Finite Group Databasebeta

← #1016827

Subgroups — #1016827

Order 512.

2922 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2764C211yesmaximal, characteristic, complemented
2C22×#397C211yesmaximal, characteristic
3#17173C212yesmaximal, complemented
4#16831C211yesmaximal, characteristic, complemented
5#16773C212yesmaximal, complemented
6#16675C211yesmaximal, characteristic, complemented
7#16378C212yesmaximal, complemented
8#15917C212yesmaximal, complemented
9#15540C212yesmaximal, complemented
10#15298C212yesmaximal, complemented
11#14826C212yesmaximal, complemented
12#14728C212yesmaximal, complemented
13#14717C211yesmaximal, characteristic
14#14581C211yesmaximal, characteristic, complemented
15#14127C212yesmaximal
16#14052C212yesmaximal, complemented
17#13901C212yesmaximal, complemented
18#13873C212yesmaximal
19#13869C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2764—28no—
26C2×#400C2212yescomplemented
27C2×#398C2212yescomplemented
28C2×#398C2212yescomplemented
29C2×#397—28no—
30C2×#397C2211yescharacteristic
31C2×#397C2211yescharacteristic
32C2×#397C2211yescharacteristic
33C2×#397C2212yes—
34C2×#397C2212yes—
35C2×#397C2211yescharacteristic
36C2×#393C2211yescharacteristic
37C2×#393C2211yescharacteristic
38C2×#391C2212yescomplemented
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#383C2212yescomplemented
46C2×#381C2211yescharacteristic
47C2×#381C2211yescharacteristic
48C2×#380C2212yes—
49C2×#379C2212yes—
50C2×#379C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C22×#95C2211yescharacteristic
53C22×#95C2212yes—
54#1446C2212yescomplemented
55#1445C2212yescomplemented
56#1445C2212yescomplemented
57#1444C2212yescomplemented
58#1444C2212yescomplemented
59#1443C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1441C2212yescomplemented
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2211yescharacteristic
85#1439C2212yes—
86#1439C2212yes—
87#1439C2211yescharacteristic
88#1439C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93C4⋊#95C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2212yescomplemented
97C22⋊#95C2212yes—
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—42no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—28no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—28no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—44no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164#400—28no—
165#398—28no—
166#398—44no—
167#397—24no—
168#397—28no—
169#397—24no—
170#397—24no—
171#397—28no—
172#397D418yes—
173#393—24no—
174#393—42no—
175#391—28no—
176#388—28no—
177#388—44no—
178#385—28no—
179#385—44no—
180#385—44no—
181#385—44no—
182#383—28no—
183#381—24no—
184#381—42no—
185#380—44no—
186#379—28no—
187#379—42no—
188C4×C22⋊C4—28no—
189C2×#95—24no—
190C2×#95—28no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
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×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C25—22no—
238C25—22no—
239C25—24no—
240C25—22no—
241C25—22no—
242C25—24no—
243C25—41no—
244C25—42no—
245C25—41no—
246C25—42no—
247C25#4114yes—
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×Q8—22no—
252C22×Q8—24no—
253C22×Q8—41no—
254C22×Q8—42no—
255C22×Q8—41no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—41no—
289C23×C4—41no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C22⋊Q8—416no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
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—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—416no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
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—42no—
341C2×C4⋊C4C2×D414yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
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—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—432no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—416no—
390C2×C22⋊C4—416no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4C2×D418yes—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4#4118yes—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411#95—24no—
412#95—22no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—41no—
454#95—42no—
455#95C2×D414yes—
456#95C2×D418yes—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—22no—
471C24—28no—
472C24—21no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—28no—
483C24—216no—
484C24—48no—
485C24—44no—
486C24—44no—
487C24—48no—
488C24—44no—
489C24—48no—
490C24—48no—
491C24—44no—
492C24—48no—
493C24—44no—
494C24—48no—
495C24—44no—
496C24—44no—
497C24—84no—
498C24—84no—
499C24—82no—
500C24—84no—
501C24—82no—
502C24—84no—
503C24—84no—
504C24C22×D412yes—
505C24C2×#4112yes—
506C24C2×#4112yes—
507C24C2×#4112yes—
508C24C2×#4114yes—
509C24H(5,𝔽2)12yes—
510C24H(5,𝔽2)12yes—
511C24H(5,𝔽2)12yes—
512C242−1+414yes—
513C24C2511yescharacteristic
514C2×Q8—44no—
515C2×Q8—48no—
516C2×Q8—82no—
