Finite Group Databasebeta

← #637521

Subgroups — #637521

Order 512.

5718 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2579C212yesmaximal, complemented
3C22×#385C211yesmaximal, characteristic, complemented
4#16264C212yesmaximal, complemented
5#16261C212yesmaximal, complemented
6#16257C214yesmaximal, complemented
7#15114C212yesmaximal, complemented
8#14914C211yesmaximal, characteristic, complemented
9#14913C211yesmaximal, characteristic, complemented
10#14889C212yesmaximal, complemented
11#14720C211yesmaximal, characteristic, complemented
12#14719C211yesmaximal, characteristic, complemented
13#14718C212yesmaximal, complemented
14#14718C212yesmaximal, complemented
15#14680C211yesmaximal, characteristic, complemented
16#14300C214yesmaximal, complemented
17#13960C212yesmaximal, complemented
18C23×#41C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C2×#525—28no—
21C2×#525—216no—
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#120C2212yes—
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2579—216no—
36C2×#398C2214yescomplemented
37C2×#396C2214yescomplemented
38C2×#395C2212yescomplemented
39C2×#394C2214yes—
40C2×#394C2214yes—
41C2×#394C2212yescomplemented
42C2×#387C2214yescomplemented
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385—28no—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#385C2214yescomplemented
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#379C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1446C2212yescomplemented
62#1444C2212yescomplemented
63#1444C2214yescomplemented
64#1442C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yescomplemented
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yescomplemented
75#1439C2214yescomplemented
76#1438C2214yes—
77#1438C2214yes—
78#1438C2212yescomplemented
79#1434C2214yescomplemented
80C22⋊#95C2212yes—
81C22⋊#95C2211yescharacteristic
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2214yescomplemented
87C26C2311yescharacteristic
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—44no—
91C22×#41—44no—
92C23×Q8C2311yescharacteristic
93C23×D4C2312yes—
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4—28no—
98C24×C4—44no—
99C24×C4—44no—
100C24×C4D418yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2311yescharacteristic
112#525—2128no—
113C2×#123—28no—
114C2×#123—28no—
115C2×#123—28no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×#121—28no—
121C2×#121—24no—
122C2×#121—24no—
123C2×#121—28no—
124C2×#120—28no—
125C2×#120—28no—
126C2×#120—28no—
127C2×C4×D4—28no—
128C2×C4×D4—28no—
129C2×C4×D4—28no—
130C2×C4×D4—28no—
131C2×C4×D4—28no—
132C2×C4×D4D4116yes—
133C2×#117—24no—
134C2×#117—28no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—44no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—28no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—44no—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2314yes—
171C22×C42C2312yes—
172#398—216no—
173#396—216no—
174#395—44no—
175#394—216no—
176#394—44no—
177#394—48no—
178#387—216no—
179#386—28no—
180#386—28no—
181#386—44no—
182#386—44no—
183#385—216no—
184#385—28no—
185#385—28no—
186#385—28no—
187#385—28no—
188#385—28no—
189#385—28no—
190#380—28no—
191#380—44no—
192#380—44no—
193#379—44no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C25—24no—
216C25—24no—
217C25—24no—
218C25—24no—
219C25—22no—
220C25—22no—
221C25—42no—
222C25—42no—
223C25C2×D414yes—
224C25C2412yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C2×#41—232no—
229C2×#41—464no—
230C2×#41—416no—
231C2×#41—416no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—42no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—44no—
254C22×D4—42no—
255C22×D4—44no—
256C22×D4C2×D418yes—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—232no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—416no—
283C23×C4—42no—
284C23×C4—416no—
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—44no—
294C23×C4—44no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—464no—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4C2×D418yes—
306C23×C4C2×D414yes—
307C23×C4C2×D418yes—
308C23×C4C2414yes—
309C23×C4C2414yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321#123—264no—
322C22⋊Q8—232no—
323C22⋊Q8—232no—
324#121—232no—
325#121—232no—
326#120—264no—
327C4×D4—264no—
328C4×D4—264no—
329#117—232no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—416no—
355C2×C4⋊C4—416no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2×D418yes—
361C2×C22⋊C4—232no—
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—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—416no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4C2×D418yes—
410C2×C22⋊C4C2×D418yes—
411C2×C22⋊C4#4118yescomplemented
412C2×C42—24no—
413C2×C42—24no—
414C2×C42C2×D418yes—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—44no—
428#95—42no—
429#95—42no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—232no—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—28no—
457C24—28no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—22no—
462C24—24no—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—24no—
468C24—44no—
469C24—44no—
