Finite Group Databasebeta

← #947349

Subgroups — #947349

Order 512.

2902 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic, complemented
2C2×#2427C211yesmaximal, characteristic, complemented
3#17095C214yesmaximal, complemented
4#16592C214yesmaximal, complemented
5#16268C214yesmaximal, complemented
6#15442C214yesmaximal, complemented
7#15241C211yesmaximal, characteristic, complemented
8#15227C211yesmaximal, characteristic, complemented
9#15217C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15153C211yesmaximal, characteristic, complemented
12#15124C211yesmaximal, characteristic
13#14273C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14138C211yesmaximal, characteristic, complemented
16#14136C211yesmaximal, characteristic, complemented
17#14025C211yesmaximal, characteristic, complemented
18#13941C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2500—28no—
29#2427—28no—
30C2×#400C2214yes—
31C2×#397C2212yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#392C2214yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#386C2212yes—
51C2×#386C2214yes—
52C2×#384C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×#376C2211yescharacteristic
60#1445C2214yes—
61#1443C2212yes—
62#1443C2214yes—
63#1443C2214yes—
64#1442C2212yes—
65#1440C2212yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2314yes—
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×#127—24no—
102C2×#127—42no—
103C2×#127—42no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—42no—
107C2×#124—42no—
108C2×#124—42no—
109C2×#124—42no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—42no—
117C2×#121—42no—
118C2×#121—42no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—42no—
122C2×#117—24no—
123C2×#117—42no—
124C2×#117—42no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
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⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163#400—48no—
164#397—28no—
165#394—28no—
166#394—28no—
167#394—28no—
168#392—48no—
169#391—24no—
170#391—42no—
171#391—42no—
172#391—42no—
173#390—24no—
174#390—24no—
175#390—24no—
176#390—42no—
177#390—42no—
178#390—42no—
179#390—42no—
180#389—24no—
181#388—28no—
182#388—28no—
183#386—28no—
184#386—48no—
185#384—24no—
186#382—24no—
187#380—28no—
188C4×C4⋊C4—42no—
189C4×C22⋊C4—42no—
190C4×C22⋊C4—42no—
191C4×C22⋊C4D418yescomplemented
192#376—42no—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C25C2412yes—
219C25C2411yescharacteristic
220C25C2412yes—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×D4—24no—
229C22×D4—28no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—28no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4#4114yes—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4C2×D414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287#127—416no—
288#124—416no—
289#124—416no—
290C22⋊Q8—416no—
291#121—416no—
292#121—416no—
293C4×D4—416no—
294#117—416no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
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—24no—
304C2×C4⋊C4—22no—
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—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4#4114yes—
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—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—24no—
409#95—42no—
410#95—44no—
411#95—42no—
412#95—44no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95C2×D414yes—
424#95C2×D414yes—
425C24—22no—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24C22×D412yes—
457C24C2×#4114yes—
458C24C2511yescharacteristic
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—416no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—88no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4—88no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—84no—
587C22×C4—88no—
588C22×C4—88no—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—416no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C22⋊C4—88no—
634C42—28no—
635C42—28no—
636C42—48no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42—44no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—28no—
652C23—28no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23C23×D411yescharacteristic
711C23C22×#4111yescharacteristic
712C23C22×#4111yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)12yes—
718C23#58512yes—
719C23#58512yes—
720C23#58512yes—
721Q8—88no—
722D4—416no—
723D4—832no—
724D4—816no—
725D4—816no—
726D4—88no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—416no—
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—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—42no—
789C2×C4—42no—
790C2×C4—42no—
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—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—816no—
816C2×C4#53514yes—
817C2×C4#53814yes—
818C2×C4#54014yes—
819C2×C4#54614yes—
820C2×C4#54614yes—
821C2×C4#55314yes—
822C2×C4#56014yes—
823C22—48no—
824C22—42no—
825C22—44no—
826C22—48no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—82no—
836C22—84no—
837C22—82no—
838C22—82no—
839C22—84no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—82no—
848C22—84no—
849C22—84no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22C2×#53511yescharacteristic
857C22#344911yescharacteristic
858C22#344911yescharacteristic
859C22C2×#53811yescharacteristic
860C22C2×#54011yescharacteristic
861C22C2×#54611yescharacteristic
862C22C2×#54611yescharacteristic
863C22C2×#55311yescharacteristic
864C22#349811yescharacteristic
865C22#350011yescharacteristic
866C22#351312yes—
867C22#351412yes—
868C22#352112yes—
869C22#352412yes—
870C22C2×#56011yescharacteristic
871C22#353912yes—
872C22#354012yes—
873C22#354212yes—
874C22#354612yes—
875C22#354612yes—
876C22#355812yes—
877C22#356212yes—
878C22#356212yes—
879C4—42no—
880C4—44no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4#270318yes—
895C2—84no—
896C2—82no—
897C2—162no—
898C2#3730511yescharacteristic
899C2#3754411yescharacteristic
900C2#3809011yescharacteristic
901C2#3809211yescharacteristic
902C2#3809511yescharacteristic
903C2#3894511yescharacteristic
904C2#4262712yes—
905C2#4275912yes—
906C2#4506812yes—
907C2C2×#270311yescharacteristic
908C2#5306312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15124C2
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×#2500C2semidirect
2. C2×#2427C2semidirect
3. #17095C2semidirect
4. #16592C2semidirect
5. #16268C2semidirect
6. #15442C2semidirect
7. #15241C2semidirect
8. #15227C2semidirect
9. #15217C2semidirect
10. #15215C2semidirect
11. #15153C2semidirect
13. #14273C2semidirect
14. #14260C2semidirect
15. #14138C2semidirect
16. #14136C2semidirect
17. #14025C2semidirect
18. #13941C2semidirect
19. #13842C2semidirect
191. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#24272
#170952
#165922
#162682
#154422
#152412
#152272
#152172
#152152
#151532
#151242
#142732
#142602
#141382
#141362
#140252
#139412
#138422