Finite Group Databasebeta

← #365408

Subgroups — #365408

Order 512.

1864 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2352C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1854C211yesmaximal, characteristic, complemented
4C2×#1853C211yesmaximal, characteristic, complemented
5C2×#1807C211yesmaximal, characteristic, complemented
6C2×#1735C211yesmaximal, characteristic, complemented
7#13871C211yesmaximal, characteristic
8#11325C211yesmaximal, characteristic, complemented
9#11268C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28#2352—24no—
29#2352—24no—
30C2×#388—21no—
31C2×#387—21no—
32C2×#386—21no—
33C2×#382C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4—21no—
41#1869C418yescomplemented
42#1854—24no—
43#1853—24no—
44#1807—24no—
45#1735—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1440—21no—
61#1438—21no—
62#1437—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8C2×C414yescomplemented
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4C2×C414yes—
86C2×C4×D4Q814yes—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—41no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117—41no—
98C2×#117D414yes—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—41no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4D411yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4D411yescharacteristic
123C22×C22⋊C4D411yescharacteristic
124C22×C42—21no—
125C22×C42—21no—
126C22×C42—21no—
127C22×C42C2311yescharacteristic
128C2×#107—22no—
129C2×#107—41no—
130C2×#107—41no—
131C2×#106—22no—
132C2×#106—22no—
133C2×#106—22no—
134C2×#106—22no—
135C2×#106—22no—
136C2×#106—22no—
137C2×#106—22no—
138C2×#106—41no—
139C2×#106—41no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—41no—
145C2×C22⋊C8—41no—
146C2×C22⋊C8C2×C414yes—
147C2×C22⋊C8C2×C414yes—
148C2×C22⋊C8C2×C414yescomplemented
149#388—28no—
150#387—28no—
151#386—28no—
152#382—22no—
153#382—22no—
154#380—22no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—22no—
159#380—22no—
160#380—22no—
161#380—41no—
162#380—41no—
163#380D414yes—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C22⋊C4—28no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—41no—
189#340—41no—
190#340D414yescomplemented
191#336C2×C414yescomplemented
192#336C2×C414yescomplemented
193C25C2×D411yescharacteristic
194C25C2×D411yescharacteristic
195C22×D4—22no—
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—41no—
200C22×D4—41no—
201C22×D4C4⋊C414yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
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—24no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—81no—
236C23×C4—81no—
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—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
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—21no—
264C22×C8—21no—
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—28no—
274C22×C8—44no—
275C22×C8—44no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8C22×C412yes—
280C22×C8C22×C412yes—
281C22×C8C22×C412yes—
282C22×C8C22×C412yes—
283C22×C8C2×D412yes—
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—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
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—24no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
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—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C4⋊C414yes—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D412yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4#4112yes—
354C2×C4⋊C4#4112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
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—81no—
375C2×C22⋊C4—81no—
376C2×C22⋊C4—81no—
377C2×C22⋊C4—81no—
378C2×C22⋊C4—81no—
379C2×C22⋊C4—81no—
380C2×C22⋊C4C4⋊C414yes—
381C2×C22⋊C4C4⋊C414yes—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—81no—
394C2×C42—81no—
395C2×C42C22×C412yes—
396C2×C42C2×Q812yes—
397#107—44no—
398#106—44no—
399#106—44no—
400#106—44no—
401C22⋊C8—28no—
402C22⋊C8—28no—
403C22⋊C8—44no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—81no—
415#95—81no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
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—
440C24C2×C4⋊C412yes—
441C24C2×C4⋊C412yes—
442C24#12012yes—
443C24#12312yes—
444C24#13512yes—
445C24#13512yes—
446C24C22×D411yescharacteristic
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
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—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
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—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—48no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
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—48no—
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—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
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×C4C23×C411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×Q811yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4C2×#4111yescharacteristic
608C22×C4C2×#4111yescharacteristic
609C22×C4C2×#4111yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4H(5,𝔽2)11yescharacteristic
612C22×C4H(5,𝔽2)11yescharacteristic
613C22×C4H(5,𝔽2)11yescharacteristic
614C22×C42−1+411yescharacteristic
