Finite Group Databasebeta

← #365613

Subgroups — #365613

Order 512.

1868 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#442C211yesmaximal, characteristic
2C2×#1972C211yesmaximal, characteristic
3C2×#1970C211yesmaximal, characteristic
4C2×#1944C211yesmaximal, characteristic, complemented
5C2×#1864C211yesmaximal, characteristic, complemented
6C2×#1862C211yesmaximal, characteristic, complemented
7C2×#1847C211yesmaximal, characteristic, complemented
8#13979C211yesmaximal, characteristic, complemented
9#13977C211yesmaximal, characteristic, complemented
10#11123C211yesmaximal, characteristic, complemented
11#11121C211yesmaximal, characteristic, complemented
12#11051C211yesmaximal, characteristic, complemented
13#11049C211yesmaximal, characteristic, complemented
14#10861C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×D8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#442—24no—
20C2×#442—24no—
21C2×#442—24no—
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#385—22no—
43C2×#384C2211yescharacteristic
44C2×#382C2211yescharacteristic
45#1972C418yescomplemented
46#1970—24no—
47#1944—24no—
48#1864—24no—
49#1862—24no—
50#1847—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1439—22no—
59#1439—22no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—22no—
63C4×#95C2211yescharacteristic
64C23×D4C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C22×D8—22no—
69C22×D8—22no—
70C22×D8—22no—
71C22×D8—22no—
72C22×D8C2×C414yes—
73C22×D8D414yes—
74C22×D8Q814yes—
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×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C2×C4×D4—41no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—22no—
105C22×C22⋊C4—22no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109#442—232no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—41no—
116C2×#106—22no—
117C2×#106—22no—
118C2×#106—22no—
119C2×#106—22no—
120C2×#106—22no—
121C2×#106—22no—
122C2×#106—41no—
123C2×#106C2×C414yescomplemented
124C2×#106D414yes—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—41no—
140C2×#102—41no—
141C2×#102C2×C414yescomplemented
142C2×#102C2×C414yescomplemented
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97C2×C414yescomplemented
148C2×#97D414yes—
149C2×C4×C8—22no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152#390—22no—
153#390—22no—
154#390—22no—
155#390—22no—
156#390—41no—
157#390—41no—
158#390C2×C414yescomplemented
159#390C2×C414yescomplemented
160#389—22no—
161#389—22no—
162#389—22no—
163#389—22no—
164#385—48no—
165#384—22no—
166#384—41no—
167#382—22no—
168#382—41no—
169C2×#95—21no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—21no—
173C2×#95—22no—
174C2×#95D412yes—
175C2×#95D412yes—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#336—22no—
181#336—22no—
182#336D414yes—
183C25—21no—
184C25—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
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×D4C22×C412yes—
208C22×D4C22×C412yes—
209C22×D4C2×D412yes—
210C22×D4C2×D412yes—
211C22×D4C2×Q812yes—
212C22×D4C2×Q812yes—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4—42no—
223C23×C4—44no—
224C23×C4—44no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—82no—
228C23×C4—82no—
229C23×C4C2×D412yes—
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D412yes—
233C23×C4C2411yescharacteristic
234C2×D8—28no—
235C2×D8—28no—
236C2×D8—28no—
237C2×D8—28no—
238C2×D8—28no—
239C2×D8—28no—
240C2×D8C4⋊C4116yescomplemented
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×C8C22×C412yes—
258C22×C8C22×C412yes—
259C22×C8C2×D412yes—
260C22×C8C2×D412yes—
261C22×C8C2×D412yes—
262C22×C8C2×D412yes—
263C22×C8C2×D412yes—
264C22×C8C2×D412yes—
265C22×C8C2×Q812yes—
266C22×C8#4112yes—
267C22×C8#4112yes—
268C22×C8#4112yes—
269C4×D4—28no—
270C4×D4—28no—
271C4×D4—44no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C4×D4—44no—
276C4×D4—44no—
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—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—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—82no—
315C2×C4⋊C4—82no—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—82no—
335C2×C22⋊C4—82no—
336C2×C22⋊C4—82no—
337C2×C22⋊C4—82no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42C22×C412yes—
353C2×C42C2×D412yes—
354C2×C42C2×D412yes—
355C2×C42#4112yes—
356#107—44no—
357#107—44no—
358#106—28no—
359#106—28no—
360#106—44no—
361#102—28no—
362#102—28no—
363#102—28no—
364#102—28no—
365#102—44no—
366#102—44no—
367#97—28no—
368#97—28no—
369C4×C8—44no—
370#95—24no—
371#95—42no—
372#95—44no—
373#95—42no—
374#95—42no—
375#95—44no—
376#95—82no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24C22×D411yescharacteristic
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×C4⋊C414yes—
