Finite Group Databasebeta

← #4457918

Subgroups — #4457918

Order 512.

2806 conjugacy classes of subgroups.

The subgroup lattice has 967 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16707C211yesmaximal, characteristic, complemented
2#16706C211yesmaximal, characteristic, complemented
3#16405C212yesmaximal, complemented
4#16405C212yesmaximal, complemented
5#16404C212yesmaximal, complemented
6#16404C212yesmaximal, complemented
7#16403C212yesmaximal, complemented
8#16402C212yesmaximal, complemented
9#16358C211yesmaximal, characteristic, complemented
10#16339C211yesmaximal, characteristic, complemented
11#14920C212yesmaximal, complemented
12#14822C212yesmaximal, complemented
13#14767C212yesmaximal, complemented
14#14766C212yesmaximal, complemented
15#14338C211yesmaximal, characteristic
16#14127C212yesmaximal
17#13877C212yesmaximal
18C2×#1439C211yesmaximal, characteristic
19#13794C211yesmaximal, characteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2212yes—
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C2×#400C2212yescomplemented
26C2×#400C2212yescomplemented
27C2×#400C2212yescomplemented
28C2×#398C2212yescomplemented
29C2×#385C2212yes—
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#379C2212yes—
40C22×#95C2211yescharacteristic
41C22×#95C2212yes—
42#1445C2212yescomplemented
43#1445C2212yescomplemented
44#1445C2212yescomplemented
45#1445C2212yescomplemented
46#1444C2212yescomplemented
47#1443C2212yescomplemented
48#1443C2212yescomplemented
49#1442C2212yescomplemented
50#1442C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1441C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1439C2211yescharacteristic
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2212yes—
74#1439C2211yescharacteristic
75#1439C2211yescharacteristic
76#1439C2212yes—
77#1439C2211yescharacteristic
78#1439C2212yes—
79#1439C2211yescharacteristic
80#1439C2211yescharacteristic
81#1439C2211yescharacteristic
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2211yescharacteristic
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C26C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C22×C4⋊C4—44no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—44no—
135C22×C22⋊C4—44no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4Q818yes—
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⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162#400—44no—
163#400—44no—
164#400—44no—
165#398—44no—
166#385—44no—
167#385—44no—
168#385—44no—
169#385—44no—
170#385—44no—
171#385—44no—
172#380—44no—
173#380—44no—
174#380—42no—
175#380—42no—
176#379—28no—
177C2×#95—44no—
178C2×#95—42no—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
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×#95C2311yescharacteristic
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—42no—
230C25—42no—
231C25—42no—
232C25—42no—
233C25C2×Q814yes—
234C25#4114yes—
235C25#4114yes—
236C25C2411yescharacteristic
237C25C2411yescharacteristic
238C25C2411yescharacteristic
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—41no—
261C23×C4—41no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4C2×Q814yes—
279C23×C4C2×Q814yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
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×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
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—432no—
363C2×C22⋊C4—416no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
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—416no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4C2×Q814yes—
393C2×C22⋊C4C2×Q814yes—
394C2×C22⋊C4C2×Q814yes—
395C2×C22⋊C4C2×Q814yes—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—42no—
403#95—42no—
404#95—41no—
405#95—42no—
406#95—41no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
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—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—82no—
475C24—82no—
476C24—84no—
477C24—84no—
478C24—84no—
479C24—84no—
480C24—82no—
481C24—82no—
482C24—84no—
483C24—84no—
484C24#125116yes—
485C24C22×Q812yes—
486C24C22×Q812yes—
487C24C22×Q812yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24H(5,𝔽2)12yes—
