Finite Group Databasebeta

← #772934

Subgroups — #772934

Order 512.

3346 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2484C212yesmaximal, complemented
2C2×#2342C212yesmaximal
3#16339C211yesmaximal, characteristic, complemented
4#16321C211yesmaximal, characteristic, complemented
5#15977C212yesmaximal, complemented
6#15781C212yesmaximal, complemented
7#15408C212yesmaximal, complemented
8#15402C212yesmaximal, complemented
9#14918C212yesmaximal
10#14810C212yesmaximal, complemented
11#14753C212yesmaximal, complemented
12#14734C211yesmaximal, characteristic
13#14215C211yesmaximal, characteristic, complemented
14#14143C211yesmaximal, characteristic, complemented
15#14127C211yesmaximal, characteristic
16#14004C212yesmaximal, complemented
17#13972C212yesmaximal, complemented
18#13878C212yesmaximal, complemented
19C2×#1439C211yesmaximal, characteristic
20C22×#117C2212yes—
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2484—216no—
26C2×#400C2212yescomplemented
27C2×#400C2212yescomplemented
28C2×#399C2211yescharacteristic
29C2×#399C2211yescharacteristic
30C2×#398C2212yescomplemented
31C2×#398C2212yescomplemented
32#2342—216no—
33C2×#389C2212yescomplemented
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#387C2212yescomplemented
39C2×#387C2212yescomplemented
40C2×#387C2212yescomplemented
41C2×#387C2212yescomplemented
42C2×#385C2211yescharacteristic
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2211yescharacteristic
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#381C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#379C2211yescharacteristic
55C2×#379C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2212yes—
60C22×#95C2211yescharacteristic
61#1444C2212yescomplemented
62#1444C2212yescomplemented
63#1444C2212yescomplemented
64#1443C2212yescomplemented
65#1443C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2211yescharacteristic
80#1439C2212yes—
81#1439C2211yescharacteristic
82#1439C2211yescharacteristic
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2211yescharacteristic
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101C4⋊#95C2212yescomplemented
102#1434C2212yescomplemented
103#1434C2212yescomplemented
104C22⋊#95C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2211yescharacteristic
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C26C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C2×#117—28no—
117C2×#117—28no—
118C2×#117—44no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4—28no—
137C22×C22⋊C4—28no—
138C22×C22⋊C4—28no—
139C22×C22⋊C4—28no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168#400—28no—
169#400—28no—
170#399—24no—
171#399—42no—
172#398—28no—
173#398—28no—
174#389—44no—
175#388—28no—
176#388—28no—
177#388—28no—
178#388—28no—
179#387—28no—
180#387—28no—
181#387—28no—
182#387—28no—
183#385—28no—
184#385—28no—
185#385—28no—
186#385—24no—
187#385—28no—
188#385—28no—
189#385—42no—
190#381—28no—
191#381—28no—
192#381D4116yes—
193#380—28no—
194#380—42no—
195#379—24no—
196#379—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—28no—
199C4×C22⋊C4—28no—
200C2×#95—28no—
201C2×#95—42no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C25—22no—
244C25—22no—
245C25—24no—
246C25—24no—
247C25—22no—
248C25—22no—
249C25—41no—
250C25—42no—
251C25—42no—
252C25—41no—
253C25#4114yes—
254C25C2411yescharacteristic
255C25C2411yescharacteristic
256C25C2411yescharacteristic
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—42no—
277C23×C4—41no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4C2×D418yes—
290C23×C4#4118yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307#117—432no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—416no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—41no—
351C2×C22⋊C4—264no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
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—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—416no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—416no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4C2×D418yes—
412C2×C22⋊C4C2×D418yes—
413C2×C22⋊C4#4114yes—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—22no—
450#95—24no—
451#95—41no—
452#95—41no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—41no—
463#95C2×D418yes—
464#95C2×D418yes—
465#95C2×D418yes—
466#95C2×D418yes—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—28no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—216no—
493C24—28no—
494C24—48no—
495C24—44no—
496C24—44no—
497C24—48no—
498C24—48no—
499C24—48no—
500C24—48no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—48no—
506C24—44no—
507C24—84no—
508C24—84no—
509C24—84no—
510C24—84no—
511C24—82no—
512C24—82no—
513C24—84no—
514C24C22×D414yes—
515C24C2×#4112yes—
516C24C2×#4112yes—
517C24C2×#4112yes—
518C24C2×#4112yes—
519C24C2×#4114yes—
