Finite Group Databasebeta

← #429318

Subgroups — #429318

Order 512.

1092 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1934C211yesmaximal, characteristic
2C2×#1926C211yesmaximal, characteristic
3#15136C211yesmaximal, characteristic
4#14132C211yesmaximal, characteristic, complemented
5#11323C211yesmaximal, characteristic, complemented
6#11292C211yesmaximal, characteristic, complemented
7#11267C211yesmaximal, characteristic, complemented
8#11220C211yesmaximal, characteristic, complemented
9#11189C211yesmaximal, characteristic
10#11121C211yesmaximal, characteristic
11#11121C211yesmaximal, characteristic
12#11066C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic, complemented
14#10861C211yesmaximal, characteristic, complemented
15#10797C211yesmaximal, characteristic, complemented
16C22×#106C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C2×#397—21no—
25C2×#397—21no—
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33#1934—24no—
34#1926—24no—
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1445—21no—
50#1441—21no—
51#1439—21no—
52#1439—21no—
53#1436—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60C4×#95C2211yescharacteristic
61C23×D4C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4—21no—
81C22×C22⋊C4—21no—
82C22×C22⋊C4—21no—
83C22×C42—21no—
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C2×#106—22no—
88C2×#106—22no—
89C2×#106—22no—
90C2×#106—22no—
91C2×#106—22no—
92C2×#106—41no—
93C2×#106—41no—
94C2×#106—41no—
95C2×#106—41no—
96C2×#102—22no—
97C2×#102—22no—
98C2×#102—22no—
99C2×#102—22no—
100C2×#102—22no—
101C2×#102—22no—
102C2×#102—22no—
103C2×#102—22no—
104C2×#102—22no—
105C2×#102—41no—
106C2×#102—41no—
107C2×#102D414yes—
108C2×C4×C8—22no—
109C2×C4×C8—22no—
110C2×C4×C8—22no—
111#397—44no—
112#397—44no—
113#390—22no—
114#390—22no—
115#390—41no—
116#390—41no—
117#390—41no—
118#390—41no—
119#389—22no—
120#389—22no—
121#389—22no—
122#389—41no—
123#384—41no—
124#384—41no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—41no—
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×#95—21no—
139C2×#95—21no—
140C2×#95D411yescharacteristic
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
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#336—22no—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158C25—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4C2×D412yes—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2411yescharacteristic
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8C2×D412yes—
211C22×C8#4112yes—
212C22×C8#4112yes—
213C22×C8#4112yes—
214C22×C8#4112yes—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
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—24no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—81no—
261C2×C4⋊C4—81no—
262C2×C4⋊C4—81no—
263C2×C4⋊C4—81no—
264C2×C4⋊C4—81no—
265C2×C4⋊C4C2×D412yes—
266C2×C4⋊C4#4112yes—
267C2×C4⋊C4#4112yes—
268C2×C4⋊C4#4112yes—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—81no—
284C2×C22⋊C4—81no—
285C2×C22⋊C4—81no—
286C2×C22⋊C4—81no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—81no—
308#106—44no—
309#106—44no—
310#106—44no—
311#102—28no—
312#102—28no—
313#102—44no—
314#102—44no—
315C4×C8—44no—
316#95—24no—
317#95—22no—
318#95—22no—
319#95—41no—
320#95—42no—
321#95—42no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—81no—
328#95—81no—
329#95—81no—
330#95—81no—
331#95—81no—
332#95SD1614yes—
333C24—22no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24—41no—
339C24—41no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24C22×D411yescharacteristic
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
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×C4C2×SD1612yes—
464C22×C4C2×SD1612yes—
465C22×C4C2×SD1612yes—
466C22×C4#13512yes—
467C22×C4AGL(1,ℤ/8)12yes—
468C22×C4C22×D411yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4H(5,𝔽2)11yescharacteristic
477C22×C4H(5,𝔽2)11yescharacteristic
478C22×C4H(5,𝔽2)11yescharacteristic
479C22×C42−1+411yescharacteristic
480C22×C42−1+411yescharacteristic
481C22×C42−1+411yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8#12314yes—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—84no—
539C4⋊C4—84no—
540C4⋊C4—84no—
541C4⋊C4—84no—
542C22⋊C4—84no—
543C22⋊C4—84no—
544C22⋊C4—84no—
545C22⋊C4—84no—
546C22⋊C4—84no—
547C22⋊C4—84no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—84no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—81no—
