Finite Group Databasebeta

← #394923

Subgroups — #394923

Order 512.

1720 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q16C211yesmaximal, characteristic, complemented
2C2×#2423C211yesmaximal, characteristic
3C2×#2036C211yesmaximal, characteristic
4C2×#2001C211yesmaximal, characteristic
5C2×#1863C211yesmaximal, characteristic, complemented
6#13969C211yesmaximal, characteristic
7#11324C211yesmaximal, characteristic, complemented
8#11190C211yesmaximal, characteristic, complemented
9#11096C211yesmaximal, characteristic
10#11050C211yesmaximal, characteristic, complemented
11#11024C211yesmaximal, characteristic, complemented
12#10970C211yesmaximal, characteristic
13#10921C211yesmaximal, characteristic
14#10880C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×Q16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C2×C4×Q16—24no—
22C2×C4×Q16—24no—
23C2×C4×Q16—24no—
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35#2423—24no—
36#2423—24no—
37C2×#399—21no—
38C2×#398—21no—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#388—21no—
43C2×#387—21no—
44C2×#384C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48#2036—24no—
49#2001—24no—
50#1863—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1441—21no—
62#1439—21no—
63#1437—21no—
64#1436—21no—
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67C23×Q8C2311yescharacteristic
68C23×Q8C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C22×Q16—22no—
71C22×Q16—22no—
72C22×Q16—22no—
73C22×Q16—22no—
74C22×Q16—22no—
75C22×Q16—22no—
76C22×Q16D414yes—
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8—22no—
85C2×C22⋊Q8—22no—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—41no—
90C2×C22⋊Q8—41no—
91C2×C22⋊Q8—41no—
92C2×C22⋊Q8—41no—
93C2×C4×Q8—22no—
94C2×C4×Q8—22no—
95C2×C4×Q8—22no—
96C2×C4×Q8—22no—
97C2×C4×Q8—22no—
98C2×C4×Q8—22no—
99C2×C4×Q8—22no—
100C2×C4×Q8—41no—
101C2×C4×Q8—41no—
102C2×C4×Q8—41no—
103C2×C4×Q8—41no—
104C2×C4×Q8D414yes—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4D411yescharacteristic
123C22×C22⋊C4D411yescharacteristic
124C22×C42—21no—
125C22×C42—21no—
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C4×Q16—232no—
129C2×#107—22no—
130C2×#107—22no—
131C2×#107—22no—
132C2×#107—22no—
133C2×#107—22no—
134C2×#107—41no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—41no—
150C2×#103—41no—
151C2×#103—41no—
152C2×#103D414yes—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—41no—
159C2×C4×C8—22no—
160C2×C4×C8—22no—
161C2×C4×C8—22no—
162#399—28no—
163#398—28no—
164#391—22no—
165#391—22no—
166#391—22no—
167#391—41no—
168#389—22no—
169#389D414yes—
170#388—28no—
171#387—28no—
172#384—22no—
173#384—22no—
174#380—22no—
175#380—22no—
176#380—22no—
177#380—41no—
178C4×C22⋊C4—22no—
179C4×C22⋊C4—22no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95D411yescharacteristic
192C2×#95D411yescharacteristic
193#340—22no—
194#340—22no—
195#340—22no—
196#340—22no—
197#340—22no—
198#340—41no—
199#340—41no—
200#336—22no—
201#336—22no—
202#336—41no—
203C25C2×D411yescharacteristic
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8C2×D412yes—
227C22×Q8C2×D412yes—
228C22×Q8C2×D412yes—
229C22×Q8C2×D412yes—
230C22×Q8#4112yes—
231C22×Q8#4112yes—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2411yescharacteristic
260C2×Q16—28no—
261C2×Q16—28no—
262C2×Q16—28no—
263C2×Q16—28no—
264C2×Q16—28no—
265C2×Q16—28no—
266C2×Q16—28no—
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×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22×C8#4112yes—
293C22×C8#4112yes—
294C22×C8#4112yes—
295C22⋊Q8—44no—
296C22⋊Q8—44no—
297C22⋊Q8—44no—
298C22⋊Q8—44no—
299C22⋊Q8—44no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C22⋊Q8—44no—
303C4×Q8—28no—
304C4×Q8—28no—
305C4×Q8—44no—
306C4×Q8—44no—
307C4×Q8—44no—
308C4×Q8—44no—
309C4×Q8—44no—
310C4×Q8—44no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—81no—
360C2×C4⋊C4—81no—
361C2×C4⋊C4—81no—
362C2×C4⋊C4—81no—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2×D412yes—
365C2×C4⋊C4C2×D412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4#4112yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—81no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4Q1614yescomplemented
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D412yes—
403C2×C42C2×D412yes—
404#107—28no—
405#107—44no—
406#103—28no—
407#103—28no—
408#103—28no—
409#103—44no—
410#103—44no—
411#103—44no—
412C22⋊C8—44no—
413C22⋊C8—44no—
414C4×C8—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—81no—
427#95—81no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24C2×Q1612yes—
443C24C22×D411yescharacteristic
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8#12014yes—
499C2×Q8#12314yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
