Finite Group Databasebeta

← #383875

Subgroups — #383875

Order 512.

1764 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
1C2×#1928C211yesmaximal, characteristic, complemented
2C2×#1787C211yesmaximal, characteristic
3C2×#1787C211yesmaximal, characteristic
4#13974C211yesmaximal, characteristic
5#13922C211yesmaximal, characteristic
6#11199C211yesmaximal, characteristic
7#11190C211yesmaximal, characteristic, complemented
8#11124C211yesmaximal, characteristic, complemented
9#11096C211yesmaximal, characteristic
10#11067C211yesmaximal, characteristic, complemented
11#11067C211yesmaximal, characteristic, complemented
12#10932C211yesmaximal, characteristic, complemented
13#10928C211yesmaximal, characteristic, complemented
14#10928C211yesmaximal, characteristic, complemented
15#10922C211yesmaximal, characteristic
16C24×Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#103C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40#1928—24no—
41#1787—24no—
42#1787C418yescomplemented
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1446—21no—
54#1446—21no—
55#1443—21no—
56#1440—21no—
57#1436—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C23×Q8—21no—
63C23×Q8—22no—
64C23×Q8—22no—
65C23×Q8—22no—
66C23×Q8—22no—
67C23×Q8—22no—
68C23×Q8—41no—
69C23×Q8—41no—
70C23×Q8—41no—
71C23×Q8—41no—
72C23×Q8—41no—
73C23×Q8—41no—
74C23×Q8—41no—
75C23×Q8—41no—
76C23×Q8C2×C414yes—
77C23×Q8C2311yescharacteristic
78C23×Q8C2311yescharacteristic
79C24×C4—21no—
80C24×C4C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C22×C4⋊C4—21no—
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4D411yescharacteristic
96C22×C22⋊C4D411yescharacteristic
97C22×C42—21no—
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×#107—22no—
101C2×#107—41no—
102C2×#107—41no—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103—41no—
116C2×#103—41no—
117C2×#103—41no—
118C2×#103—41no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103C2×C414yes—
123C2×#103C2×C414yes—
124C2×#103C2×C414yes—
125C2×#103C2×C414yes—
126C2×#103D414yes—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2×C414yes—
133C2×#97—41no—
134C2×#97—41no—
135C2×#97—41no—
136#391—22no—
137#391—22no—
138#391—22no—
139#391—22no—
140#391—41no—
141#391—41no—
142#391—41no—
143#391—41no—
144#389—41no—
145#389—41no—
146#388—44no—
147#380—22no—
148#380—22no—
149#380—41no—
150#380—41no—
151#380—41no—
152#380C2×C414yes—
153C4×C4⋊C4—22no—
154C4×C4⋊C4—41no—
155C4×C22⋊C4—41no—
156C4×C22⋊C4—41no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95D411yescharacteristic
175C2×#95D411yescharacteristic
176#340—22no—
177#340—41no—
178#340—41no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340—41no—
183#336—22no—
184#336—41no—
185#336—41no—
186C25C2×D411yescharacteristic
187C22×Q8—24no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—28no—
195C22×Q8—28no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
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—42no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8—42no—
216C22×Q8—44no—
217C22×Q8—44no—
218C22×Q8—44no—
219C22×Q8—44no—
220C22×Q8—44no—
221C22×Q8—44no—
222C22×Q8—44no—
223C22×Q8—44no—
224C22×Q8—42no—
225C22×Q8—42no—
226C22×Q8—44no—
227C22×Q8—44no—
228C22×Q8—44no—
229C22×Q8—44no—
230C22×Q8—44no—
231C22×Q8—44no—
232C22×Q8—44no—
233C22×Q8—44no—
234C22×Q8—44no—
235C22×Q8—44no—
236C22×Q8—44no—
237C22×Q8—44no—
238C22×Q8—44no—
239C22×Q8—44no—
240C22×Q8—44no—
241C22×Q8—44no—
242C22×Q8—44no—
243C22×Q8—44no—
244C22×Q8C22×C412yes—
245C22×Q8C22×C412yes—
246C22×Q8C2×D412yes—
247C22×Q8#4112yes—
248C22×Q8#4112yes—
249C22×Q8#4112yes—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—24no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4C22×C412yes—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4#4112yes—
284C23×C4C2411yescharacteristic
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8C22×C412yes—
311C22×C8C22×C412yes—
312C22×C8C2×D412yes—
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—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
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—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C22×C412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—81no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—81no—
382#107—44no—
383#103—28no—
384#103—44no—
385#103—44no—
386#103—44no—
387#103—44no—
388#103—44no—
389#103—44no—
390#103—44no—
391C22⋊C8—44no—
392C22⋊C8—44no—
393#97—44no—
394#95—24no—
395#95—41no—
396#95—41no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—81no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24C4×D412yes—
426C24AGL(1,ℤ/8)12yes—
427C24#13712yes—
428C24C22×D411yescharacteristic
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
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—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8—416no—
463C2×Q8—416no—
464C2×Q8—416no—
465C2×Q8—416no—
466C2×Q8—416no—
467C2×Q8—416no—
468C2×Q8—416no—
469C2×Q8—416no—
470C2×Q8—48no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—48no—
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#11714yes—
499C2×Q8C4×D414yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
