Finite Group Databasebeta

← #395852

Subgroups — #395852

Order 512.

1456 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#427C211yesmaximal, characteristic
2C2×#2085C211yesmaximal, characteristic, complemented
3C2×#2083C211yesmaximal, characteristic, complemented
4C2×#1854C211yesmaximal, characteristic
5#13951C211yesmaximal, characteristic
6#13879C211yesmaximal, characteristic
7#11325C211yesmaximal, characteristic, complemented
8#11323C211yesmaximal, characteristic, complemented
9#11257C211yesmaximal, characteristic, complemented
10#11256C211yesmaximal, characteristic, complemented
11#11220C211yesmaximal, characteristic, complemented
12#11219C211yesmaximal, characteristic, complemented
13#10731C211yesmaximal, characteristic
14#10721C211yesmaximal, characteristic
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C2×#427—24no—
20C2×#427—24no—
21C2×#427—24no—
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#2085—24no—
37#2083—24no—
38#1854—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1439—21no—
54#1439—21no—
55#1439—21no—
56#1439—21no—
57#1436—21no—
58#1436—21no—
59C4⋊#95—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434—21no—
65C24×C4C2311yescharacteristic
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8Q814yes—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—41no—
85C2×#117—41no—
86C2×#117—41no—
87C2×#117—41no—
88C2×#117D414yes—
89C22×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4D411yescharacteristic
106C22×C22⋊C4D411yescharacteristic
107C22×C42—21no—
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#427—232no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—22no—
120C2×#107D414yes—
121C2×#106—22no—
122C2×#106—22no—
123C2×#106—22no—
124C2×#106—22no—
125C2×#106—22no—
126C2×#106—22no—
127C2×#106—41no—
128C2×#106—41no—
129C2×#106D414yes—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8Q814yes—
133#389—22no—
134#389—22no—
135#389—41no—
136#389—41no—
137#384—22no—
138#384—41no—
139#382—22no—
140#382—41no—
141#380—22no—
142#380—22no—
143#380—22no—
144#380—22no—
145C4×C22⋊C4—22no—
146C4×C22⋊C4—22no—
147C2×#95—21no—
148C2×#95—21no—
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×#95D411yescharacteristic
162C2×#95D411yescharacteristic
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—41no—
172#340—41no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177C25C2×D411yescharacteristic
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D412yes—
200C23×C4C2×Q812yes—
201C23×C4C2×Q812yes—
202C23×C4#4112yes—
203C23×C4#4112yes—
204C23×C4#4112yes—
205C23×C4C2411yescharacteristic
206C22×C8—28no—
207C22×C8—28no—
208C22×C8—28no—
209C22×C8—28no—
210C22×C8—28no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—28no—
220C22×C8—28no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8C2×D412yes—
234C22×C8C2×D412yes—
235C22×C8C2×Q812yes—
236C22×C8C2×Q812yes—
237C22×C8C2×Q812yes—
238C22×C8C2×Q812yes—
239C22×C8#4112yes—
240C22×C8#4112yes—
241#117—28no—
242#117—28no—
243#117—44no—
244#117—44no—
245#117—44no—
246#117—44no—
247#117—44no—
248#117—44no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
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—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
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—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—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4C2×D412yes—
304C2×C4⋊C4C2×D412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—81no—
324C2×C22⋊C4—81no—
325C2×C22⋊C4—81no—
326C2×C22⋊C4—81no—
327C2×C42—24no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42—42no—
345#107—28no—
346#107—28no—
347#107—44no—
348#106—28no—
349#106—28no—
350#106—44no—
351C22⋊C8—28no—
352#95—22no—
353#95—22no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—81no—
365#95—81no—
366#95—81no—
367#95—81no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24#12112yes—
381C24#12312yes—
382C24C4⋊Q812yes—
383C24C22×D411yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
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—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
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—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#12112yes—
495C22×C4C22⋊Q814yes—
496C22×C4C22⋊Q814yes—
497C22×C4#12312yes—
498C22×C4#12514yes—
499C22×C4#12514yes—
500C22×C4C4⋊Q812yes—
501C22×C4#13512yes—
502C22×C4#13512yes—
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×Q811yescharacteristic
