Finite Group Databasebeta

← #395864

Subgroups — #395864

Order 512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2349C211yesmaximal, characteristic
2C2×#2086C211yesmaximal, characteristic, complemented
3C2×#1864C211yesmaximal, characteristic
4C2×#1862C211yesmaximal, characteristic
5C2×#1804C211yesmaximal, characteristic
6#15221C211yesmaximal, characteristic, complemented
7#11327C211yesmaximal, characteristic, complemented
8#11325C211yesmaximal, characteristic, complemented
9#11293C211yesmaximal, characteristic, complemented
10#11268C211yesmaximal, characteristic, complemented
11#11208C211yesmaximal, characteristic, complemented
12#11202C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26#2349—24no—
27#2349—24no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#385—21no—
33C2×#385—21no—
34C2×#382C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×#380—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38C22×#95—21no—
39#2086—24no—
40#1864—24no—
41#1862—24no—
42#1804—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1445—21no—
59#1444—21no—
60#1442—21no—
61#1442—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C24×C4—21no—
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4D414yes—
90C2×C4×D4Q814yes—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—41no—
113C2×#106—22no—
114C2×#106—41no—
115C2×#106—41no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—41no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102D414yes—
130C2×#102Q814yes—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—22no—
135#389—22no—
136#389—22no—
137#389—41no—
138#389D414yes—
139#385—28no—
140#385—28no—
141#382—22no—
142#382—22no—
143#382—22no—
144#382—41no—
145#380—28no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—22no—
148C2×#95—28no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95D411yescharacteristic
164C2×#95D411yescharacteristic
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—41no—
175#336—22no—
176#336—22no—
177#336—22no—
178#336—22no—
179#336—41no—
180C25—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4C2×D412yes—
189C22×D4C2×D412yes—
190C22×D4C2×Q812yes—
191C22×D4C2×Q812yes—
192C22×D4#4112yes—
193C22×D4#4112yes—
194C22×D4#4112yes—
195C23×C4—21no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—81no—
216C23×C4—81no—
217C23×C4—81no—
218C23×C4—81no—
219C23×C4—81no—
220C23×C4—81no—
221C23×C4—81no—
222C23×C4—81no—
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2411yescharacteristic
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×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8C2×D412yes—
257C22×C8C2×Q812yes—
258C4×D4—28no—
259C4×D4—28no—
260C4×D4—28no—
261C4×D4—28no—
262C4×D4—28no—
263C4×D4—44no—
264C4×D4—44no—
265C4×D4—44no—
266C4×D4—44no—
267C4×D4—44no—
268C4×D4—44no—
269C4×D4—44no—
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—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
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—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—81no—
317C2×C4⋊C4—81no—
318C2×C4⋊C4—81no—
319C2×C4⋊C4—81no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4C2×D412yes—
324C2×C4⋊C4C2×D412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4C2×D412yes—
327C2×C4⋊C4C2×Q812yes—
328C2×C4⋊C4C2×Q812yes—
329C2×C4⋊C4#4112yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
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—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42C2×D412yes—
354C2×C42C2×D412yes—
355C2×C42C2×Q812yes—
356C2×C42#4112yes—
357#107—44no—
358#106—44no—
359C4⋊C8—44no—
360#102—28no—
361#102—28no—
362#102—44no—
363#102—44no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—22no—
368#95—24no—
369#95—22no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—81no—
378#95—81no—
379#95—81no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24C22×D411yescharacteristic
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4#12114yes—
418C2×D4C22⋊Q814yes—
419C2×D4C22⋊Q814yes—
420C2×D4#12314yes—
421C2×D4#12514yes—
422C2×D4#12514yes—
423C2×D4C4⋊Q814yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
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—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—216no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—48no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—48no—
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—84no—
516C22×C4—84no—
517C22×C4—84no—
518C22×C4—84no—
519C22×C4—84no—
520C22×C4—84no—
521C22×C4—84no—
522C22×C4—84no—
523C22×C4—84no—
524C22×C4—84no—
525C22×C4—84no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4#12012yes—
532C22×C4#12012yes—
533C22×C4C22⋊Q812yes—
534C22×C4C22⋊Q812yes—
