Finite Group Databasebeta

← #530300

Subgroups — #530300

Order 512.

3802 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2346C211yesmaximal, characteristic, complemented
2C2×#2280C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic
4#14680C211yesmaximal, characteristic
5#14368C214yesmaximal, complemented
6#14366C214yesmaximal
7#14264C212yesmaximal, complemented
8#13993C212yesmaximal, complemented
9#13974C212yesmaximal, complemented
10#13951C211yesmaximal, characteristic, complemented
11#13939C211yesmaximal, characteristic, complemented
12#13917C212yesmaximal, complemented
13#13915C212yesmaximal, complemented
14#13898C212yesmaximal, complemented
15#13895C212yesmaximal, complemented
16#13801C211yesmaximal, characteristic, complemented
17#13777C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#117C2212yes—
20C22×#117C2211yescharacteristic
21C22×#117C2211yescharacteristic
22#2346—28no—
23C2×#389C2212yescomplemented
24C2×#389C2212yescomplemented
25C2×#388C2214yes—
26C2×#388C2214yes—
27C2×#382C2212yescomplemented
28#2280—28no—
29#2280C4116yescomplemented
30C2×#381C2211yescharacteristic
31C2×#381C2211yescharacteristic
32C2×#381C2212yes—
33C2×#380C2212yes—
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#379C2212yes—
45C2×#379C2212yes—
46C2×#379C2212yes—
47C2×C4×C4⋊C4C2212yescomplemented
48C2×C4×C4⋊C4C2212yescomplemented
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×#376C2212yescomplemented
55#1444C2214yescomplemented
56#1443C2214yescomplemented
57#1443C2214yescomplemented
58#1442C2214yescomplemented
59#1440C2214yes—
60#1440C2214yes—
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1437C2214yes—
66#1437C2214yes—
67#1437C2214yes—
68#1437C2214yes—
69#1436C2214yescomplemented
70#1436C2214yescomplemented
71#1436C2214yescomplemented
72#1436C2214yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78#1434C2212yescomplemented
79#1434C2212yescomplemented
80#1434C2212yescomplemented
81#1434C2212yescomplemented
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C4×#95C2212yescomplemented
86C26C2311yescharacteristic
87C24×C4—24no—
88C24×C4—28no—
89C24×C4—24no—
90C24×C4—44no—
91C24×C4C2×C418yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C2×#117—24no—
99C2×#117—24no—
100C2×#117—28no—
101C2×#117—28no—
102C2×#117—44no—
103C2×#117—44no—
104C2×#117C2×C418yes—
105C2×#117C2×C418yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2314yes—
136C22×C42C2314yes—
137C22×C42C2312yes—
138#389—28no—
139#389—44no—
140#388—216no—
141#388—48no—
142#382—28no—
143#381—24no—
144#381—24no—
145#381C2×C4116yes—
146#380—24no—
147#380—28no—
148#380—24no—
149#380—28no—
150#380—24no—
151#380—24no—
152#380—44no—
153#380C2×C418yes—
154#380C2×C418yes—
155#380C2×C418yes—
156#380C2×C418yes—
157#379—28no—
158#379—44no—
159#379C2×C4116yes—
160C4×C4⋊C4—28no—
161C4×C4⋊C4—44no—
162C4×C22⋊C4—24no—
163C4×C22⋊C4—28no—
164C4×C22⋊C4C2×C4116yes—
165C4×C22⋊C4C2×C4116yes—
166C4×C22⋊C4D418yes—
167#376—28no—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2311yescharacteristic
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C25—22no—
195C25—24no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—42no—
200C25—41no—
201C25—41no—
202C25—42no—
203C25—42no—
204C25C22×C414yes—
205C25C2411yescharacteristic
206C25C2411yescharacteristic
207C25C2411yescharacteristic
208C23×C4—22no—
209C23×C4—24no—
210C23×C4—22no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—22no—
214C23×C4—24no—
215C23×C4—22no—
216C23×C4—232no—
217C23×C4—232no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—24no—
228C23×C4—416no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—432no—
233C23×C4—432no—
234C23×C4C22×C414yes—
235C23×C4C22×C414yes—
236C23×C4C22×C414yes—
237C23×C4C22×C414yes—
238C23×C4C22×C414yes—
239C23×C4C22×C414yes—
240C23×C4C2×D414yes—
241C23×C4#4118yes—
242C23×C4#4114yes—
243C23×C4C2414yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257#117—232no—
258#117—432no—
259#117—416no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4C22×C414yes—
285C2×C4⋊C4C22×C414yes—
286C2×C4⋊C4C22×C414yes—
287C2×C4⋊C4C22×C414yes—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4C22×C418yes—
327C2×C22⋊C4C22×C418yes—
328C2×C22⋊C4C22×C418yes—
329C2×C22⋊C4C22×C418yes—
330C2×C22⋊C4C22×C418yes—
331C2×C22⋊C4C22×C418yes—
332C2×C22⋊C4C2×D418yes—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—28no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42—44no—
344C2×C42—44no—
345C2×C42—44no—
346C2×C42—44no—
347C2×C42C22×C418yes—
348C2×C42C22×C418yes—
349C2×C42C2×D418yes—
350#95—24no—
351#95—28no—
352#95—24no—
353#95—24no—
354#95—22no—
355#95—22no—
356#95—28no—
357#95—28no—
