Finite Group Databasebeta

← #414627

Subgroups — #414627

Order 512.

2042 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#475C211yesmaximal, characteristic, complemented
2C2×#2857C211yesmaximal, characteristic
3C2×C4×C22⋊Q8C211yesmaximal, characteristic
4C2×#1988C211yesmaximal, characteristic, complemented
5C2×#1803C211yesmaximal, characteristic, complemented
6C2×#1797C211yesmaximal, characteristic
7#11327C212yesmaximal, complemented
8#11095C212yesmaximal
9#11067C212yesmaximal, complemented
10#10970C212yesmaximal
11#10849C211yesmaximal, characteristic, complemented
12C22×C4⋊Q8C2211yescharacteristic
13C22×C22⋊Q8—21no—
14C22×C22⋊Q8C2211yescharacteristic
15C22×C4×Q8C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#475—24no—
18C2×#475—24no—
19C2×#475—24no—
20C22×#106C2212yes—
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×C22⋊C8C2212yes—
26#2857—24no—
27#2857—24no—
28C4×C22⋊Q8—24no—
29C4×C22⋊Q8—24no—
30C2×#391—21no—
31C2×#391C2211yescharacteristic
32C2×#389—21no—
33C2×#389C2212yes—
34C2×#389C2211yescharacteristic
35C2×#387—21no—
36C2×#385—21no—
37C2×#384C2211yescharacteristic
38C2×#380—21no—
39C2×#380C2212yes—
40C2×#380C2211yescharacteristic
41C2×C4×C4⋊C4—21no—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4—21no—
44#1988—24no—
45#1803—24no—
46#1797—24no—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#340C2212yes—
50C2×#340C2212yes—
51C2×#340C2212yes—
52C2×#336C2212yes—
53C23×Q8—21no—
54C23×Q8C2311yescharacteristic
55C24×C4D411yescharacteristic
56C24×C4D411yescharacteristic
57C24×C4C2311yescharacteristic
58C23×C8C2312yes—
59C23×C8C2312yes—
60C2×C4⋊Q8—22no—
61C2×C4⋊Q8—22no—
62C2×C4⋊Q8—22no—
63C2×C4⋊Q8—22no—
64C2×C4⋊Q8—22no—
65C2×C4⋊Q8D414yes—
66C2×C22⋊Q8—22no—
67C2×C22⋊Q8—22no—
68C2×C22⋊Q8—22no—
69C2×C22⋊Q8—28no—
70C2×C22⋊Q8—22no—
71C2×C22⋊Q8—22no—
72C2×C22⋊Q8—44no—
73C2×C22⋊Q8—44no—
74C2×C22⋊Q8Q814yescomplemented
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8D414yes—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4C2312yes—
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C22⋊C4—21no—
94C22×C22⋊C4—22no—
95C22×C22⋊C4—21no—
96C22×C42—21no—
97C22×C42—21no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42D411yescharacteristic
105C22×C42D411yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108#475—232no—
109C2×#106—24no—
110C2×#106—24no—
111C2×#106—24no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8D414yes—
118C2×#103—24no—
119C2×#103—24no—
120C2×#103—24no—
121C2×#103—24no—
122C2×#103—24no—
123C2×#103—42no—
124C2×C22⋊C8—24no—
125C2×C22⋊C8—24no—
126C2×C22⋊C8—42no—
127#391—28no—
128#391—22no—
129#391—22no—
130#389—28no—
131#389—24no—
132#389—24no—
133#389—22no—
134#389—22no—
135#387—28no—
136#385—28no—
137#384—22no—
138#384D414yes—
139#380—28no—
140#380—24no—
141#380—24no—
142#380—22no—
143#380—22no—
144C4×C4⋊C4—28no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4D414yes—
147C4×C22⋊C4—28no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—22no—
154C2×#95—22no—
155#340—24no—
156#340—24no—
157#340—24no—
158#340—24no—
159#340—42no—
160#336—24no—
161C25C2×D411yescharacteristic
162C22×Q8—24no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—42no—
175C22×Q8—42no—
176C22×Q8—42no—
177C22×Q8—42no—
178C22×Q8—42no—
179C22×Q8—42no—
180C22×Q8C2×D412yes—
181C22×Q8C2×Q812yes—
182C22×Q8#4112yes—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—41no—
213C23×C4—41no—
214C23×C4SD1614yes—
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×Q812yes—
221C23×C4#4112yes—
222C23×C4C2411yescharacteristic
