Finite Group Databasebeta

← #391364

Subgroups — #391364

Order 512.

1086 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2092C211yesmaximal, characteristic
2#14707C211yesmaximal, characteristic, complemented
3#14700C211yesmaximal, characteristic
4#11372C211yesmaximal, characteristic, complemented
5#11268C211yesmaximal, characteristic, complemented
6#11220C211yesmaximal, characteristic, complemented
7#11220C211yesmaximal, characteristic, complemented
8#11219C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11189C211yesmaximal, characteristic
11#11189C211yesmaximal, characteristic
12#11066C211yesmaximal, characteristic
13#11066C211yesmaximal, characteristic
14#11051C211yesmaximal, characteristic
15#10795C211yesmaximal, characteristic, complemented
16C22×#107C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#102C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C2×#390C2211yescharacteristic
23C2×#390C2211yescharacteristic
24C2×#390C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#388—21no—
29C2×#388—21no—
30C2×#382C2211yescharacteristic
31C2×#382C2211yescharacteristic
32C2×C43C2211yescharacteristic
33#2092C418yescomplemented
34C2×#340C2211yescharacteristic
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
49C2×#336C2211yescharacteristic
50#1437—21no—
51#1437—21no—
52#1436—21no—
53#1436—21no—
54#1436—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C23×D4C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C22⋊C4—21no—
76C22×C22⋊C4—21no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4—21no—
81C22×C42D411yescharacteristic
82C22×C42D411yescharacteristic
83C22×C42D411yescharacteristic
84C22×C42D411yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C2×#107—41no—
89C2×#107—41no—
90C2×#107C2×C414yes—
91C2×#106—41no—
92C2×#106—41no—
93C2×#106C2×C414yes—
94C2×#102—41no—
95C2×#102—41no—
96C2×#102—41no—
97C2×#102—41no—
98C2×#102—41no—
99C2×#102—41no—
100C2×#102—41no—
101C2×#102—41no—
102C2×#102—41no—
103C2×#102—41no—
104C2×#102C2×C414yes—
105C2×#102C2×C414yes—
106#390—22no—
107#390—41no—
108#390—41no—
109#390—41no—
110#390—41no—
111#390C2×C414yes—
112#389—41no—
113#389—41no—
114#389—41no—
115#389—41no—
116#389—41no—
117#389—41no—
118#388—44no—
119#388—44no—
120#382—22no—
121#382—41no—
122#382—41no—
123#382C2×C414yes—
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×#95—21no—
139C43—41no—
140C43—41no—
141#340—41no—
142#340—41no—
143#340—41no—
144#340—41no—
145#340—41no—
146#340—41no—
147#340—41no—
148#340—41no—
149#340—41no—
150#340—41no—
151#336—22no—
152#336—41no—
153#336—41no—
154#336—41no—
155#336—41no—
156#336C2×C414yes—
157C25—21no—
158C22×D4—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×D4C22×C412yes—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2411yescharacteristic
186C22×C8—21no—
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×C8—21no—
211C22×C8—21no—
212C22×C8C22×C412yes—
213C22×C8C22×C412yes—
214C2×C4⋊C4—21no—
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—42no—
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—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4C22×C412yes—
263C2×C4⋊C4C22×C412yes—
264C2×C4⋊C4C22×C412yes—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—42no—
268C2×C22⋊C4—42no—
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×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—22no—
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—41no—
304C2×C42—41no—
305C2×C42—41no—
306C2×C42—41no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42C22×C412yes—
312C2×C42#4112yes—
313#107—44no—
314#106—44no—
315#102—44no—
316#102—44no—
317#102—44no—
318#102—44no—
319#95—24no—
320#95—24no—
321#95—42no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—42no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334C24—22no—
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—
348C24—41no—
349C24C22×D411yescharacteristic
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
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—
377C2×D4—41no—
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—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—41no—
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×C4C4×D412yes—
464C22×C4C4×D412yes—
465C22×C4#13512yes—
466C22×C4#13512yes—
467C22×C4AGL(1,ℤ/8)12yes—
468C22×C4AGL(1,ℤ/8)12yes—
469C22×C4C23×C411yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4H(5,𝔽2)11yescharacteristic
472C22×C4H(5,𝔽2)11yescharacteristic
473C22×C4H(5,𝔽2)11yescharacteristic
474C22×C4H(5,𝔽2)11yescharacteristic
475C22×C4H(5,𝔽2)11yescharacteristic
476C22×C4H(5,𝔽2)11yescharacteristic
477C22×C4H(5,𝔽2)11yescharacteristic
478C22×C42−1+411yescharacteristic
479C22×C42−1+411yescharacteristic
480C22×C42−1+411yescharacteristic
481C22×C42−1+411yescharacteristic
482C22×C42−1+411yescharacteristic