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—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4C4×D412yes—
625C22×C4#13712yes—
626C22×C4C23×C411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C22×C4H(5,𝔽2)11yescharacteristic
634C22×C4H(5,𝔽2)11yescharacteristic
635C22×C4H(5,𝔽2)11yescharacteristic
636C22×C4H(5,𝔽2)11yescharacteristic
637C22×C4H(5,𝔽2)11yescharacteristic
638C22×C4H(5,𝔽2)11yescharacteristic
639C22×C4H(5,𝔽2)11yescharacteristic
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
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—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
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—41no—
692C4⋊C4—84no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—48no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—41no—
705C42—41no—
706C42—84no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
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#44014yes—
742C23C2×C4×D411yescharacteristic
743C23#53411yescharacteristic
744C23#53511yescharacteristic
745C23D4211yescharacteristic
746C23#54611yescharacteristic
747C23#54611yescharacteristic
748C23#54611yescharacteristic
749C23C2×AGL(1,ℤ/8)11yescharacteristic
750C23C2×#13711yescharacteristic
751C23C2×#13711yescharacteristic
752C23#57511yescharacteristic
753C23#57711yescharacteristic
754C23#57811yescharacteristic
755C23#57811yescharacteristic
756C23#57811yescharacteristic
757Q8—24no—
758Q8—24no—
759Q8—24no—
760Q8—24no—
761Q8—432no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—42no—
770Q8—42no—
771Q8—42no—
772Q8—42no—
773Q8—42no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—432no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
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—81no—
874C2×C4C2×#11711yescharacteristic
875C2×C4C2×C4×D411yescharacteristic
876C2×C4#51811yescharacteristic
877C2×C4#51811yescharacteristic
878C2×C4#51811yescharacteristic
879C2×C4#51811yescharacteristic
880C2×C4#53411yescharacteristic
881C2×C4#53511yescharacteristic
882C2×C4#53811yescharacteristic
883C2×C4#53811yescharacteristic
884C2×C4#53811yescharacteristic
885C2×C4#53811yescharacteristic
886C2×C4#53811yescharacteristic
887C2×C4#53811yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#53811yescharacteristic
890C2×C4#54611yescharacteristic
891C2×C4#54611yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#55111yescharacteristic
894C2×C4#55111yescharacteristic
895C2×C4#55111yescharacteristic
896C2×C4#55111yescharacteristic
897C2×C4#55111yescharacteristic
898C2×C4#56011yescharacteristic
899C2×C4#56011yescharacteristic
900C2×C4#56011yescharacteristic
901C2×C4H(3,𝔽4)11yescharacteristic
902C8—42no—
903C8—42no—
904C8—42no—
905C8—81no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22#232111yescharacteristic
922C22#234211yescharacteristic
923C22#235811yescharacteristic
924C22#267811yescharacteristic
925C22#267811yescharacteristic
926C22#268411yescharacteristic
927C22#268511yescharacteristic
928C22C2×#44011yescharacteristic
929C22C4×#13711yescharacteristic
930C22#294711yescharacteristic
931C22#295011yescharacteristic
932C22#319311yescharacteristic
933C22#319611yescharacteristic
934C22#320111yescharacteristic
935C22#320211yescharacteristic
936C22#321311yescharacteristic
937C22#321811yescharacteristic
938C22#322311yescharacteristic
939C22#322511yescharacteristic
940C22#326511yescharacteristic
941C22#326911yescharacteristic
942C22#327011yescharacteristic
943C22#327011yescharacteristic
944C22#330811yescharacteristic
945C22#330811yescharacteristic
946C22#330811yescharacteristic
947C22#331211yescharacteristic
948C22#331211yescharacteristic
949C22#331311yescharacteristic
950C22#332011yescharacteristic
951C22#332011yescharacteristic
952C22#332611yescharacteristic
953C22#332711yescharacteristic
954C22#332811yescharacteristic
955C22#332811yescharacteristic
956C4—42no—
957C4—44no—
958C4—44no—
959C4—42no—
960C4—82no—
961C4—82no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—82no—
966C4—161no—
967C4—161no—
968C4—161no—
969C4#231211yescharacteristic
970C4#232111yescharacteristic
971C4#234211yescharacteristic
972C4#237511yescharacteristic
973C4#268411yescharacteristic
974C4#268511yescharacteristic
975C4#273511yescharacteristic
976C4#273511yescharacteristic
977C2—44no—
978C2#1436511yescharacteristic
979C2#2204711yescharacteristic
980C2#2205411yescharacteristic
981C2#2256311yescharacteristic
982C2#2258111yescharacteristic
983C2#2285511yescharacteristic
984C2#2288111yescharacteristic
985C2#3100611yescharacteristic
986C2#3101011yescharacteristic
987C2#3103911yescharacteristic
988C2#3104311yescharacteristic
989C2#3127311yescharacteristic
990C2#3127711yescharacteristic
991C2#3130811yescharacteristic
992C2#3131211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×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. C2×#1928C2semidirect
7. #11190C2semidirect
8. #11124C2semidirect
10. #11067C2semidirect
11. #11067C2semidirect
12. #10932C2semidirect
13. #10928C2semidirect
14. #10928C2semidirect
42. #1787C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19282
C2×#17872
#139742
#139222
#111992
#111902
#111242
#110962
#110672
#109322
#109282
#109222