Finite Group Databasebeta

← #396782

Subgroups — #396782

Order 512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2101C211yesmaximal, characteristic, complemented
2C2×#1736C211yesmaximal, characteristic
3#14129C211yesmaximal, characteristic
4#13881C211yesmaximal, characteristic
5#11372C211yesmaximal, characteristic, complemented
6#11316C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11292C211yesmaximal, characteristic, complemented
10#11268C211yesmaximal, characteristic, complemented
11#11208C211yesmaximal, characteristic, complemented
12#10731C211yesmaximal, characteristic
13#10730C211yesmaximal, characteristic
14#10722C211yesmaximal, characteristic
15#10715C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×#382C2211yescharacteristic
24C2×#380C2211yescharacteristic
25C2×#380C2211yescharacteristic
26C2×C4×C22⋊C4C2211yescharacteristic
27#2101—24no—
28#1736—24no—
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1442—21no—
50#1442—21no—
51#1439—21no—
52#1439—21no—
53#1436—21no—
54#1436—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C22⋊#95—21no—
60C22⋊#95—21no—
61C24×C4—21no—
62C24×C4C2311yescharacteristic
63C22×M16—22no—
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—41no—
69C22×M16—41no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—41no—
79C2×#117—41no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—41no—
88C22×C4⋊C4—41no—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4D411yescharacteristic
101C22×C22⋊C4D411yescharacteristic
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108#389—22no—
109#389—22no—
110#389—41no—
111#389—41no—
112#382—22no—
113#382—22no—
114#382—41no—
115#382—41no—
116#380—22no—
117#380—22no—
118#380—22no—
119#380Q814yes—
120C4×C22⋊C4—22no—
121C4×C22⋊C4—22no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95D411yescharacteristic
139C2×#95D411yescharacteristic
140#340—22no—
141#340—22no—
142#340—22no—
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—41no—
150#340—41no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340D414yes—
156#336—22no—
157#336—22no—
158#336—41no—
159#336—41no—
160C25C2×D411yescharacteristic
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—42no—
178C23×C4—42no—
179C23×C4—42no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—81no—
183C23×C4—81no—
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×Q812yes—
190C23×C4#4112yes—
191C23×C4#4112yes—
192C23×C4#4112yes—
193C23×C4#4112yes—
194C23×C4#4112yes—
195C23×C4C2411yescharacteristic
196C2×M16—28no—
197C2×M16—44no—
198C2×M16—44no—
199C2×M16—44no—
200C2×M16—44no—
201C2×M16—44no—
202C2×M16—44no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
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—21no—
220C22×C8—21no—
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×C8C2×D412yes—
230C22×C8#4112yes—
231#117—28no—
232#117—44no—
233#117—44no—
234#117—44no—
235C2×C4⋊C4—28no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
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—44no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×Q812yes—
293C2×C4⋊C4C2×Q812yes—
294C2×C4⋊C4#4112yes—
295C2×C4⋊C4#4112yes—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—41no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—41no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—42no—
326C22⋊C8—44no—
327#95—24no—
328#95—22no—
329#95—22no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—81no—
340#95—81no—
341#95—81no—
342#95—81no—
343#95—81no—
344#95—81no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24C22⋊Q812yes—
358C24#12312yes—
359C24#12412yes—
360C24C22×D411yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—48no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
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—84no—
475C22×C4—84no—
476C22×C4—84no—
477C22×C4—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4C22⋊Q812yes—
481C22×C4#12312yes—
482C22×C4#12412yes—
483C22×C4#12514yes—
484C22×C4#12514yes—
485C22×C4#12614yes—
486C22×C4#12614yes—
487C22×C4C22×D411yescharacteristic
488C22×C4C22×Q811yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4H(5,𝔽2)11yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C42−1+411yescharacteristic
501M16—416no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—48no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