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8C2×D414yes—
237C4⋊Q8—28no—
238C4⋊Q8—28no—
239C4⋊Q8—44no—
240C4⋊Q8—44no—
241C22⋊Q8—28no—
242C22⋊Q8—28no—
243C22⋊Q8—28no—
244C22⋊Q8—28no—
245C22⋊Q8—432no—
246C4×Q8—28no—
247C4×Q8—28no—
248C4×Q8—44no—
249C4×Q8—44no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4C2×D412yes—
295C2×C4⋊C4C2×D414yes—
296C2×C4⋊C4C2×D412yes—
297C2×C4⋊C4C2×D414yes—
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—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—42no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
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—42no—
327C2×C42—42no—
328C2×C42—44no—
329C2×C42—44no—
330C2×C42—44no—
331C2×C42—44no—
332C2×C42C2×D412yes—
333C2×C42C2×D412yes—
334C2×C42C2×D412yes—
335C2×C42C2×D412yes—
336C2×C42C2×D412yes—
337C2×C42#4112yes—
338#106—216no—
339C4⋊C8—28no—
340C4⋊C8—44no—
341#103—216no—
342#103—48no—
343C22⋊C8—48no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—28no—
349#95—28no—
350#95—24no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24C22⋊Q812yes—
364C24C2×SD1612yes—
365C24#13712yes—
366C24C22×D411yescharacteristic
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—48no—
397C2×Q8—84no—
398C2×Q8—84no—
399C2×Q8—84no—
400C2×Q8—84no—
401C2×Q8C22⋊Q814yescomplemented
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—28no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
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—21no—
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—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
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—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4#12012yes—
509C22×C4#12012yes—
510C22×C4#12012yes—
511C22×C4#12012yes—
512C22×C4#12112yes—
513C22×C4#12112yes—
514C22×C4C22⋊Q812yes—
515C22×C4C2×SD1612yes—
516C22×C4C2×SD1612yes—
517C22×C4#13512yes—
518C22×C4AGL(1,ℤ/8)12yes—
519C22×C4#13712yes—
520C22×C4#13712yes—
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×Q811yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C42−1+411yescharacteristic
533C22×C42−1+411yescharacteristic
534C22×C42−1+411yescharacteristic
535C2×C8—24no—
536C2×C8—24no—
537C2×C8—24no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C4⋊C4—216no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—416no—
564C4⋊C4—41no—
565C4⋊C4—42no—
566C4⋊C4—41no—
567C4⋊C4—42no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4C22⋊Q814yescomplemented
576C22⋊C4—216no—
577C22⋊C4—48no—
578C22⋊C4—416no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—44no—
584C42—44no—
585C42—48no—
586C42—48no—
587C42#12014yes—
588C42#12114yes—
589C42#12114yes—
590C42#12714yes—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23#47514yescomplemented
626C23C2×#12011yescharacteristic
627C23C2×#12011yescharacteristic
628C23C2×#12111yescharacteristic
629C23C2×C22⋊Q811yescharacteristic
630C23#52511yescharacteristic
631C23#53611yescharacteristic
632C23#53711yescharacteristic
633C23C22×SD1611yescharacteristic
634C23C2×#13511yescharacteristic
635C23C2×AGL(1,ℤ/8)11yescharacteristic
636C23C2×#13711yescharacteristic
637C23C2×#13711yescharacteristic
638C23C2×#13711yescharacteristic
639C23#57511yescharacteristic
640C23#57511yescharacteristic
641Q8—24no—
642Q8—24no—
643Q8—42no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—816no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
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—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—81no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4#39214yes—
