Finite Group Databasebeta

← #369474

Subgroups — #369474

Order 512.

1540 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1862C211yesmaximal, characteristic
2C2×#1804C211yesmaximal, characteristic
3C2×C4×#102C211yesmaximal, characteristic
4#14030C211yesmaximal, characteristic, complemented
5D4×#95C211yesmaximal, characteristic
6#11372C211yesmaximal, characteristic, complemented
7#11316C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11232C211yesmaximal, characteristic, complemented
10#10907C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10820C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#382C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C22×#95—21no—
30#1862—24no—
31#1804C418yescomplemented
32C4×#102—24no—
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48#1443—21no—
49#1442—21no—
50#1436—21no—
51C4⋊#95C2211yescharacteristic
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57#1434—21no—
58C22⋊#95—21no—
59C22⋊#95—21no—
60C22⋊#95—21no—
61C4×#95C2211yescharacteristic
62C23×D4C2311yescharacteristic
63C24×C4—21no—
64C24×C4—21no—
65C24×C4—21no—
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—41no—
81C2×C4×D4—41no—
82C2×C4×D4—41no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4C2×C414yes—
87C2×C4×D4Q814yes—
88C22×C4⋊C4—21no—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×#107—22no—
104C2×#107—22no—
105C2×#107—41no—
106C2×C4⋊C8—41no—
107C2×C4⋊C8—41no—
108C2×C4⋊C8C2×C414yescomplemented
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102C2×C414yes—
119C2×#102C2×C414yes—
120C2×#102D414yes—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—41no—
124#389—22no—
125#389—41no—
126#382—22no—
127#382C2×C414yescomplemented
128C4×C4⋊C4—22no—
129C4×C4⋊C4—41no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—44no—
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
150C2×#95D411yescharacteristic
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340—41no—
159#340—41no—
160#340C2×C414yescomplemented
161#340C2×C414yescomplemented
162#336—22no—
163#336—22no—
164#336—22no—
165#336—41no—
166C25—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4C22×C412yes—
175C22×D4C2×D412yes—
176C22×D4C2×Q812yes—
177C22×D4#4112yes—
178C22×D4#4112yes—
179C22×D4#4112yes—
180C22×D4#4112yes—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—24no—
190C23×C4—21no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—81no—
204C23×C4—81no—
205C23×C4—81no—
206C23×C4—81no—
207C23×C4—81no—
208C23×C4—81no—
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2411yescharacteristic
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8C22×C412yes—
242C22×C8C22×C412yes—
243C22×C8C2×D412yes—
244C4×D4—28no—
245C4×D4—28no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—44no—
250C4×D4—44no—
251C4×D4—44no—
252C4×D4—44no—
253C4×D4—44no—
254C4×D4—44no—
255C4×D4—44no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
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—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4C22×C412yes—
296C2×C4⋊C4C22×C412yes—
297C2×C4⋊C4C22×C412yes—
298C2×C4⋊C4C2×D412yes—
299C2×C4⋊C4C2×Q812yes—
300C2×C4⋊C4#4112yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—81no—
327C2×C42C22×C412yes—
328C2×C42C2×Q812yes—
329C2×C42#4112yes—
330C2×C42#4112yes—
331#107—44no—
332C4⋊C8—44no—
333#102—28no—
334#102—28no—
335#102—28no—
336#102—44no—
337C4×C8—44no—
338#95—24no—
339#95—24no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—41no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—81no—
352#95—81no—
353#95—81no—
354#95—81no—
355#95—81no—
356#95—81no—
357#95—81no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C22×D411yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4#11714yes—
396C2×D4C4×D414yes—
397C2×D4C4×Q814yes—
398C2×D4C22⋊Q814yes—
399C2×D4#12314yes—
400C2×D4#12514yes—
401C2×D4#12614yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—48no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4—84no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4—84no—
506C22×C4—84no—
507C22×C4C4×D412yes—
508C22×C4C4×D412yes—
509C22×C4C22⋊Q812yes—
510C22×C4C22⋊Q812yes—
511C22×C4#13512yes—
512C22×C4#13512yes—
513C22×C4AGL(1,ℤ/8)12yes—
514C22×C4C23×C411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×Q811yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4H(5,𝔽2)11yescharacteristic
525C22×C4H(5,𝔽2)11yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C42−1+411yescharacteristic
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
