Finite Group Databasebeta

← #618585

Subgroups — #618585

Order 512.

4304 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#126C211yesmaximal, characteristic, complemented
2C2×#2534C211yesmaximal, characteristic
3C2×#2487C211yesmaximal, characteristic, complemented
4C2×#2322C211yesmaximal, characteristic, complemented
5#16102C214yesmaximal, complemented
6#16004C214yesmaximal, complemented
7#15940C214yesmaximal, complemented
8#15939C214yesmaximal, complemented
9#15073C211yesmaximal, characteristic, complemented
10#15069C211yesmaximal, characteristic, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14911C211yesmaximal, characteristic
13#14706C211yesmaximal, characteristic, complemented
14#14705C211yesmaximal, characteristic, complemented
15#14339C211yesmaximal, characteristic, complemented
16#14262C211yesmaximal, characteristic, complemented
17#14255C211yesmaximal, characteristic
18#13924C211yesmaximal, characteristic, complemented
19#13903C211yesmaximal, characteristic, complemented
20C22×#126—28no—
21C22×#126—28no—
22C22×#126—28no—
23C22×#126C2214yes—
24C22×#126C2214yes—
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2534—28no—
37#2487—28no—
38C2×#400C2212yescomplemented
39C2×#399C2212yescomplemented
40C2×#396C2212yes—
41C2×#394C2212yes—
42#2322—28no—
43C2×#389C2212yescomplemented
44C2×#389C2212yescomplemented
45C2×#388C2212yes—
46C2×#388C2212yescomplemented
47C2×#387C2212yescomplemented
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2212yescomplemented
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#381C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2212yescomplemented
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×#379C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69#1445C2214yescomplemented
70#1444C2214yescomplemented
71#1442C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1441C2214yescomplemented
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yescomplemented
83#1438C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1437C2214yescomplemented
87#1436C2214yescomplemented
88#1436C2214yescomplemented
89#1436C2214yescomplemented
90C4⋊#95C2214yescomplemented
91C22⋊#95C2211yescharacteristic
92C22⋊#95C2211yescharacteristic
93C22⋊#95C2211yescharacteristic
94C22⋊#95C2211yescharacteristic
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2211yescharacteristic
97C26C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C2×#126—2128no—
108C2×#126—216no—
109C2×#126—216no—
110C2×#126—216no—
111C2×#126—216no—
112C2×#126—216no—
113C2×#126—216no—
114C2×#123—24no—
115C2×#123—24no—
116C2×#123—24no—
117C2×#123—24no—
118C2×#123—24no—
119C2×#123—42no—
120C2×#120—24no—
121C2×#120—24no—
122C2×#120—42no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4D418yescomplemented
134C22×C4⋊C4D418yescomplemented
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4D418yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2314yes—
179C22×C42—24no—
180C22×C42—24no—
181C22×C42—24no—
182C22×C42C2314yes—
183C22×C42C2311yescharacteristic
184C22×C42C2312yes—
185#400—28no—
186#399—28no—
187#396—28no—
188#394—28no—
189#389—28no—
190#389—28no—
191#388—28no—
192#388—28no—
193#387—28no—
194#386—24no—
195#386—24no—
196#386—24no—
197#386—28no—
198#385—24no—
199#385—24no—
200#385—24no—
201#385—28no—
202#381—24no—
203#381—24no—
204#381—24no—
205#381—42no—
206#381—42no—
207#381—42no—
208#380—24no—
209#380—24no—
210#380—28no—
211#379—24no—
212#379—24no—
213#379—42no—
214C4×C22⋊C4—24no—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—44no—
245C25—44no—
246C25C2×D414yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—42no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4#4114yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312#126—2128no—
313#126—2128no—
314#123—232no—
315#123—416no—
316#120—416no—
317C4×D4—416no—
318C2×C4⋊C4—232no—
319C2×C4⋊C4—232no—
320C2×C4⋊C4—232no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D418yes—
352C2×C4⋊C4C2×D418yes—
353C2×C4⋊C4C2×D418yes—
354C2×C4⋊C4C2×D418yes—
355C2×C22⋊C4—232no—
356C2×C22⋊C4—232no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—232no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
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—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4C2×D418yes—
417C2×C22⋊C4C2×D418yes—
418C2×C22⋊C4#4114yes—
419C2×C42—232no—
420C2×C42—28no—
421C2×C42—28no—
422C2×C42—28no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—44no—
