Finite Group Databasebeta

← #945561

Subgroups — #945561

Order 512.

3052 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2414C211yesmaximal, characteristic
4C2×#2620C211yesmaximal, characteristic, complemented
5#17123C214yesmaximal, complemented
6#16530C214yesmaximal, complemented
7#16277C214yesmaximal, complemented
8#15396C214yesmaximal, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic, complemented
13#15215C211yesmaximal, characteristic, complemented
14#15188C211yesmaximal, characteristic, complemented
15#14258C211yesmaximal, characteristic, complemented
16#14138C211yesmaximal, characteristic, complemented
17#14048C211yesmaximal, characteristic, complemented
18#14002C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32#2620—28no—
33#2542—28no—
34#2499—28no—
35#2414—28no—
36C2×#399C2212yes—
37C2×#399C2212yes—
38C2×#397C2214yes—
39C2×#396C2214yes—
40C2×#394C2214yes—
41C2×#394C2212yes—
42C2×#392C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2212yes—
52C2×#390C2211yescharacteristic
53C2×#390C2212yes—
54C2×#389C2211yescharacteristic
55C2×#388C2212yes—
56C2×#387C2214yes—
57C2×#384C2212yes—
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1442C2214yes—
66#1442C2214yes—
67#1441C2212yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2212yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1438C2212yes—
83#1438C2214yes—
84#1438C2214yes—
85#1438C2214yes—
86#1437C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—42no—
105C2×C4⋊Q8—42no—
106C2×#124—24no—
107C2×#124—42no—
108C2×#124—42no—
109C2×#124—42no—
110C2×#124—42no—
111C2×#124—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—42no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121—24no—
127C2×#121—42no—
128C2×#121—42no—
129C2×#121—42no—
130C2×C4×D4—42no—
131C2×C4×D4—42no—
132C2×C4×D4D418yes—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—42no—
137C2×#117—42no—
138C2×#117—42no—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181#399—28no—
182#399—28no—
183#397—216no—
184#396—216no—
185#394—216no—
186#394—28no—
187#392—28no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—42no—
192#391—42no—
193#391—42no—
194#390—28no—
195#390—24no—
196#390—24no—
197#390—28no—
198#390—24no—
199#389—24no—
200#388—28no—
201#387—216no—
202#384—28no—
203#384D418yescomplemented
204#382—24no—
205#380—24no—
206C4×C4⋊C4—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—42no—
209C4×C22⋊C4—42no—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—41no—
260C22×D4—41no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4C2×D414yes—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C4⋊Q8—416no—
301#124—416no—
302#124—416no—
303C22⋊Q8—416no—
304C22⋊Q8—416no—
305C22⋊Q8—416no—
306C22⋊Q8—416no—
307#121—416no—
308#121—416no—
309C4×D4—416no—
310#117—416no—
311#117—416no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
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—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D4116yes—
355C2×C4⋊C4#4114yes—
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—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×D414yes—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—42no—
430C2×C42—44no—
431C2×C42C2×D414yes—
432C2×C42C2×D414yes—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—24no—
440#95—28no—
441#95—24no—
442#95—24no—
443#95—44no—
444#95—42no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—44no—
452#95—44no—
453#95—44no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—24no—
482C24—24no—
483C24—24no—
484C24—24no—
485C24C22×D412yes—
486C24C22×D412yes—
487C24C2511yescharacteristic
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×D4—28no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—88no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4—84no—
521C2×D4—88no—
522C2×D4—88no—
523C2×D4—88no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
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—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
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—22no—
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—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D412yes—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4112yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+414yes—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—416no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—84no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—416no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—416no—
666C22⋊C4—48no—
667C22⋊C4—88no—
668C22⋊C4—84no—
669C22⋊C4—88no—
670C22⋊C4—84no—
671C42—28no—
672C42—28no—
673C42—48no—
674C42—48no—
675C42—44no—
676C42—44no—
677C42—44no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—41no—
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—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—42no—
735C23—42no—
736C23—44no—
737C23—44no—
738C23—42no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C22×#4111yescharacteristic
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)11yescharacteristic
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)11yescharacteristic
754C23C2×2−1+412yes—
755C23#58512yes—
756C23#58512yes—
757C23#58512yes—
758Q8—88no—
759Q8—88no—
760D4—416no—
761D4—816no—
762D4—816no—
763D4—88no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—416no—
810C2×C4—416no—
811C2×C4—42no—
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—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4#53414yes—
857C2×C4#53514yes—
858C2×C4#53614yes—
859C2×C4#54014yes—
860C2×C4D4214yes—
861C2×C4#54614yes—
862C2×C4#55014yes—
863C2×C4#56014yes—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—84no—
888C22—82no—
889C22—82no—
890C22—84no—
891C22—82no—
892C22—82no—
893C22—84no—
894C22—82no—
895C22—82no—
896C22—84no—
897C22C2×#53411yescharacteristic
898C22C2×#53511yescharacteristic
899C22C2×#53611yescharacteristic
900C22#344911yescharacteristic
901C22C2×#54011yescharacteristic
902C22C2×D4211yescharacteristic
903C22C2×#54611yescharacteristic
904C22C2×#55011yescharacteristic
905C22#348512yes—
906C22#349712yes—
907C22#350011yescharacteristic
908C22#350011yescharacteristic
909C22#351812yes—
910C22#352112yes—
911C22C2×#56011yescharacteristic
912C22#353912yes—
913C22#354012yes—
914C22#354112yes—
915C22#354112yes—
916C22#354712yes—
917C22#355112yes—
918C22#355412yes—
919C22#356212yes—
920C4—24no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—42no—
925C4—42no—
926C4—44no—
927C4—44no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4#267318yes—
936C2—82no—
937C2—82no—
938C2—162no—
939C2#3741911yescharacteristic
940C2#3744911yescharacteristic
941C2#3768211yescharacteristic
942C2#3809211yescharacteristic
943C2#3895811yescharacteristic
944C2#3936311yescharacteristic
945C2#4264312yes—
946C2#4271912yes—
947C2#4510112yes—
948C2C2×#267311yescharacteristic
949C2#5305112yes—
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×#2542C2semidirect
2. C2×#2499C2semidirect
4. C2×#2620C2semidirect
5. #17123C2semidirect
6. #16530C2semidirect
7. #16277C2semidirect
8. #15396C2semidirect
9. #15243C2semidirect
10. #15236C2semidirect
11. #15215C2semidirect
12. #15215C2semidirect
13. #15215C2semidirect
14. #15188C2semidirect
15. #14258C2semidirect
16. #14138C2semidirect
17. #14048C2semidirect
18. #14002C2semidirect
19. #13839C2semidirect
203. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#24992
C2×#24142
C2×#26202
#171232
#165302
#162772
#153962
#152432
#152362
#152152
#151882
#142582
#141382
#140482
#140022
#138392