Finite Group Databasebeta

← #375969

Subgroups — #375969

Order 512.

1590 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2367C211yesmaximal, characteristic
2C2×#2042C211yesmaximal, characteristic
3C2×#1926C211yesmaximal, characteristic
4C2×#1763C211yesmaximal, characteristic, complemented
5#14042C211yesmaximal, characteristic, complemented
6#11190C211yesmaximal, characteristic, complemented
7#11122C211yesmaximal, characteristic, complemented
8#11009C211yesmaximal, characteristic
9#10927C211yesmaximal, characteristic
10#10908C211yesmaximal, characteristic, complemented
11#10885C211yesmaximal, characteristic, complemented
12#10875C211yesmaximal, characteristic, complemented
13#10789C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×#124C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#97C2211yescharacteristic
29#2367—24no—
30#2367—24no—
31C2×#391C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#388—21no—
36C2×#387—21no—
37C2×#385—21no—
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4—21no—
42#2042C418yescomplemented
43#1926—24no—
44#1763—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1443—21no—
58#1441—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#124—22no—
72C2×#124—22no—
73C2×#124—22no—
74C2×#124—22no—
75C2×#124—22no—
76C2×#124C2×C414yes—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C2×C4×Q8D414yes—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4D411yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C42—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—41no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103C2×C414yescomplemented
124C2×#103C2×C414yescomplemented
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—41no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102—41no—
135C2×#102C2×C414yes—
136C2×#102C2×C414yes—
137C2×#97—22no—
138C2×#97—41no—
139C2×#97—41no—
140#391—22no—
141#391—22no—
142#390—22no—
143#390D414yes—
144#389—22no—
145#389C2×C414yescomplemented
146#388—28no—
147#388—28no—
148#387—44no—
149#385—28no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C4×C22⋊C4—28no—
157C2×#95—21no—
158C2×#95—21no—
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×#95D411yescharacteristic
171C2×#95D411yescharacteristic
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—41no—
179#336—22no—
180#336—22no—
181#336—41no—
182#336—41no—
183#336C2×C414yescomplemented
184C25—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8C22×C412yes—
197C22×Q8C2×D412yes—
198C22×Q8#4112yes—
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—21no—
210C22×D4C22×C412yes—
211C22×D4C2×D412yes—
212C22×D4#4112yes—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—24no—
220C23×C4—21no—
221C23×C4—42no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—81no—
226C23×C4—81no—
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2411yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
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×C8C22×C412yes—
260C22×C8C22×C412yes—
261C22×C8#4112yes—
262#124—28no—
263#124—28no—
264#124—28no—
265#124—28no—
266C4×Q8—28no—
267C4×Q8—44no—
268C4×Q8—44no—
269C4×Q8—44no—
270C4×D4—44no—
271C4×D4—44no—
272C4×D4—44no—
273C4×D4—44no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
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—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4C22×C412yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C2×D412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4#4112yes—
320C2×C4⋊C4#4112yes—
321C2×C4⋊C4#4112yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—24no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—24no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—81no—
359C2×C42—81no—
360C2×C42C22×C412yes—
361C2×C42C2×D412yes—
362C2×C42C2×D412yes—
363C2×C42#4112yes—
364#106—44no—
365#103—28no—
366#103—28no—
367#103—44no—
368#103—44no—
369#102—28no—
370#102—44no—
371#102—44no—
372#102—44no—
373#97—44no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—22no—
379#95—22no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—81no—
387#95—81no—
388#95—81no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24C22×D411yescharacteristic
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8C4×D414yes—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C4×D414yes—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
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—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—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
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—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—84no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4C4×D412yes—
555C22×C4C4×D412yes—
556C22×C4#12012yes—
557C22×C4#12012yes—