495C24H(5,𝔽2)12yes—
496C24H(5,𝔽2)12yes—
497C242−1+412yes—
498C24C2511yescharacteristic
499C22×C4—28no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
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—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—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—82no—
621C22×C4—84no—
622C22×C4—82no—
623C22×C4—84no—
624C22×C4—84no—
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—82no—
635C22×C4—82no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4C22×Q812yes—
639C22×C4C22×Q812yes—
640C22×C4C22×Q812yes—
641C22×C4C22×Q812yes—
642C22×C4H(5,𝔽2)14yes—
643C22×C4H(5,𝔽2)14yes—
644C4⋊C4—44no—
645C4⋊C4—48no—
646C4⋊C4—44no—
647C4⋊C4—84no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—82no—
653C4⋊C4—84no—
654C4⋊C4—82no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C22⋊C4—216no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—232no—
718C23—432no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—88no—
740C23—88no—
741C23—816no—
742C23—88no—
743C23—816no—
744C23—88no—
745C23—816no—
746C23—88no—
747C23—88no—
748C23C2×#12514yes—
749C23C2×#12514yes—
750C23C2×#12514yes—
751C23#53814yes—
752C23#53814yes—
753C23#53914yes—
754C23#53914yes—
755C23#54314yes—
756C23#54414yes—
757C23C23×Q811yescharacteristic
758C23C22×#4111yescharacteristic
759C23C22×#4111yescharacteristic
760C23C2×H(5,𝔽2)11yescharacteristic
761C23C2×H(5,𝔽2)11yescharacteristic
762C23C2×H(5,𝔽2)11yescharacteristic
763C23C2×H(5,𝔽2)12yes—
764C23C2×H(5,𝔽2)12yes—
765C23C2×2−1+411yescharacteristic
766C23#58512yes—
767C23#58512yes—
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—416no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
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—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—88no—
874C2×C4—816no—
875C2×C4—816no—
876C2×C4—816no—
877C2×C4—88no—
878C2×C4—88no—
879C22—24no—
880C22—28no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—28no—
892C22—28no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—44no—
898C22—44no—
899C22—42no—
900C22—42no—
901C22—44no—
902C22—44no—
903C22—42no—
904C22—42no—
905C22—44no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—832no—
912C22#264618yes—
913C22C22×#12511yescharacteristic
914C22C2×#53811yescharacteristic
915C22C2×#53811yescharacteristic
916C22C2×#53911yescharacteristic
917C22C2×#53911yescharacteristic
918C22C2×#54311yescharacteristic
919C22C2×#54411yescharacteristic
920C22#349012yes—
921C22#349112yes—
922C22#350112yes—
923C22#350112yes—
924C22#350512yes—
925C22#350512yes—
926C22#353211yescharacteristic
927C22#353311yescharacteristic
928C22#353412yes—
929C22#353412yes—
930C22#353612yes—
931C22#354212yes—
932C22#354311yescharacteristic
933C22#354511yescharacteristic
934C22#355812yes—
935C22#356412yes—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—44no—
941C4—44no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C2—28no—
953C2—44no—
954C2—44no—
955C2C2×#264611yescharacteristic
956C2#3536812yes—
957C2#3674711yescharacteristic
958C2#3675012yes—
959C2#3713411yescharacteristic
960C2#4063811yescharacteristic
961C2#4064112yes—
962C2#4065912yes—
963C2#4066011yescharacteristic
964C2#4066211yescharacteristic
965C2#4142611yescharacteristic
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. #16707C2semidirect
2. #16706C2semidirect
3. #16405C2semidirect
4. #16405C2semidirect
5. #16404C2semidirect
6. #16404C2semidirect
7. #16403C2semidirect
8. #16402C2semidirect
9. #16358C2semidirect
10. #16339C2semidirect
11. #14920C2semidirect
12. #14822C2semidirect
13. #14767C2semidirect
14. #14766C2semidirect
25. C2×#400C22semidirect
26. C2×#400C22semidirect
27. C2×#400C22semidirect
28. C2×#398C22semidirect
42. #1445C22semidirect
43. #1445C22semidirect
44. #1445C22semidirect
45. #1445C22semidirect
46. #1444C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1442C22semidirect
50. #1442C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect

Maximal subgroups

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

subgroupindex
#167072
#167062
#164052
#164042
#164032
#164022
#163582
#163392
#149202
#148222
#147672
#147662
#143382
#141272
#138772
C2×#14392
#137942