Finite Group Databasebeta

← #678155

Subgroups — #678155

Order 512.

3318 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2563C211yesmaximal, characteristic, complemented
3C2×#2354C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#15832C214yesmaximal, complemented
6#15613C214yesmaximal, complemented
7#15138C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15126C212yesmaximal
11#14161C211yesmaximal, characteristic, complemented
12#14151C211yesmaximal, characteristic, complemented
13#14006C212yesmaximal, complemented
14#13951C212yesmaximal, complemented
15#13875C212yesmaximal, complemented
16#13871C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×#121C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×#117C2212yes—
24C23×C42C2211yescharacteristic
25#2857—28no—
26#2563—28no—
27C2×#397C2214yes—
28C2×#394C2214yes—
29C2×#393C2214yes—
30#2354—28no—
31C4×#121—28no—
32C2×#391C2212yes—
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#388C2214yes—
42C2×#388C2212yes—
43C2×#386C2212yes—
44C2×#384C2211yescharacteristic
45C2×#382C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60#1446C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2214yes—
83#1434C2214yes—
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2312yes—
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—44no—
99C2×C22⋊Q8—44no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—24no—
103C2×C4×D4—28no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—44no—
108C2×C4×D4D418yes—
109C2×#117—28no—
110C2×#117—28no—
111C2×#117—44no—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C42—24no—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2314yes—
149C22×C42C2311yescharacteristic
150#397—48no—
151#394—48no—
152#393—216no—
153#391—28no—
154#390—28no—
155#390—24no—
156#390—28no—
157#389—28no—
158#389—28no—
159#389—24no—
160#389—28no—
161#389—44no—
162#388—216no—
163#388—28no—
164#386—28no—
165#384D418yescomplemented
166#382—28no—
167#380—28no—
168#380—28no—
169#380—24no—
170#380—28no—
171#380—28no—
172#380—28no—
173#380—24no—
174#380—24no—
175C4×C4⋊C4—28no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—24no—
178C4×C4⋊C4—24no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—28no—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C22×Q8—24no—
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8—42no—
210C22×Q8—42no—
211C22×Q8—42no—
212C22×Q8—42no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—24no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4C2×D414yes—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—41no—
251C23×C4—41no—
252C23×C4C2×D418yes—
253C23×C4#4114yes—
254C23×C4#4114yes—
255C23×C4C2414yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C4⋊Q8—416no—
271C22⋊Q8—432no—
272#121—232no—
273C4×D4—232no—
274C4×D4—432no—
275#117—432no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×D418yes—
318C2×C4⋊C4C2×D418yes—
319C2×C4⋊C4#4114yes—
320C2×C4⋊C4#4114yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×D418yes—
357C2×C42—28no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—28no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—44no—
378C2×C42—416no—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42#4114yes—
382#95—24no—
383#95—24no—
384#95—28no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—24no—
398#95—42no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×D414yes—
432C24C2×#4112yes—
433C24C2×#4112yes—
434C24H(5,𝔽2)12yes—
435C24C2511yescharacteristic
436C2×Q8—48no—
437C2×Q8—48no—
438C2×Q8—48no—
439C2×Q8—84no—
440C2×Q8—84no—
441C2×Q8—84no—
442C2×Q8—84no—
443C2×D4—216no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—216no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
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—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
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—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4C22×D414yes—
567C22×C4C22×D418yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
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×C4C2×#4112yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C42−1+412yes—
588C22×C42−1+412yes—
589C22×C42−1+412yes—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—216no—
593C4⋊C4—28no—
594C4⋊C4—216no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—416no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—88no—
605C22⋊C4—216no—
606C22⋊C4—216no—
607C22⋊C4—416no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—88no—
615C22⋊C4—88no—
616C22⋊C4—88no—
617C42—416no—
618C42—44no—
619C42—44no—
620C42—44no—
621C42—48no—
622C42—48no—
623C42—48no—
624C42#121116yes—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23#55514yes—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C22×#4111yescharacteristic
702C23C2×H(5,𝔽2)11yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23C2×2−1+411yescharacteristic
707C23C2×2−1+411yescharacteristic
708C23#58511yescharacteristic
709C23#58511yescharacteristic
710Q8—816no—
711D4—432no—
712D4—416no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—432no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
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×C4C2×#12114yes—
808C2×C4C2×#12114yes—
809C2×C4C2×#12114yes—
810C2×C4#52514yes—
811C2×C4#52914yes—
812C2×C4#53614yes—
813C2×C4#54214yes—
814C2×C4#54614yes—
815C2×C4#54614yes—
816C2×C4#54714yes—
817C2×C4#54714yes—
818C2×C4#54814yes—
819C2×C4#54814yes—
820C2×C4#55214yes—
821C2×C4#55614yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22C22×#12111yescharacteristic
853C22C2×#52511yescharacteristic
854C22C2×#52911yescharacteristic
855C22C2×#53611yescharacteristic
856C22C2×#54211yescharacteristic
857C22C2×#54611yescharacteristic
858C22C2×#54611yescharacteristic
859C22C2×#54711yescharacteristic
860C22C2×#54711yescharacteristic
861C22C2×#54811yescharacteristic
862C22C2×#54811yescharacteristic
863C22C2×#55211yescharacteristic
864C22C2×#55511yescharacteristic
865C22C2×#55611yescharacteristic
866C22#347511yescharacteristic
867C22#347511yescharacteristic
868C22#348311yescharacteristic
869C22#348411yescharacteristic
870C22#348711yescharacteristic
871C22#348811yescharacteristic
872C22#348811yescharacteristic
873C22#349411yescharacteristic
874C22#349411yescharacteristic
875C22#350611yescharacteristic
876C22#350711yescharacteristic
877C22#351111yescharacteristic
878C22#351111yescharacteristic
879C22#351511yescharacteristic
880C22#351811yescharacteristic
881C22#351911yescharacteristic
882C22#352211yescharacteristic
883C22#354411yescharacteristic
884C22#354711yescharacteristic
885C22#354811yescharacteristic
886C22#355511yescharacteristic
887C4—24no—
888C4—44no—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—48no—
894C4—42no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—84no—
899C4—82no—
900C4#241518yes—
901C4#242718yes—
902C2—44no—
903C2—84no—
904C2C2×#242711yescharacteristic
905C2C2×#241511yescharacteristic
906C2#3556311yescharacteristic
907C2#3616011yescharacteristic
908C2#3617611yescharacteristic
909C2#3641111yescharacteristic
910C2#3645911yescharacteristic
911C2#3892111yescharacteristic
912C2#3915811yescharacteristic
913C2#3947011yescharacteristic
914C2#3947911yescharacteristic
915C2#5903411yescharacteristic
916C2#5903911yescharacteristic
917C2#5906511yescharacteristic
918C2#5913511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
2. C2×#2563C2semidirect
3. C2×#2354C2semidirect
5. #15832C2semidirect
6. #15613C2semidirect
7. #15138C2semidirect
8. #15132C2semidirect
9. #15129C2semidirect
11. #14161C2semidirect
12. #14151C2semidirect
13. #14006C2semidirect
14. #13951C2semidirect
15. #13875C2semidirect
16. #13871C2semidirect
17. C4×#380C2semidirect
165. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25632
C2×#23542
C2×C4×#1212
#158322
#156132
#151382
#151322
#151292
#151262
#141612
#141512
#140062
#139512
#138752
#138712
C4×#3802