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×C8—41no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
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—84no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—84no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23C2×C4×D411yescharacteristic
637C23C2×C22⋊Q811yescharacteristic
638C23#52511yescharacteristic
639C23D4211yescharacteristic
640C23#54611yescharacteristic
641C23#54611yescharacteristic
642C23#54811yescharacteristic
643C23C2×#13511yescharacteristic
644C23C2×#13511yescharacteristic
645C23C2×AGL(1,ℤ/8)11yescharacteristic
646C23#57511yescharacteristic
647C23#57611yescharacteristic
648C23#57611yescharacteristic
649C23#57711yescharacteristic
650C23#57811yescharacteristic
651D4—24no—
652D4—24no—
653D4—24no—
654D4—24no—
655D4—24no—
656D4—24no—
657D4—24no—
658D4#38718yes—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—816no—
719C2×C4—816no—
720C2×C4—816no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4#47814yes—
753C2×C4C2×#11711yescharacteristic
754C2×C4C2×C4×D411yescharacteristic
755C2×C4C2×C4×Q811yescharacteristic
756C2×C4C4×#4111yescharacteristic
757C2×C4#51811yescharacteristic
758C2×C4#52011yescharacteristic
759C2×C4C2×C22⋊Q811yescharacteristic
760C2×C4C2×#12311yescharacteristic
761C2×C4C2×#12511yescharacteristic
762C2×C4C2×#12611yescharacteristic
763C2×C4#52911yescharacteristic
764C2×C4#53311yescharacteristic
765C2×C4#53811yescharacteristic
766C2×C4#53911yescharacteristic
767C2×C4#54311yescharacteristic
768C2×C4#54411yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54711yescharacteristic
772C2×C4#55111yescharacteristic
773C2×C4#55111yescharacteristic
774C2×C4#55111yescharacteristic
775C2×C4#55111yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55211yescharacteristic
778C2×C4#55311yescharacteristic
779C2×C4#55311yescharacteristic
780C2×C4#55311yescharacteristic
781C8—42no—
782C8—42no—
783C8—42no—
784C8—81no—
785C22—28no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C4×C22⋊Q811yescharacteristic
801C22#234211yescharacteristic
802C22#236111yescharacteristic
803C22#241811yescharacteristic
804C22#243711yescharacteristic
805C22#244211yescharacteristic
806C22#248111yescharacteristic
807C22C4×#13511yescharacteristic
808C22C4×AGL(1,ℤ/8)11yescharacteristic
809C22#294611yescharacteristic
810C22#295111yescharacteristic
811C22C2×#47811yescharacteristic
812C22#307611yescharacteristic
813C22#308111yescharacteristic
814C22#308311yescharacteristic
815C22#310211yescharacteristic
816C22#310511yescharacteristic
817C22#312011yescharacteristic
818C22#312211yescharacteristic
819C22#326411yescharacteristic
820C22#326911yescharacteristic
821C22#328011yescharacteristic
822C22#328211yescharacteristic
823C22#329711yescharacteristic
824C22#329711yescharacteristic
825C22#330211yescharacteristic
826C22#330211yescharacteristic
827C22#331011yescharacteristic
828C22#331911yescharacteristic
829C22#332311yescharacteristic
830C22#332511yescharacteristic
831C22#336011yescharacteristic
832C22#336111yescharacteristic
833C22#336711yescharacteristic
834C22#337011yescharacteristic
835C4—24no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—81no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—161no—
848C4C2×#38711yescharacteristic
849C4#232911yescharacteristic
850C4#234311yescharacteristic
851C4#236411yescharacteristic
852C4#241911yescharacteristic
853C4#243811yescharacteristic
854C4#251011yescharacteristic
855C4#256911yescharacteristic
856C2—48no—
857C2#1402811yescharacteristic
858C2C4×#47811yescharacteristic
859C2#2162011yescharacteristic
860C2#2257611yescharacteristic
861C2#2258411yescharacteristic
862C2#2299911yescharacteristic
863C2#2301111yescharacteristic
864C2#2489711yescharacteristic
865C2#2490311yescharacteristic
866C2#2595411yescharacteristic
867C2#2596011yescharacteristic
868C2#2611111yescharacteristic
869C2#2611711yescharacteristic
870C2#2755511yescharacteristic
871C2#2756011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
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. #14030C2semidirect
6. #11372C2semidirect
7. #11316C2semidirect
8. #11293C2semidirect
9. #11232C2semidirect
10. #10907C2semidirect
11. #10876C2semidirect
12. #10820C2semidirect
31. #1804C4semidirect
108. C2×C4⋊C8C2×C4semidirect
127. #382C2×C4semidirect
160. #340C2×C4semidirect
161. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18622
C2×#18042
C2×C4×#1022
#140302
D4×#952
#113722
#113162
#112932
#112322
#109072
#108762
#108202
#107882