Finite Group Databasebeta

← #360015

Subgroups — #360015

Order 512.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2324C211yesmaximal, characteristic
2C2×#2314C211yesmaximal, characteristic, complemented
3C2×#1804C211yesmaximal, characteristic, complemented
4C2×#1802C211yesmaximal, characteristic, complemented
5C2×#1798C211yesmaximal, characteristic, complemented
6#11200C211yesmaximal, characteristic, complemented
7#11199C211yesmaximal, characteristic, complemented
8#10969C211yesmaximal, characteristic
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10931C211yesmaximal, characteristic, complemented
12#10885C211yesmaximal, characteristic, complemented
13#10884C211yesmaximal, characteristic, complemented
14#10850C211yesmaximal, characteristic, complemented
15#10849C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27#2324—24no—
28#2324C418yescomplemented
29#2314—24no—
30#2314—24no—
31C2×#390—21no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#388—21no—
36C2×#388—21no—
37C2×#387—21no—
38C2×#387—21no—
39C2×#386—21no—
40C2×#385—21no—
41C2×#384C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49#1804—24no—
50#1802—24no—
51#1798—24no—
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62C2×#340C2211yescharacteristic
63C2×#340C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C23×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#121—22no—
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121C2×C414yes—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4C2×C414yes—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117C2×C414yes—
91C2×#117D414yes—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4D411yescharacteristic
112C22×C22⋊C4D411yescharacteristic
113C22×C42—21no—
114C22×C42—21no—
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102—41no—
135C2×#102—41no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—41no—
139C2×C22⋊C8—41no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8—41no—
142#390—28no—
143#390—22no—
144#390C2×C414yes—
145#389—22no—
146#389C2×C414yes—
147#388—28no—
148#388—28no—
149#388—28no—
150#387—28no—
151#387—28no—
152#386—28no—
153#385—28no—
154#384—22no—
155#384D414yescomplemented
156#382—22no—
157#382D414yescomplemented
158#380—22no—
159#380—22no—
160#380—22no—
161#380—22no—
162#380—22no—
163#380C2×C414yes—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4—22no—
167C4×C4⋊C4—22no—
168C4×C4⋊C4—22no—
169C4×C4⋊C4C2×C414yes—
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—41no—
188#340—41no—
189#340—41no—
190#340—41no—
191#336—22no—
192#336—22no—
193C25—21no—
194C25C2×D411yescharacteristic
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—81no—
210C22×D4—81no—
211C22×D4—81no—
212C22×D4—81no—
213C22×D4C22×C412yes—
214C22×D4#4112yes—
215C22×D4#4112yes—
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—24no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4C22×C412yes—
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2411yescharacteristic
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—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278#121—28no—
279#121—28no—
280#121—28no—
281#121—28no—
282C4×D4—28no—
283C4×D4—28no—
284C4×D4—44no—
285C4×D4—44no—
286#117—28no—
287#117—28no—
288#117—28no—
289#117—28no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
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—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—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4—81no—
332C2×C4⋊C4—81no—
333C2×C4⋊C4—81no—
334C2×C4⋊C4—81no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4C22⋊C414yes—
337C2×C4⋊C4C22⋊C414yes—
338C2×C4⋊C4C22×C412yes—
339C2×C4⋊C4C22×C412yes—
340C2×C4⋊C4C22×C412yes—
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×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4—81no—
365C2×C22⋊C4—81no—
366C2×C22⋊C4—81no—
367C2×C22⋊C4—81no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C22⋊C4C22⋊C414yes—
373C2×C22⋊C4C22⋊C414yes—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—81no—
382C2×C42—81no—
383C2×C42—81no—
384C2×C42—81no—
385C2×C42—81no—
386C2×C42—81no—
387C2×C42C22×C412yes—
388C2×C42C22×C412yes—
389C2×C42C2×D412yes—
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393C2×C42#4112yes—
394C2×C42#4112yes—
395C4⋊C8—44no—
396C4⋊C8—44no—
397#102—44no—
398#102—44no—
399#102—44no—
400#102—44no—
401C22⋊C8—44no—
402C22⋊C8—44no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
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—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24—41no—
441C24C2×C22⋊C412yes—
442C24C22×D411yescharacteristic
443C2×D4—216no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—84no—
472C2×D4—84no—
473C2×D4—84no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4#11714yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
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—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
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—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
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—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—48no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4C2×C22⋊C412yes—
589C22×C4C2×C22⋊C412yes—
590C22×C4C2×C22⋊C412yes—
591C22×C4C2×C22⋊C412yes—
592C22×C4C2×C22⋊C412yes—
593C22×C4#12012yes—
594C22×C4#12012yes—
595C22×C4#12312yes—
596C22×C4#12312yes—
597C22×C4C23×C411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4H(5,𝔽2)11yescharacteristic
608C22×C4H(5,𝔽2)11yescharacteristic