520C24H(5,𝔽2)12yes—
521C242−1+412yes—
522C242−1+412yes—
523C24C2511yescharacteristic
524C22×C4—28no—
525C22×C4—216no—
526C22×C4—216no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—216no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—44no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—44no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—44no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—84no—
642C22×C4—82no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—82no—
648C22×C4—82no—
649C22×C4—82no—
650C22×C4—82no—
651C22×C4C22×D414yes—
652C22×C4C22×D414yes—
653C22×C4C22×D414yes—
654C22×C4C22×D414yes—
655C22×C4C22×D414yes—
656C22×C4C22×D414yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4114yes—
659C22×C4C2×#4112yes—
660C22×C4C2×#4112yes—
661C22×C4H(5,𝔽2)12yes—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—84no—
673C4⋊C4—82no—
674C4⋊C4—84no—
675C4⋊C4—84no—
676C4⋊C4—82no—
677C22⋊C4—216no—
678C22⋊C4—216no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—44no—
684C22⋊C4—48no—
685C22⋊C4—44no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—44no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C42—48no—
698C42—48no—
699C42—84no—
700C42—84no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—24no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—22no—
736C23—432no—
737C23—416no—
738C23—41no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—416no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—41no—
757C23—42no—
758C23—42no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—42no—
767C23—816no—
768C23—88no—
769C23—88no—
770C23—88no—
771C23—816no—
772C23—816no—
773C23—88no—
774C23—88no—
775C23#52518yes—
776C23#53914yes—
777C23D4214yes—
778C23#54718yes—
779C23#55214yes—
780C23#55914yes—
781C23C23×D412yes—
782C23C22×#4111yescharacteristic
783C23C22×#4112yes—
784C23C22×#4111yescharacteristic
785C23C2×H(5,𝔽2)11yescharacteristic
786C23C2×H(5,𝔽2)11yescharacteristic
787C23C2×2−1+411yescharacteristic
788C23C2×2−1+411yescharacteristic
789C23#58512yes—
790C23#58512yes—
791C23#58511yescharacteristic
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—416no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—432no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
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—42no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—41no—
898C2×C4—816no—
899C2×C4—88no—
900C2×C4—88no—
901C2×C4—88no—
902C22—24no—
903C22—24no—
904C22—28no—
905C22—28no—
906C22—28no—
907C22—28no—
908C22—24no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—28no—
913C22—24no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—44no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—832no—
929C22—81no—
930C22—81no—
931C22—82no—
932C22—82no—
933C22—81no—
934C22—81no—
935C22#245518yes—
936C22C2×#52512yes—
937C22C2×#53911yescharacteristic
938C22C2×D4211yescharacteristic
939C22C2×#54712yes—
940C22D4×#4112yes—
941C22C2×#55211yescharacteristic
942C22#347512yes—
943C22C2×#55911yescharacteristic
944C22#348812yes—
945C22#348912yes—
946C22#349011yescharacteristic
947C22#349112yes—
948C22#349112yes—
949C22#349512yes—
950C22#349511yescharacteristic
951C22#350012yes—
952C22#350512yes—
953C22#350511yescharacteristic
954C22#353311yescharacteristic
955C22#353511yescharacteristic
956C22#353811yescharacteristic
957C22#354511yescharacteristic
958C22#356412yes—
959C4—44no—
960C4—44no—
961C4—42no—
962C4—42no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—42no—
969C4—44no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—81no—
974C4—82no—
975C2—28no—
976C2—44no—
977C2—82no—
978C2C2×#245511yescharacteristic
979C2#3575312yes—
980C2#3622312yes—
981C2#3788011yescharacteristic
982C2#4142611yescharacteristic
983C2#4359811yescharacteristic
984C2#4393512yes—
985C2#4476011yescharacteristic
986C2#5899211yescharacteristic
987C2#5931012yes—
988C2#5986111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2484C2semidirect
3. #16339C2semidirect
4. #16321C2semidirect
5. #15977C2semidirect
6. #15781C2semidirect
7. #15408C2semidirect
8. #15402C2semidirect
10. #14810C2semidirect
11. #14753C2semidirect
13. #14215C2semidirect
14. #14143C2semidirect
16. #14004C2semidirect
17. #13972C2semidirect
18. #13878C2semidirect
26. C2×#400C22semidirect
27. C2×#400C22semidirect
30. C2×#398C22semidirect
31. C2×#398C22semidirect
33. C2×#389C22semidirect
38. C2×#387C22semidirect
39. C2×#387C22semidirect
40. C2×#387C22semidirect
41. C2×#387C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1444C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. C4⋊#95C22semidirect
102. #1434C22semidirect
103. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24842
C2×#23422
#163392
#163212
#159772
#157812
#154082
#154022
#149182
#148102
#147532
#147342
#142152
#141432
#141272
#140042
#139722
#138782
C2×#14392