Finite Group Databasebeta

← #874262

Subgroups — #874262

Order 512.

3024 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic
2C2×#2483C211yesmaximal, characteristic
3#16787C212yesmaximal, complemented
4#16722C212yesmaximal, complemented
5#15930C211yesmaximal, characteristic, complemented
6#15750C212yesmaximal, complemented
7#15722C211yesmaximal, characteristic, complemented
8#15645C212yesmaximal, complemented
9#15622C211yesmaximal, characteristic, complemented
10#15539C211yesmaximal, characteristic, complemented
11#15019C212yesmaximal, complemented
12#14820C212yesmaximal
13#14758C212yesmaximal, complemented
14#14685C212yesmaximal, complemented
15#14541C212yesmaximal, complemented
16#14383C212yesmaximal, complemented
17#14047C212yesmaximal, complemented
18#13877C212yesmaximal
19C2×#1437C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C23×C22⋊C4C2212yes—
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2561—28no—
26#2483—28no—
27C2×#397C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#395C2212yescomplemented
34C2×#393C2211yescharacteristic
35C2×#393C2211yescharacteristic
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#387C2212yescomplemented
39C2×#385C2211yescharacteristic
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2211yescharacteristic
43C2×#385C2212yes—
44C2×#381C2212yes—
45C2×#381C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#381C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#379C2212yes—
52C2×#379C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C22×#95C2212yes—
55C22×#95C2211yescharacteristic
56#1446C2212yescomplemented
57#1445C2212yescomplemented
58#1445C2212yescomplemented
59#1445C2212yescomplemented
60#1444C2212yescomplemented
61#1444C2212yescomplemented
62#1444C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1443C2212yescomplemented
66#1443C2212yescomplemented
67#1443C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
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#1439C2212yes—
85#1437C2211yescharacteristic
86#1437C2211yescharacteristic
87#1437C2212yes—
88#1437C2211yescharacteristic
89#1437C2212yes—
90#1437C2211yescharacteristic
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93C4⋊#95C2212yescomplemented
94C4⋊#95C2212yescomplemented
95C4⋊#95C2212yescomplemented
96C4⋊#95C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99#1434C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8—42no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—28no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4D418yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C42—28no—
160C22×C42—42no—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165#397—24no—
166#397—24no—
167#397—28no—
168#397—28no—
169#397—28no—
170#397—44no—
171#395—44no—
172#393—24no—
173#393—24no—
174#388—28no—
175#388—28no—
176#387—44no—
177#385—28no—
178#385—24no—
179#385—24no—
180#385—28no—
181#385—44no—
182#381—28no—
183#381—28no—
184#381—24no—
185#381—24no—
186#380—28no—
187#380—44no—
188#380—44no—
189#379—28no—
190#379—24no—
191C4×C22⋊C4—24no—
192C2×#95—44no—
193C2×#95—42no—
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
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×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C25—24no—
240C25—24no—
241C25—22no—
242C25—22no—
243C25—24no—
244C25—42no—
245C25—42no—
246C25—42no—
247C25C2×D414yes—
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×Q8—22no—
252C22×Q8—41no—
253C22×Q8—41no—
254C22×Q8—42no—
255C22×Q8—42no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—41no—
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×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4#4118yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C22⋊Q8—416no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
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—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
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×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
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—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—432no—
370C2×C22⋊C4—416no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—416no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4#4118yes—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—41no—
404C2×C42—42no—
405C2×C42—41no—
406C2×C42—416no—
407C2×C42—42no—
408C2×C42—42no—
409#95—22no—
410#95—22no—
411#95—24no—
412#95—24no—
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—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—42no—
433#95—42no—
434#95—41no—
435#95—42no—
436#95—41no—
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—42no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—28no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—28no—