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
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—416no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8C4×D414yes—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—28no—
648C4⋊C4—22no—
649C4⋊C4—22no—
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—48no—
659C4⋊C4—41no—
660C4⋊C4—41no—
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#12114yes—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—48no—
692C42—48no—
693C42—84no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
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—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
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#38514yes—
763C23#42714yes—
764C23C22×C4⋊C411yescharacteristic
765C23C2×#12011yescharacteristic
766C23C2×#12311yescharacteristic
767C23D4211yescharacteristic
768C23#54611yescharacteristic
769C23#54611yescharacteristic
770C23#54711yescharacteristic
771C23C2×#13511yescharacteristic
772C23C2×#13511yescharacteristic
773C23#57511yescharacteristic
774C23#57511yescharacteristic
775C23#57711yescharacteristic
776C23#57711yescharacteristic
777C23#57711yescharacteristic
778C23#57711yescharacteristic
779D4—416no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
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—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—816no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
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#38514yes—
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C2×C4×D411yescharacteristic
883C2×C4C2×C4×D411yescharacteristic
884C2×C4C4×#4111yescharacteristic
885C2×C4#51811yescharacteristic
886C2×C4#52011yescharacteristic
887C2×C4C2×#12111yescharacteristic
888C2×C4C2×C22⋊Q811yescharacteristic
889C2×C4C2×C22⋊Q811yescharacteristic
890C2×C4#52511yescharacteristic
891C2×C4#52911yescharacteristic
892C2×C4#53211yescharacteristic
893C2×C4#53411yescharacteristic
894C2×C4#53711yescharacteristic
895C2×C4#53811yescharacteristic
896C2×C4#53911yescharacteristic
897C2×C4D4211yescharacteristic
898C2×C4#54611yescharacteristic
899C2×C4#54611yescharacteristic
900C2×C4#54611yescharacteristic
901C2×C4#54711yescharacteristic
902C2×C4D4×Q811yescharacteristic
903C2×C4#55111yescharacteristic
904C2×C4#55111yescharacteristic
905C2×C4#55211yescharacteristic
906C2×C4#55411yescharacteristic
907C2×C4#55411yescharacteristic
908C2×C4#55411yescharacteristic
909C8—24no—
910C8—42no—
911C8—42no—
912C8—42no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—42no—
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—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22C2×#38511yescharacteristic
944C22D4×C4⋊C411yescharacteristic
945C22#234911yescharacteristic
946C22#241011yescharacteristic
947C22#241811yescharacteristic
948C22#241911yescharacteristic
949C22#243011yescharacteristic
950C22C2×#42711yescharacteristic
951C22#291111yescharacteristic
952C22#291211yescharacteristic
953C22#291211yescharacteristic
954C22#300211yescharacteristic
955C22#300211yescharacteristic
956C22#300911yescharacteristic
957C22#301011yescharacteristic
958C22#309111yescharacteristic
959C22#309111yescharacteristic
960C22#309911yescharacteristic
961C22#309911yescharacteristic
962C22#326711yescharacteristic
963C22#327111yescharacteristic
964C22#328211yescharacteristic
965C22#328211yescharacteristic
966C22#329611yescharacteristic
967C22#329611yescharacteristic
968C22#330111yescharacteristic
969C22#330111yescharacteristic
970C22#330711yescharacteristic
971C22#331111yescharacteristic
972C22#331711yescharacteristic
973C22#332111yescharacteristic
974C22#333711yescharacteristic
975C22#333711yescharacteristic
976C22#334811yescharacteristic
977C22#335011yescharacteristic
978C4—24no—
979C4—42no—
980C4—42no—
981C4—44no—
982C4—42no—
983C4—82no—
984C4—82no—
985C4—82no—
986C4—82no—
987C4—82no—
988C4—161no—
989C4—161no—
990C4C4×#12111yescharacteristic
991C4#232511yescharacteristic
992C4#235811yescharacteristic
993C4#235911yescharacteristic
994C4#241711yescharacteristic
995C4#244911yescharacteristic
996C4#245011yescharacteristic
997C4#256411yescharacteristic
998C2—44no—
999C2—44no—
1000C2#1397511yescharacteristic
1001C2#2084311yescharacteristic
1002C2#2084811yescharacteristic
1003C2#2265411yescharacteristic
1004C2#2266211yescharacteristic
1005C2#2270611yescharacteristic
1006C2#2271011yescharacteristic
1007C2#2442511yescharacteristic
1008C2#2443611yescharacteristic
1009C2#2486211yescharacteristic
1010C2#2486811yescharacteristic
1011C2#2493611yescharacteristic
1012C2#2493811yescharacteristic
1013C2#2553211yescharacteristic
1014C2#2554411yescharacteristic
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
3. C2×#1854C2semidirect
4. C2×#1853C2semidirect
5. C2×#1807C2semidirect
6. C2×#1735C2semidirect
8. #11325C2semidirect
9. #11268C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10908C2semidirect
13. #10908C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
41. #1869C4semidirect
76. C23×C8C2×C4semidirect
148. C2×C22⋊C8C2×C4semidirect
190. #340D4semidirect
191. #336C2×C4semidirect
192. #336C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23522
C2×#18692
C2×#18542
C2×#18532
C2×#18072
C2×#17352
#138712
#113252
#112682
#110962
#110952
#109082
#107312
#107302