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
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—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—41no—
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—41no—
539C4⋊C4—84no—
540C4⋊C4—84no—
541C4⋊C4—84no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—84no—
545C22⋊C4—84no—
546C22⋊C4—84no—
547C22⋊C4—84no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—44no—
553C42—44no—
554C42—44no—
555C42—44no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
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—81no—
597C23—81no—
598C23—81no—
599C23C2×C4×D411yescharacteristic
600C23#53411yescharacteristic
601C23#53511yescharacteristic
602C23#53511yescharacteristic
603C23#53611yescharacteristic
604C23#53611yescharacteristic
605C23#53711yescharacteristic
606C23C2×#13511yescharacteristic
607C23C2×#13511yescharacteristic
608C23C2×AGL(1,ℤ/8)11yescharacteristic
609C23C2×AGL(1,ℤ/8)11yescharacteristic
610C23#57511yescharacteristic
611C23#57511yescharacteristic
612C23#57511yescharacteristic
613C23#57511yescharacteristic
614D4—42no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—81no—
619D4—81no—
620D4—81no—
621D4—81no—
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
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—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
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×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4#51811yescharacteristic
714C2×C4#51811yescharacteristic
715C2×C4#51911yescharacteristic
716C2×C4#52011yescharacteristic
717C2×C4#52011yescharacteristic
718C2×C4#52011yescharacteristic
719C2×C4#53911yescharacteristic
720C2×C4#53911yescharacteristic
721C2×C4#54011yescharacteristic
722C2×C4#54011yescharacteristic
723C2×C4#54111yescharacteristic
724C2×C4#54211yescharacteristic
725C2×C4#56011yescharacteristic
726C2×C4#56011yescharacteristic
727C2×C4#56211yescharacteristic
728C2×C4#56211yescharacteristic
729C2×C4#56211yescharacteristic
730C2×C4#56211yescharacteristic
731C2×C4#56211yescharacteristic
732C2×C4#56211yescharacteristic
733C2×C4#56211yescharacteristic
734C2×C4#56211yescharacteristic
735C2×C4#56311yescharacteristic
736C2×C4#56311yescharacteristic
737C2×C4#56311yescharacteristic
738C2×C4#56311yescharacteristic
739C2×C4#56311yescharacteristic
740C2×C4#56311yescharacteristic
741C8—42no—
742C8—42no—
743C8—81no—
744C8—81no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—161no—
753C22—161no—
754C22—161no—
755C22—161no—
756C22—161no—
757C22—161no—
758C22—161no—
759C22—161no—
760C22#232211yescharacteristic
761C22#232311yescharacteristic
762C22#232811yescharacteristic
763C22#281311yescharacteristic
764C22#281611yescharacteristic
765C22#282011yescharacteristic
766C22#282111yescharacteristic
767C22C4×#13511yescharacteristic
768C22#294311yescharacteristic
769C22C4×AGL(1,ℤ/8)11yescharacteristic
770C22C4×AGL(1,ℤ/8)11yescharacteristic
771C22#318811yescharacteristic
772C22#319111yescharacteristic
773C22#319411yescharacteristic
774C22#319711yescharacteristic
775C22#321111yescharacteristic
776C22#321111yescharacteristic
777C22#321211yescharacteristic
778C22#321211yescharacteristic
779C22#321311yescharacteristic
780C22#321411yescharacteristic
781C22#321711yescharacteristic
782C22#321911yescharacteristic
783C22#322811yescharacteristic
784C22#322811yescharacteristic
785C22#323211yescharacteristic
786C22#323311yescharacteristic
787C22#323411yescharacteristic
788C22#323511yescharacteristic
789C22#324011yescharacteristic
790C22#324011yescharacteristic
791C22#324711yescharacteristic
792C22#325011yescharacteristic
793C22#325111yescharacteristic
794C22#325611yescharacteristic
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—161no—
805C4—161no—
806C4—161no—
807C4—161no—
808C4#237611yescharacteristic
809C4#237611yescharacteristic
810C4#237811yescharacteristic
811C4#237811yescharacteristic
812C4#283611yescharacteristic
813C4#283611yescharacteristic
814C4#283711yescharacteristic
815C4#283711yescharacteristic
816C2—162no—
817C2#1462811yescharacteristic
818C2#2208011yescharacteristic
819C2#2208611yescharacteristic
820C2#2211411yescharacteristic
821C2#2212011yescharacteristic
822C2#2227111yescharacteristic
823C2#2227211yescharacteristic
824C2#3272611yescharacteristic
825C2#3272711yescharacteristic
826C2#3277611yescharacteristic
827C2#3277811yescharacteristic
828C2#3282211yescharacteristic
829C2#3282311yescharacteristic
830C2#3283611yescharacteristic
831C2#3284011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14707C2semidirect
4. #11372C2semidirect
5. #11268C2semidirect
6. #11220C2semidirect
7. #11220C2semidirect
8. #11219C2semidirect
9. #11219C2semidirect
15. #10795C2semidirect
33. #2092C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20922
#147072
#147002
#113722
#112682
#112202
#112192
#111892
#110662
#110512
#107952