Finite Group Databasebeta

← #649234

Subgroups — #649234

Order 512.

3328 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic
2C2×#2426C211yesmaximal, characteristic
3C2×#2360C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#15397C214yesmaximal, complemented
6#15365C214yesmaximal, complemented
7#15243C211yesmaximal, characteristic, complemented
8#15215C211yesmaximal, characteristic
9#15184C211yesmaximal, characteristic, complemented
10#15178C211yesmaximal, characteristic, complemented
11#14793C214yesmaximal, complemented
12#14700C211yesmaximal, characteristic, complemented
13#14153C211yesmaximal, characteristic, complemented
14#14139C211yesmaximal, characteristic, complemented
15#14095C214yesmaximal, complemented
16#14049C211yesmaximal, characteristic, complemented
17#14026C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#123C2214yes—
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2501—28no—
31#2426—28no—
32C2×#399C2214yes—
33C2×#396C2212yes—
34C2×#394C2212yes—
35#2360—28no—
36C4×C4⋊Q8—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2212yes—
49C2×#389C2214yes—
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#388C2214yes—
55C2×#387C2212yes—
56C2×#387C2214yes—
57C2×#385C2212yes—
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×C4×C4⋊C4C2214yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1445C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1437C2212yes—
83#1437C2214yes—
84#1437C2214yes—
85#1436C2214yes—
86#1436C2212yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#124—42no—
108C2×#124—42no—
109C2×#124—42no—
110C2×#123—216no—
111C2×#123—216no—
112C2×#123—48no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—42no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—42no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8—42no—
127C2×C4×Q8—42no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173#399—216no—
174#396—28no—
175#394—28no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—42no—
181#391—42no—
182#390—24no—
183#390—24no—
184#390—28no—
185#390—24no—
186#390—24no—
187#389—216no—
188#389—24no—
189#389—24no—
190#389—28no—
191#388—28no—
192#388—28no—
193#388—48no—
194#387—28no—
195#387—48no—
196#385—28no—
197#384—24no—
198#384D418yes—
199C4×C4⋊C4—216no—
200C4×C4⋊C4—24no—
201C4×C4⋊C4—42no—
202C4×C22⋊C4—28no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—42no—
205C4×C22⋊C4D418yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C43—24no—
230C25C2412yes—
231C25C2411yescharacteristic
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—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8#4114yes—
245C22×Q8#4114yes—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—42no—
257C22×D4—44no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—28no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4C2×D414yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C4⋊Q8—232no—
288#124—416no—
289#124—416no—
290#123—464no—
291C22⋊Q8—232no—
292C22⋊Q8—416no—
293#121—416no—
294C4×Q8—416no—
295C4×Q8—416no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
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—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
341C2×C4⋊C4C2×D4116yes—
342C2×C4⋊C4#4114yes—
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—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4#4118yes—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—44no—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—24no—
428#95—28no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95C2×D414yes—
438#95C2×D414yes—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—24no—
459C24C22×D412yes—
460C24C2×#4114yes—
461C24C2511yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×D4—48no—
477C2×D4—416no—
478C2×D4—48no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—84no—
487C2×D4—88no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
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—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—48no—
570C22×C4—416no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—88no—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D414yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)14yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C42−1+414yes—
600C22×C42−1+414yes—
601C4⋊C4—216no—
602C4⋊C4—232no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—232no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—416no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C22⋊C4—216no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—216no—
621C22⋊C4—416no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—84no—
632C42—216no—
633C42—28no—
634C42—28no—
635C42—28no—
636C42—48no—
637C42—48no—
638C42—44no—
639C42—48no—
640C42—44no—
641C42—44no—
642C42—84no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23#53214yes—
689C23C23×D411yescharacteristic
690C23C23×D411yescharacteristic
691C23C22×#4111yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×2−1+412yes—
699C23C2×2−1+412yes—
700Q8—416no—
701Q8—416no—
702D4—816no—
703D4—88no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
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—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—416no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—816no—
798C2×C4#52514yes—
799C2×C4#52514yes—
800C2×C4#53614yes—
801C2×C4#53814yes—
802C2×C4D4214yes—
803C2×C4#54618yes—
804C2×C4#54614yes—
805C2×C4#55014yes—
806C2×C4#55314yes—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—44no—
811C22—42no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—42no—
816C22—44no—
817C22—42no—
818C22—84no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—84no—
824C22—84no—
825C22—82no—
826C22—82no—
827C22—84no—
828C22—82no—
829C22C2×#52511yescharacteristic
830C22C2×#52511yescharacteristic
831C22C2×#53211yescharacteristic
832C22C2×#53611yescharacteristic
833C22C2×#53811yescharacteristic
834C22C2×D4211yescharacteristic
835C22C2×#54611yescharacteristic
836C22C2×#54612yes—
837C22C2×#55011yescharacteristic
838C22C2×#55311yescharacteristic
839C22#348212yes—
840C22#348212yes—
841C22#348212yes—
842C22#348612yes—
843C22#349811yescharacteristic
844C22#349911yescharacteristic
845C22#350812yes—
846C22#352012yes—
847C22#352012yes—
848C22#352212yes—
849C22#352212yes—
850C22#354812yes—
851C22#355212yes—
852C4—24no—
853C4—28no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—44no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4#245618yes—
869C2—44no—
870C2—162no—
871C2C2×#245611yescharacteristic
872C2#3497211yescharacteristic
873C2#3553511yescharacteristic
874C2#3612111yescharacteristic
875C2#3637611yescharacteristic
876C2#3642212yes—
877C2#3767511yescharacteristic
878C2#3895211yescharacteristic
879C2#4021412yes—
880C2#5904012yes—
881C2#5969712yes—
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
3. C2×#2360C2semidirect
4. C2×C4×C4⋊Q8C2semidirect
5. #15397C2semidirect
6. #15365C2semidirect
7. #15243C2semidirect
9. #15184C2semidirect
10. #15178C2semidirect
11. #14793C2semidirect
12. #14700C2semidirect
13. #14153C2semidirect
14. #14139C2semidirect
15. #14095C2semidirect
16. #14049C2semidirect
17. #14026C2semidirect
18. #13976C2semidirect
19. C4×#388C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24262
C2×#23602
C2×C4×C4⋊Q82
#153972
#153652
#152432
#152152
#151842
#151782
#147932
#147002
#141532
#141392
#140952
#140492
#140262
#139762
C4×#3882