517C2×Q8—84no—
518C2×Q8—82no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
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—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
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—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
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—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—44no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—48no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4—84no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—84no—
642C22×C4—84no—
643C22×C4—82no—
644C22×C4—82no—
645C22×C4—82no—
646C22×C4—84no—
647C22×C4—82no—
648C22×C4—82no—
649C22×C4—82no—
650C22×C4—82no—
651C22×C4—84no—
652C22×C4C22×D414yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C22×D414yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4H(5,𝔽2)12yes—
659C4⋊C4—44no—
660C4⋊C4—48no—
661C4⋊C4—44no—
662C4⋊C4—48no—
663C4⋊C4—44no—
664C4⋊C4—84no—
665C4⋊C4—84no—
666C4⋊C4—84no—
667C4⋊C4—84no—
668C4⋊C4—84no—
669C4⋊C4—84no—
670C22⋊C4—216no—
671C22⋊C4—216no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—84no—
690C42—48no—
691C42—84no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—416no—
728C23—432no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—41no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—416no—
750C23—41no—
751C23—41no—
752C23—42no—
753C23—42no—
754C23—41no—
755C23—41no—
756C23—42no—
757C23—42no—
758C23—88no—
759C23—816no—
760C23—88no—
761C23—816no—
762C23—816no—
763C23—88no—
764C23—88no—
765C23—88no—
766C23#53814yes—
767C23#54218yes—
768C23#54614yes—
769C23#55114yes—
770C23#55218yes—
771C23#56314yes—
772C23C23×D411yescharacteristic
773C23C22×#4111yescharacteristic
774C23C22×#4112yes—
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)11yescharacteristic
779C23C2×2−1+412yes—
780C23#58512yes—
781C23#58511yescharacteristic
782C23#58512yes—
783Q8—88no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
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—416no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
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—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
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—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—88no—
890C2×C4—816no—
891C2×C4—816no—
892C2×C4—88no—
893C2×C4—88no—
894C22—24no—
895C22—24no—
896C22—28no—
897C22—28no—
898C22—24no—
899C22—28no—
900C22—24no—
901C22—24no—
902C22—24no—
903C22—28no—
904C22—24no—
905C22—28no—
906C22—42no—
907C22—44no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—44no—
915C22—42no—
916C22—44no—
917C22—42no—
918C22—42no—
919C22—44no—
920C22—832no—
921C22—81no—
922C22—82no—
923C22—82no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22#276418yescomplemented
928C22C2×#53811yescharacteristic
929C22C2×#54212yes—
930C22C2×#54611yescharacteristic
931C22D4×#4112yes—
932C22C2×#55111yescharacteristic
933C22C2×#55212yes—
934C22#348411yescharacteristic
935C22#348811yescharacteristic
936C22#348912yes—
937C22#349112yes—
938C22#350511yescharacteristic
939C22#351312yes—
940C22#351412yes—
941C22#352112yes—
942C22C2×#56311yescharacteristic
943C22#353311yescharacteristic
944C22#353411yescharacteristic
945C22#353512yes—
946C22#353512yes—
947C22#353711yescharacteristic
948C22#354511yescharacteristic
949C22#356012yes—
950C22#356412yes—
951C4—42no—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—42no—
956C4—42no—
957C4—44no—
958C4—81no—
959C4—82no—
960C4—82no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C2—28no—
968C2—44no—
969C2—82no—
970C2#3769311yescharacteristic
971C2#3772612yes—
972C2#4081312yes—
973C2#4142711yescharacteristic
974C2#4324411yescharacteristic
975C2#4350712yes—
976C2#4545611yescharacteristic
977C2C2×#276411yescharacteristic
978C2#5260311yescharacteristic
979C2#5901212yes—
980C2#5916211yescharacteristic
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×#2764C2semidirect
3. #17173C2semidirect
4. #16831C2semidirect
5. #16773C2semidirect
6. #16675C2semidirect
7. #16378C2semidirect
8. #15917C2semidirect
9. #15540C2semidirect
10. #15298C2semidirect
11. #14826C2semidirect
12. #14728C2semidirect
14. #14581C2semidirect
16. #14052C2semidirect
17. #13901C2semidirect
26. C2×#400C22semidirect
27. C2×#398C22semidirect
28. C2×#398C22semidirect
38. C2×#391C22semidirect
45. C2×#383C22semidirect
54. #1446C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1443C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. C4⋊#95C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
927. C22#2764semidirect

Maximal subgroups

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

subgroupindex
C2×#27642
C22×#3972
#171732
#168312
#167732
#166752
#163782
#159172
#155402
#152982
#148262
#147282
#147172
#145812
#141272
#140522
#139012
#138732
#138692