Finite Group Databasebeta

← #392858

Subgroups — #392858

Order 512.

1632 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2276C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3C2×#1878C211yesmaximal, characteristic
4C2×#1878C211yesmaximal, characteristic
5C2×#1878C211yesmaximal, characteristic
6C2×#1863C211yesmaximal, characteristic
7#14261C211yesmaximal, characteristic
8#10932C211yesmaximal, characteristic
9#10932C211yesmaximal, characteristic
10#10907C211yesmaximal, characteristic
11#10884C211yesmaximal, characteristic
12#10806C211yesmaximal, characteristic
13#10796C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#389C2211yescharacteristic
31#2276—24no—
32#2276—24no—
33C2×C4×C4⋊C4—21no—
34C2×C4×C4⋊C4—21no—
35C2×C4×C4⋊C4—21no—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×#376—21no—
40C2×#376C2211yescharacteristic
41#1928—24no—
42#1878—24no—
43#1878—24no—
44#1878C418yescomplemented
45#1863—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#1443—21no—
61#1443—21no—
62#1442—21no—
63#1442—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×Q8C2311yescharacteristic
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—22no—
71C22×Q16—22no—
72C22×Q16—22no—
73C22×Q16—22no—
74C22×Q16C2×C414yes—
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8—22no—
84C2×C4×Q8—22no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8C2×C414yes—
95C2×C4×Q8D414yes—
96C2×C4×Q8D414yes—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C42—21no—
108C22×C42—21no—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42—21no—
112C22×C42—21no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103C2×C414yes—
136C2×#103C2×C414yes—
137#391—22no—
138#391—22no—
139#391—22no—
140#391—22no—
141#391—22no—
142#391C2×C414yes—
143#389—22no—
144#389—22no—
145C4×C4⋊C4—28no—
146C4×C4⋊C4—28no—
147C4×C4⋊C4—28no—
148C4×C4⋊C4—22no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4D414yes—
154#376—28no—
155#376—22no—
156#376—22no—
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×#95D411yescharacteristic
172C2×#95D411yescharacteristic
173C2×#95D411yescharacteristic
174C2×#95D411yescharacteristic
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340C2×C414yes—
183#336—22no—
184#336—22no—
185#336—22no—
186#336—22no—
187#336—22no—
188#336C2×C414yes—
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×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×Q8C22×C412yes—
210C22×Q8C22×C412yes—
211C22×Q8C2×D412yes—
212C22×Q8C2×D412yes—
213C22×Q8#4112yes—
214C22×Q8#4112yes—
215C22×Q8#4112yes—
216C22×Q8#4112yes—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2411yescharacteristic
232C2×Q16—28no—
233C2×Q16—28no—
234C2×Q16—28no—
235C2×Q16—44no—
236C2×Q16—44no—
237C2×Q16—44no—
238C2×Q16—44no—
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×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×C8C22×C412yes—
266C22×C8C22×C412yes—
267C4×Q8—28no—
268C4×Q8—28no—
269C4×Q8—28no—
270C4×Q8—28no—
271C4×Q8—28no—
272C4×Q8—28no—
273C4×Q8—28no—
274C4×Q8—28no—
275C4×Q8—28no—
276C4×Q8—28no—
277C4×Q8—28no—
278C4×Q8—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
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—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—81no—
316C2×C4⋊C4—81no—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C4⋊C4C2×D412yes—
321C2×C4⋊C4C2×D412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4#4112yes—
324C2×C4⋊C4#4112yes—
325C2×C4⋊C4#4112yes—
326C2×C4⋊C4#4112yes—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—81no—
352C2×C42—81no—
353C2×C42—81no—
354C2×C42—81no—
355C2×C42—81no—
356C2×C42—81no—
357C2×C42C22×C412yes—
358C2×C42C2×D412yes—
359C2×C42C2×D412yes—
360C2×C42C2×D412yes—
361C2×C42#4112yes—
362C2×C42#4112yes—
363#107—44no—
364#103—28no—
365#103—28no—
366#103—44no—
367#103—44no—
368#103—44no—
369#103—44no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—81no—
385#95—81no—
386#95—81no—
387#95—81no—
388C24C22×D411yescharacteristic
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
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—41no—
417C2×Q8—41no—
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—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8#11714yes—
439C2×Q8C4×D414yes—
440C2×Q8C4×D414yes—
441C2×Q8#12114yes—
442C2×Q8#12314yes—
443C2×Q8#12414yes—
444C2×Q8#12614yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
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—22no—
498C22×C4—22no—
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×C4C4×D412yes—
538C22×C4C4×D412yes—
539C22×C4#12012yes—
