Finite Group Databasebeta

← #674638

Subgroups — #674638

Order 512.

3410 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×#2352C211yesmaximal, characteristic, complemented
5#15649C214yesmaximal, complemented
6#15611C214yesmaximal, complemented
7#15219C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#14778C214yesmaximal, complemented
12#14708C211yesmaximal, characteristic, complemented
13#14153C211yesmaximal, characteristic, complemented
14#14139C211yesmaximal, characteristic, complemented
15#14136C211yesmaximal, characteristic, complemented
16#14095C214yesmaximal, complemented
17#13909C211yesmaximal, characteristic, complemented
18C4×#384C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×#123C2214yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2540—28no—
30#2501—28no—
31#2499—28no—
32C2×#399C2212yes—
33C2×#399C2214yes—
34C2×#397C2214yes—
35C2×#394C2214yes—
36C2×#392C2212yes—
37#2352—28no—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#388C2212yes—
50C2×#387C2214yes—
51C2×#387C2212yes—
52C2×#386C2212yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2214yes—
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C43C2211yescharacteristic
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2212yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85#1437C2214yes—
86#1437C2212yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2212yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#124—24no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#123—216no—
107C2×#123—216no—
108C2×#123—48no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—42no—
120C2×#121—42no—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4D418yes—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—42no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—42no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2311yescharacteristic
173#399—216no—
174#399—28no—
175#397—216no—
176#394—48no—
177#392—28no—
178#391—24no—
179#391—24no—
180#391—42no—
181#391—42no—
182#390—24no—
183#390—28no—
184#390—28no—
185#390—28no—
186#390—24no—
187#390—42no—
188#390—42no—
189#388—28no—
190#387—28no—
191#387—216no—
192#386—28no—
193#384—24no—
194#384—24no—
195#384D418yescomplemented
196#382—24no—
197#382—24no—
198#380—24no—
199#380—24no—
200C4×C4⋊C4—24no—
201C4×C4⋊C4—24no—
202C4×C4⋊C4—24no—
203C4×C4⋊C4—48no—
204C4×C22⋊C4—28no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—42no—
208C4×C22⋊C4—42no—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C43—24no—
230C25C2412yes—
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—28no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4C2×D414yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—28no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—44no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297#124—416no—
298#123—464no—
299C22⋊Q8—416no—
300C22⋊Q8—416no—
301#121—416no—
302#121—416no—
303C4×D4—232no—
304#117—416no—
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—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—22no—
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—24no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—416no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D4116yes—
347C2×C4⋊C4#4114yes—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
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—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4C2×D414yes—
402C2×C22⋊C4#4118yes—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—44no—
426C2×C42—44no—
427C2×C42C2×D414yes—
428C2×C42C2×D414yes—
429C2×C42#4114yes—
430C2×C42#4114yes—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—28no—
441#95—28no—
442#95—24no—
443#95—44no—
444#95—42no—
445#95—42no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—24no—
475C24—22no—
476C24—24no—
477C24—22no—
478C24—22no—
479C24—24no—
480C24—24no—
481C24C22×D412yes—
482C24C22×D412yes—
483C24C2×#4114yes—
484C24C2511yescharacteristic
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—44no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—416no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—88no—
510C2×D4—84no—
511C2×D4—84no—
512C2×D4—88no—
513C2×D4—88no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—48no—
594C22×C4—416no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—48no—
604C22×C4—84no—
605C22×C4—88no—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D414yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4H(5,𝔽2)14yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C42−1+414yes—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—232no—
633C4⋊C4—28no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—416no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—216no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—416no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—416no—
659C22⋊C4—88no—
660C22⋊C4—84no—
661C22⋊C4—88no—
662C42—216no—
663C42—28no—
664C42—48no—
665C42—48no—
666C42—44no—
667C42—44no—
668C42—44no—
669C42—84no—
670C42—84no—
671C42#123116yescomplemented
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—44no—
727C23—44no—
728C23—42no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—42no—
733C23—42no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23#53214yes—
741C23C23×D411yescharacteristic
742C23C23×D411yescharacteristic
743C23C22×#4111yescharacteristic
744C23C22×#4111yescharacteristic
745C23C22×#4112yes—
746C23C22×#4111yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)11yescharacteristic
749C23C2×H(5,𝔽2)12yes—
750C23C2×2−1+412yes—
751C23#58512yes—
752Q8—88no—
753D4—416no—
754D4—816no—
755D4—816no—
756D4—88no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—416no—
815C2×C4—416no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—816no—
846C2×C4C2×#12314yes—
847C2×C4C2×#12314yes—
848C2×C4C2×#12314yes—
849C2×C4#53214yes—
850C2×C4#54014yes—
851C2×C4D4214yes—
852C2×C4#54618yes—
853C2×C4#54614yes—
854C2×C4#55014yes—
855C2×C4#55914yes—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—44no—
860C22—42no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—44no—
866C22—44no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—84no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—84no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—84no—
887C22—82no—
888C22—84no—
889C22C22×#12311yescharacteristic
890C22C2×#53211yescharacteristic
891C22C2×#53211yescharacteristic
892C22#344911yescharacteristic
893C22C2×#54011yescharacteristic
894C22C2×D4211yescharacteristic
895C22C2×#54612yes—
896C22C2×#54611yescharacteristic
897C22C2×#55011yescharacteristic
898C22#347512yes—
899C22#347512yes—
900C22C2×#55911yescharacteristic
901C22#348212yes—
902C22#349212yes—
903C22#349712yes—
904C22#349811yescharacteristic
905C22#349911yescharacteristic
906C22#350812yes—
907C22#351112yes—
908C22#351312yes—
909C22#352012yes—
910C22#354612yes—
911C22#356112yes—
912C4—28no—
913C4—24no—
914C4—24no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4—44no—
919C4—42no—
920C4—42no—
921C4—44no—
922C4—82no—
923C4—82no—
924C4—82no—
925C4—82no—
926C4—82no—
927C4#244518yes—
928C2—44no—
929C2—82no—
930C2—162no—
931C2C2×#244511yescharacteristic
932C2#3481011yescharacteristic
933C2#3553011yescharacteristic
934C2#3612111yescharacteristic
935C2#3637611yescharacteristic
936C2#3642412yes—
937C2#3894511yescharacteristic
938C2#3935611yescharacteristic
939C2#3992612yes—
940C2#5941012yes—
941C2#5964312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2540C2
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×#2499C2semidirect
3. C2×#2501C2semidirect
4. C2×#2352C2semidirect
5. #15649C2semidirect
6. #15611C2semidirect
7. #15219C2semidirect
8. #15182C2semidirect
9. #15182C2semidirect
10. #15130C2semidirect
11. #14778C2semidirect
12. #14708C2semidirect
13. #14153C2semidirect
14. #14139C2semidirect
15. #14136C2semidirect
16. #14095C2semidirect
17. #13909C2semidirect
18. C4×#384C2semidirect
19. C4×#390C2semidirect
195. #384D4semidirect
671. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#24992
C2×#25012
C2×#23522
#156492
#156112
#152192
#151822
#151302
#147782
#147082
#141532
#141392
#141362
#140952
#139092
C4×#3842
C4×#3902