470C24—416no—
471C24—416no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—416no—
477C24—48no—
478C24—48no—
479C24C22×D414yes—
480C24C22×D412yes—
481C24C22×D412yes—
482C24C22×D414yes—
483C24C22×D412yes—
484C24C2×#4114yes—
485C24H(5,𝔽2)14yes—
486C24H(5,𝔽2)12yes—
487C242−1+414yes—
488C242−1+412yes—
489C24C2511yescharacteristic
490#41—4128no—
491C2×Q8—28no—
492C2×Q8—416no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×D4—216no—
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—216no—
499C2×D4—216no—
500C2×D4—216no—
501C2×D4—416no—
502C2×D4—416no—
503C2×D4—416no—
504C2×D4—44no—
505C2×D4—416no—
506C2×D4—416no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—44no—
516C22×C4—232no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—216no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—416no—
595C22×C4—416no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—416no—
601C22×C4—416no—
602C22×C4—4128no—
603C22×C4—416no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—416no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—88no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4#120116yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D414yes—
625C22×C4C22×D412yes—
626C22×C4C22×D414yes—
627C22×C4C22×D412yes—
628C22×C4C22×D414yes—
629C22×C4C22×D412yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C4H(5,𝔽2)14yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—216no—
636C4⋊C4—216no—
637C4⋊C4—416no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—88no—
643C4⋊C4—88no—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—416no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—88no—
657C22⋊C4—88no—
658C22⋊C4—88no—
659C22⋊C4—88no—
660C22⋊C4—88no—
661C42—216no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—28no—
667C23—28no—
668C23—28no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—28no—
674C23—232no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—28no—
699C23—28no—
700C23—416no—
701C23—416no—
702C23—416no—
703C23—416no—
704C23—416no—
705C23—464no—
706C23—464no—
707C23—416no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—44no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23C2×#12014yes—
739C23#52514yes—
740C23#53414yes—
741C23#53618yes—
742C23#53614yes—
743C23#53718yes—
744C23#53714yes—
745C23C23×D411yescharacteristic
746C23C23×D412yes—
747C23C22×#4112yes—
748C23C2×H(5,𝔽2)12yes—
749C23C2×H(5,𝔽2)12yes—
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×2−1+412yes—
752C23C2×2−1+411yescharacteristic
753C23#58512yes—
754Q8—416no—
755D4—416no—
756D4—432no—
757D4—432no—
758D4—432no—
759C2×C4—232no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—416no—
789C2×C4—432no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—88no—
835C2×C4—88no—
836C2×C4C2×#12014yes—
837C2×C4C2×#12014yes—
838C2×C4#53414yes—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—216no—
845C22—216no—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—464no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—48no—
863C22—48no—
864C22—48no—
865C22—48no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—48no—
870C22—48no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—84no—
875C22—84no—
876C22—82no—
877C22#261618yes—
878C22C22×#12011yescharacteristic
879C22C2×#52511yescharacteristic
880C22C2×#53411yescharacteristic
881C22C2×#53411yescharacteristic
882C22C2×#53611yescharacteristic
883C22C2×#53612yes—
884C22C2×#53711yescharacteristic
885C22C2×#53712yes—
886C22#344911yescharacteristic
887C22D4×#4114yes—
888C22#348414yes—
889C22#349214yes—
890C22#351912yes—
891C22#352012yes—
892C22#353412yes—
893C22#353512yes—
894C22#354114yes—
895C4—24no—
896C4—24no—
897C4—24no—
898C4—44no—
899C4—44no—
900C4—42no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—82no—
905C4—82no—
906C4—84no—
907C4—84no—
908C2—28no—
909C2—44no—
910C2—44no—
911C2—84no—
912C2C2×#261611yescharacteristic
913C2#3473611yescharacteristic
914C2#3498011yescharacteristic
915C2#3505711yescharacteristic
916C2#3507711yescharacteristic
917C2#3744911yescharacteristic
918C2#3745211yescharacteristic
919C2#3835714yes—
920C2#3835914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
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×#2579C2semidirect
3. C22×#385C2semidirect
4. #16264C2semidirect
5. #16261C2semidirect
6. #16257C2semidirect
7. #15114C2semidirect
8. #14914C2semidirect
9. #14913C2semidirect
10. #14889C2semidirect
11. #14720C2semidirect
12. #14719C2semidirect
13. #14718C2semidirect
14. #14718C2semidirect
15. #14680C2semidirect
16. #14300C2semidirect
17. #13960C2semidirect
36. C2×#398C22semidirect
37. C2×#396C22semidirect
38. C2×#395C22semidirect
41. C2×#394C22semidirect
42. C2×#387C22semidirect
54. C2×#385C22semidirect
61. #1446C22semidirect
62. #1444C22semidirect
63. #1444C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
71. #1440C22semidirect
74. #1439C22semidirect
75. #1439C22semidirect
78. #1438C22semidirect
79. #1434C22semidirect
86. C22⋊#95C22semidirect
411. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#25792
C22×#3852
#162642
#162612
#162572
#151142
#149142
#149132
#148892
#147202
#147192
#147182
#146802
#143002
#139602