Finite Group Databasebeta

← #219724

Subgroups — #219724

Order 512.

1742 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2361C211yesmaximal, characteristic
2D4×C22⋊C8C212yesmaximal, complemented
3C2×#1459C211yesmaximal, characteristic, complemented
4C22×#324C211yesmaximal, characteristic, complemented
5#9651C212yesmaximal, complemented
6#9081C212yesmaximal, complemented
7#9079C212yesmaximal, complemented
8#8560C211yesmaximal, characteristic, complemented
9#8301C211yesmaximal, characteristic, complemented
10#8299C211yesmaximal, characteristic, complemented
11C4×#324C211yesmaximal, characteristic, complemented
12C22×#121C411yescharacteristic
13C22×C4×D4C411yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C22×C4×D4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C2×C8×D4—22no—
18C22×C22⋊C8C2212yes—
19C22×C22⋊C8C2212yes—
20#2361—22no—
21#2361—22no—
22#2361—22no—
23#2361—22no—
24C2×#390C411yescharacteristic
25C2×#389C411yescharacteristic
26C2×#388C411yescharacteristic
27C2×#388C2211yescharacteristic
28C2×#386C411yescharacteristic
29C2×#386C2211yescharacteristic
30C2×#385C411yescharacteristic
31C2×#385C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C411yescharacteristic
34#1954—22no—
35#1869—22no—
36#1869—22no—
37#1797C2212yes—
38#1779C2212yes—
39#1779C2212yes—
40C4×C22⋊C8C2212yes—
41#1459—24no—
42C2×#324—24no—
43C2×#324C2211yescharacteristic
44C2×#324C2211yescharacteristic
45C2×#324C2211yescharacteristic
46C2×#324C2212yes—
47C2×#324C2212yes—
48C2×#324C2211yescharacteristic
49C2×#323C2212yes—
50C2×#323C2212yes—
51#1280C2212yes—
52#1280C2212yes—
53C23×D4C2×C411yescharacteristic
54C23×D4C2×C411yescharacteristic
55C23×D4C2×C411yescharacteristic
56C24×C4C2×C411yescharacteristic
57C24×C4C2×C411yescharacteristic
58C24×C4C2×C411yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C23×C8—22no—
62C23×C8—22no—
63C2×#121—22no—
64C2×#121—22no—
65C2×#121—24no—
66C2×#121C818yescomplemented
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—21no—
75C2×C4×D4—42no—
76C2×C4×D4—44no—
77C2×C4×D4—44no—
78C2×C4×D4D412yes—
79C2×C4×D4D412yes—
80C2×C4×D4D412yes—
81C2×C4×D4D412yes—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C22⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C411yescharacteristic
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2311yescharacteristic
104C22×C42C2×C411yescharacteristic
105C22×C42C2×C411yescharacteristic
106C22×C42C2×C411yescharacteristic
107C22×C42C2311yescharacteristic
108C8×D4—48no—
109C2×C4⋊C8—22no—
110C2×C22⋊C8—24no—
111C2×C22⋊C8—24no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—42no—
119C2×C22⋊C8—42no—
120C2×C22⋊C8C2312yes—
121C2×C22⋊C8C2312yes—
122C2×C22⋊C8C2312yes—
123C2×C22⋊C8C2312yes—
124C2×C4×C8—22no—
125#390—22no—
126#390—22no—
127#389—22no—
128#389—22no—
129#388—22no—
130#388—22no—
131#388—22no—
132#388—22no—
133#386—22no—
134#386—22no—
135#386—22no—
136#386—22no—
137#385—22no—
138#385—22no—
139#385—22no—
140#385—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C22⋊C4—21no—
144C4×C22⋊C4—21no—
145C4×C22⋊C4—21no—
146C4×C22⋊C4—21no—
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2311yescharacteristic
153#336—22no—
154#336—22no—
155#324—22no—
156#324—22no—
157#324—22no—
158#324—24no—
159#324—42no—
160#324D414yescomplemented
161#323—24no—
162#323—42no—
163C25C22×C411yescharacteristic
164C25C22×C411yescharacteristic
165C25C22×C411yescharacteristic
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—22no—
169C22×D4—22no—
170C22×D4—22no—
171C22×D4—22no—
172C22×D4—22no—
173C22×D4—41no—
174C22×D4—41no—
175C22×D4—42no—
176C22×D4—42no—
177C22×D4—42no—
178C22×D4—42no—
179C22×D4C22⋊C412yes—
180C22×D4C22⋊C412yes—
181C22×D4C2×C814yes—
182C22×D4C2×C814yescomplemented
183C22×D4C2×C814yescomplemented
184C22×D4M1614yes—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—42no—
203C23×C4—41no—
204C23×C4—41no—
205C23×C4—41no—
206C23×C4—41no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—81no—
211C23×C4—81no—
212C23×C4—81no—
213C23×C4—81no—
214C23×C4C2×C814yescomplemented
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C2×D412yes—
227C23×C4C2×D412yes—
228C23×C4C2×D412yes—
229C23×C4C2×D412yes—
230C23×C4C2411yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—44no—
236C22×C8—44no—
237C22×C8—44no—
238C22×C8—44no—
239C22×C8—82no—
240C22×C8—82no—
241#121—216no—
242#121—216no—
243C4×D4—28no—
244C4×D4—44no—
245C4×D4—44no—
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—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—44no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4C22⋊C412yes—
278C2×C4⋊C4C22⋊C412yes—
279C2×C4⋊C4C2×C814yescomplemented
280C2×C4⋊C4C2×D412yes—
281C2×C4⋊C4#4112yes—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—81no—
304C2×C22⋊C4—81no—
305C2×C22⋊C4C22⋊C411yescharacteristic
306C2×C22⋊C4C22⋊C411yescharacteristic
307C2×C22⋊C4C22⋊C411yescharacteristic
308C2×C22⋊C4C22⋊C412yes—
309C2×C22⋊C4C22⋊C412yes—
310C2×C22⋊C4C22⋊C411yescharacteristic
311C2×C22⋊C4C2×C814yescomplemented
312C2×C22⋊C4C2×C814yescomplemented
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—42no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—42no—
