Finite Group Databasebeta

← #365185

Subgroups — #365185

Order 512.

1318 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1854C211yesmaximal, characteristic
2C2×#1825C211yesmaximal, characteristic
3C2×#1735C211yesmaximal, characteristic
4#13939C211yesmaximal, characteristic
5#13801C211yesmaximal, characteristic
6#11316C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11256C211yesmaximal, characteristic, complemented
9#11256C211yesmaximal, characteristic, complemented
10#10908C211yesmaximal, characteristic, complemented
11#10908C211yesmaximal, characteristic, complemented
12#10807C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10721C211yesmaximal, characteristic
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C2×#380C2211yescharacteristic
23C2×#380C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C22⋊C4C2211yescharacteristic
27#1854—24no—
28#1825C418yescomplemented
29#1735—24no—
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×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48#1440—21no—
49#1440—21no—
50#1437—21no—
51#1437—21no—
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58#1434—21no—
59#1434—21no—
60#1434—21no—
61C4×#95—21no—
62C24×C4C2311yescharacteristic
63C23×C8—22no—
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—41no—
69C23×C8—41no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—41no—
83C2×#117—41no—
84C2×#117C2×C414yes—
85C2×#117D414yes—
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4D411yescharacteristic
99C22×C22⋊C4D411yescharacteristic
100C22×C42—21no—
101C22×C42—21no—
102C22×C42—21no—
103C22×C42—21no—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×#107—22no—
107C2×#107—41no—
108C2×#107—41no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8C2×C414yes—
115#380—22no—
116#380—22no—
117#380—22no—
118#380C2×C414yes—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—41no—
122C4×C4⋊C4—41no—
123C4×C22⋊C4—22no—
124C4×C22⋊C4—22no—
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—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—41no—
152#340—41no—
153#340C2×C414yes—
154#340C2×C414yes—
155#340C2×C414yes—
156#340C2×C414yes—
157#336—22no—
158#336—22no—
159#336—41no—
160#336—41no—
161C25C2×D411yescharacteristic
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—21no—
178C23×C4C22×C412yes—
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D412yes—
185C23×C4#4112yes—
186C23×C4#4112yes—
187C23×C4#4112yes—
188C23×C4#4112yes—
189C23×C4C2411yescharacteristic
190C22×C8—28no—
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×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—44no—
216C22×C8—44no—
217C22×C8—44no—
218C22×C8—44no—
219C22×C8—44no—
220C22×C8—44no—
221C22×C8C22×C412yes—
222C22×C8C22×C412yes—
223C22×C8#4112yes—
224C22×C8#4112yes—
225#117—28no—
226#117—28no—
227#117—28no—
228#117—44no—
229#117—44no—
230#117—44no—
231#117—44no—
232#117—44no—
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—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C22×C412yes—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C2×D412yes—
278C2×C4⋊C4C2×D412yes—
279C2×C4⋊C4#4112yes—
280C2×C4⋊C4#4112yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—41no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—81no—
296C2×C22⋊C4—81no—
297C2×C22⋊C4—81no—
298C2×C22⋊C4—81no—
299C2×C42—24no—
300C2×C42—24no—
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—21no—
312C2×C42—21no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—81no—
322C2×C42—81no—
323#107—44no—
324#106—44no—
325C22⋊C8—28no—
326#95—24no—
327#95—22no—
328#95—22no—
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—
340#95—81no—
341#95—81no—
342#95—81no—
343#95—81no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24C4×D412yes—
357C24#12112yes—
358C24#12312yes—
359C24C22×D411yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
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—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
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—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
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—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#11714yes—
471C22×C4C4×D414yes—
472C22×C4C4×D412yes—
473C22×C4#12112yes—
474C22×C4#12312yes—
475C22×C4#12414yes—
476C22×C4#12614yes—
477C22×C4#13512yes—
478C22×C4#13512yes—
479C22×C4C23×C411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4C2×#4111yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C22×C4H(5,𝔽2)11yescharacteristic
490C22×C4H(5,𝔽2)11yescharacteristic
491C22×C42−1+411yescharacteristic
492C22×C42−1+411yescharacteristic
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—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—416no—
