Finite Group Databasebeta

← #370932

Subgroups — #370932

Order 512.

1696 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2295C211yesmaximal, characteristic, complemented
2C2×#1880C211yesmaximal, characteristic
3C2×#1877C211yesmaximal, characteristic
4C2×#1864C211yesmaximal, characteristic
5C4×#390C211yesmaximal, characteristic
6#11292C211yesmaximal, characteristic, complemented
7#11122C211yesmaximal, characteristic, complemented
8#11066C211yesmaximal, characteristic
9#11023C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic, complemented
11#10931C211yesmaximal, characteristic
12#10908C211yesmaximal, characteristic, complemented
13#10885C211yesmaximal, characteristic, complemented
14#10795C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26#2295—24no—
27#2295—24no—
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#387—21no—
35C2×#387—21no—
36C2×C4×C4⋊C4—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4—21no—
40C2×C4×C22⋊C4—21no—
41C2×#376—21no—
42C2×C43C2211yescharacteristic
43#1880C418yescomplemented
44#1877—24no—
45#1864—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1437—21no—
61#1437—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16—41no—
72C22×SD16—41no—
73C22×SD16C2×C414yes—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8C2×C414yescomplemented
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C42—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42D411yescharacteristic
108C22×C42D411yescharacteristic
109C22×C42D411yescharacteristic
110C22×C42D411yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—41no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103—41no—
125C2×#103C2×C414yescomplemented
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—41no—
133C2×#102—41no—
134C2×#102C2×C414yes—
135#391—22no—
136#391—22no—
137#391—22no—
138#391D414yes—
139#390—22no—
140#390—22no—
141#390—22no—
142#390C2×C414yes—
143#389—22no—
144#389—22no—
145#389—22no—
146#389D414yes—
147#387—28no—
148#387—28no—
149C4×C4⋊C4—28no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4—41no—
153C4×C4⋊C4—41no—
154C4×C22⋊C4—44no—
155C4×C22⋊C4—44no—
156#376—28no—
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—
169C43—22no—
170C43—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340C2×C414yescomplemented
179#336—22no—
180#336—22no—
181#336—22no—
182#336—41no—
183#336—41no—
184#336C2×C414yescomplemented
185C25—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8C22×C412yes—
198C22×Q8C2×D412yes—
199C22×Q8#4112yes—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C22×C412yes—
212C22×D4#4112yes—
213C22×D4#4112yes—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—24no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2411yescharacteristic
235C2×SD16—28no—
236C2×SD16—28no—
237C2×SD16—44no—
238C2×SD16—44no—
239C2×SD16—44no—
240C2×SD16—44no—
241C2×SD16—44no—
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×C8C22×C412yes—
269C22×C8C22×C412yes—
270C4×Q8—28no—
271C4×Q8—28no—
272C4×Q8—28no—
273C4×Q8—28no—
274C4×D4—44no—
275C4×D4—44no—
276C4×D4—44no—
277C4×D4—44no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4C22×C412yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C2×D412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C4⋊C4#4112yes—
321C2×C4⋊C4#4112yes—
322C2×C4⋊C4#4112yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—22no—
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—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—41no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42SD1614yescomplemented
373C2×C42C22×C412yes—
374C2×C42C2×D412yes—
375C2×C42C2×D412yes—
376C2×C42#4112yes—
377#106—44no—
378#103—44no—
379#103—44no—
380#103—44no—
381#102—28no—
382#102—44no—
383#102—44no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24C22×D411yescharacteristic
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8C4×D414yes—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4#11714yes—
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—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
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—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
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—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4C4×D412yes—
557C22×C4C4×D412yes—
558C22×C4#12012yes—
559C22×C4#12012yes—
560C22×C4C2×SD1612yes—
561C22×C4C2×SD1612yes—
562C22×C4C2×SD1612yes—
563C22×C4#13512yes—
564C22×C4AGL(1,ℤ/8)12yes—
565C22×C4#13712yes—
566C22×C4C23×C411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C2×#4111yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4H(5,𝔽2)11yescharacteristic
577C22×C4H(5,𝔽2)11yescharacteristic
578C22×C4H(5,𝔽2)11yescharacteristic
579C22×C42−1+411yescharacteristic
580SD16—416no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
