Finite Group Databasebeta

← #612707

Subgroups — #612707

Order 512.

3554 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2487C211yesmaximal, characteristic
3C2×#2417C211yesmaximal, characteristic
4C2×C42×D4C211yesmaximal, characteristic
5#15196C211yesmaximal, characteristic, complemented
6#15195C211yesmaximal, characteristic, complemented
7#15184C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#14871C214yesmaximal, complemented
10#14771C214yesmaximal, complemented
11#14712C211yesmaximal, characteristic, complemented
12#14703C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14686C211yesmaximal, characteristic, complemented
16#14004C214yesmaximal, complemented
17#13899C214yesmaximal
18#13880C211yesmaximal, characteristic, complemented
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2502—28no—
29#2487—28no—
30#2417—28no—
31C2×#400C2212yes—
32C2×#399C2212yes—
33C2×#398C2212yes—
34C2×#398C2214yes—
35C2×#396C2212yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2214yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2214yes—
48C2×#385C2214yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2214yes—
60C42×D4—28no—
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2211yescharacteristic
67C22×#95C2214yes—
68C2×C43C2211yescharacteristic
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81C4⋊#95C2214yes—
82C4⋊#95C2214yes—
83C4⋊#95C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—42no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—28no—
112C2×C4×D4—28no—
113C2×C4×D4D418yes—
114C2×C4×D4Q8116yescomplemented
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42—42no—
156C22×C42—42no—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#400—28no—
167#399—28no—
168#398—28no—
169#398—216no—
170#396—28no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—42no—
176#389—24no—
177#389—24no—
178#389—24no—
179#389—48no—
180#386—28no—
181#386—28no—
182#385—28no—
183#385—216no—
184#385—216no—
185#384—24no—
186#384—24no—
187#384—24no—
188#384—42no—
189#380—24no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—28no—
194#380—48no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4D418yes—
201C2×#95—48no—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C43—24no—
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4C2×D414yes—
240C22×D4C2×Q818yes—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—28no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×Q818yes—
277C23×C4C2×Q818yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C22⋊Q8—416no—
297C22⋊Q8—416no—
298C4×D4—232no—
299C4×D4—264no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—416no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×Q818yes—
358C2×C4⋊C4#4114yes—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4C2×D414yes—
380C2×C22⋊C4C2×D414yes—
381C2×C22⋊C4C2×D418yes—
382C2×C22⋊C4C2×Q818yes—
383C2×C22⋊C4C2×Q818yes—
384C2×C22⋊C4#4118yes—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—416no—
405C2×C42—416no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42C2×Q818yes—
413C2×C42#4114yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95C2×D418yes—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24C22×D412yes—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×Q814yes—
457C24C22×Q814yes—
458C24C2×#4112yes—
459C24C2×#4114yes—
460C24C2511yescharacteristic
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×D4—28no—
469C2×D4—216no—
470C2×D4—28no—
471C2×D4—216no—
472C2×D4C4⋊Q8116yes—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—216no—
524C22×C4—216no—
525C22×C4—22no—
526C22×C4—22no—
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—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
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—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—416no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—416no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—84no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4#121116yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D414yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×Q814yes—
597C22×C4C22×Q814yes—
598C22×C4C22×Q814yes—
599C22×C4C22×Q814yes—
600C22×C4C22×Q814yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4H(5,𝔽2)14yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C42−1+412yes—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—28no—
615C4⋊C4—416no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—88no—
627C4⋊C4—88no—
628C4⋊C4—88no—
629C4⋊C4—84no—
630C4⋊C4—84no—
631C4⋊C4—84no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—216no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4C22⋊Q8132yescomplemented
642C42—28no—
643C42—216no—
644C42—28no—
645C42—28no—
646C42—28no—
647C42—48no—
648C42—48no—
649C42—48no—
650C42—44no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C2×#12114yes—
692C23C2×C22⋊Q818yes—
693C23C2×C4⋊Q814yes—
694C23C2×C4⋊Q814yes—
695C23#53214yes—
696C23#53318yes—
697C23C23×D411yescharacteristic
698C23C23×D411yescharacteristic
699C23C23×Q812yes—
700C23C22×#4111yescharacteristic
701C23C22×#4112yes—
702C23C22×#4111yescharacteristic
703C23C22×#4111yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)12yes—
706C23C2×2−1+411yescharacteristic
707C23#58512yes—
708Q8—88no—
709D4—232no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—232no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—416no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—816no—
804C2×C4—816no—
805C2×C4C2×#12114yes—
806C2×C4C2×#12114yes—
807C2×C4C2×C22⋊Q818yes—
808C2×C4C2×C22⋊Q818yes—
809C2×C4#52914yes—
810C2×C4C2×C4⋊Q814yes—
811C2×C4#53914yes—
812C2×C4#54614yes—
813C2×C4#54614yes—
814C2×C4#54714yes—
815C2×C4#54714yes—
816C2×C4#55418yes—
817C22—24no—
818C22—28no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—28no—
823C22—24no—
824C22—24no—
825C22—28no—
826C22—28no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—44no—
838C22#285718yes—
839C22C22×#12111yescharacteristic
840C22C22×C22⋊Q812yes—
841C22C2×#52911yescharacteristic
842C22C22×C4⋊Q811yescharacteristic
843C22C2×#53211yescharacteristic
844C22C2×#53312yes—
845C22C2×#53911yescharacteristic
846C22#346012yes—
847C22C2×#54611yescharacteristic
848C22C2×#54611yescharacteristic
849C22C2×#54711yescharacteristic
850C22C2×#54711yescharacteristic
851C22C2×#55412yes—
852C22#347512yes—
853C22Q8×#4112yes—
854C22#348112yes—
855C22#348812yes—
856C22#349811yescharacteristic
857C22#350011yescharacteristic
858C22#350112yes—
859C22#350312yes—
860C22#351512yes—
861C22#351912yes—
862C4—24no—
863C4—28no—
864C4—28no—
865C4—24no—
866C4—28no—
867C4—44no—
868C4—44no—
869C4—42no—
870C4—42no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4#242518yes—
879C2—28no—
880C2—44no—
881C2C2×#242511yescharacteristic
882C2#3477212yes—
883C2#3501712yes—
884C2#3525611yescharacteristic
885C2#3615412yes—
886C2#3618011yescharacteristic
887C2#3618411yescharacteristic
888C2#3627512yes—
889C2#3627611yescharacteristic
890C2#3636211yescharacteristic
891C2C2×#285711yescharacteristic
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
1. C2×#2502C2semidirect
5. #15196C2semidirect
6. #15195C2semidirect
7. #15184C2semidirect
8. #15182C2semidirect
9. #14871C2semidirect
10. #14771C2semidirect
11. #14712C2semidirect
12. #14703C2semidirect
13. #14702C2semidirect
14. #14702C2semidirect
15. #14686C2semidirect
16. #14004C2semidirect
18. #13880C2semidirect
19. C2×C4⋊#95C2semidirect
114. C2×C4×D4Q8semidirect
641. C22⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24872
C2×#24172
C2×C42×D42
#151962
#151952
#151842
#151822
#148712
#147712
#147122
#147032
#147022
#146862
#140042
#138992
#138802
C2×C4⋊#952