
1013C2#2409311yescharacteristic
1014C2#2409611yescharacteristic
1015C2#2613511yescharacteristic
1016C2#2613711yescharacteristic
1017C2#2613911yescharacteristic
1018C2#2614111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#427C2semidirect
4. C2×#1854C2semidirect
5. C2×#1854C2semidirect
6. C2×#1854C2semidirect
8. #11324C2semidirect
9. #11323C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10908C2semidirect
13. #10907C2semidirect
14. #10731C2semidirect
15. #10721C2semidirect
46. #1869C4semidirect
141. C2×#107D4semidirect
150. C2×#106D4semidirect
884. C2×C4#427semidirect

Maximal subgroups

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

subgroupindex
C22×#4272
C2×#23542
C2×#18692
C2×#18542
#138712
#113242
#113232
#110962
#110952
#109082
#109072
#107312
#107212