558C22×C4AGL(1,ℤ/8)12yes—
559C22×C4C23×C411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4C2×#4111yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C22×C42−1+411yescharacteristic
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—44no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4#12314yes—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—84no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—48no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—84no—
648C42—84no—
649C23—24no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—81no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C2×C4×D411yescharacteristic
685C23C2×#12011yescharacteristic
686C23#52511yescharacteristic
687C23#54611yescharacteristic
688C23#54611yescharacteristic
689C23#54811yescharacteristic
690C23#55011yescharacteristic
691C23C2×AGL(1,ℤ/8)11yescharacteristic
692C23#57511yescharacteristic
693C23#57511yescharacteristic
694C23#57511yescharacteristic
695C23#57711yescharacteristic
696C23#57711yescharacteristic
697C23#57711yescharacteristic
698C23#57811yescharacteristic
699Q8—24no—
700Q8—24no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707D4—24no—
708D4—24no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—816no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4C2×C4×D411yescharacteristic
808C2×C4C2×C4×D411yescharacteristic
809C2×C4C4×#4111yescharacteristic
810C2×C4C4×#4111yescharacteristic
811C2×C4#51811yescharacteristic
812C2×C4#52011yescharacteristic
813C2×C4C2×#12311yescharacteristic
814C2×C4#52511yescharacteristic
815C2×C4#52511yescharacteristic
816C2×C4#52511yescharacteristic
817C2×C4#52911yescharacteristic
818C2×C4#52911yescharacteristic
819C2×C4#53411yescharacteristic
820C2×C4#53711yescharacteristic
821C2×C4#53811yescharacteristic
822C2×C4#53911yescharacteristic
823C2×C4#54611yescharacteristic
824C2×C4#54611yescharacteristic
825C2×C4#54611yescharacteristic
826C2×C4#54711yescharacteristic
827C2×C4#55111yescharacteristic
828C2×C4#55211yescharacteristic
829C2×C4#55311yescharacteristic
830C2×C4#55311yescharacteristic
831C2×C4#55311yescharacteristic
832C2×C4#55511yescharacteristic
833C2×C4#55611yescharacteristic
834C2×C4#55911yescharacteristic
835C8—42no—
836C8—42no—
837C8—42no—
838C8—81no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22C4×#12011yescharacteristic
855C22#236311yescharacteristic
856C22#236711yescharacteristic
857C22#240511yescharacteristic
858C22#240711yescharacteristic
859C22#246011yescharacteristic
860C22#246711yescharacteristic
861C22#294311yescharacteristic
862C22C4×AGL(1,ℤ/8)11yescharacteristic
863C22#294711yescharacteristic
864C22#295211yescharacteristic
865C22#300511yescharacteristic
866C22#300611yescharacteristic
867C22#300911yescharacteristic
868C22#301311yescharacteristic
869C22#311111yescharacteristic
870C22#311511yescharacteristic
871C22#312011yescharacteristic
872C22#312511yescharacteristic
873C22#330611yescharacteristic
874C22#330611yescharacteristic
875C22#331311yescharacteristic
876C22#332111yescharacteristic
877C22#332311yescharacteristic
878C22#332311yescharacteristic
879C22#332611yescharacteristic
880C22#332711yescharacteristic
881C22#336711yescharacteristic
882C22#337111yescharacteristic
883C22#337111yescharacteristic
884C22#337611yescharacteristic
885C22#339711yescharacteristic
886C22#340111yescharacteristic
887C22#340111yescharacteristic
888C22#340211yescharacteristic
889C4—44no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—44no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—161no—
902C4C4×#12311yescharacteristic
903C4#232511yescharacteristic
904C4#235911yescharacteristic
905C4#236411yescharacteristic
906C4#245911yescharacteristic
907C4#246611yescharacteristic
908C4#248511yescharacteristic
909C4#260011yescharacteristic
910C2—84no—
911C2#1417311yescharacteristic
912C2#2145611yescharacteristic
913C2#2146111yescharacteristic
914C2#2310311yescharacteristic
915C2#2310911yescharacteristic
916C2#2322511yescharacteristic
917C2#2322611yescharacteristic
918C2#2404711yescharacteristic
919C2#2404811yescharacteristic
920C2#2420211yescharacteristic
921C2#2420511yescharacteristic
922C2#2678011yescharacteristic
923C2#2678111yescharacteristic
924C2#2709011yescharacteristic
925C2#2709111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1763C2semidirect
5. #14042C2semidirect
6. #11190C2semidirect
7. #11122C2semidirect
10. #10908C2semidirect
11. #10885C2semidirect
12. #10875C2semidirect
13. #10789C2semidirect
42. #2042C4semidirect
123. C2×#103C2×C4semidirect
124. C2×#103C2×C4semidirect
145. #389C2×C4semidirect
183. #336C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23672
C2×#20422
C2×#19262
C2×#17632
#140422
#111902
#111222
#110092
#109272
#109082
#108852
#108752
#107892
#107882