325C2×C42C2×D412yes—
326C2×C42C2×D412yes—
327C4⋊C8—44no—
328C22⋊C8—22no—
329C22⋊C8—22no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334C22⋊C8—22no—
335C22⋊C8—44no—
336C22⋊C8—44no—
337C22⋊C8—44no—
338C22⋊C8—44no—
339C22⋊C8—82no—
340C22⋊C8—82no—
341C22⋊C8C2×D414yes—
342C4×C8—44no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—22no—
356C24—22no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24C2×C22⋊C412yes—
378C24C2×C22⋊C411yescharacteristic
379C24C2×C22⋊C411yescharacteristic
380C24C22×C812yes—
381C24C22×C812yes—
382C24C22×C812yes—
383C24C2×M1612yes—
384C24C2×M1612yes—
385C24C23×C411yescharacteristic
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—28no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—48no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—48no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—48no—
407C2×D4C22⋊C818yes—
408C2×D4C22⋊C818yes—
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—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—28no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—82no—
495C22×C4—82no—
496C22×C4—84no—
497C22×C4—82no—
498C22×C4—82no—
499C22×C4—84no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4—84no—
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C412yes—
509C22×C4C2×C22⋊C412yes—
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C4×D412yes—
513C22×C4C4×D412yes—
514C22×C4C22×C812yes—
515C22×C4C22×C812yes—
516C22×C4C22×C812yes—
517C22×C4C22×C812yes—
518C22×C4C2×M1612yes—
519C22×C4#13112yes—
520C22×C4C22×D412yes—
521C22×C4C22×D411yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4H(5,𝔽2)12yes—
524C2×C8—24no—
525C2×C8—42no—
526C2×C8—42no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8—42no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—88no—
537C2×C8—88no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—28no—
541C4⋊C4—24no—
542C4⋊C4—42no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C22⋊C4—28no—
550C22⋊C4—22no—
551C22⋊C4—28no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—24no—
555C22⋊C4—42no—
556C22⋊C4—44no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—82no—
564C22⋊C4—82no—
565C22⋊C4#9914yes—
566C42—24no—
567C42—42no—
568C42—42no—
569C42—42no—
570C42—42no—
571C42—42no—
572C42—42no—
573C42—42no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—21no—
587C23—22no—
588C23—22no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—21no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—42no—
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—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23C2×C22⋊C814yes—
650C23C2×C22⋊C812yes—
651C23C2×C22⋊C812yes—
652C23C2×#9912yes—
653C23#41312yes—
654C23C22×C22⋊C411yescharacteristic
655C23C2×C4×D411yescharacteristic
656C23#51811yescharacteristic
657C23C23×C811yescharacteristic
658C23C22×M1611yescharacteristic
659C23C2×#13111yescharacteristic
660C23#56811yescharacteristic
661D4—216no—
662D4—48no—
663D4—416no—
664D4—48no—
665D4—48no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—84no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4C2×C22⋊C814yes—
747C2×C4C2×#9912yes—
748C2×C4C2×#9912yes—
749C2×C4C8×D414yescomplemented
750C2×C4D4212yes—
751C2×C4#54612yes—
752C8—44no—
753C8—82no—
754C8—82no—
755C8—82no—
756C22—21no—
757C22—21no—
758C22—22no—
759C22—21no—
760C22—21no—
761C22—22no—
762C22—22no—
763C22—21no—
764C22—21no—
765C22—22no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—24no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22#145914yescomplemented
808C22D4×C22⋊C411yescharacteristic
809C22C22×C22⋊C811yescharacteristic
810C22#288011yescharacteristic
811C22C22×#9911yescharacteristic
812C22#288311yescharacteristic
813C22C2×#41311yescharacteristic
814C22#288911yescharacteristic
815C22C2×C8×D411yescharacteristic
816C22D4×M1611yescharacteristic
817C22#297211yescharacteristic
818C22#297411yescharacteristic
819C4—22no—
820C4—24no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—24no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—24no—
839C2—42no—
840C2—44no—
841C2—82no—
842C2C2×#145911yescharacteristic
843C2#1735111yescharacteristic
844C2#1741611yescharacteristic
845C2#1742711yescharacteristic
846C2D4×C22⋊C811yescharacteristic
847C2D4×#9911yescharacteristic
848C2#2241011yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC23C23×C8
Frattini, cosocleC23×C4C24
prime radicalC22×#121C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. D4×C22⋊C8C2semidirect
3. C2×#1459C2semidirect
4. C22×#324C2semidirect
5. #9651C2semidirect
6. #9081C2semidirect
7. #9079C2semidirect
8. #8560C2semidirect
9. #8301C2semidirect
10. #8299C2semidirect
11. C4×#324C2semidirect
66. C2×#121C8semidirect
160. #324D4semidirect
182. C22×D4C2×C8semidirect
183. C22×D4C2×C8semidirect
214. C23×C4C2×C8semidirect
279. C2×C4⋊C4C2×C8semidirect
311. C2×C22⋊C4C2×C8semidirect
312. C2×C22⋊C4C2×C8semidirect
749. C2×C4C8×D4semidirect
807. C22#1459semidirect

Maximal subgroups

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

subgroupindex
C2×#23612
D4×C22⋊C82
C2×#14592
C22×#3242
#96512
#90812
#90792
#85602
#83012
#82992
C4×#3242