Finite Group Databasebeta

← #368212

Subgroups — #368212

Order 512.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1008 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×#1735C211yesmaximal, characteristic, complemented
5#13871C211yesmaximal, characteristic
6#11268C211yesmaximal, characteristic, complemented
7#11268C211yesmaximal, characteristic, complemented
8#11096C211yesmaximal, characteristic, complemented
9#11095C211yesmaximal, characteristic, complemented
10#10908C211yesmaximal, characteristic, complemented
11#10907C211yesmaximal, characteristic, complemented
12#10731C211yesmaximal, characteristic, complemented
13#10730C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26#2352—24no—
27#2352—24no—
28C2×#388—21no—
29C2×#387—21no—
30C2×#386—21no—
31C2×#382C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4—21no—
39#1869C418yescomplemented
40#1854—24no—
41#1735—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1440—21no—
59#1438—21no—
60#1437—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×D4D411yescharacteristic
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—41no—
71C23×C8—41no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8C2×C414yescomplemented
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4C2×C414yes—
84C2×C4×D4Q814yes—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—41no—
93C2×#117—41no—
94C2×#117—41no—
95C2×#117—41no—
96C2×#117D414yes—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—41no—
103C22×C4⋊C4—41no—
104C22×C4⋊C4D411yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4D411yescharacteristic
121C22×C22⋊C4D411yescharacteristic
122C22×C42—21no—
123C22×C42—21no—
124C22×C42—21no—
125C22×C42C2311yescharacteristic
126C2×#107—22no—
127C2×#107—22no—
128C2×#107—41no—
129C2×#106—22no—
130C2×#106—22no—
131C2×#106—41no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—41no—
135C2×C22⋊C8—41no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8—41no—
138C2×C22⋊C8C2×C414yes—
139C2×C22⋊C8C2×C414yes—
140C2×C22⋊C8C2×C414yescomplemented
141#388—28no—
142#387—28no—
143#386—28no—
144#382—22no—
145#382—22no—
146#380—22no—
147#380—22no—
148#380—22no—
149#380—22no—
150#380—22no—
151#380—22no—
152#380—22no—
153#380—41no—
154#380—41no—
155#380D414yes—
156C4×C4⋊C4—22no—
157C4×C4⋊C4—22no—
158C4×C22⋊C4—28no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340—41no—
183#340—41no—
184#340—41no—
185#336C2×C414yescomplemented
186#336C2×C414yescomplemented
187C25C2×D411yescharacteristic
188C25C2×D411yescharacteristic
189C22×D4—22no—
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—41no—
194C22×D4—41no—
195C22×D4C4⋊C414yes—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
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—24no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—81no—
230C23×C4—81no—
231C23×C4C22×C412yes—
232C23×C4C22×C412yes—
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D412yes—
238C23×C4C2×D412yes—
239C23×C4C2×Q812yes—
240C23×C4C2×Q812yes—
241C23×C4#4112yes—
242C23×C4#4112yes—
243C23×C4C2411yescharacteristic
244C22×C8—28no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
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—44no—
270C22×C8—44no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C4×D4—28no—
280C4×D4—28no—
281C4×D4—28no—
282C4×D4—28no—
283#117—28no—
284#117—28no—
285#117—44no—
286#117—44no—
287#117—44no—
288#117—44no—
289#117—44no—
290#117—44no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
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—24no—
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—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—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C4⋊C414yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4C2×D412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4#4112yes—
346C2×C4⋊C4#4112yes—
347C2×C4⋊C4#4112yes—
348C2×C4⋊C4#4112yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
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—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C22⋊C4—81no—
373C2×C22⋊C4—81no—
374C2×C22⋊C4C4⋊C414yes—
375C2×C22⋊C4C4⋊C414yes—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—81no—
388C2×C42—81no—
389C2×C42C22×C412yes—
390C2×C42C2×Q812yes—
391#107—44no—
392#106—44no—
393C22⋊C8—28no—
394C22⋊C8—44no—
395C22⋊C8—44no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—81no—
407#95—81no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
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—
432C24C2×C4⋊C412yes—
433C24C2×C4⋊C412yes—
434C24#12012yes—
435C24#12312yes—
436C24#13512yes—
437C24#13512yes—
438C24C22×D411yescharacteristic
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
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—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
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—22no—
512C22×C4—48no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
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—48no—
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—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4C2×C4⋊C412yes—
584C22×C4C2×C4⋊C412yes—
585C22×C4C2×C4⋊C412yes—
586C22×C4C2×C4⋊C412yes—
587C22×C4C4×D414yes—
588C22×C4C4×D414yes—
589C22×C4#12012yes—