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—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C4⋊C4—216no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4C4×D414yes—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C42—216no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—28no—
651C42—44no—
652C42—44no—
653C42—48no—
654C42—44no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—84no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23C2×C4×D411yescharacteristic
696C23C2×#12011yescharacteristic
697C23#52511yescharacteristic
698C23#52511yescharacteristic
699C23#52511yescharacteristic
700C23#53511yescharacteristic
701C23#53711yescharacteristic
702C23C22×SD1611yescharacteristic
703C23C2×#13511yescharacteristic
704C23C2×AGL(1,ℤ/8)11yescharacteristic
705C23C2×#13711yescharacteristic
706C23#57511yescharacteristic
707C23#57511yescharacteristic
708C23#57511yescharacteristic
709C23#57511yescharacteristic
710Q8—24no—
711Q8—24no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716Q8—42no—
717Q8—42no—
718D4—24no—
719D4—24no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—42no—
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—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—816no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4C4×SD1614yes—
817C2×C4#44814yes—
818C2×C4C2×#11711yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4C4×#4111yescharacteristic
822C2×C4#51811yescharacteristic
823C2×C4#52011yescharacteristic
824C2×C4#52511yescharacteristic
825C2×C4#52511yescharacteristic
826C2×C4#52911yescharacteristic
827C2×C4#52911yescharacteristic
828C2×C4#54011yescharacteristic
829C2×C4#54211yescharacteristic
830C2×C4#54611yescharacteristic
831C2×C4#54611yescharacteristic
832C2×C4#54611yescharacteristic
833C2×C4#54611yescharacteristic
834C2×C4#54611yescharacteristic
835C2×C4#54711yescharacteristic
836C2×C4#54811yescharacteristic
837C2×C4#55011yescharacteristic
838C2×C4#55111yescharacteristic
839C2×C4#55111yescharacteristic
840C2×C4#55111yescharacteristic
841C2×C4#55211yescharacteristic
842C2×C4#55211yescharacteristic
843C2×C4#55311yescharacteristic
844C2×C4#55311yescharacteristic
845C2×C4#55511yescharacteristic
846C8—42no—
847C8—42no—
848C8—81no—
849C8—81no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22#229011yescharacteristic
866C22C4×#12011yescharacteristic
867C22#232411yescharacteristic
868C22#240411yescharacteristic
869C22#240711yescharacteristic
870C22#259811yescharacteristic
871C22#260911yescharacteristic
872C22C2×C4×SD1611yescharacteristic
873C22#294311yescharacteristic
874C22C4×AGL(1,ℤ/8)11yescharacteristic
875C22C4×#13711yescharacteristic
876C22C2×#44811yescharacteristic
877C22#300211yescharacteristic
878C22#300511yescharacteristic
879C22#300611yescharacteristic
880C22#310111yescharacteristic
881C22#310111yescharacteristic
882C22#310211yescharacteristic
883C22#310211yescharacteristic
884C22#310311yescharacteristic
885C22#310811yescharacteristic
886C22#311011yescharacteristic
887C22#311111yescharacteristic
888C22#311111yescharacteristic
889C22#311411yescharacteristic
890C22#311511yescharacteristic
891C22#311611yescharacteristic
892C22#320811yescharacteristic
893C22#321211yescharacteristic
894C22#321511yescharacteristic
895C22#321911yescharacteristic
896C22#324611yescharacteristic
897C22#324711yescharacteristic
898C22#325211yescharacteristic
899C22#325611yescharacteristic
900C4—24no—
901C4—24no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—44no—
907C4—44no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4#234211yescharacteristic
914C4#235211yescharacteristic
915C4#235911yescharacteristic
916C4#236311yescharacteristic
917C4#247011yescharacteristic
918C4#247111yescharacteristic
919C4#247611yescharacteristic
920C4#247711yescharacteristic
921C2—84no—
922C2#1406411yescharacteristic
923C2#2111711yescharacteristic
924C2#2112111yescharacteristic
925C2C4×#44811yescharacteristic
926C2#2145611yescharacteristic
927C2#2214711yescharacteristic
928C2#2215611yescharacteristic
929C2#2393311yescharacteristic
930C2#2393811yescharacteristic
931C2#2415111yescharacteristic
932C2#2415911yescharacteristic
933C2#2936611yescharacteristic
934C2#2937411yescharacteristic
935C2#2953411yescharacteristic
936C2#2953811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2295C2semidirect
6. #11292C2semidirect
7. #11122C2semidirect
10. #10932C2semidirect
12. #10908C2semidirect
13. #10885C2semidirect
14. #10795C2semidirect
15. #10789C2semidirect
43. #1880C4semidirect
83. C2×C4×Q8C2×C4semidirect
125. C2×#103C2×C4semidirect
178. #340C2×C4semidirect
184. #336C2×C4semidirect
372. C2×C42SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#22952
C2×#18802
C2×#18772
C2×#18642
C4×#3902
#112922
#111222
#110662
#110232
#109322
#109312
#109082
#108852
#107952
#107892