609C22×C42−1+411yescharacteristic
610C22×C42−1+411yescharacteristic
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
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—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
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—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—84no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C4⋊C4#11714yes—
672C22⋊C4—216no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—48no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—84no—
686C42—84no—
687C42—84no—
688C42C4×D414yes—
689C42C4×D414yes—
690C42#12114yes—
691C42#12114yes—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—42no—
713C23—41no—
714C23—42no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23—42no—
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—42no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23—81no—
762C23C22×C22⋊C411yescharacteristic
763C23C2×#12011yescharacteristic
764C23C2×#12311yescharacteristic
765C23#52511yescharacteristic
766C23#52511yescharacteristic
767C23#53711yescharacteristic
768C23#53711yescharacteristic
769C23#57611yescharacteristic
770C23#57611yescharacteristic
771C23#57611yescharacteristic
772C23#57711yescharacteristic
773C23#57711yescharacteristic
774C23#57711yescharacteristic
775C23#57711yescharacteristic
776C23#57811yescharacteristic
777D4—24no—
778D4—24no—
779D4—42no—
780D4—42no—
781D4—42no—
782D4—42no—
783D4—42no—
784D4—42no—
785D4—816no—
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—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—816no—
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#38614yes—
878C2×C4#38614yes—
879C2×C4C2×#11711yescharacteristic
880C2×C4C2×#11711yescharacteristic
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C2×C4×D411yescharacteristic
883C2×C4#52011yescharacteristic
884C2×C4#52011yescharacteristic
885C2×C4C2×#12111yescharacteristic
886C2×C4C2×#12111yescharacteristic
887C2×C4#52511yescharacteristic
888C2×C4#52511yescharacteristic
889C2×C4#53511yescharacteristic
890C2×C4#53611yescharacteristic
891C2×C4#54611yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#54711yescharacteristic
894C2×C4#54711yescharacteristic
895C2×C4#54811yescharacteristic
896C2×C4#54811yescharacteristic
897C2×C4#55011yescharacteristic
898C2×C4#55011yescharacteristic
899C2×C4#55211yescharacteristic
900C2×C4#55211yescharacteristic
901C2×C4#55311yescharacteristic
902C2×C4#55311yescharacteristic
903C2×C4#55511yescharacteristic
904C2×C4#55511yescharacteristic
905C2×C4#55611yescharacteristic
906C2×C4#55611yescharacteristic
907C8—81no—
908C8—81no—
909C8—81no—
910C8—81no—
911C22—42no—
912C22—44no—
913C22—42no—
914C22—44no—
915C22—42no—
916C22—44no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—81no—
922C22—82no—
923C22—81no—
924C22—82no—
925C22—81no—
926C22—82no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—81no—
934C22—82no—
935C22—81no—
936C22—82no—
937C22—81no—
938C22—82no—
939C22—81no—
940C22—82no—
941C22#228011yescharacteristic
942C22C2×#38611yescharacteristic
943C22#231111yescharacteristic
944C22#240711yescharacteristic
945C22#240711yescharacteristic
946C22#248511yescharacteristic
947C22#248511yescharacteristic
948C22#289711yescharacteristic
949C22#289711yescharacteristic
950C22#289711yescharacteristic
951C22#289811yescharacteristic
952C22#300811yescharacteristic
953C22#301011yescharacteristic
954C22#301211yescharacteristic
955C22#301311yescharacteristic
956C22#309611yescharacteristic
957C22#309611yescharacteristic
958C22#309811yescharacteristic
959C22#309911yescharacteristic
960C22#311811yescharacteristic
961C22#311811yescharacteristic
962C22#311911yescharacteristic
963C22#312011yescharacteristic
964C22#312211yescharacteristic
965C22#312311yescharacteristic
966C22#312411yescharacteristic
967C22#312511yescharacteristic
968C22#325711yescharacteristic
969C22#325711yescharacteristic
970C22#325711yescharacteristic
971C22#325811yescharacteristic
972C22#325911yescharacteristic
973C22#326011yescharacteristic
974C22#326211yescharacteristic
975C22#326311yescharacteristic
976C4—24no—
977C4—24no—
978C4—44no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—82no—
983C4—82no—
984C4—82no—
985C4—82no—
986C4—82no—
987C4—82no—
988C4#235211yescharacteristic
989C4#235211yescharacteristic
990C4#235411yescharacteristic
991C4#235411yescharacteristic
992C4#241411yescharacteristic
993C4#241411yescharacteristic
994C4#241511yescharacteristic
995C4#241511yescharacteristic
996C2—82no—
997C2—84no—
998C2#1387111yescharacteristic
999C2#2074411yescharacteristic
1000C2#2074611yescharacteristic
1001C2#2091411yescharacteristic
1002C2#2091511yescharacteristic
1003C2#2189611yescharacteristic
1004C2#2189711yescharacteristic
1005C2#2416211yescharacteristic
1006C2#2416311yescharacteristic
1007C2#2416611yescharacteristic
1008C2#2416711yescharacteristic
1009C2#2763611yescharacteristic
1010C2#2763711yescharacteristic
1011C2#2764011yescharacteristic
1012C2#2764111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2314C2semidirect
3. C2×#1804C2semidirect
4. C2×#1802C2semidirect
5. C2×#1798C2semidirect
6. #11200C2semidirect
7. #11199C2semidirect
10. #10931C2semidirect
11. #10931C2semidirect
12. #10885C2semidirect
13. #10884C2semidirect
14. #10850C2semidirect
15. #10849C2semidirect
28. #2324C4semidirect
155. #384D4semidirect
157. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23242
C2×#23142
C2×#18042
C2×#18022
C2×#17982
#112002
#111992
#109692
#109312
#108852
#108842
#108502
#108492