590C22×C4C22⋊Q814yes—
591C22×C4C22⋊Q814yes—
592C22×C4#12312yes—
593C22×C4C23×C411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×Q811yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C4H(5,𝔽2)11yescharacteristic
605C22×C4H(5,𝔽2)11yescharacteristic
606C22×C4H(5,𝔽2)11yescharacteristic
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—416no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—28no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—48no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
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#12314yes—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—48no—
684C42—48no—
685C42—84no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
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—41no—
723C23—41no—
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#38514yes—
755C23#42714yes—
756C23C22×C4⋊C411yescharacteristic
757C23C2×#12011yescharacteristic
758C23C2×#12311yescharacteristic
759C23#54611yescharacteristic
760C23#54611yescharacteristic
761C23#54611yescharacteristic
762C23#54611yescharacteristic
763C23C2×#13511yescharacteristic
764C23C2×#13511yescharacteristic
765C23#57511yescharacteristic
766C23#57511yescharacteristic
767C23#57611yescharacteristic
768C23#57711yescharacteristic
769C23#57711yescharacteristic
770C23#57811yescharacteristic
771D4—416no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
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—816no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
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#38514yes—
873C2×C4C2×C4×D411yescharacteristic
874C2×C4C2×C4×D411yescharacteristic
875C2×C4C4×#4111yescharacteristic
876C2×C4C4×#4111yescharacteristic
877C2×C4#51811yescharacteristic
878C2×C4#51811yescharacteristic
879C2×C4C2×C22⋊Q811yescharacteristic
880C2×C4C2×C22⋊Q811yescharacteristic
881C2×C4C2×#12311yescharacteristic
882C2×C4#52511yescharacteristic
883C2×C4#52911yescharacteristic
884C2×C4#52911yescharacteristic
885C2×C4#53411yescharacteristic
886C2×C4#53511yescharacteristic
887C2×C4#53811yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#54611yescharacteristic
890C2×C4#54611yescharacteristic
891C2×C4#54611yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#55311yescharacteristic
894C2×C4#55311yescharacteristic
895C2×C4#55311yescharacteristic
896C2×C4#55311yescharacteristic
897C2×C4#55411yescharacteristic
898C2×C4#55411yescharacteristic
899C2×C4#55411yescharacteristic
900C2×C4#55411yescharacteristic
901C8—42no—
902C8—42no—
903C8—42no—
904C8—42no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—24no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
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—
935C22C2×#38511yescharacteristic
936C22#234911yescharacteristic
937C22#234911yescharacteristic
938C22#240411yescharacteristic
939C22#240511yescharacteristic
940C22#244411yescharacteristic
941C22#244411yescharacteristic
942C22C2×#42711yescharacteristic
943C22#291111yescharacteristic
944C22#291211yescharacteristic
945C22#291311yescharacteristic
946C22#300211yescharacteristic
947C22#300211yescharacteristic
948C22#301211yescharacteristic
949C22#301311yescharacteristic
950C22#309111yescharacteristic
951C22#309111yescharacteristic
952C22#309611yescharacteristic
953C22#309711yescharacteristic
954C22#329611yescharacteristic
955C22#329611yescharacteristic
956C22#329711yescharacteristic
957C22#329711yescharacteristic
958C22#330011yescharacteristic
959C22#330011yescharacteristic
960C22#330111yescharacteristic
961C22#330111yescharacteristic
962C22#330711yescharacteristic
963C22#330911yescharacteristic
964C22#331111yescharacteristic
965C22#331311yescharacteristic
966C22#331511yescharacteristic
967C22#331711yescharacteristic
968C22#331911yescharacteristic
969C22#332111yescharacteristic
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—44no—
975C4—82no—
976C4—82no—
977C4—82no—
978C4—82no—
979C4—82no—
980C4—161no—
981C4—161no—
982C4C4×#12311yescharacteristic
983C4#232111yescharacteristic
984C4#236411yescharacteristic
985C4#236411yescharacteristic
986C4#245011yescharacteristic
987C4#245011yescharacteristic
988C4#248711yescharacteristic
989C4#257911yescharacteristic
990C2—44no—
991C2—44no—
992C2#1401611yescharacteristic
993C2#2084311yescharacteristic
994C2#2084911yescharacteristic
995C2#2270411yescharacteristic
996C2#2270611yescharacteristic
997C2#2271011yescharacteristic
998C2#2271211yescharacteristic
999C2#2396211yescharacteristic
1000C2#2397111yescharacteristic
1001C2#2403711yescharacteristic
1002C2#2404011yescharacteristic
1003C2#2619911yescharacteristic
1004C2#2620111yescharacteristic
1005C2#2620311yescharacteristic
1006C2#2620511yescharacteristic
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×#1735C2semidirect
6. #11268C2semidirect
7. #11268C2semidirect
8. #11096C2semidirect
9. #11095C2semidirect
10. #10908C2semidirect
11. #10907C2semidirect
12. #10731C2semidirect
13. #10730C2semidirect
14. #10730C2semidirect
15. #10721C2semidirect
39. #1869C4semidirect
74. C23×C8C2×C4semidirect
140. C2×C22⋊C8C2×C4semidirect
185. #336C2×C4semidirect
186. #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×#17352
#138712
#112682
#110962
#110952
#109082
#109072
#107312
#107302
#107212