358#95—24no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95C22×C418yes—
371#95C22×C418yes—
372#95C22×C418yes—
373#95C22×C418yes—
374#95C2×D414yes—
375#95C2×D414yes—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—44no—
405C24—44no—
406C24—44no—
407C24—44no—
408C24—48no—
409C24—48no—
410C24—44no—
411C24—44no—
412C24—48no—
413C24—44no—
414C24—48no—
415C24—44no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24C23×C412yes—
425C24C23×C412yes—
426C24C23×C412yes—
427C24C22×D412yes—
428C24C2×#4114yes—
429C24C2×#4112yes—
430C24H(5,𝔽2)12yes—
431C242−1+412yes—
432C24C2511yescharacteristic
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—216no—
443C22×C4—216no—
444C22×C4—216no—
445C22×C4—216no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—4128no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4#117116yes—
530C22×C4C4×D4116yes—
531C22×C4C23×C412yes—
532C22×C4C23×C414yes—
533C22×C4C23×C414yes—
534C22×C4C23×C414yes—
535C22×C4C23×C414yes—
536C22×C4C23×C412yes—
537C22×C4C23×C412yes—
538C22×C4C23×C412yes—
539C22×C4C22×D414yes—
540C22×C4C22×D414yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C2×#4114yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4114yes—
546C22×C4C2×#4112yes—
547C22×C4H(5,𝔽2)14yes—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—88no—
557C4⋊C4—88no—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—84no—
571C22⋊C4—88no—
572C22⋊C4—84no—
573C22⋊C4—88no—
574C42—216no—
575C42—216no—
576C42—48no—
577C42—416no—
578C42—48no—
579C42—88no—
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—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—416no—
621C23—416no—
622C23—416no—
623C23—416no—
624C23—416no—
625C23—416no—
626C23—416no—
627C23—432no—
628C23—432no—
629C23—432no—
630C23—432no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—41no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×#11714yes—
658C23C2×C4×D414yes—
659C23#52014yes—
660C23C24×C411yescharacteristic
661C23C23×D411yescharacteristic
662C23C22×#4112yes—
663C23C22×#4111yescharacteristic
664C23C2×H(5,𝔽2)12yes—
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23#58512yes—
668C23#58512yes—
669C23#58511yescharacteristic
670C23#58511yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—232no—
680C2×C4—232no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—416no—
703C2×C4—416no—
704C2×C4—416no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—416no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4C2×#11714yes—
755C2×C4C2×#11714yes—
756C2×C4C2×C4×D414yes—
757C2×C4C2×C4×D414yes—
758C2×C4#51814yes—
759C2×C4#54618yes—
760C2×C4#55118yes—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—464no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22C22×#11711yescharacteristic
796C22C22×C4×D411yescharacteristic
797C22C2×#51811yescharacteristic
798C22C2×#52011yescharacteristic
799C22#342811yescharacteristic
800C22#342811yescharacteristic
801C22#342811yescharacteristic
802C22#344912yes—
803C22#345512yes—
804C22C2×#54612yes—
805C22C2×#55112yes—
806C22#348811yescharacteristic
807C22#348911yescharacteristic
808C22#349312yes—
809C22#349312yes—
810C22#349412yes—
811C22#349411yescharacteristic
812C22#349512yes—
813C22#349511yescharacteristic
814C22#353912yes—
815C22#354012yes—
816C22#354112yes—
817C22#354212yes—
818C4—24no—
819C4—24no—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—44no—
826C4—44no—
827C4—84no—
828C4—82no—
829C4—82no—
830C4—84no—
831C4#234218yes—
832C2—44no—
833C2—44no—
834C2—44no—
835C2#3406511yescharacteristic
836C2C2×#234211yescharacteristic
837C2#3417911yescharacteristic
838C2#3418011yescharacteristic
839C2#3420211yescharacteristic
840C2#3439111yescharacteristic
841C2#3440411yescharacteristic
842C2#3784512yes—
843C2#3784712yes—
844C2#3785712yes—
845C2#3785912yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2346C2semidirect
5. #14368C2semidirect
7. #14264C2semidirect
8. #13993C2semidirect
9. #13974C2semidirect
10. #13951C2semidirect
11. #13939C2semidirect
12. #13917C2semidirect
13. #13915C2semidirect
14. #13898C2semidirect
15. #13895C2semidirect
16. #13801C2semidirect
17. #13777C2semidirect
23. C2×#389C22semidirect
24. C2×#389C22semidirect
27. C2×#382C22semidirect
29. #2280C4semidirect
47. C2×C4×C4⋊C4C22semidirect
48. C2×C4×C4⋊C4C22semidirect
54. C2×#376C22semidirect
55. #1444C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
69. #1436C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. #1434C22semidirect
79. #1434C22semidirect
80. #1434C22semidirect
81. #1434C22semidirect
85. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#23462
C2×#22802
#146802
#143682
#143662
#142642
#139932
#139742
#139512
#139392
#139172
#139152
#138982
#138952
#138012
#137772