730C2×C4#39214yes—
731C2×C4#44814yes—
732C2×C4#44914yes—
733C2×C4#45014yes—
734C2×C4#45214yes—
735C2×C4#46514yes—
736C2×C4#46814yes—
737C2×C4C2×#12011yescharacteristic
738C2×C4C2×#12111yescharacteristic
739C2×C4C2×#12111yescharacteristic
740C2×C4C2×C22⋊Q811yescharacteristic
741C2×C4C2×C22⋊Q811yescharacteristic
742C2×C4#52511yescharacteristic
743C2×C4#52511yescharacteristic
744C2×C4C2×#12711yescharacteristic
745C2×C4#53611yescharacteristic
746C2×C4#53611yescharacteristic
747C2×C4#53711yescharacteristic
748C2×C4#53711yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54711yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#54811yescharacteristic
754C2×C4#54811yescharacteristic
755C2×C4#54811yescharacteristic
756C2×C4#54811yescharacteristic
757C2×C4D4×Q811yescharacteristic
758C2×C4D4×Q811yescharacteristic
759C2×C4D4×Q811yescharacteristic
760C2×C4#55011yescharacteristic
761C2×C4#55211yescharacteristic
762C2×C4#55211yescharacteristic
763C2×C4#55411yescharacteristic
764C2×C4#55611yescharacteristic
765C8—44no—
766C8—82no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22C2×#39211yescharacteristic
783C22#240711yescharacteristic
784C22#240911yescharacteristic
785C22#241511yescharacteristic
786C22#241711yescharacteristic
787C22#261611yescharacteristic
788C22#284811yescharacteristic
789C22C2×#45011yescharacteristic
790C22C2×#44811yescharacteristic
791C22C2×#44911yescharacteristic
792C22C2×#45211yescharacteristic
793C22#300411yescharacteristic
794C22#300511yescharacteristic
795C22#300711yescharacteristic
796C22#300711yescharacteristic
797C22C2×#46511yescharacteristic
798C22C2×#46811yescharacteristic
799C22#305611yescharacteristic
800C22#305611yescharacteristic
801C22C2×#47511yescharacteristic
802C22#307611yescharacteristic
803C22#307811yescharacteristic
804C22#307911yescharacteristic
805C22#310311yescharacteristic
806C22#310711yescharacteristic
807C22#311311yescharacteristic
808C22#311511yescharacteristic
809C22#322911yescharacteristic
810C22#323311yescharacteristic
811C22#323711yescharacteristic
812C22#323911yescharacteristic
813C22#324611yescharacteristic
814C22#324811yescharacteristic
815C22#325111yescharacteristic
816C22#325511yescharacteristic
817C4—24no—
818C4—42no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—44no—
823C4—84no—
824C4—84no—
825C4—82no—
826C4—82no—
827C4#200018yes—
828C4#240711yescharacteristic
829C4#240911yescharacteristic
830C4#241511yescharacteristic
831C4#241711yescharacteristic
832C4#253611yescharacteristic
833C4#253811yescharacteristic
834C4#254011yescharacteristic
835C4#254211yescharacteristic
836C2—44no—
837C2#1517711yescharacteristic
838C2C2×#200011yescharacteristic
839C2#2339211yescharacteristic
840C2#2415411yescharacteristic
841C2#2415711yescharacteristic
842C2#2430111yescharacteristic
843C2#2430311yescharacteristic
844C2#2470311yescharacteristic
845C2#2471011yescharacteristic
846C2#2483811yescharacteristic
847C2#2484511yescharacteristic
848C2#2968811yescharacteristic
849C2#2968911yescharacteristic
850C2#3295411yescharacteristic
851C2#3295511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#475C2semidirect
4. C2×#1988C2semidirect
5. C2×#1803C2semidirect
7. #11327C2semidirect
9. #11067C2semidirect
11. #10849C2semidirect
74. C2×C22⋊Q8Q8semidirect
401. C2×Q8C22⋊Q8semidirect
575. C4⋊C4C22⋊Q8semidirect
625. C23#475semidirect

Maximal subgroups

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

subgroupindex
C22×#4752
C2×#28572
C2×C4×C22⋊Q82
C2×#19882
C2×#18032
C2×#17972
#113272
#110952
#110672
#109702
#108492