Finite Group Databasebeta

← #530317

Subgroups — #530317

Order 512.

4314 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2342C212yesmaximal
2C22×#380C211yesmaximal, characteristic
3#14680C211yesmaximal, characteristic
4#14423C212yesmaximal, complemented
5#14422C212yesmaximal, complemented
6#14369C214yesmaximal, complemented
7#14275C212yesmaximal, complemented
8#14047C214yesmaximal, complemented
9#13882C212yesmaximal, complemented
10#13878C212yesmaximal, complemented
11#13874C212yesmaximal, complemented
12#13870C212yesmaximal, complemented
13#13869C212yesmaximal
14#13778C212yesmaximal, complemented
15C2×C22⋊#95C211yesmaximal, characteristic
16C25×C4C2211yescharacteristic
17C22×#117C2212yes—
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2342—216no—
24C2×#388C2214yes—
25C2×#388C2214yes—
26C2×#387C2214yescomplemented
27C2×#385C2214yes—
28C2×#381C2212yes—
29C2×#381C2212yes—
30C2×#381C2212yes—
31C2×#380C4116yescomplemented
32C2×#380C2212yes—
33C2×#380C2212yes—
34C2×#380C2212yes—
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#379C2212yes—
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2214yes—
46C22×#95C2212yes—
47C22×#95C2212yes—
48C22×#95C2212yes—
49#1445C2214yescomplemented
50#1444C2214yescomplemented
51#1443C2214yescomplemented
52#1442C2214yescomplemented
53#1442C2214yescomplemented
54#1441C2214yescomplemented
55#1441C2214yescomplemented
56#1441C2214yescomplemented
57#1440C2214yes—
58#1440C2214yes—
59#1436C2214yescomplemented
60#1436C2214yescomplemented
61#1436C2214yescomplemented
62#1436C2214yescomplemented
63#1436C2214yescomplemented
64#1436C2214yescomplemented
65#1434C2214yescomplemented
66C22⋊#95C2212yes—
67C22⋊#95C2212yes—
68C22⋊#95C2212yes—
69C22⋊#95C2214yes—
70C22⋊#95C2214yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C26C2311yescharacteristic
78C24×C4—28no—
79C24×C4—44no—
80C24×C4—42no—
81C24×C4—42no—
82C24×C4C2×C418yes—
83C24×C4C2311yescharacteristic
84C24×C4C2312yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C2×#117—28no—
94C2×#117—44no—
95C2×#117—44no—
96C22×C4⋊C4—44no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4C2×C418yescomplemented
100C22×C4⋊C4C2×C418yescomplemented
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C22⋊C4—28no—
112C22×C22⋊C4—28no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—42no—
115C22×C22⋊C4—42no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4C2×C4116yes—
119C22×C22⋊C4D418yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C42C2314yes—
133C22×C42C2314yes—
134#388—216no—
135#388—216no—
136#387—48no—
137#385—216no—
138#381—28no—
139#381—44no—
140#381—44no—
141#380—28no—
142#380—28no—
143#380—44no—
144#380—42no—
145#380—42no—
146#380C2×C4116yes—
147#380C2×C418yes—
148#380C2×C418yes—
149#380C2×C4116yescomplemented
150#380C2×C418yescomplemented
151#380C2×C418yescomplemented
152#379—28no—
153C4×C22⋊C4—216no—
154C4×C22⋊C4—28no—
155C2×#95—28no—
156C2×#95—44no—
157C2×#95C2×C4116yescomplemented
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C25—24no—
183C25—22no—
184C25—22no—
185C25—22no—
186C25—24no—
187C25—22no—
188C25—42no—
189C25—42no—
190C25C22×C414yes—
191C25C2×D414yes—
192C25#4114yes—
193C25C2411yescharacteristic
194C25C2411yescharacteristic
195C25C2411yescharacteristic
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—232no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—416no—
223C23×C4—416no—
224C23×C4—42no—
225C23×C4—41no—
226C23×C4—41no—
227C23×C4—41no—
228C23×C4—41no—
229C23×C4—42no—
230C23×C4—41no—
231C23×C4—41no—
232C23×C4—42no—
233C23×C4—41no—
234C23×C4—41no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—44no—
240C23×C4—44no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—432no—
246C23×C4—432no—
247C23×C4C22×C418yes—
248C23×C4C22×C414yes—
249C23×C4C22×C414yes—
250C23×C4C22×C414yes—
251C23×C4C22×C414yes—
252C23×C4C22×C418yes—
253C23×C4C22×C414yes—
254C23×C4C22×C414yes—
255C23×C4C2×D418yes—
256C23×C4#4118yes—
257C23×C4C2414yes—
258C23×C4C2414yes—
259C23×C4C2414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2414yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269#117—432no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—416no—
276C2×C4⋊C4—416no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4C22×C418yes—
294C2×C4⋊C4C22×C414yes—
295C2×C4⋊C4C22×C414yes—
296C2×C4⋊C4C22×C414yes—
297C2×C4⋊C4C22×C414yes—
298C2×C4⋊C4C22×C418yes—
299C2×C22⋊C4—264no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—416no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—416no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4C22×C418yes—
333C2×C22⋊C4C22×C418yes—
334C2×C22⋊C4C22×C418yes—
335C2×C22⋊C4C22×C418yes—
336C2×C22⋊C4C2×D418yes—
337C2×C22⋊C4C2×D418yes—
338C2×C42—28no—
339C2×C42—28no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42—44no—
344#95—28no—
345#95—28no—
346#95—28no—
347#95—28no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—28no—
352#95—28no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95—42no—
357#95—42no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95C22×C418yes—
365#95C22×C418yes—
366#95C22×C418yes—
367#95C22×C418yes—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—28no—
379C24—28no—