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—84no—
564C4⋊C4—84no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—48no—
568C22⋊C4—84no—
569C22⋊C4—84no—
570C42—48no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23#40014yes—
614C23C2×C22⋊Q811yescharacteristic
615C23C2×#12311yescharacteristic
616C23C2×#12411yescharacteristic
617C23D4211yescharacteristic
618C23#54611yescharacteristic
619C23#54611yescharacteristic
620C23#54711yescharacteristic
621C23#57511yescharacteristic
622C23#57511yescharacteristic
623C23#57511yescharacteristic
624C23#57511yescharacteristic
625C23#57611yescharacteristic
626C23#57711yescharacteristic
627C23#57711yescharacteristic
628C23#57811yescharacteristic
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—816no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
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#40014yes—
729C2×C4#52511yescharacteristic
730C2×C4#52511yescharacteristic
731C2×C4#52511yescharacteristic
732C2×C4C2×#12511yescharacteristic
733C2×C4C2×#12511yescharacteristic
734C2×C4C2×#12611yescharacteristic
735C2×C4C2×#12611yescharacteristic
736C2×C4#52911yescharacteristic
737C2×C4#52911yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#53811yescharacteristic
740C2×C4#53811yescharacteristic
741C2×C4#53811yescharacteristic
742C2×C4#53911yescharacteristic
743C2×C4#53911yescharacteristic
744C2×C4#53911yescharacteristic
745C2×C4#54611yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4D4×Q811yescharacteristic
748C2×C4#55111yescharacteristic
749C2×C4#55111yescharacteristic
750C2×C4#55111yescharacteristic
751C2×C4#55111yescharacteristic
752C2×C4#55211yescharacteristic
753C2×C4#55211yescharacteristic
754C2×C4#55411yescharacteristic
755C2×C4#55411yescharacteristic
756C2×C4#55411yescharacteristic
757C8—42no—
758C8—42no—
759C8—81no—
760C8—81no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22C2×#40011yescharacteristic
777C22#241811yescharacteristic
778C22#241911yescharacteristic
779C22#244911yescharacteristic
780C22#245011yescharacteristic
781C22#247211yescharacteristic
782C22#248811yescharacteristic
783C22#308011yescharacteristic
784C22#308011yescharacteristic
785C22#308111yescharacteristic
786C22#308211yescharacteristic
787C22#309311yescharacteristic
788C22#309311yescharacteristic
789C22#309811yescharacteristic
790C22#309911yescharacteristic
791C22#313611yescharacteristic
792C22#313711yescharacteristic
793C22#314011yescharacteristic
794C22#314011yescharacteristic
795C22#326711yescharacteristic
796C22#326811yescharacteristic
797C22#327511yescharacteristic
798C22#327711yescharacteristic
799C22#331311yescharacteristic
800C22#331511yescharacteristic
801C22#331711yescharacteristic
802C22#332111yescharacteristic
803C22#332211yescharacteristic
804C22#332211yescharacteristic
805C22#332311yescharacteristic
806C22#332611yescharacteristic
807C22#334711yescharacteristic
808C22#335011yescharacteristic
809C22#335111yescharacteristic
810C22#335211yescharacteristic
811C4—24no—
812C4—81no—
813C4—82no—
814C4—81no—
815C4—82no—
816C4—82no—
817C4—81no—
818C4—81no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—161no—
823C4—161no—
824C4#247311yescharacteristic
825C4#247311yescharacteristic
826C4#248011yescharacteristic
827C4#249311yescharacteristic
828C4#250511yescharacteristic
829C4#250511yescharacteristic
830C4#264311yescharacteristic
831C4#285211yescharacteristic
832C2—44no—
833C2#1473811yescharacteristic
834C2#2374611yescharacteristic
835C2#2374911yescharacteristic
836C2#2488511yescharacteristic
837C2#2488711yescharacteristic
838C2#2496111yescharacteristic
839C2#2496311yescharacteristic
840C2#2636111yescharacteristic
841C2#2636511yescharacteristic
842C2#2643511yescharacteristic
843C2#2643911yescharacteristic
844C2#2727111yescharacteristic
845C2#2728511yescharacteristic
846C2#2770311yescharacteristic
847C2#2772311yescharacteristic
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
1. C2×#2101C2semidirect
5. #11372C2semidirect
6. #11316C2semidirect
7. #11315C2semidirect
8. #11293C2semidirect
9. #11292C2semidirect
10. #11268C2semidirect
11. #11208C2semidirect

Maximal subgroups

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

subgroupindex
C2×#21012
C2×#17362
#141292
#138812
#113722
#113162
#113152
#112932
#112922
#112682
#112082
#107312
#107302
#107222
#107152