507C22×C4C22×Q811yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C42−1+411yescharacteristic
516C22×C42−1+411yescharacteristic
517C2×C8—232no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8C22⋊Q814yes—
545C2×C8C22⋊Q814yes—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—84no—
578C4⋊C4—84no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4#12014yes—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C42—48no—
589C42—48no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23#39814yes—
633C23C2×#12111yescharacteristic
634C23C2×#12311yescharacteristic
635C23C2×C4⋊Q811yescharacteristic
636C23D4211yescharacteristic
637C23D4211yescharacteristic
638C23#54711yescharacteristic
639C23#54711yescharacteristic
640C23C2×#13511yescharacteristic
641C23C2×#13511yescharacteristic
642C23#57511yescharacteristic
643C23#57511yescharacteristic
644C23#57611yescharacteristic
645C23#57711yescharacteristic
646C23#57711yescharacteristic
647C23#57811yescharacteristic
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4#39814yes—
747C2×C4C2×#12011yescharacteristic
748C2×C4C2×C22⋊Q811yescharacteristic
749C2×C4C2×C22⋊Q811yescharacteristic
750C2×C4C2×C22⋊Q811yescharacteristic
751C2×C4C2×C22⋊Q811yescharacteristic
752C2×C4#52511yescharacteristic
753C2×C4#52511yescharacteristic
754C2×C4#52511yescharacteristic
755C2×C4C2×#12511yescharacteristic
756C2×C4C2×#12511yescharacteristic
757C2×C4#53411yescharacteristic
758C2×C4#53611yescharacteristic
759C2×C4#53911yescharacteristic
760C2×C4#53911yescharacteristic
761C2×C4#54411yescharacteristic
762C2×C4#54411yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#54611yescharacteristic
765C2×C4#54811yescharacteristic
766C2×C4#54811yescharacteristic
767C2×C4D4×Q811yescharacteristic
768C2×C4D4×Q811yescharacteristic
769C2×C4#55211yescharacteristic
770C2×C4#55211yescharacteristic
771C2×C4#55311yescharacteristic
772C2×C4#55311yescharacteristic
773C2×C4#55411yescharacteristic
774C2×C4#55411yescharacteristic
775C8—24no—
776C8—24no—
777C8—42no—
778C8—42no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22C2×#39811yescharacteristic
795C22#241011yescharacteristic
796C22#241311yescharacteristic
797C22#244011yescharacteristic
798C22#244011yescharacteristic
799C22#244311yescharacteristic
800C22#244311yescharacteristic
801C22#303511yescharacteristic
802C22#303511yescharacteristic
803C22#304511yescharacteristic
804C22#304611yescharacteristic
805C22#309111yescharacteristic
806C22#309111yescharacteristic
807C22#309611yescharacteristic
808C22#309711yescharacteristic
809C22#316011yescharacteristic
810C22#316211yescharacteristic
811C22#316311yescharacteristic
812C22#316411yescharacteristic
813C22#326711yescharacteristic
814C22#326811yescharacteristic
815C22#326911yescharacteristic
816C22#327111yescharacteristic
817C22#328011yescharacteristic
818C22#328411yescharacteristic
819C22#328411yescharacteristic
820C22#328511yescharacteristic
821C22#333711yescharacteristic
822C22#333711yescharacteristic
823C22#334111yescharacteristic
824C22#334211yescharacteristic
825C22#334711yescharacteristic
826C22#334811yescharacteristic
827C22#334911yescharacteristic
828C22#335011yescharacteristic
829C4—24no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—81no—
834C4—81no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—161no—
839C4—161no—
840C4—161no—
841C4—161no—
842C4#240911yescharacteristic
843C4#244211yescharacteristic
844C4#244211yescharacteristic
845C4#247311yescharacteristic
846C4#247311yescharacteristic
847C4#257911yescharacteristic
848C4#262711yescharacteristic
849C4#284811yescharacteristic
850C2—44no—
851C2#1472811yescharacteristic
852C2#2365611yescharacteristic
853C2#2366211yescharacteristic
854C2#2436311yescharacteristic
855C2#2436411yescharacteristic
856C2#2458411yescharacteristic
857C2#2458711yescharacteristic
858C2#2606311yescharacteristic
859C2#2606411yescharacteristic
860C2#2606911yescharacteristic
861C2#2607011yescharacteristic
862C2#2612911yescharacteristic
863C2#2613111yescharacteristic
864C2#2613511yescharacteristic
865C2#2614111yescharacteristic
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×#2085C2semidirect
3. C2×#2083C2semidirect
7. #11325C2semidirect
8. #11323C2semidirect
9. #11257C2semidirect
10. #11256C2semidirect
11. #11220C2semidirect
12. #11219C2semidirect

Maximal subgroups

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

subgroupindex
C22×#4272
C2×#20852
C2×#20832
C2×#18542
#139512
#138792
#113252
#113232
#112572
#112562
#112202
#112192
#107312
#107212
#107142