Finite Group Databasebeta

← #719718

Subgroups — #719718

Order 512.

3466 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2504C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5#16528C214yesmaximal, complemented
6#15327C214yesmaximal, complemented
7#15269C214yesmaximal, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15195C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14721C214yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13909C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#123C2214yes—
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2535—28no—
29#2504—28no—
30#2501—28no—
31C2×#399C2214yes—
32C2×#397C2212yes—
33C2×#397C2214yes—
34C2×#394C2214yes—
35C2×#392C2212yes—
36D4×C4⋊C4—28no—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2214yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2214yes—
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2214yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×#376C2211yescharacteristic
68#1445C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1443C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2212yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C24×C4C2312yes—
104C2×#123—216no—
105C2×#123—48no—
106C2×#123—48no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—42no—
112C2×#121—42no—
113C2×C4×D4—28no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—48no—
120C2×C4×D4D418yes—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4—42no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#399—216no—
167#397—28no—
168#397—216no—
169#394—48no—
170#392—28no—
171#390—24no—
172#390—24no—
173#390—24no—
174#390D418yescomplemented
175#389—28no—
176#386—216no—
177#386—28no—
178#386—28no—
179#385—28no—
180#385—28no—
181#385—48no—
182#384—24no—
183#384—24no—
184#384—24no—
185#384—42no—
186#382—24no—
187#382—24no—
188#382—24no—
189#382—42no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—48no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—24no—
201#376—24no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—28no—
235C22×D4—28no—
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—42no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4C2×D414yes—
249C22×D4C2×D414yes—
250C23×C4—22no—
251C23×C4—22no—
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—24no—
263C23×C4—24no—
264C23×C4—28no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295#123—464no—
296#121—416no—
297#121—416no—
298C4×D4—232no—
299C4×D4—432no—
300C4×D4—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—416no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D4116yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—44no—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42#4114yes—
411C2×C42#4114yes—
412C2×C42#4114yes—
413#95—24no—
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—24no—
428#95—24no—
429#95—28no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—24no—
464C24C22×D414yes—
465C24C22×D412yes—
466C24C22×D412yes—
467C24H(5,𝔽2)14yes—
468C242−1+414yes—
469C24C2511yescharacteristic
470C2×D4—216no—
471C2×D4—216no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—416no—
481C2×D4—416no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
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—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—22no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
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—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—416no—
576C22×C4—416no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—88no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—88no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—88no—
595C22×C4—88no—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)14yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C42−1+412yes—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—416no—
621C4⋊C4—48no—
622C4⋊C4—416no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—84no—
630C4⋊C4—88no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—416no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—88no—
645C22⋊C4—88no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C42—28no—
649C42—28no—
650C42—48no—
651C42—44no—
652C42—44no—
653C42#123116yescomplemented
654C23—22no—
655C23—22no—
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—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—28no—
682C23—28no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
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—44no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—42no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23#53514yes—
722C23#53614yes—
723C23C23×D411yescharacteristic
724C23C23×D411yescharacteristic
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C22×#4111yescharacteristic
728C23C2×H(5,𝔽2)12yes—
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)12yes—
731C23C2×2−1+412yes—
732C23C2×2−1+411yescharacteristic
733C23#58512yes—
734D4—232no—
735D4—416no—
736D4—816no—
737D4—816no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
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—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—416no—
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—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—42no—
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—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—816no—
826C2×C4—816no—
827C2×C4—816no—
828C2×C4C2×#12314yes—
829C2×C4C2×#12314yes—
830C2×C4C2×#12314yes—
831C2×C4#53214yes—
832C2×C4#54214yes—
833C2×C4D4214yes—
834C2×C4#54714yes—
835C2×C4#54714yes—
836C2×C4#55314yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—48no—
862C22—44no—
863C22—48no—
864C22—84no—
865C22—84no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22C22×#12311yescharacteristic
871C22C2×#53211yescharacteristic
872C22C2×#53511yescharacteristic
873C22C2×#53611yescharacteristic
874C22C2×#54211yescharacteristic
875C22C2×D4211yescharacteristic
876C22C2×#54711yescharacteristic
877C22C2×#54711yescharacteristic
878C22C2×#55311yescharacteristic
879C22#348412yes—
880C22#348912yes—
881C22#349212yes—
882C22#349212yes—
883C22#349212yes—
884C22#349412yes—
885C22#349412yes—
886C22#349811yescharacteristic
887C22#350011yescharacteristic
888C22#350612yes—
889C22#354312yes—
890C22#355212yes—
891C22#355912yes—
892C22#356112yes—
893C4—24no—
894C4—24no—
895C4—44no—
896C4—44no—
897C4—42no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4#242218yes—
909C2—44no—
910C2—44no—
911C2—84no—
912C2C2×#242211yescharacteristic
913C2#3522711yescharacteristic
914C2#3553111yescharacteristic
915C2#3592312yes—
916C2#3767411yescharacteristic
917C2#3767611yescharacteristic
918C2#3786211yescharacteristic
919C2#3786411yescharacteristic
920C2#4251412yes—
921C2#4492212yes—
922C2#4525512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2535C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2504C2semidirect
3. C2×#2501C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. #16528C2semidirect
6. #15327C2semidirect
7. #15269C2semidirect
8. #15233C2semidirect
9. #15219C2semidirect
10. #15195C2semidirect
11. #15130C2semidirect
12. #14721C2semidirect
13. #14354C2semidirect
14. #13909C2semidirect
15. #13906C2semidirect
16. #13881C2semidirect
17. #13880C2semidirect
18. #13847C2semidirect
19. #13785C2semidirect
174. #390D4semidirect
653. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#25042
C2×#25012
C2×D4×C4⋊C42
#165282
#153272
#152692
#152332
#152192
#151952
#151302
#147212
#143542
#139092
#139062
#138812
#138802
#138472
#137852