Finite Group Databasebeta

← #664671

Subgroups — #664671

Order 512.

3086 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2417C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3#15811C214yesmaximal, complemented
4#15555C214yesmaximal, complemented
5#15197C211yesmaximal, characteristic, complemented
6#15195C211yesmaximal, characteristic, complemented
7#15185C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#14920C214yesmaximal, complemented
10#14702C211yesmaximal, characteristic, complemented
11#14139C211yesmaximal, characteristic, complemented
12#14139C211yesmaximal, characteristic, complemented
13#14048C211yesmaximal, characteristic, complemented
14#14016C214yesmaximal
15#14000C211yesmaximal, characteristic, complemented
16#13924C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18C4×#386C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2417—28no—
29C2×#398C2212yes—
30C2×#396C2212yes—
31D4×C4⋊C4—28no—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2214yes—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C22×#95C2214yes—
56#1445C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1437C2212yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C22⋊#95C2214yes—
87C22⋊#95C2214yes—
88C22⋊#95C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—42no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—28no—
110C2×C4×D4—48no—
111C2×C4×D4D418yes—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C42—24no—
150C22×C42—42no—
151C22×C42—42no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159#398—28no—
160#396—28no—
161#391—24no—
162#391—24no—
163#391—42no—
164#391—42no—
165#391—42no—
166#389—28no—
167#389—24no—
168#386—28no—
169#386Q8116yescomplemented
170#385—28no—
171#385—28no—
172#385—48no—
173#384—24no—
174#384—24no—
175#384—42no—
176#380—24no—
177#380—24no—
178#380—24no—
179#380—28no—
180C4×C4⋊C4—24no—
181C4×C22⋊C4—24no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—42no—
184C2×#95—48no—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C25C2411yescharacteristic
214C25C2411yescharacteristic
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4C2×D414yes—
226C22×D4C2×Q818yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×Q818yes—
261C23×C4#4114yes—
262C23×C4#4114yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C22⋊Q8—416no—
281C22⋊Q8—416no—
282C4×D4—232no—
283C4×D4—432no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—416no—
321C2×C4⋊C4—416no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4#4114yes—
337C2×C4⋊C4#4114yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
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—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×D414yes—
361C2×C22⋊C4C2×D414yes—
362C2×C22⋊C4C2×Q818yes—
363C2×C22⋊C4C2×Q818yes—
364C2×C22⋊C4C2×Q818yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—44no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—416no—
385C2×C42C2×D414yes—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—42no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95C2×Q818yes—
413#95C2×Q818yes—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C22×Q814yes—
432C24C22×Q814yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24H(5,𝔽2)14yes—
436C24C2511yescharacteristic
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—216no—
447C2×D4—216no—
448C2×D4C4⋊Q8116yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—216no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
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—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—416no—
546C22×C4—416no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—88no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4—88no—
565C22×C4#123116yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×Q814yes—
572C22×C4C22×Q814yes—
573C22×C4C22×Q814yes—
574C22×C4C22×Q814yes—
575C22×C4C22×Q814yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—48no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—84no—
601C4⋊C4—84no—
602C4⋊C4—88no—
603C4⋊C4—88no—
604C22⋊C4—28no—
605C22⋊C4—216no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—84no—
614C42—28no—
615C42—48no—
616C42—48no—
617C42—44no—
618C42—44no—
619C42—44no—
620C42—44no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C2×#12314yes—
662C23C2×C4⋊Q814yes—
663C23C2×C4⋊Q814yes—
664C23#53514yes—
665C23#55418yes—
666C23#55418yes—
667C23C23×D411yescharacteristic
668C23C23×Q812yes—
669C23C22×#4111yescharacteristic
670C23C22×#4111yescharacteristic
671C23C22×#4111yescharacteristic
672C23C22×#4111yescharacteristic
673C23C2×H(5,𝔽2)12yes—
674C23C2×H(5,𝔽2)11yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23#58512yes—
677C23#58512yes—
678Q8—88no—
679D4—232no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—232no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—432no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—416no—
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—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—816no—
776C2×C4—816no—
777C2×C4—816no—
778C2×C4C2×#12314yes—
779C2×C4C2×#12314yes—
780C2×C4#52914yes—
781C2×C4C2×C4⋊Q814yes—
782C2×C4#53814yes—
783C2×C4#54614yes—
784C2×C4#54614yes—
785C2×C4#55314yes—
786C2×C4#55314yes—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—24no—
793C22—24no—
794C22—28no—
795C22—28no—
796C22—28no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22#250218yes—
809C22C22×#12311yescharacteristic
810C22C2×#52911yescharacteristic
811C22C22×C4⋊Q811yescharacteristic
812C22C2×#53511yescharacteristic
813C22C2×#53811yescharacteristic
814C22C2×#54611yescharacteristic
815C22C2×#54611yescharacteristic
816C22C2×#55311yescharacteristic
817C22C2×#55311yescharacteristic
818C22C2×#55412yes—
819C22C2×#55412yes—
820C22Q8×#4112yes—
821C22Q8×#4112yes—
822C22#349312yes—
823C22#350011yescharacteristic
824C22#350011yescharacteristic
825C22#350112yes—
826C22#350112yes—
827C22#351212yes—
828C22#351312yes—
829C22#351312yes—
830C22#354212yes—
831C22#354212yes—
832C4—24no—
833C4—24no—
834C4—42no—
835C4—42no—
836C4—44no—
837C4—44no—
838C4—44no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4#244418yes—
849C2—28no—
850C2—44no—
851C2C2×#244411yescharacteristic
852C2C2×#250211yescharacteristic
853C2#3561811yescharacteristic
854C2#3627611yescharacteristic
855C2#3627611yescharacteristic
856C2#3655312yes—
857C2#3808211yescharacteristic
858C2#3808411yescharacteristic
859C2#3960512yes—
860C2#5985612yes—
861C2#5985612yes—
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. #15811C2semidirect
4. #15555C2semidirect
5. #15197C2semidirect
6. #15195C2semidirect
7. #15185C2semidirect
8. #15182C2semidirect
9. #14920C2semidirect
10. #14702C2semidirect
11. #14139C2semidirect
12. #14139C2semidirect
13. #14048C2semidirect
15. #14000C2semidirect
16. #13924C2semidirect
17. #13880C2semidirect
19. C2×C4⋊#95C2semidirect
169. #386Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24172
C2×D4×C4⋊C42
#158112
#155552
#151972
#151952
#151852
#151822
#149202
#147022
#141392
#140482
#140162
#140002
#139242
#138802
C4×#3862
C2×C4⋊#952