Finite Group Databasebeta

← #626405

Subgroups — #626405

Order 512.

2968 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2536C211yesmaximal, characteristic
3C2×#2327C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic
5#15839C214yesmaximal, complemented
6#15823C214yesmaximal, complemented
7#15812C214yesmaximal, complemented
8#15803C214yesmaximal
9#15233C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14348C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14258C211yesmaximal, characteristic, complemented
18#13942C211yesmaximal, characteristic, complemented
19#13926C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2538—28no—
31#2536—28no—
32C2×#398C2212yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#394C2212yes—
36#2327—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2212yes—
44C2×#389C2212yes—
45#2290—28no—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2214yes—
50C2×#387C2214yes—
51C2×#387C2212yes—
52C2×#386C2212yes—
53C2×#385C2212yes—
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1444C2214yes—
66#1444C2214yes—
67#1443C2214yes—
68#1443C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C4×Q8—24no—
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×D4—24no—
123C2×C4×D4—24no—
124C2×C4×D4D418yes—
125C2×#117—24no—
126C2×#117—42no—
127C2×#117—42no—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C42—24no—
160C22×C42—42no—
161C22×C42—42no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170#398—28no—
171#396—28no—
172#396—28no—
173#394—28no—
174#391—24no—
175#391—24no—
176#391—42no—
177#391—42no—
178#391—42no—
179#391—42no—
180#390—28no—
181#389—28no—
182#388—28no—
183#388—28no—
184#388—28no—
185#387—216no—
186#387—216no—
187#387—28no—
188#386—28no—
189#385—28no—
190#384—24no—
191#382—24no—
192#382—24no—
193#380—24no—
194#380—24no—
195#380—24no—
196#380—24no—
197C4×C4⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200#376D418yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8#4114yes—
242C22×Q8#4114yes—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4C2×D414yes—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C4⋊Q8—232no—
287C22⋊Q8—416no—
288C22⋊Q8—416no—
289C22⋊Q8—416no—
290C22⋊Q8—416no—
291C4×Q8—416no—
292C4×Q8—416no—
293C4×D4—232no—
294#117—416no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
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—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
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—28no—
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—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4C2×D414yes—
381C2×C22⋊C4C2×D414yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406C2×C42#4114yes—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95C2×D418yes—
432#95C2×D418yes—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24C22×D412yes—
453C24C22×D412yes—
454C242−1+414yes—
455C24C2511yescharacteristic
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—48no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
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—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
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—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4C22×D414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C42−1+414yes—
599C4⋊C4—232no—
600C4⋊C4—28no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—84no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C42—28no—
631C42—28no—
632C42—48no—
633C42—48no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42#121116yes—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23#53614yes—
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4111yescharacteristic
688C23C22×#4111yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)11yescharacteristic
691C23C2×2−1+412yes—
692C23C2×2−1+412yes—
693C23#58512yes—
694C23#58512yes—
695Q8—416no—
696Q8—416no—
697D4—416no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—432no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—416no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4C2×#12114yes—
796C2×C4C2×#12114yes—
797C2×C4C2×#12114yes—
798C2×C4#52514yes—
799C2×C4#53514yes—
800C2×C4#54614yes—
801C2×C4#54614yes—
802C2×C4#55314yes—
803C2×C4#55314yes—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22C22×#12111yescharacteristic
827C22C2×#52511yescharacteristic
828C22C2×#53511yescharacteristic
829C22C2×#53611yescharacteristic
830C22#344911yescharacteristic
831C22#346112yes—
832C22C2×#54611yescharacteristic
833C22C2×#54611yescharacteristic
834C22C2×#55311yescharacteristic
835C22C2×#55311yescharacteristic
836C22#348912yes—
837C22#348912yes—
838C22#349512yes—
839C22#349911yescharacteristic
840C22#350011yescharacteristic
841C22#351612yes—
842C22#351812yes—
843C22#352312yes—
844C22#352412yes—
845C22#353812yes—
846C22#353912yes—
847C22#354112yes—
848C22#354112yes—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4#253518yes—
866C2—44no—
867C2—82no—
868C2C2×#253511yescharacteristic
869C2#3530611yescharacteristic
870C2#3530811yescharacteristic
871C2#3566312yes—
872C2#3737512yes—
873C2#3808111yescharacteristic
874C2#3808311yescharacteristic
875C2#3809111yescharacteristic
876C2#3809311yescharacteristic
877C2#3925712yes—
878C2#3926312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2327C2semidirect
5. #15839C2semidirect
6. #15823C2semidirect
7. #15812C2semidirect
9. #15233C2semidirect
10. #15233C2semidirect
11. #15178C2semidirect
12. #15178C2semidirect
13. #14702C2semidirect
14. #14702C2semidirect
15. #14348C2semidirect
16. #14258C2semidirect
17. #14258C2semidirect
18. #13942C2semidirect
19. #13926C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#25362
C2×#23272
C2×#22902
#158392
#158232
#158122
#158032
#152332
#151782
#147022
#143482
#142582
#139422
#139262