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—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4#12012yes—
614C22×C4#12012yes—
615C22×C4C2×Q1612yes—
616C22×C4C2×Q1612yes—
617C22×C4#13512yes—
618C22×C4#13712yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4H(5,𝔽2)11yescharacteristic
630C22×C4H(5,𝔽2)11yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C42−1+411yescharacteristic
633Q16—232no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8#12314yes—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4—84no—
692C4⋊C4—84no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—84no—
698C22⋊C4—84no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—48no—
704C42—48no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23C2×#12011yescharacteristic
745C23#52511yescharacteristic
746C23#53211yescharacteristic
747C23D4211yescharacteristic
748C23D4211yescharacteristic
749C23#54611yescharacteristic
750C23#54711yescharacteristic
751C23C22×Q1611yescharacteristic
752C23C2×#13511yescharacteristic
753C23C2×#13711yescharacteristic
754C23#57511yescharacteristic
755C23#57611yescharacteristic
756C23#57711yescharacteristic
757C23#57811yescharacteristic
758C23#57811yescharacteristic
759Q8—24no—
760Q8—24no—
761Q8—24no—
762Q8—24no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—42no—
770Q8—42no—
771Q8—42no—
772Q8—42no—
773Q8—42no—
774Q8—42no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4#45114yes—
874C2×C4C2×#12011yescharacteristic
875C2×C4C2×#12311yescharacteristic
876C2×C4C2×#12311yescharacteristic
877C2×C4#52511yescharacteristic
878C2×C4#52511yescharacteristic
879C2×C4#52511yescharacteristic
880C2×C4#52511yescharacteristic
881C2×C4#52511yescharacteristic
882C2×C4#53211yescharacteristic
883C2×C4#53211yescharacteristic
884C2×C4#53411yescharacteristic
885C2×C4#53711yescharacteristic
886C2×C4#53811yescharacteristic
887C2×C4#53911yescharacteristic
888C2×C4#54011yescharacteristic
889C2×C4#54211yescharacteristic
890C2×C4D4211yescharacteristic
891C2×C4D4211yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#54611yescharacteristic
894C2×C4#54711yescharacteristic
895C2×C4#54711yescharacteristic
896C2×C4#54811yescharacteristic
897C2×C4#55011yescharacteristic
898C2×C4#55111yescharacteristic
899C2×C4#55311yescharacteristic
900C2×C4#55311yescharacteristic
901C2×C4#55911yescharacteristic
902C8—24no—
903C8—42no—
904C8—42no—
905C8—81no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22#238811yescharacteristic
922C22#240311yescharacteristic
923C22#240711yescharacteristic
924C22#241811yescharacteristic
925C22#242211yescharacteristic
926C22#245511yescharacteristic
927C22#246411yescharacteristic
928C22C2×#45111yescharacteristic
929C22#300211yescharacteristic
930C22#301111yescharacteristic
931C22#301211yescharacteristic
932C22#310411yescharacteristic
933C22#310711yescharacteristic
934C22#312111yescharacteristic
935C22#312411yescharacteristic
936C22#317011yescharacteristic
937C22#317211yescharacteristic
938C22#317511yescharacteristic
939C22#317811yescharacteristic
940C22#326811yescharacteristic
941C22#327011yescharacteristic
942C22#327011yescharacteristic
943C22#327111yescharacteristic
944C22#328411yescharacteristic
945C22D4×Q1611yescharacteristic
946C22D4×Q1611yescharacteristic
947C22#328711yescharacteristic
948C22#329911yescharacteristic
949C22#330011yescharacteristic
950C22#332711yescharacteristic
951C22#333311yescharacteristic
952C22#333611yescharacteristic
953C22#333811yescharacteristic
954C22#335211yescharacteristic
955C22#335611yescharacteristic
956C4—24no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—44no—
961C4—44no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4—81no—
968C4—161no—
969C4#243011yescharacteristic
970C4#244311yescharacteristic
971C4#244511yescharacteristic
972C4#245611yescharacteristic
973C4#246111yescharacteristic
974C4#260211yescharacteristic
975C4#263011yescharacteristic
976C4#284911yescharacteristic
977C2—82no—
978C2#1472111yescharacteristic
979C2#2357111yescharacteristic
980C2#2358511yescharacteristic
981C2#2385611yescharacteristic
982C2#2385711yescharacteristic
983C2#2412211yescharacteristic
984C2#2412711yescharacteristic
985C2#2490411yescharacteristic
986C2#2490611yescharacteristic
987C2#2503511yescharacteristic
988C2#2503911yescharacteristic
989C2#2655911yescharacteristic
990C2#2656011yescharacteristic
991C2#2696511yescharacteristic
992C2#2697311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q16C2semidirect
5. C2×#1863C2semidirect
7. #11324C2semidirect
8. #11190C2semidirect
10. #11050C2semidirect
11. #11024C2semidirect
14. #10880C2semidirect
15. #10789C2semidirect
385. C2×C22⋊C4Q16semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q162
C2×#24232
C2×#20362
C2×#20012
C2×#18632
#139692
#113242
#111902
#110962
#110502
#110242
#109702
#109212
#108802
#107892