Finite Group Databasebeta

← #384013

Subgroups — #384013

Order 512.

1214 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1918C211yesmaximal, characteristic, complemented
2C2×#1808C211yesmaximal, characteristic
3C2×#1808C211yesmaximal, characteristic
4#13994C211yesmaximal, characteristic
5#13974C211yesmaximal, characteristic
6#11379C211yesmaximal, characteristic, complemented
7#11328C211yesmaximal, characteristic, complemented
8#11256C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11199C211yesmaximal, characteristic
11#11199C211yesmaximal, characteristic
12#10907C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10907C211yesmaximal, characteristic, complemented
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#388—21no—
25C2×#388—21no—
26C2×#380C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33#1918—24no—
34#1808—24no—
35#1808C418yescomplemented
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1443—21no—
53#1442—21no—
54#1440—21no—
55#1440—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62C24×C4C2311yescharacteristic
63C23×C8—22no—
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—41no—
68C23×C8—41no—
69C23×C8C2×C414yes—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C22⋊C4D411yescharacteristic
89C22×C22⋊C4D411yescharacteristic
90C22×C42—21no—
91C22×C42—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C2×#107—22no—
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#107—22no—
99C2×#107—22no—
100C2×#107—41no—
101C2×#107—41no—
102C2×#107—41no—
103C2×#107—41no—
104C2×#107C2×C414yes—
105C2×#107C2×C414yes—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—41no—
108C2×C22⋊C8—41no—
109#389—22no—
110#389—41no—
111#389—41no—
112#389—41no—
113#388—44no—
114#388—44no—
115#380—22no—
116#380—22no—
117#380—22no—
118#380—22no—
119#380—41no—
120#380—41no—
121#380C2×C414yes—
122#380C2×C414yes—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—41no—
125C4×C4⋊C4—41no—
126C4×C4⋊C4—41no—
127C4×C22⋊C4—41no—
128C4×C22⋊C4—41no—
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×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95D411yescharacteristic
146C2×#95D411yescharacteristic
147#340—22no—
148#340—22no—
149#340—22no—
150#340—41no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340C2×C414yes—
157#340C2×C414yes—
158#340D414yes—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—22no—
163C25C2×D411yescharacteristic
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—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4C22×C412yes—
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4#4112yes—
191C23×C4C2411yescharacteristic
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—28no—
201C22×C8—28no—
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×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—44no—
217C22×C8—44no—
218C22×C8—44no—
219C22×C8—44no—
220C22×C8—44no—
221C22×C8C22×C412yes—
222C22×C8C22×C412yes—
223C22×C8C2×D412yes—
224C22×C8#4112yes—
225C22×C8#4112yes—
226C22×C8#4112yes—
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—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—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—81no—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C22×C412yes—
279C2×C4⋊C4C2×D412yes—
280C2×C4⋊C4C2×D412yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—81no—
297C2×C22⋊C4—81no—
298C2×C22⋊C4D814yes—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—81no—
317#107—28no—
318#107—44no—
319#107—44no—
320#107—44no—
321C22⋊C8—44no—
322#95—24no—
323#95—24no—
324#95—41no—
325#95—41no—
326#95—42no—
327#95—42no—
328#95—42no—
329#95—42no—
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—81no—
339#95—81no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24C4×D412yes—
353C24C2×D812yes—
354C24#13512yes—
355C24C22×D411yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
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—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
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—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
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×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×C4C4×D412yes—
473C22×C4C2×D812yes—
474C22×C4C2×D812yes—
475C22×C4C23×C411yescharacteristic
476C22×C4C22×D411yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4H(5,𝔽2)11yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C42−1+411yescharacteristic
486C22×C42−1+411yescharacteristic
487C22×C42−1+411yescharacteristic
488C22×C42−1+411yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—416no—