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—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
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—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
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—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4#12314yes—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—84no—
559C22⋊C4—84no—
560C42—48no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—41no—
568C42—41no—
569C42—48no—
570C42—84no—
571C42—84no—
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—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23#38814yes—
607C23C2×C4×D411yescharacteristic
608C23C2×#12111yescharacteristic
609C23C2×#12311yescharacteristic
610C23#54611yescharacteristic
611C23#54611yescharacteristic
612C23#54711yescharacteristic
613C23#54711yescharacteristic
614C23C2×#13511yescharacteristic
615C23C2×#13511yescharacteristic
616C23#57511yescharacteristic
617C23#57511yescharacteristic
618C23#57611yescharacteristic
619C23#57711yescharacteristic
620C23#57711yescharacteristic
621C23#57811yescharacteristic
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
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—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
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×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4#38814yes—
721C2×C4C2×#11711yescharacteristic
722C2×C4C2×C4×D411yescharacteristic
723C2×C4C4×#4111yescharacteristic
724C2×C4C4×#4111yescharacteristic
725C2×C4#52011yescharacteristic
726C2×C4#52011yescharacteristic
727C2×C4C2×#12311yescharacteristic
728C2×C4#52511yescharacteristic
729C2×C4C2×#12411yescharacteristic
730C2×C4C2×#12611yescharacteristic
731C2×C4#52911yescharacteristic
732C2×C4#52911yescharacteristic
733C2×C4#53411yescharacteristic
734C2×C4#53611yescharacteristic
735C2×C4#53911yescharacteristic
736C2×C4#53911yescharacteristic
737C2×C4#55111yescharacteristic
738C2×C4#55111yescharacteristic
739C2×C4#55111yescharacteristic
740C2×C4#55111yescharacteristic
741C2×C4#55111yescharacteristic
742C2×C4#55111yescharacteristic
743C2×C4#55211yescharacteristic
744C2×C4#55211yescharacteristic
745C2×C4#55211yescharacteristic
746C2×C4#55211yescharacteristic
747C2×C4#55211yescharacteristic
748C2×C4#55211yescharacteristic
749C8—42no—
750C8—42no—
751C8—42no—
752C8—42no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×#38811yescharacteristic
769C22#235911yescharacteristic
770C22#235911yescharacteristic
771C22#241211yescharacteristic
772C22#241311yescharacteristic
773C22#241911yescharacteristic
774C22#241911yescharacteristic
775C22C4×#13511yescharacteristic
776C22#294311yescharacteristic
777C22#294611yescharacteristic
778C22#294711yescharacteristic
779C22#303511yescharacteristic
780C22#303511yescharacteristic
781C22#304511yescharacteristic
782C22#304611yescharacteristic
783C22#309111yescharacteristic
784C22#309111yescharacteristic
785C22#309811yescharacteristic
786C22#309911yescharacteristic
787C22#329611yescharacteristic
788C22#330111yescharacteristic
789C22#330211yescharacteristic
790C22#330511yescharacteristic
791C22#330911yescharacteristic
792C22#331111yescharacteristic
793C22#331511yescharacteristic
794C22#332111yescharacteristic
795C22#333711yescharacteristic
796C22#333711yescharacteristic
797C22#334111yescharacteristic
798C22#334211yescharacteristic
799C22#334711yescharacteristic
800C22#334811yescharacteristic
801C22#334911yescharacteristic
802C22#335011yescharacteristic
803C4—24no—
804C4—42no—
805C4—42no—
806C4—44no—
807C4—82no—
808C4—82no—
809C4—81no—
810C4—81no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—161no—
815C4—161no—
816C4C4×#12311yescharacteristic
817C4#232211yescharacteristic
818C4#234311yescharacteristic
819C4#234311yescharacteristic
820C4#249311yescharacteristic
821C4#249311yescharacteristic
822C4#250311yescharacteristic
823C4#256111yescharacteristic
824C2—44no—
825C2#1397211yescharacteristic
826C2#2105811yescharacteristic
827C2#2106211yescharacteristic
828C2#2291911yescharacteristic
829C2#2292111yescharacteristic
830C2#2293311yescharacteristic
831C2#2293911yescharacteristic
832C2#2453511yescharacteristic
833C2#2453611yescharacteristic
834C2#2458411yescharacteristic
835C2#2458711yescharacteristic
836C2#2493611yescharacteristic
837C2#2493811yescharacteristic
838C2#2494211yescharacteristic
839C2#2494811yescharacteristic
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
6. #11316C2semidirect
7. #11315C2semidirect
8. #11256C2semidirect
9. #11256C2semidirect
10. #10908C2semidirect
11. #10908C2semidirect
12. #10807C2semidirect
13. #10806C2semidirect
28. #1825C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18542
C2×#18252
C2×#17352
#139392
#138012
#113162
#113152
#112562
#109082
#108072
#108062
#107212
#107142