455C2×D4C2×C4⋊C414yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
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—48no—
481C22×C4—48no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—84no—
512C22×C4—88no—
513C22×C4—88no—
514C22×C4—88no—
515C22×C4—88no—
516C22×C4C4×D414yes—
517C22×C4#12712yes—
518C22×C4#12712yes—
519C22×C4AGL(1,ℤ/8)14yes—
520C22×C4C23×C411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×Q811yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C42−1+411yescharacteristic
533C22×C42−1+411yescharacteristic
534D8—232no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8C2×C4⋊C414yes—
556C2×C8C4×D414yes—
557C2×C8C4×D414yes—
558C2×C8C4×D414yes—
559C2×C8#12014yes—
560C2×C8C22⋊Q814yes—
561C2×C8C22⋊Q814yes—
562C2×C8#12314yes—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C4⋊C4—88no—
590C22⋊C4—416no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—88no—
594C22⋊C4—88no—
595C22⋊C4—88no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C23—24no—
609C23—24no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—44no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—44no—
626C23—42no—
627C23—42no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23C2×C4×D411yescharacteristic
655C23C2×#12711yescharacteristic
656C23#53211yescharacteristic
657C23D4211yescharacteristic
658C23D4211yescharacteristic
659C23#54711yescharacteristic
660C23D4×Q811yescharacteristic
661C23C2×AGL(1,ℤ/8)12yes—
662C23#57512yes—
663C23#57612yes—
664C23#57712yes—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—816no—
714C2×C4—816no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4C22×C4⋊C411yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4#52011yescharacteristic
742C2×C4#52011yescharacteristic
743C2×C4C2×#12011yescharacteristic
744C2×C4C2×C22⋊Q811yescharacteristic
745C2×C4C2×C22⋊Q811yescharacteristic
746C2×C4C2×#12311yescharacteristic
747C2×C4#53211yescharacteristic
748C2×C4#53211yescharacteristic
749C2×C4#53511yescharacteristic
750C2×C4#53611yescharacteristic
751C2×C4#54211yescharacteristic
752C2×C4#54211yescharacteristic
753C2×C4D4211yescharacteristic
754C2×C4D4211yescharacteristic
755C2×C4#54711yescharacteristic
756C2×C4#54711yescharacteristic
757C2×C4#54711yescharacteristic
758C2×C4#54811yescharacteristic
759C2×C4#54811yescharacteristic
760C2×C4D4×Q811yescharacteristic
761C2×C4#55311yescharacteristic
762C2×C4#55311yescharacteristic
763C2×C4#55411yescharacteristic
764C2×C4#55411yescharacteristic
765C8—24no—
766C8—42no—
767C8—42no—
768C8#38518yescomplemented
769C22—48no—
770C22—48no—
771C22—44no—
772C22—44no—
773C22—84no—
774C22—84no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—84no—
788C22—84no—
789C22—84no—
790C22—84no—
791C22C4×#12711yescharacteristic
792C22D4×C4⋊C411yescharacteristic
793C22#236111yescharacteristic
794C22#242211yescharacteristic
795C22#243311yescharacteristic
796C22#245211yescharacteristic
797C22#254211yescharacteristic
798C22C4×AGL(1,ℤ/8)12yes—
799C22#294612yes—
800C22#315111yescharacteristic
801C22#315311yescharacteristic
802C22#315411yescharacteristic
803C22#315511yescharacteristic
804C22#317912yes—
805C22#318012yes—
806C22#326412yes—
807C22#326712yes—
808C22#327412yes—
809C22#327512yes—
810C22#334512yes—
811C22#334712yes—
812C22#338412yes—
813C22#338912yes—
814C4—42no—
815C4—42no—
816C4—44no—
817C4—44no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—161no—
823C4—161no—
824C4C2×#38511yescharacteristic
825C4#232611yescharacteristic
826C4D4×C4⋊C411yescharacteristic
827C4#236111yescharacteristic
828C4#242211yescharacteristic
829C4#243211yescharacteristic
830C4#245211yescharacteristic
831C4#256611yescharacteristic
832C2—84no—
833C2—84no—
834C2#1397711yescharacteristic
835C2#2170111yescharacteristic
836C2#2170411yescharacteristic
837C2#2267612yes—
838C2#2303912yes—
839C2#2504212yes—
840C2#2579411yescharacteristic
841C2#2579611yescharacteristic
842C2#2649612yes—
843C2#2854411yescharacteristic
844C2#2854811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1944C2semidirect
5. C2×#1864C2semidirect
6. C2×#1862C2semidirect
7. C2×#1847C2semidirect
8. #13979C2semidirect
9. #13977C2semidirect
10. #11123C2semidirect
11. #11121C2semidirect
12. #11051C2semidirect
13. #11049C2semidirect
14. #10861C2semidirect
15. #10696C2semidirect
45. #1972C4semidirect
123. C2×#106C2×C4semidirect
141. C2×#102C2×C4semidirect
142. C2×#102C2×C4semidirect
147. C2×#97C2×C4semidirect
158. #390C2×C4semidirect
159. #390C2×C4semidirect
240. C2×D8C4⋊C4semidirect
768. C8#385semidirect

Maximal subgroups

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

subgroupindex
C22×#4422
C2×#19722
C2×#19702
C2×#19442
C2×#18642
C2×#18622
C2×#18472
#139792
#139772
#111232
#111212
#110512
#110492
#108612
#106962