Finite Group Databasebeta

← #437909

Subgroups — #437909

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2423C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic, complemented
3C2×#2035C211yesmaximal, characteristic
4C2×#1933C211yesmaximal, characteristic, complemented
5C2×#1865C211yesmaximal, characteristic, complemented
6#15131C211yesmaximal, characteristic
7#11327C211yesmaximal, characteristic, complemented
8#11292C211yesmaximal, characteristic, complemented
9#11199C211yesmaximal, characteristic
10#11095C211yesmaximal, characteristic
11#11050C211yesmaximal, characteristic, complemented
12#10970C211yesmaximal, characteristic
13#10921C211yesmaximal, characteristic
14#10841C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2423—24no—
28#2423—24no—
29C2×#399—21no—
30C2×#398—21no—
31C2×#396—21no—
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#388—21no—
37C2×#387—21no—
38C2×#384C2211yescharacteristic
39C2×#384C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44#2084—24no—
45#2035—24no—
46#1933—24no—
47#1865—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1441—21no—
62#1441—21no—
63#1439—21no—
64C4⋊#95C2211yescharacteristic
65C23×Q8C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C22⋊Q8—22no—
72C2×C22⋊Q8—22no—
73C2×C22⋊Q8—22no—
74C2×C22⋊Q8—22no—
75C2×C22⋊Q8—41no—
76C2×C22⋊Q8—41no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—41no—
82C2×C4×Q8—41no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
104C22×C22⋊C4D411yescharacteristic
105C22×C42—21no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C2×#106—22no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—41no—
113C2×#106—41no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—41no—
124C2×#103—41no—
125C2×#103D414yes—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C4×C8—22no—
133C2×C4×C8—22no—
134C2×C4×C8—41no—
135#399—28no—
136#398—28no—
137#396—44no—
138#391—22no—
139#391D414yes—
140#389—22no—
141#389—22no—
142#389—22no—
143#389—22no—
144#389—22no—
145#389—41no—
146#388—28no—
147#387—28no—
148#384—22no—
149#384—22no—
150#384—41no—
151#384D414yes—
152#380—22no—
153#380—22no—
154#380—22no—
155#380—22no—
156#380—41no—
157#380—41no—
158C4×C22⋊C4—22no—
159C4×C22⋊C4—22no—
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×#95D411yescharacteristic
171C2×#95D411yescharacteristic
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—41no—
181#340—41no—
182#336—22no—
183#336—22no—
184#336—41no—
185C25C2×D411yescharacteristic
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×Q8C2×D412yes—
198C22×Q8C2×D412yes—
199C22×Q8#4112yes—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2411yescharacteristic
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
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×C8C2×D412yes—
253C22×C8#4112yes—
254C22×C8#4112yes—
255C22×C8#4112yes—
256C22⋊Q8—44no—
257C22⋊Q8—44no—
258C22⋊Q8—44no—
259C22⋊Q8—44no—
260C4×Q8—44no—
261C4×Q8—44no—
262C4×Q8—44no—
263C4×Q8—44no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
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—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4C2×D412yes—
329C2×C4⋊C4C2×D412yes—
330C2×C4⋊C4C2×D412yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4#4112yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—81no—
347C2×C22⋊C4—81no—
348C2×C22⋊C4—81no—
349C2×C22⋊C4—81no—
350C2×C22⋊C4SD1614yes—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—24no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42C2×D412yes—
365C2×C42C2×D412yes—
366#106—44no—
367#106—44no—
368#103—28no—
369#103—28no—
370#103—44no—
371#103—44no—
372C22⋊C8—44no—
373C22⋊C8—44no—
374C4×C8—44no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—22no—
380#95—22no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—81no—
387C24—21no—
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—21no—
401C24C2×SD1612yes—
402C24C22×D411yescharacteristic
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8#12114yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
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—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
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#12012yes—
544C22×C4#12012yes—
545C22×C4C2×SD1612yes—
546C22×C4C2×SD1612yes—
547C22×C4#13512yes—
548C22×C4#13712yes—
549C22×C4#13712yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4H(5,𝔽2)11yescharacteristic
559C22×C4H(5,𝔽2)11yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C42−1+411yescharacteristic