540C22×C4#12012yes—
541C22×C4#12112yes—
542C22×C4#12112yes—
543C22×C4C23×C411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557Q16—416no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
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—
586C4⋊C4—216no—
587C4⋊C4—216no—
588C4⋊C4—216no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
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—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—84no—
611C4⋊C4C4×D414yes—
612C4⋊C4#12114yes—
613C4⋊C4#12314yes—
614C42—216no—
615C42—216no—
616C42—216no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—84no—
630C42—84no—
631C42—84no—
632C23C2×C4×D411yescharacteristic
633C23C2×#12011yescharacteristic
634C23C2×#12111yescharacteristic
635C23#52511yescharacteristic
636C23#52511yescharacteristic
637C23#52511yescharacteristic
638C23#52511yescharacteristic
639C23#57611yescharacteristic
640C23#57711yescharacteristic
641C23#57711yescharacteristic
642C23#57811yescharacteristic
643C23#57811yescharacteristic
644C23#57811yescharacteristic
645C23#57811yescharacteristic
646C23#57811yescharacteristic
647Q8—24no—
648Q8—24no—
649Q8—24no—
650Q8—24no—
651Q8—24no—
652Q8—24no—
653Q8—24no—
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—81no—
659Q8—81no—
660Q8—81no—
661Q8—81no—
662Q8#38818yes—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4C2×#11711yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C2×C4×D411yescharacteristic
764C2×C4C2×C4×D411yescharacteristic
765C2×C4C4×#4111yescharacteristic
766C2×C4C4×#4111yescharacteristic
767C2×C4C2×#12111yescharacteristic
768C2×C4C2×#12111yescharacteristic
769C2×C4C2×#12311yescharacteristic
770C2×C4C2×#12311yescharacteristic
771C2×C4#52511yescharacteristic
772C2×C4#52511yescharacteristic
773C2×C4#52511yescharacteristic
774C2×C4#52511yescharacteristic
775C2×C4#52511yescharacteristic
776C2×C4#52511yescharacteristic
777C2×C4C2×#12411yescharacteristic
778C2×C4C2×#12611yescharacteristic
779C2×C4#52911yescharacteristic
780C2×C4#52911yescharacteristic
781C2×C4#52911yescharacteristic
782C2×C4#52911yescharacteristic
783C2×C4#52911yescharacteristic
784C2×C4#52911yescharacteristic
785C2×C4#52911yescharacteristic
786C2×C4#52911yescharacteristic
787C2×C4#53211yescharacteristic
788C2×C4#53211yescharacteristic
789C8—42no—
790C8—42no—
791C8—81no—
792C8—81no—
793C22#229011yescharacteristic
794C22C4×#12011yescharacteristic
795C22C4×#12111yescharacteristic
796C22#284711yescharacteristic
797C22#284911yescharacteristic
798C22#285011yescharacteristic
799C22#285211yescharacteristic
800C22#294711yescharacteristic
801C22#294711yescharacteristic
802C22#295011yescharacteristic
803C22#295111yescharacteristic
804C22#301111yescharacteristic
805C22#301111yescharacteristic
806C22#301211yescharacteristic
807C22#301311yescharacteristic
808C22#304411yescharacteristic
809C22#304411yescharacteristic
810C22#304511yescharacteristic
811C22#304611yescharacteristic
812C22#312011yescharacteristic
813C22#312011yescharacteristic
814C22#312011yescharacteristic
815C22#312111yescharacteristic
816C22#312111yescharacteristic
817C22#312111yescharacteristic
818C22#312411yescharacteristic
819C22#312411yescharacteristic
820C22#312411yescharacteristic
821C22#312411yescharacteristic
822C22#312511yescharacteristic
823C22#312711yescharacteristic
824C22#312711yescharacteristic
825C22#312711yescharacteristic
826C22#312711yescharacteristic
827C22#312711yescharacteristic
828C4—28no—
829C4—42no—
830C4—42no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—44no—
837C4—42no—
838C4—82no—
839C4—82no—
840C4—161no—
841C4—161no—
842C4C2×#38811yescharacteristic
843C4#229011yescharacteristic
844C4C4×#12111yescharacteristic
845C4C4×#12311yescharacteristic
846C4#285011yescharacteristic
847C4#285211yescharacteristic
848C4#285311yescharacteristic
849C4#285411yescharacteristic
850C2#1469611yescharacteristic
851C2#2112711yescharacteristic
852C2#2113511yescharacteristic
853C2#2146311yescharacteristic
854C2#2146511yescharacteristic
855C2#2151211yescharacteristic
856C2#2151611yescharacteristic
857C2#3291511yescharacteristic
858C2#3291911yescharacteristic
859C2#3301711yescharacteristic
860C2#3301911yescharacteristic
861C2#3303511yescharacteristic
862C2#3304111yescharacteristic
863C2#3309111yescharacteristic
864C2#3309311yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
44. #1878C4semidirect

Maximal subgroups

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

subgroupindex
C2×#22762
C2×#19282
C2×#18782
C2×#18632
#142612
#109322
#109072
#108842
#108062
#107962
#107892