Finite Group Databasebeta

← #392751

Subgroups — #392751

Order 512.

1718 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×M16C211yesmaximal, characteristic
2C2×#1917C211yesmaximal, characteristic, complemented
3C2×#1916C211yesmaximal, characteristic, complemented
4C2×#1851C211yesmaximal, characteristic
5C4×#385C211yesmaximal, characteristic
6#10877C211yesmaximal, characteristic, complemented
7#10876C211yesmaximal, characteristic, complemented
8#10875C211yesmaximal, characteristic, complemented
9#10874C211yesmaximal, characteristic, complemented
10#10798C211yesmaximal, characteristic, complemented
11#10797C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic
13#10715C211yesmaximal, characteristic
14#10715C211yesmaximal, characteristic
15#10712C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C2×C4×M16—24no—
24C2×C4×M16—24no—
25C2×C4×M16—24no—
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C2×#385C411yescharacteristic
31C2×#385C411yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#1917—24no—
37#1916—24no—
38#1851—24no—
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59#1436C411yescharacteristic
60#1436C411yescharacteristic
61C22⋊#95C411yescharacteristic
62C22⋊#95C411yescharacteristic
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2311yescharacteristic
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16D414yes—
81C22×M16Q814yes—
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C4⋊C4C2×C411yescharacteristic
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42C2×C411yescharacteristic
105C22×C42C2×C411yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C4×M16—232no—
125C2×#97—22no—
126C2×#97—22no—
127C2×#97—22no—
128C2×#97—22no—
129C2×#97—22no—
130C2×#97D414yes—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—22no—
134C2×C4×C8—22no—
135C2×C4×C8—22no—
136C2×C4×C8D414yes—
137#385—24no—
138#385—24no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C22⋊C4—22no—
144C4×C22⋊C4—22no—
145C4×C22⋊C4—22no—
146C4×C22⋊C4—22no—
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162C2×#95C2×C411yescharacteristic
163#336—22no—
164#336—22no—
165#336—22no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178#336—22no—
179#336—22no—
180#336—22no—
181C25C22×C411yescharacteristic
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4—41no—
203C23×C4—41no—
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C2×D412yes—
218C23×C4C2×Q812yes—
219C23×C4#4112yes—
220C23×C4#4112yes—
221C23×C4#4112yes—
222C23×C4#4112yes—
223C23×C4C2411yescharacteristic
224C2×M16—28no—
225C2×M16—28no—
226C2×M16—28no—
227C2×M16—28no—
228C2×M16—28no—
229C2×M16—28no—
230C2×M16—28no—
231C2×M16—28no—
232C2×M16—28no—
233C2×M16—28no—
234C2×M16—28no—
235C2×M16—28no—
236C2×M16—28no—
237C2×M16—28no—
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×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—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8C2×D412yes—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8C2×D412yes—
286C22×C8C2×D412yes—
287C22×C8C2×D412yes—
288C22×C8C2×Q812yes—
289C22×C8C2×Q812yes—
290C22×C8#4112yes—
291C22×C8#4112yes—
292C22×C8#4112yes—
293C22×C8#4112yes—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4M1614yescomplemented
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C42—28no—
319C2×C42—28no—
320C2×C42—28no—
321C2×C42—28no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
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—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42C2×D412yes—
361C2×C42C2×D412yes—
362C2×C42#4112yes—
363C2×C42#4112yes—
364C4⋊C8—44no—
365C4⋊C8—44no—
366C22⋊C8—44no—
367C22⋊C8—44no—
368#97—28no—
369#97—28no—
370C4×C8—28no—
371C4×C8—28no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—41no—
386#95—41no—
387#95M1614yescomplemented
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24#11712yes—
401C24C4×D412yes—
402C24C4×Q812yes—
403C24C23×C411yescharacteristic
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—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—21no—
443C22×C4—21no—
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—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
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—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—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4#11712yes—
519C22×C4C4×D412yes—
520C22×C4C4×D412yes—
521C22×C4C4×D412yes—
522C22×C4C4×D412yes—
523C22×C4C4×D412yes—
524C22×C4C4×Q812yes—
525C22×C4C22⋊Q814yes—
526C22×C4#12314yes—
527C22×C4#12514yes—
528C22×C4#12614yes—
529C22×C4C2×M1612yes—
530C22×C4C2×M1612yes—
531C22×C4C2×M1612yes—
532C22×C4C2×M1612yes—
533C22×C4C2×M1612yes—
534C22×C4C2×M1612yes—
535C22×C4#13112yes—