535C22×C4#13512yes—
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×Q811yescharacteristic
540C22×C4C22×Q811yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4H(5,𝔽2)11yescharacteristic
547C22×C4H(5,𝔽2)11yescharacteristic
548C22×C42−1+411yescharacteristic
549C22×C42−1+411yescharacteristic
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
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—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C4⋊C4—84no—
610C4⋊C4—84no—
611C4⋊C4C22⋊Q814yes—
612C22⋊C4—216no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23C2×#12011yescharacteristic
663C23C2×C22⋊Q811yescharacteristic
664C23#52511yescharacteristic
665C23D4211yescharacteristic
666C23#54611yescharacteristic
667C23#54811yescharacteristic
668C23D4×Q811yescharacteristic
669C23C2×#13511yescharacteristic
670C23#57511yescharacteristic
671C23#57511yescharacteristic
672C23#57511yescharacteristic
673C23#57611yescharacteristic
674C23#57611yescharacteristic
675C23#57711yescharacteristic
676C23#57711yescharacteristic
677D4—24no—
678D4—24no—
679D4—24no—
680D4—24no—
681D4—24no—
682D4—24no—
683D4—24no—
684D4#39818yes—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—816no—
747C2×C4—816no—
748C2×C4—816no—
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×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×C4C2×#12111yescharacteristic
780C2×C4C2×C22⋊Q811yescharacteristic
781C2×C4C2×C22⋊Q811yescharacteristic
782C2×C4C2×C22⋊Q811yescharacteristic
783C2×C4C2×#12311yescharacteristic
784C2×C4#52511yescharacteristic
785C2×C4#52511yescharacteristic
786C2×C4C2×#12511yescharacteristic
787C2×C4C2×#12511yescharacteristic
788C2×C4C2×C4⋊Q811yescharacteristic
789C2×C4#53411yescharacteristic
790C2×C4#53611yescharacteristic
791C2×C4#53911yescharacteristic
792C2×C4#53911yescharacteristic
793C2×C4#54411yescharacteristic
794C2×C4#54411yescharacteristic
795C2×C4D4211yescharacteristic
796C2×C4#54611yescharacteristic
797C2×C4#54711yescharacteristic
798C2×C4#54711yescharacteristic
799C2×C4#54811yescharacteristic
800C2×C4D4×Q811yescharacteristic
801C2×C4#55211yescharacteristic
802C2×C4#55211yescharacteristic
803C2×C4#55311yescharacteristic
804C2×C4#55311yescharacteristic
805C2×C4#55411yescharacteristic
806C2×C4#55411yescharacteristic
807C8—42no—
808C8—42no—
809C8—81no—
810C8—81no—
811C22—28no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22#240911yescharacteristic
827C22#241011yescharacteristic
828C22#244011yescharacteristic
829C22#244211yescharacteristic
830C22#244311yescharacteristic
831C22#247311yescharacteristic
832C22#284811yescharacteristic
833C22#300211yescharacteristic
834C22#300511yescharacteristic
835C22#300811yescharacteristic
836C22#300911yescharacteristic
837C22#307611yescharacteristic
838C22#308011yescharacteristic
839C22#308111yescharacteristic
840C22#308111yescharacteristic
841C22#310211yescharacteristic
842C22#311111yescharacteristic
843C22#311811yescharacteristic
844C22#311811yescharacteristic
845C22#326711yescharacteristic
846C22#326811yescharacteristic
847C22#327511yescharacteristic
848C22#328011yescharacteristic
849C22#329711yescharacteristic
850C22#331111yescharacteristic
851C22#331911yescharacteristic
852C22#332311yescharacteristic
853C22#336011yescharacteristic
854C22#337011yescharacteristic
855C22#337011yescharacteristic
856C22#337611yescharacteristic
857C22#338111yescharacteristic
858C22#338811yescharacteristic
859C22#338911yescharacteristic
860C22#338911yescharacteristic
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—44no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—81no—
871C4—82no—
872C4—161no—
873C4—161no—
874C4C2×#39811yescharacteristic
875C4#241311yescharacteristic
876C4#244011yescharacteristic
877C4#244211yescharacteristic
878C4#244311yescharacteristic
879C4#247311yescharacteristic
880C4#257911yescharacteristic
881C4#262711yescharacteristic
882C2—48no—
883C2#1472811yescharacteristic
884C2#2433711yescharacteristic
885C2#2433911yescharacteristic
886C2#2442811yescharacteristic
887C2#2444211yescharacteristic
888C2#2604911yescharacteristic
889C2#2605911yescharacteristic
890C2#2611711yescharacteristic
891C2#2612511yescharacteristic
892C2#2616011yescharacteristic
893C2#2618411yescharacteristic
894C2#2730411yescharacteristic
895C2#2732311yescharacteristic
896C2#3296111yescharacteristic
897C2#3296211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2086C2semidirect
6. #15221C2semidirect
7. #11327C2semidirect
8. #11325C2semidirect
9. #11293C2semidirect
10. #11268C2semidirect
11. #11208C2semidirect
12. #11202C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23492
C2×#20862
C2×#18642
C2×#18622
C2×#18042
#152212
#113272
#113252
#112932
#112682
#112082
#112022
#107882