Finite Group Databasebeta

← #674687

Subgroups — #674687

Order 512.

3352 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×#2352C211yesmaximal, characteristic, complemented
5#15641C214yesmaximal, complemented
6#15611C214yesmaximal, complemented
7#15219C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15195C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#14743C214yesmaximal, complemented
12#14687C211yesmaximal, characteristic, complemented
13#14096C214yesmaximal, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13909C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18C4×#390C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic, complemented
20C22×#123C2214yes—
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2535—28no—
28#2501—28no—
29#2500—28no—
30C2×#399C2214yes—
31C2×#397C2212yes—
32C2×#397C2214yes—
33C2×#394C2214yes—
34C2×#392C2212yes—
35#2352—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#388C2214yes—
42C2×#388C2212yes—
43C2×#387C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2214yes—
67C2×C43C2211yescharacteristic
68#1445C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2212yes—
80#1437C2214yes—
81#1437C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×#123—216no—
104C2×#123—216no—
105C2×#123—48no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C2×#121—42no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4D418yes—
118C2×#117—24no—
119C2×#117—24no—
120C2×#117—42no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164#399—216no—
165#397—28no—
166#397—48no—
167#394—216no—
168#392—28no—
169#390—24no—
170#390—24no—
171#390—28no—
172#390—24no—
173#390D418yescomplemented
174#388—28no—
175#388—216no—
176#387—28no—
177#386—28no—
178#386—28no—
179#386—28no—
180#384—24no—
181#384—24no—
182#384—24no—
183#382—24no—
184#382—24no—
185#382—24no—
186#382—42no—
187#382—42no—
188#380—24no—
189#380—24no—
190#380—24no—
191#380—24no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—24no—
194C4×C22⋊C4—28no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—48no—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C43—24no—
224C25C2411yescharacteristic
225C25C2412yes—
226C25C2411yescharacteristic
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—28no—
232C22×D4—24no—
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—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4C2×D414yes—
248C22×D4C2×D414yes—
249C23×C4—22no—
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—24no—
262C23×C4—28no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289#123—464no—
290#121—416no—
291#121—416no—
292C4×D4—232no—
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—24no—
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—22no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—416no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
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—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D4116yes—
384C2×C22⋊C4#4118yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—44no—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408C2×C42#4114yes—
409C2×C42#4114yes—
410C2×C42#4114yes—
411#95—24no—
412#95—24no—
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—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—21no—
456C24—22no—
457C24—21no—
458C24—22no—
459C24—24no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24C22×D414yes—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2511yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—416no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
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—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—48no—
570C22×C4—416no—
571C22×C4—416no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—88no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—88no—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4H(5,𝔽2)14yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C42−1+412yes—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—416no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—416no—
619C4⋊C4—44no—
620C4⋊C4—88no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—232no—
624C22⋊C4—216no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—88no—
638C22⋊C4—84no—
639C42—28no—
640C42—28no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—44no—
645C42—44no—
646C42—84no—
647C42#123116yescomplemented
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—28no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—28no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—44no—
706C23—42no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—44no—
714C23—42no—
715C23—44no—
716C23#53214yes—
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C22×#4112yes—
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)12yes—
725C23C2×2−1+411yescharacteristic
726C23#58512yes—
727C23#58512yes—
728D4—416no—
729D4—416no—
730D4—816no—
731D4—816no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—416no—
780C2×C4—416no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—816no—
819C2×C4—816no—
820C2×C4C2×#12314yes—
821C2×C4C2×#12314yes—
822C2×C4C2×#12314yes—
823C2×C4#53214yes—
824C2×C4#54214yes—
825C2×C4D4214yes—
826C2×C4#54618yes—
827C2×C4#54714yes—
828C2×C4#54714yes—
829C2×C4#55314yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—42no—
844C22—48no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—48no—
849C22—42no—
850C22—44no—
851C22—42no—
852C22—42no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—82no—
858C22—82no—
859C22—84no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22C22×#12311yescharacteristic
864C22C2×#53211yescharacteristic
865C22C2×#53211yescharacteristic
866C22#344911yescharacteristic
867C22C2×#54211yescharacteristic
868C22C2×D4211yescharacteristic
869C22C2×#54612yes—
870C22C2×#54711yescharacteristic
871C22C2×#54711yescharacteristic
872C22C2×#55311yescharacteristic
873C22#347512yes—
874C22#347512yes—
875C22#347512yes—
876C22#349412yes—
877C22#349811yescharacteristic
878C22#350012yes—
879C22#350011yescharacteristic
880C22#350612yes—
881C22#350612yes—
882C22#350812yes—
883C22#351512yes—
884C22#355912yes—
885C22#356212yes—
886C4—28no—
887C4—24no—
888C4—24no—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—44no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4#242218yes—
902C2—44no—
903C2—84no—
904C2—82no—
905C2C2×#242211yescharacteristic
906C2#3481011yescharacteristic
907C2#3553111yescharacteristic
908C2#3612111yescharacteristic
909C2#3618411yescharacteristic
910C2#3641512yes—
911C2#3935711yescharacteristic
912C2#3948311yescharacteristic
913C2#4000312yes—
914C2#5930712yes—
915C2#5931812yes—
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×#2500C2semidirect
3. C2×#2501C2semidirect
4. C2×#2352C2semidirect
5. #15641C2semidirect
6. #15611C2semidirect
7. #15219C2semidirect
8. #15219C2semidirect
9. #15195C2semidirect
10. #15150C2semidirect
11. #14743C2semidirect
12. #14687C2semidirect
13. #14096C2semidirect
14. #13941C2semidirect
15. #13909C2semidirect
16. #13881C2semidirect
17. #13879C2semidirect
18. C4×#390C2semidirect
19. C4×#390C2semidirect
173. #390D4semidirect
647. 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×#25002
C2×#25012
C2×#23522
#156412
#156112
#152192
#151952
#151502
#147432
#146872
#140962
#139412
#139092
#138812
#138792
C4×#3902