562C22×C42−1+411yescharacteristic
563C22×C42−1+411yescharacteristic
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—41no—
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—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—48no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C22⋊C4—28no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—48no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
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—41no—
678C23—41no—
679C23C2×#12011yescharacteristic
680C23#53211yescharacteristic
681C23#53611yescharacteristic
682C23D4211yescharacteristic
683C23#54611yescharacteristic
684C23#54611yescharacteristic
685C23#54711yescharacteristic
686C23C22×SD1611yescharacteristic
687C23C2×#13511yescharacteristic
688C23C2×#13711yescharacteristic
689C23C2×#13711yescharacteristic
690C23#57611yescharacteristic
691C23#57711yescharacteristic
692C23#57711yescharacteristic
693C23#57811yescharacteristic
694Q8—24no—
695Q8—24no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
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—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4#44814yes—
800C2×C4#45214yes—
801C2×C4C2×#12111yescharacteristic
802C2×C4#52511yescharacteristic
803C2×C4#52911yescharacteristic
804C2×C4#53211yescharacteristic
805C2×C4#53511yescharacteristic
806C2×C4#53611yescharacteristic
807C2×C4#53711yescharacteristic
808C2×C4#53911yescharacteristic
809C2×C4#53911yescharacteristic
810C2×C4#53911yescharacteristic
811C2×C4#54011yescharacteristic
812C2×C4#54211yescharacteristic
813C2×C4D4211yescharacteristic
814C2×C4#54611yescharacteristic
815C2×C4#54611yescharacteristic
816C2×C4#54611yescharacteristic
817C2×C4#54711yescharacteristic
818C2×C4#54711yescharacteristic
819C2×C4#54711yescharacteristic
820C2×C4#54711yescharacteristic
821C2×C4#54811yescharacteristic
822C2×C4#54811yescharacteristic
823C2×C4#55111yescharacteristic
824C2×C4#55211yescharacteristic
825C2×C4#55211yescharacteristic
826C2×C4#55311yescharacteristic
827C2×C4#56211yescharacteristic
828C2×C4#56311yescharacteristic
829C8—42no—
830C8—42no—
831C8—42no—
832C8—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22#240811yescharacteristic
849C22#243011yescharacteristic
850C22#243211yescharacteristic
851C22#246411yescharacteristic
852C22#255311yescharacteristic
853C22#268011yescharacteristic
854C22#268711yescharacteristic
855C22C2×#44811yescharacteristic
856C22C2×#45211yescharacteristic
857C22#301211yescharacteristic
858C22#301311yescharacteristic
859C22#316711yescharacteristic
860C22#317811yescharacteristic
861C22#317911yescharacteristic
862C22#318511yescharacteristic
863C22#322911yescharacteristic
864C22#323111yescharacteristic
865C22#324311yescharacteristic
866C22#324411yescharacteristic
867C22#327611yescharacteristic
868C22#327811yescharacteristic
869C22D4×SD1611yescharacteristic
870C22#328711yescharacteristic
871C22#329511yescharacteristic
872C22#329611yescharacteristic
873C22#329811yescharacteristic
874C22#330411yescharacteristic
875C22#331211yescharacteristic
876C22#331611yescharacteristic
877C22#332911yescharacteristic
878C22#333311yescharacteristic
879C22#333511yescharacteristic
880C22#333611yescharacteristic
881C22#334411yescharacteristic
882C22#334611yescharacteristic
883C4—24no—
884C4—24no—
885C4—42no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—161no—
895C4—161no—
896C4#241311yescharacteristic
897C4#242511yescharacteristic
898C4#246111yescharacteristic
899C4#255811yescharacteristic
900C4#268111yescharacteristic
901C4#270611yescharacteristic
902C4#270711yescharacteristic
903C4#271811yescharacteristic
904C2—82no—
905C2#1561211yescharacteristic
906C2#2423911yescharacteristic
907C2#2424211yescharacteristic
908C2#2554111yescharacteristic
909C2#2554311yescharacteristic
910C2#2567211yescharacteristic
911C2#2568411yescharacteristic
912C2#2696211yescharacteristic
913C2#2698811yescharacteristic
914C2#2884711yescharacteristic
915C2#2887111yescharacteristic
916C2#3108311yescharacteristic
917C2#3108911yescharacteristic
918C2#3135311yescharacteristic
919C2#3135411yescharacteristic
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
2. C2×#2084C2semidirect
4. C2×#1933C2semidirect
5. C2×#1865C2semidirect
7. #11327C2semidirect
8. #11292C2semidirect
11. #11050C2semidirect
14. #10841C2semidirect
15. #10789C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24232
C2×#20842
C2×#20352
C2×#19332
C2×#18652
#151312
#113272
#112922
#111992
#110952
#110502
#109702
#109212
#108412
#107892