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—28no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451C24—24no—
452C24—24no—
453C24—28no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—24no—
467C24—24no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24—24no—
472C24—28no—
473C24—28no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—88no—
485C24—88no—
486C24—88no—
487C24—88no—
488C24C22×D414yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24C2×#4112yes—
495C24H(5,𝔽2)12yes—
496C242−1+412yes—
497C24C2511yescharacteristic
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—84no—
508C2×D4—88no—
509C2×D4—88no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
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—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
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—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4#120116yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4112yes—
626C4⋊C4—232no—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—216no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—44no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C22⋊C4—232no—
640C22⋊C4—232no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—88no—
659C22⋊C4—84no—
660C22⋊C4—88no—
661C42—232no—
662C42—44no—
663C42—84no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—28no—
685C23—416no—
686C23—416no—
687C23—416no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—44no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—816no—
718C23—816no—
719C23—816no—
720C23—816no—
721C23—816no—
722C23—816no—
723C23C2×#12014yes—
724C23#52514yes—
725C23#53714yes—
726C23#54614yes—
727C23#54714yes—
728C23#54814yes—
729C23#55014yes—
730C23C23×D411yescharacteristic
731C23C23×D411yescharacteristic
732C23C23×D411yescharacteristic
733C23C22×#4111yescharacteristic
734C23C22×#4111yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×2−1+411yescharacteristic
737C23#58514yes—
738C23#58514yes—
739D4—416no—
740D4—816no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—41no—
795C2×C4—41no—
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—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—44no—
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—88no—
828C2×C4C2×#12014yes—
829C2×C4C2×#12014yes—
830C22—24no—
831C22—24no—
832C22—28no—
833C22—28no—
834C22—28no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—832no—
850C22—81no—
851C22—81no—
852C22—82no—
853C22—84no—
854C22—84no—
855C22—82no—
856C22—84no—
857C22—82no—
858C22—84no—
859C22#240718yes—
860C22C22×#12011yescharacteristic
861C22C2×#52511yescharacteristic
862C22C2×#53711yescharacteristic
863C22#344912yes—
864C22#344912yes—
865C22C2×#54611yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54811yescharacteristic
868C22C2×#55011yescharacteristic
869C22#348512yes—
870C22#348512yes—
871C22#348512yes—
872C22#348712yes—
873C22#352114yes—
874C22#352114yes—
875C22#356014yes—
876C22#356414yes—
877C4—24no—
878C4—24no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—42no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C2—28no—
894C2—82no—
895C2—84no—
896C2C2×#240711yescharacteristic
897C2#3508811yescharacteristic
898C2#3514911yescharacteristic
899C2#3545412yes—
900C2#3697112yes—
901C2#3803012yes—
902C2#3804612yes—
903C2#3911712yes—
904C2#3912912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#126C2semidirect
3. C2×#2487C2semidirect
4. C2×#2322C2semidirect
5. #16102C2semidirect
6. #16004C2semidirect
7. #15940C2semidirect
8. #15939C2semidirect
9. #15073C2semidirect
10. #15069C2semidirect
11. #14918C2semidirect
13. #14706C2semidirect
14. #14705C2semidirect
15. #14339C2semidirect
16. #14262C2semidirect
18. #13924C2semidirect
19. #13903C2semidirect
38. C2×#400C22semidirect
39. C2×#399C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
46. C2×#388C22semidirect
47. C2×#387C22semidirect
55. C2×#385C22semidirect
64. C2×#380C22semidirect
69. #1445C22semidirect
70. #1444C22semidirect
71. #1442C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
82. #1439C22semidirect
86. #1437C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. C4⋊#95C22semidirect
133. C22×C4⋊C4D4semidirect
134. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C23×#1262
C2×#25342
C2×#24872
C2×#23222
#161022
#160042
#159402
#159392
#150732
#150692
#149182
#149112
#147062
#147052
#143392
#142622
#142552
#139242
#139032