475C24—216no—
476C24—44no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—48no—
485C24—44no—
486C24—44no—
487C24—84no—
488C24—84no—
489C24—84no—
490C24—82no—
491C24—82no—
492C24—84no—
493C24—84no—
494C24C22×D412yes—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C2×#4114yes—
498C24C2×#4114yes—
499C24H(5,𝔽2)12yes—
500C24H(5,𝔽2)12yes—
501C242−1+414yes—
502C24C2511yescharacteristic
503C2×Q8—44no—
504C2×Q8—84no—
505C2×Q8—84no—
506C2×Q8—82no—
507C2×Q8—82no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
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—28no—
544C22×C4—216no—
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—22no—
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—22no—
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—22no—
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—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—82no—
636C22×C4—82no—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C22×C4H(5,𝔽2)14yes—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—48no—
649C4⋊C4—84no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C4⋊C4—84no—
656C22⋊C4—216no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—44no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—44no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—84no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C42—44no—
677C42—48no—
678C42—44no—
679C42—84no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—24no—
711C23—432no—
712C23—416no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—42no—
727C23—416no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—88no—
741C23—816no—
742C23—816no—
743C23—816no—
744C23—816no—
745C23—816no—
746C23#53214yes—
747C23#53414yes—
748C23#54218yes—
749C23#54718yes—
750C23#55114yes—
751C23#56314yes—
752C23C23×D411yescharacteristic
753C23C22×#4112yes—
754C23C22×#4112yes—
755C23C2×H(5,𝔽2)11yescharacteristic
756C23C2×H(5,𝔽2)11yescharacteristic
757C23C2×H(5,𝔽2)12yes—
758C23C2×2−1+412yes—
759C23#58512yes—
760C23#58512yes—
761Q8—88no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—432no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—416no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
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—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
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—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—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—88no—
868C2×C4—816no—
869C2×C4—88no—
870C2×C4—88no—
871C2×C4#55118yes—
872C22—24no—
873C22—28no—
874C22—28no—
875C22—28no—
876C22—28no—
877C22—28no—
878C22—24no—
879C22—28no—
880C22—28no—
881C22—24no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—42no—
890C22—44no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—832no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22#271718yes—
900C22C2×#53211yescharacteristic
901C22C2×#53411yescharacteristic
902C22#344911yescharacteristic
903C22C2×#54212yes—
904C22C2×#54712yes—
905C22C2×#55111yescharacteristic
906C22C2×#55112yes—
907C22#347512yes—
908C22#349112yes—
909C22#349412yes—
910C22#349512yes—
911C22#349612yes—
912C22#351312yes—
913C22#351312yes—
914C22#352012yes—
915C22C2×#56311yescharacteristic
916C22#353412yes—
917C22#354311yescharacteristic
918C22#354511yescharacteristic
919C22#356112yes—
920C22#356412yes—
921C4—28no—
922C4—42no—
923C4—42no—
924C4—44no—
925C4—44no—
926C4—42no—
927C4—42no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C4—82no—
937C2—28no—
938C2—44no—
939C2—82no—
940C2#3506411yescharacteristic
941C2#3618312yes—
942C2#3712911yescharacteristic
943C2#3786612yes—
944C2#3805412yes—
945C2#3839212yes—
946C2#4557912yes—
947C2C2×#271711yescharacteristic
948C2#5919512yes—
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
3. #16787C2semidirect
4. #16722C2semidirect
5. #15930C2semidirect
6. #15750C2semidirect
7. #15722C2semidirect
8. #15645C2semidirect
9. #15622C2semidirect
10. #15539C2semidirect
11. #15019C2semidirect
13. #14758C2semidirect
14. #14685C2semidirect
15. #14541C2semidirect
16. #14383C2semidirect
17. #14047C2semidirect
33. C2×#395C22semidirect
38. C2×#387C22semidirect
56. #1446C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1445C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1443C22semidirect
67. #1443C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. C4⋊#95C22semidirect
94. C4⋊#95C22semidirect
95. C4⋊#95C22semidirect
96. C4⋊#95C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect
99. #1434C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24832
#167872
#167222
#159302
#157502
#157222
#156452
#156222
#155392
#150192
#148202
#147582
#146852
#145412
#143832
#140472
#138772
C2×#14372