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—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8#11714yes—
517C2×C8C4×D414yes—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
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—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—84no—
551C4⋊C4—84no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—84no—
557C22⋊C4—84no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—84no—
567C42—84no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23C4×D814yes—
603C23C2×C4×D411yescharacteristic
604C23#53411yescharacteristic
605C23#53711yescharacteristic
606C23D4211yescharacteristic
607C23#54711yescharacteristic
608C23#54711yescharacteristic
609C23#54711yescharacteristic
610C23C22×D811yescharacteristic
611C23C2×#13511yescharacteristic
612C23#57511yescharacteristic
613C23#57511yescharacteristic
614C23#57611yescharacteristic
615C23#57811yescharacteristic
616C23#57811yescharacteristic
617C23#57811yescharacteristic
618C2×C4—22no—
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—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
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—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
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—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4C2×#11711yescharacteristic
718C2×C4C2×C4×D411yescharacteristic
719C2×C4#51811yescharacteristic
720C2×C4#51911yescharacteristic
721C2×C4#52011yescharacteristic
722C2×C4#52011yescharacteristic
723C2×C4#53611yescharacteristic
724C2×C4#53711yescharacteristic
725C2×C4#53811yescharacteristic
726C2×C4#53911yescharacteristic
727C2×C4#54011yescharacteristic
728C2×C4#54111yescharacteristic
729C2×C4#54111yescharacteristic
730C2×C4#54211yescharacteristic
731C2×C4#54211yescharacteristic
732C2×C4#54211yescharacteristic
733C2×C4#54611yescharacteristic
734C2×C4#54611yescharacteristic
735C2×C4#54811yescharacteristic
736C2×C4#55111yescharacteristic
737C2×C4#55111yescharacteristic
738C2×C4#55211yescharacteristic
739C2×C4#55211yescharacteristic
740C2×C4#55311yescharacteristic
741C2×C4#56211yescharacteristic
742C2×C4#56211yescharacteristic
743C2×C4#56311yescharacteristic
744C2×C4#56311yescharacteristic
745C8—24no—
746C8—24no—
747C8—81no—
748C8—81no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22#232511yescharacteristic
765C22#234411yescharacteristic
766C22#236111yescharacteristic
767C22#267111yescharacteristic
768C22#267211yescharacteristic
769C22#271711yescharacteristic
770C22#272211yescharacteristic
771C22C2×C4×D811yescharacteristic
772C22#294311yescharacteristic
773C22#295011yescharacteristic
774C22#295111yescharacteristic
775C22#318611yescharacteristic
776C22#319111yescharacteristic
777C22#320211yescharacteristic
778C22#320311yescharacteristic
779C22#324511yescharacteristic
780C22#325011yescharacteristic
781C22#326111yescharacteristic
782C22#326211yescharacteristic
783C22#326911yescharacteristic
784C22#326911yescharacteristic
785C22D4×D811yescharacteristic
786C22#328511yescharacteristic
787C22#333411yescharacteristic
788C22#333411yescharacteristic
789C22#333411yescharacteristic
790C22#333611yescharacteristic
791C22#333611yescharacteristic
792C22#333911yescharacteristic
793C22#334711yescharacteristic
794C22#334711yescharacteristic
795C22#334911yescharacteristic
796C22#334911yescharacteristic
797C22#334911yescharacteristic
798C22#334911yescharacteristic
799C4—42no—
800C4—42no—
801C4—42no—
802C4—81no—
803C4—82no—
804C4—81no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—161no—
811C4—161no—
812C4#231411yescharacteristic
813C4#232311yescharacteristic
814C4#234211yescharacteristic
815C4#237811yescharacteristic
816C4#269011yescharacteristic
817C4#270211yescharacteristic
818C4#274111yescharacteristic
819C4#274711yescharacteristic
820C2—44no—
821C2#1436911yescharacteristic
822C2#2218111yescharacteristic
823C2#2219711yescharacteristic
824C2#2261111yescharacteristic
825C2#2261611yescharacteristic
826C2#2302511yescharacteristic
827C2#2303011yescharacteristic
828C2#3055711yescharacteristic
829C2#3056211yescharacteristic
830C2#3066111yescharacteristic
831C2#3067011yescharacteristic
832C2#3225811yescharacteristic
833C2#3226311yescharacteristic
834C2#3240611yescharacteristic
835C2#3240911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×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×#1918C2semidirect
6. #11379C2semidirect
7. #11328C2semidirect
8. #11256C2semidirect
9. #11219C2semidirect
12. #10907C2semidirect
13. #10907C2semidirect
14. #10907C2semidirect
35. #1808C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19182
C2×#18082
#139942
#139742
#113792
#113282
#112562
#112192
#111992
#109072
#107142