380C24—28no—
381C24—28no—
382C24—28no—
383C24—28no—
384C24—28no—
385C24—28no—
386C24—216no—
387C24—216no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—21no—
395C24—22no—
396C24—44no—
397C24—44no—
398C24—48no—
399C24—48no—
400C24—48no—
401C24—48no—
402C24—48no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24C4×D4116yes—
409C24C23×C412yes—
410C24C23×C412yes—
411C24C23×C412yes—
412C24C22×D412yes—
413C24C22×D412yes—
414C24C22×D412yes—
415C24C2×#4112yes—
416C24C2×#4114yes—
417C24C2×#4112yes—
418C24C2×#4112yes—
419C24H(5,𝔽2)12yes—
420C24H(5,𝔽2)12yes—
421C24H(5,𝔽2)12yes—
422C242−1+414yes—
423C242−1+412yes—
424C24C2511yescharacteristic
425C22×C4—216no—
426C22×C4—216no—
427C22×C4—28no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—216no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—216no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—4128no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—88no—
534C22×C4—88no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4—84no—
541C22×C4#117116yescomplemented
542C22×C4C23×C412yes—
543C22×C4C23×C414yes—
544C22×C4C23×C414yes—
545C22×C4C23×C414yes—
546C22×C4C23×C414yes—
547C22×C4C23×C412yes—
548C22×C4C23×C412yes—
549C22×C4C23×C412yes—
550C22×C4C22×D418yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4114yes—
553C22×C4H(5,𝔽2)14yes—
554C4⋊C4—216no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—416no—
561C4⋊C4—84no—
562C4⋊C4—84no—
563C4⋊C4—88no—
564C22⋊C4—216no—
565C22⋊C4—216no—
566C22⋊C4—216no—
567C22⋊C4—216no—
568C22⋊C4—216no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—416no—
575C22⋊C4—88no—
576C42—416no—
577C42—88no—
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—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—232no—
613C23—232no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—416no—
629C23—416no—
630C23—416no—
631C23—416no—
632C23—416no—
633C23—432no—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C2×#11714yes—
646C23C2×C4×D414yes—
647C23C2×C4×D414yes—
648C23C2×C4×D414yes—
649C23#51814yes—
650C23#51914yes—
651C23#52014yes—
652C23#53414yes—
653C23#53714yes—
654C23#53814yes—
655C23#53914yes—
656C23#54718yes—
657C23#55218yes—
658C23C24×C411yescharacteristic
659C23C23×D411yescharacteristic
660C23C22×#4112yes—
661C23C22×#4111yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×H(5,𝔽2)11yescharacteristic
664C23C2×H(5,𝔽2)12yes—
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×2−1+412yes—
667C23C2×2−1+411yescharacteristic
668C23#58512yes—
669C2×C4—232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—416no—
701C2×C4—416no—
702C2×C4—416no—
703C2×C4—416no—
704C2×C4—416no—
705C2×C4—432no—
706C2×C4—42no—
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—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—816no—
746C2×C4—816no—
747C2×C4—816no—
748C2×C4C2×#11714yes—
749C2×C4C2×#11714yes—
750C2×C4#51814yes—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—28no—
767C22—28no—
768C22—28no—
769C22—28no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—464no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22#232518yes—
784C22#234418yes—
785C22C22×#11711yescharacteristic
786C22C22×C4×D411yescharacteristic
787C22C2×#51811yescharacteristic
788C22C2×#51811yescharacteristic
789C22C2×#51911yescharacteristic
790C22C2×#52011yescharacteristic
791C22#342811yescharacteristic
792C22C2×#53411yescharacteristic
793C22C2×#53711yescharacteristic
794C22C2×#53811yescharacteristic
795C22C2×#53911yescharacteristic
796C22C2×#54712yes—
797C22C2×#55212yes—
798C22#349012yes—
799C22#349012yes—
800C22#349412yes—
801C22#349512yes—
802C22#349612yes—
803C22#350512yes—
804C22#353512yes—
805C22#353512yes—
806C22#353612yes—
807C22#353812yes—
808C4—24no—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—44no—
813C4—42no—
814C4—44no—
815C4—44no—
816C4—48no—
817C4—84no—
818C4—84no—
819C4—84no—
820C2—28no—
821C2—28no—
822C2—44no—
823C2C2×#232511yescharacteristic
824C2C2×#234411yescharacteristic
825C2#3417611yescharacteristic
826C2#3418011yescharacteristic
827C2#3420511yescharacteristic
828C2#3435911yescharacteristic
829C2#3438011yescharacteristic
830C2#3786012yes—
831C2#3786112yes—
832C2#3788012yes—
833C2#3788112yes—
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
4. #14423C2semidirect
5. #14422C2semidirect
6. #14369C2semidirect
7. #14275C2semidirect
8. #14047C2semidirect
9. #13882C2semidirect
10. #13878C2semidirect
11. #13874C2semidirect
12. #13870C2semidirect
14. #13778C2semidirect
26. C2×#387C22semidirect
31. C2×#380C4semidirect
49. #1445C22semidirect
50. #1444C22semidirect
51. #1443C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1441C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
59. #1436C22semidirect
60. #1436C22semidirect
61. #1436C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. #1436C22semidirect
65. #1434C22semidirect
99. C22×C4⋊C4C2×C4semidirect
100. C22×C4⋊C4C2×C4semidirect
149. #380C2×C4semidirect
150. #380C2×C4semidirect
151. #380C2×C4semidirect
157. C2×#95C2×C4semidirect
541. C22×C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23422
C22×#3802
#146802
#144232
#144222
#143692
#142752
#140472
#138822
#138782
#138742
#138702
#138692
#137782
C2×C22⋊#952