Finite Group Databasebeta

← #642339

Subgroups — #642339

Order 512.

4536 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2618C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic, complemented
4C2×#2280C211yesmaximal, characteristic, complemented
5#16562C214yesmaximal, complemented
6#16393C212yesmaximal, complemented
7#16259C212yesmaximal, complemented
8#14911C212yesmaximal, complemented
9#14890C214yesmaximal, complemented
10#14840C212yesmaximal, complemented
11#14764C212yesmaximal, complemented
12#14718C212yesmaximal, complemented
13#14339C211yesmaximal, characteristic, complemented
14#14275C211yesmaximal, characteristic, complemented
15#14271C211yesmaximal, characteristic, complemented
16#14019C212yesmaximal, complemented
17#13996C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#120C2212yes—
24C22×#117C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29#2847—28no—
30#2618—28no—
31C2×#398C2212yescomplemented
32C2×#396C2214yescomplemented
33C2×#394C2214yes—
34C2×#394C2212yescomplemented
35C2×#388C2214yescomplemented
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385—28no—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48#2280—28no—
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#379C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1445C2214yescomplemented
63#1445C2212yescomplemented
64#1444C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2214yescomplemented
67#1441C2212yescomplemented
68#1441C2214yescomplemented
69#1441C2212yescomplemented
70#1441C2214yescomplemented
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yescomplemented
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2212yescomplemented
82#1437C2214yescomplemented
83#1436C2214yescomplemented
84C4⋊#95C2214yescomplemented
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C23×D4C2312yes—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—44no—
95C24×C4—44no—
96C24×C4D418yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C2×#123—28no—
108C2×#123—28no—
109C2×#123—44no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—44no—
116C2×#121—44no—
117C2×#120—28no—
118C2×#120—44no—
119C2×#120—44no—
120C2×#117—28no—
121C2×#117—44no—
122C2×#117—44no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—44no—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—44no—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C42C2314yes—
163#398—28no—
164#396—216no—
165#394—28no—
166#394—48no—
167#388—48no—
168#386—28no—
169#386—28no—
170#386—28no—
171#386—28no—
172#386—28no—
173#386—44no—
174#385—28no—
175#385—28no—
176#385—28no—
177#385—28no—
178#385—44no—
179#381—28no—
180#381—44no—
181#380—24no—
182#380—24no—
183#380—24no—
184#380—24no—
185#380—28no—
186#380D418yescomplemented
187#379—28no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C25—22no—
213C25—22no—
214C25—24no—
215C25—24no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—42no—
221C25—42no—
222C25C2×D414yes—
223C25C2412yes—
224C25C2411yescharacteristic
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—44no—
248C22×D4—44no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—232no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—416no—
280C23×C4—42no—
281C23×C4—416no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—432no—
295C23×C4—432no—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4#4114yes—
306C23×C4C2414yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2414yes—
313C23×C4C2411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319#123—432no—
320#121—416no—
321#121—416no—
322#121—416no—
323#120—432no—
324#117—432no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—416no—
351C2×C4⋊C4—416no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4C2×D418yes—
356C2×C22⋊C4—232no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—416no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D418yes—
408C2×C42—28no—
409C2×C42—28no—
410C2×C42—44no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95C2×D418yes—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—216no—
436C24—216no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—28no—
459C24—28no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—24no—
467C24—22no—
468C24—22no—
469C24—24no—
470C24—24no—
471C24—44no—
472C24—44no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24H(5,𝔽2)14yes—
495C24H(5,𝔽2)12yes—
496C24H(5,𝔽2)12yes—