536C22×C4#13112yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×Q811yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551M16—232no—
552M16—232no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
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—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8#12014yes—
606C2×C8C22⋊Q814yes—
607C2×C8C22⋊Q814yes—
608C2×C8#12314yes—
609C4⋊C4—28no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C22⋊C4—28no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C42—28no—
618C42—28no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23#38714yes—
678C23C2×#11711yescharacteristic
679C23C2×C4×D411yescharacteristic
680C23C2×C4×D411yescharacteristic
681C23C2×C4×D411yescharacteristic
682C23C2×C4×Q811yescharacteristic
683C23C4×#4111yescharacteristic
684C23C4×#4111yescharacteristic
685C23C22×M1611yescharacteristic
686C23C22×M1611yescharacteristic
687C23C2×#13111yescharacteristic
688C23C2×#13111yescharacteristic
689C23#56811yescharacteristic
690C23#56811yescharacteristic
691C23#56811yescharacteristic
692C23#56811yescharacteristic
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
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—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#38714yes—
792C2×C4#43514yes—
793C2×C4#43614yes—
794C2×C4C2×#12011yescharacteristic
795C2×C4C2×C22⋊Q811yescharacteristic
796C2×C4C2×C22⋊Q811yescharacteristic
797C2×C4C2×C22⋊Q811yescharacteristic
798C2×C4C2×#12311yescharacteristic
799C2×C4C2×#12311yescharacteristic
800C2×C4#52511yescharacteristic
801C2×C4#52511yescharacteristic
802C2×C4#52511yescharacteristic
803C2×C4#52511yescharacteristic
804C2×C4#52511yescharacteristic
805C2×C4#52511yescharacteristic
806C2×C4#52511yescharacteristic
807C2×C4#52511yescharacteristic
808C2×C4#52511yescharacteristic
809C2×C4#52511yescharacteristic
810C2×C4C2×#12511yescharacteristic
811C2×C4C2×#12611yescharacteristic
812C2×C4#52911yescharacteristic
813C2×C4#52911yescharacteristic
814C2×C4#52911yescharacteristic
815C2×C4#52911yescharacteristic
816C2×C4#52911yescharacteristic
817C2×C4#52911yescharacteristic
818C2×C4#52911yescharacteristic
819C2×C4#52911yescharacteristic
820C2×C4#53311yescharacteristic
821C2×C4#53311yescharacteristic
822C8—24no—
823C8—24no—
824C8—24no—
825C8—24no—
826C8—81no—
827C8—81no—
828C8—81no—
829C8—81no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22C2×#38711yescharacteristic
846C22#229011yescharacteristic
847C22#229011yescharacteristic
848C22C4×#12011yescharacteristic
849C22C4×#12311yescharacteristic
850C22C4×C22⋊Q811yescharacteristic
851C22C4×C22⋊Q811yescharacteristic
852C22#292011yescharacteristic
853C22#292111yescharacteristic
854C22#292211yescharacteristic
855C22#292311yescharacteristic
856C22C2×#43511yescharacteristic
857C22C2×#43611yescharacteristic
858C22#293011yescharacteristic
859C22#293011yescharacteristic
860C22#293311yescharacteristic
861C22#293311yescharacteristic
862C22#293311yescharacteristic
863C22#293311yescharacteristic
864C22D4×M1611yescharacteristic
865C22D4×M1611yescharacteristic
866C22D4×M1611yescharacteristic
867C22D4×M1611yescharacteristic
868C22#296211yescharacteristic
869C22#296211yescharacteristic
870C22Q8×M1611yescharacteristic
871C22Q8×M1611yescharacteristic
872C22#296511yescharacteristic
873C22#296511yescharacteristic
874C22#296711yescharacteristic
875C22#296711yescharacteristic
876C22#296911yescharacteristic
877C22#296911yescharacteristic
878C22#297011yescharacteristic
879C22#297111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—81no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4#284811yescharacteristic
894C4#284911yescharacteristic
895C4#285111yescharacteristic
896C4#285111yescharacteristic
897C4#285211yescharacteristic
898C4#285211yescharacteristic
899C4#285311yescharacteristic
900C4#285511yescharacteristic
901C2—44no—
902C2#1469511yescharacteristic
903C2#2102211yescharacteristic
904C2#2102311yescharacteristic
905C2#2110211yescharacteristic
906C2#2110411yescharacteristic
907C2#2110611yescharacteristic
908C2#2110811yescharacteristic
909C2#2143911yescharacteristic
910C2#2144111yescharacteristic
911C2#2156211yescharacteristic
912C2#2156511yescharacteristic
913C2#2159611yescharacteristic
914C2#2159811yescharacteristic
915C2#2160011yescharacteristic
916C2#2160011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1917C2semidirect
3. C2×#1916C2semidirect
6. #10877C2semidirect
7. #10876C2semidirect
8. #10875C2semidirect
9. #10874C2semidirect
10. #10798C2semidirect
11. #10797C2semidirect
305. C2×C4⋊C4M16semidirect
387. #95M16semidirect

Maximal subgroups

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

subgroupindex
C22×C4×M162
C2×#19172
C2×#19162
C2×#18512
C4×#3852
#108772
#108762
#108752
#108742
#107982
#107972
#107152
#107122