569C23—81no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23—81no—
590C23—81no—
591C23—81no—
592C23—81no—
593C23—81no—
594C23—81no—
595C23—81no—
596C23#52511yescharacteristic
597C23#53211yescharacteristic
598C23#53511yescharacteristic
599C23D4211yescharacteristic
600C23#54711yescharacteristic
601C23#54711yescharacteristic
602C23#54811yescharacteristic
603C23C22×SD1611yescharacteristic
604C23C2×#13511yescharacteristic
605C23C2×AGL(1,ℤ/8)11yescharacteristic
606C23#57511yescharacteristic
607C23#57611yescharacteristic
608C23#57711yescharacteristic
609C23#57711yescharacteristic
610C23#57711yescharacteristic
611D4—42no—
612D4—42no—
613D4—42no—
614D4—42no—
615D4—81no—
616D4—81no—
617D4—81no—
618D4—81no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
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—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
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×C4C2×#12311yescharacteristic
711C2×C4#52511yescharacteristic
712C2×C4#52911yescharacteristic
713C2×C4#52911yescharacteristic
714C2×C4#53711yescharacteristic
715C2×C4#53811yescharacteristic
716C2×C4#53911yescharacteristic
717C2×C4#53911yescharacteristic
718C2×C4#54111yescharacteristic
719C2×C4#54111yescharacteristic
720C2×C4#54211yescharacteristic
721C2×C4#54211yescharacteristic
722C2×C4#54611yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4#54711yescharacteristic
725C2×C4#55111yescharacteristic
726C2×C4#55111yescharacteristic
727C2×C4#55211yescharacteristic
728C2×C4#55211yescharacteristic
729C2×C4#55311yescharacteristic
730C2×C4#55311yescharacteristic
731C2×C4#55511yescharacteristic
732C2×C4#55511yescharacteristic
733C2×C4#55611yescharacteristic
734C2×C4#55611yescharacteristic
735C2×C4#55911yescharacteristic
736C2×C4#56211yescharacteristic
737C2×C4#56311yescharacteristic
738C8—24no—
739C8—42no—
740C8—42no—
741C8—81no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—161no—
750C22—161no—
751C22—161no—
752C22—161no—
753C22—161no—
754C22—161no—
755C22—161no—
756C22—161no—
757C22#242211yescharacteristic
758C22#245511yescharacteristic
759C22#246911yescharacteristic
760C22#251911yescharacteristic
761C22#261011yescharacteristic
762C22#267611yescharacteristic
763C22#271811yescharacteristic
764C22#310311yescharacteristic
765C22#310611yescharacteristic
766C22#311811yescharacteristic
767C22#312511yescharacteristic
768C22#316711yescharacteristic
769C22#317311yescharacteristic
770C22#317911yescharacteristic
771C22#318011yescharacteristic
772C22#320811yescharacteristic
773C22#321111yescharacteristic
774C22#322111yescharacteristic
775C22#322411yescharacteristic
776C22#326411yescharacteristic
777C22#326711yescharacteristic
778C22D4×SD1611yescharacteristic
779C22#328411yescharacteristic
780C22#333511yescharacteristic
781C22#333511yescharacteristic
782C22#333711yescharacteristic
783C22#333911yescharacteristic
784C22#334511yescharacteristic
785C22#334711yescharacteristic
786C22#335111yescharacteristic
787C22#335411yescharacteristic
788C22#336011yescharacteristic
789C22#336211yescharacteristic
790C22#336811yescharacteristic
791C22#337611yescharacteristic
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—81no—
800C4—82no—
801C4—82no—
802C4—161no—
803C4—161no—
804C4—161no—
805C4#241911yescharacteristic
806C4#247411yescharacteristic
807C4#248511yescharacteristic
808C4#259511yescharacteristic
809C4#272211yescharacteristic
810C4#275411yescharacteristic
811C4#277511yescharacteristic
812C4#278311yescharacteristic
813C2—162no—
814C2#1540011yescharacteristic
815C2#2503011yescharacteristic
816C2#2504211yescharacteristic
817C2#2654911yescharacteristic
818C2#2655111yescharacteristic
819C2#2713011yescharacteristic
820C2#2713911yescharacteristic
821C2#2803411yescharacteristic
822C2#2805611yescharacteristic
823C2#2955511yescharacteristic
824C2#2957011yescharacteristic
825C2#3087611yescharacteristic
826C2#3088311yescharacteristic
827C2#3228211yescharacteristic
828C2#3228811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #14132C2semidirect
5. #11323C2semidirect
6. #11292C2semidirect
7. #11267C2semidirect
8. #11220C2semidirect
13. #10908C2semidirect
14. #10861C2semidirect
15. #10797C2semidirect

Maximal subgroups

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

subgroupindex
C2×#19342
C2×#19262
#151362
#141322
#113232
#112922
#112672
#112202
#111892
#111212
#110662
#109082
#108612
#107972