497C242−1+414yes—
498C24C2511yescharacteristic
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—44no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4—88no—
518C2×D4—88no—
519C2×D4—88no—
520C2×D4—88no—
521C22×C4—216no—
522C22×C4—216no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—4128no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4#121116yes—
635C22×C4C22×D412yes—
636C22×C4C22×D418yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4H(5,𝔽2)14yes—
647C4⋊C4—48no—
648C4⋊C4—416no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—44no—
656C4⋊C4—48no—
657C4⋊C4—88no—
658C22⋊C4—216no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—416no—
662C22⋊C4—416no—
663C22⋊C4—416no—
664C22⋊C4—416no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—88no—
675C22⋊C4—88no—
676C42—416no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—232no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—416no—
719C23—416no—
720C23—416no—
721C23—416no—
722C23—416no—
723C23—432no—
724C23—432no—
725C23—432no—
726C23—432no—
727C23—416no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—44no—
756C23—44no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23C2×#12114yes—
772C23#52514yes—
773C23#53414yes—
774C23#53514yes—
775C23#53614yes—
776C23#54614yes—
777C23#55014yes—
778C23#55314yes—
779C23#55514yes—
780C23C23×D411yescharacteristic
781C23C23×D411yescharacteristic
782C23C22×#4111yescharacteristic
783C23C22×#4111yescharacteristic
784C23C22×#4111yescharacteristic
785C23C2×H(5,𝔽2)12yes—
786C23C2×H(5,𝔽2)12yes—
787C23C2×H(5,𝔽2)11yescharacteristic
788C23C2×H(5,𝔽2)11yescharacteristic
789C23C2×2−1+412yes—
790C23#58512yes—
791D4—88no—
792D4—816no—
793D4—816no—
794D4—816no—
795C2×C4—232no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—416no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—416no—
825C2×C4—42no—
826C2×C4—416no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—88no—
874C2×C4—88no—
875C2×C4C2×#12114yes—
876C2×C4C2×#12114yes—
877C2×C4#53414yes—
878C22—24no—
879C22—28no—
880C22—28no—
881C22—24no—
882C22—24no—
883C22—28no—
884C22—28no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—464no—
895C22—42no—
896C22—42no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—82no—
912C22—84no—
913C22—84no—
914C22—82no—
915C22—82no—
916C22—84no—
917C22—84no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22#241418yes—
923C22C22×#12111yescharacteristic
924C22C2×#52511yescharacteristic
925C22C2×#53411yescharacteristic
926C22C2×#53411yescharacteristic
927C22C2×#53511yescharacteristic
928C22C2×#53611yescharacteristic
929C22#344911yescharacteristic
930C22#345912yes—
931C22#346012yes—
932C22C2×#54611yescharacteristic
933C22C2×#55011yescharacteristic
934C22C2×#55311yescharacteristic
935C22C2×#55511yescharacteristic
936C22#348412yes—
937C22#348912yes—
938C22#349012yes—
939C22#349212yes—
940C22#349212yes—
941C22#349512yes—
942C22#353412yes—
943C22#353412yes—
944C22#353612yes—
945C22#353612yes—
946C4—24no—
947C4—24no—
948C4—24no—
949C4—44no—
950C4—48no—
951C4—44no—
952C4—42no—
953C4—82no—
954C4—82no—
955C4—82no—
956C4—84no—
957C4—82no—
958C4—82no—
959C2—28no—
960C2—44no—
961C2—44no—
962C2—162no—
963C2#3456211yescharacteristic
964C2C2×#241411yescharacteristic
965C2#3498111yescharacteristic
966C2#3505711yescharacteristic
967C2#3530611yescharacteristic
968C2#3744011yescharacteristic
969C2#3745111yescharacteristic
970C2#3774512yes—
971C2#3776812yes—
972C2#3794112yes—
973C2#3794812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2618C2semidirect
3. C22×#385C2semidirect
4. C2×#2280C2semidirect
5. #16562C2semidirect
6. #16393C2semidirect
7. #16259C2semidirect
8. #14911C2semidirect
9. #14890C2semidirect
10. #14840C2semidirect
11. #14764C2semidirect
12. #14718C2semidirect
13. #14339C2semidirect
14. #14275C2semidirect
15. #14271C2semidirect
16. #14019C2semidirect
17. #13996C2semidirect
31. C2×#398C22semidirect
32. C2×#396C22semidirect
34. C2×#394C22semidirect
35. C2×#388C22semidirect
62. #1445C22semidirect
63. #1445C22semidirect
64. #1444C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
81. #1438C22semidirect
82. #1437C22semidirect
83. #1436C22semidirect
84. C4⋊#95C22semidirect
186. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#26182
C22×#3852
C2×#22802
#165622
#163932
#162592
#149112
#148902
#148402
#147642
#147182
#143392
#142752
#142712
#140192
#139962