Finite Group Databasebeta

← #875324

Subgroups — #875324

Order 512.

3006 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic
3#16851C214yesmaximal, complemented
4#15508C214yesmaximal, complemented
5#15496C214yesmaximal, complemented
6#15215C211yesmaximal, characteristic, complemented
7#15215C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#15153C211yesmaximal, characteristic, complemented
10#15136C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14569C214yesmaximal, complemented
15#14138C211yesmaximal, characteristic, complemented
16#14026C211yesmaximal, characteristic, complemented
17#13976C211yesmaximal, characteristic, complemented
18#13939C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2538—28no—
30#2414—28no—
31C2×#400C2214yes—
32C2×#397C2214yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#392C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#388C2212yes—
50C2×#386C2212yes—
51C2×#386C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60#1445C2214yes—
61#1444C2214yes—
62#1442C2214yes—
63#1440C2214yes—
64#1440C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2214yes—
72#1438C2214yes—
73#1437C2214yes—
74#1437C2214yes—
75#1437C2212yes—
76#1436C2214yes—
77#1436C2214yes—
78#1436C2214yes—
79#1436C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×#124—24no—
102C2×#124—42no—
103C2×#124—42no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—42no—
109C2×C22⋊Q8—42no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—42no—
114C2×#121—42no—
115C2×#121—42no—
116C2×C4×Q8—24no—
117C2×C4×Q8—42no—
118C2×C4×Q8—42no—
119C2×C4×D4—42no—
120C2×C4×D4—42no—
121C2×C4×D4D418yes—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—42no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C42—42no—
159C22×C42—42no—
160C22×C42—42no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168C22×C42C2312yes—
169#400—48no—
170#397—216no—
171#396—28no—
172#396—28no—
173#394—28no—
174#394—48no—
175#392—28no—
176#391—24no—
177#391—42no—
178#391—42no—
179#390—28no—
180#390—28no—
181#390—24no—
182#390—42no—
183#390—42no—
184#390—42no—
185#389—28no—
186#389—24no—
187#388—28no—
188#386—28no—
189#386—48no—
190#384—24no—
191#384—42no—
192#380—24no—
193#380—24no—
194#380—24no—
195C4×C22⋊C4—42no—
196C4×C22⋊C4—42no—
197C4×C22⋊C4—42no—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C25C2412yes—
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8#4114yes—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—41no—
244C22×D4—41no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4C2×D414yes—
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—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289#124—416no—
290C22⋊Q8—416no—
291C22⋊Q8—416no—
292#121—416no—
293#121—416no—
294C4×Q8—416no—
295C4×D4—416no—
296#117—416no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
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—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4#4114yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—416no—
412C2×C42C2×D414yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—42no—
425#95—44no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95#4118yes—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—24no—
464C24—24no—
465C24C22×D412yes—
466C24C22×D412yes—
467C242−1+414yes—
468C24C2511yescharacteristic
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—416no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—84no—
493C2×D4—88no—
494C2×D4—84no—
495C2×D4—84no—
496C2×D4—88no—
497C2×D4—88no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4H(5,𝔽2)14yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C4H(5,𝔽2)12yes—
615C4⋊C4—28no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—88no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—416no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—88no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C42—28no—
649C42—48no—
650C42—48no—
651C42—48no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23#53614yes—
725C23C23×D411yescharacteristic
726C23C22×#4112yes—
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23C2×2−1+412yes—
735C23#58512yes—
736Q8—416no—
737D4—416no—
738D4—816no—
739D4—816no—
740D4—88no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
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—416no—
799C2×C4—416no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4#53214yes—
833C2×C4#53414yes—
834C2×C4#53814yes—
835C2×C4#54014yes—
836C2×C4#54614yes—
837C2×C4#54614yes—
838C2×C4#55314yes—
839C2×C4#56014yes—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—84no—
863C22—82no—
864C22—84no—
865C22—82no—
866C22—82no—
867C22—84no—
868C22—82no—
869C22—82no—
870C22—84no—
871C22—82no—
872C22—82no—
873C22C2×#53211yescharacteristic
874C22C2×#53411yescharacteristic
875C22C2×#53611yescharacteristic
876C22C2×#53811yescharacteristic
877C22C2×#54011yescharacteristic
878C22C2×#54611yescharacteristic
879C22C2×#54611yescharacteristic
880C22C2×#55311yescharacteristic
881C22#348012yes—
882C22#348312yes—
883C22#349811yescharacteristic
884C22#350011yescharacteristic
885C22#350612yes—
886C22#351612yes—
887C22#351912yes—
888C22#352012yes—
889C22#352012yes—
890C22#352012yes—
891C22C2×#56011yescharacteristic
892C22#353612yes—
893C22#354112yes—
894C22#354212yes—
895C22#354612yes—
896C4—24no—
897C4—44no—
898C4—44no—
899C4—44no—
900C4—42no—
901C4—42no—
902C4—44no—
903C4—42no—
904C4—44no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4#268818yes—
912C2—44no—
913C2—82no—
914C2—162no—
915C2#3508511yescharacteristic
916C2#3641211yescharacteristic
917C2#3641911yescharacteristic
918C2#3730011yescharacteristic
919C2#3807811yescharacteristic
920C2#3808511yescharacteristic
921C2#3922012yes—
922C2#4011812yes—
923C2#4564612yes—
924C2C2×#268811yescharacteristic
925C2#5939912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2414C2
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×#2538C2semidirect
3. #16851C2semidirect
4. #15508C2semidirect
5. #15496C2semidirect
6. #15215C2semidirect
7. #15215C2semidirect
8. #15195C2semidirect
9. #15153C2semidirect
10. #15136C2semidirect
11. #15130C2semidirect
12. #14702C2semidirect
13. #14698C2semidirect
14. #14569C2semidirect
15. #14138C2semidirect
16. #14026C2semidirect
17. #13976C2semidirect
18. #13939C2semidirect
19. C4×#386C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24142
#168512
#155082
#154962
#152152
#151952
#151532
#151362
#151302
#147022
#146982
#145692
#141382
#140262
#139762
#139392
C4×#3862