Finite Group Databasebeta

← #873692

Subgroups — #873692

Order 512.

3150 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2542C211yesmaximal, characteristic
3C2×#2502C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic
5#16521C214yesmaximal, complemented
6#15766C214yesmaximal, complemented
7#15292C214yesmaximal, complemented
8#15190C211yesmaximal, characteristic, complemented
9#15188C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14407C214yesmaximal
16#14139C211yesmaximal, characteristic, complemented
17#14048C211yesmaximal, characteristic, complemented
18#14000C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C42C2211yescharacteristic
32#2857—28no—
33#2542—28no—
34#2502—28no—
35#2417—28no—
36C2×#399C2212yes—
37C2×#399C2212yes—
38C2×#398C2212yes—
39C2×#398C2214yes—
40C2×#396C2212yes—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2212yes—
51C2×#389C2214yes—
52C2×#389C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#385C2214yes—
56C2×#384C2211yescharacteristic
57C2×#384C2212yes—
58C2×#384C2211yescharacteristic
59C2×#380C2214yes—
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×C4⋊Q8—42no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—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—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×C4×D4—42no—
131C2×C4×D4—42no—
132C2×C4×D4D418yes—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—42no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C42—24no—
169C22×C42—42no—
170C22×C42—42no—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2312yes—
177C22×C42C2312yes—
178#399—28no—
179#399—28no—
180#398—28no—
181#398—216no—
182#396—28no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—42no—
190#391—42no—
191#391—42no—
192#390—28no—
193#389—216no—
194#389—24no—
195#386—28no—
196#386Q8116yescomplemented
197#385—216no—
198#384—24no—
199#384—28no—
200#384D418yescomplemented
201#380—24no—
202#380—216no—
203#380—28no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—42no—
207C4×C22⋊C4—42no—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
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×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×D4—41no—
256C22×D4—41no—
257C22×D4—42no—
258C22×D4C2×D414yes—
259C22×D4C2×Q818yes—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
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—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×Q818yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C4⋊Q8—416no—
304C4⋊Q8—416no—
305C4⋊Q8—416no—
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308C22⋊Q8—416no—
309C22⋊Q8—416no—
310C22⋊Q8—416no—
311C22⋊Q8—416no—
312C4×D4—416no—
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—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
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—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D4116yes—
372C2×C4⋊C4#4114yes—
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—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×Q818yes—
406C2×C22⋊C4C2×Q818yes—
407C2×C22⋊C4C2×Q818yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—416no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—44no—
427C2×C42C2×D414yes—
428C2×C42C2×D414yes—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—28no—
433#95—28no—
434#95—24no—
435#95—28no—
436#95—28no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—24no—
441#95—28no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95C2×Q818yes—
452#95C2×Q818yes—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C22×D412yes—
472C24C22×D412yes—
473C24C22×Q814yes—
474C24C22×Q814yes—
475C24C2511yescharacteristic
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
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×D4—44no—
498C2×D4—44no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4C4⋊Q8116yescomplemented
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
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—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—216no—
562C22×C4—22no—
563C22×C4—22no—
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—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—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—88no—
610C22×C4—84no—
611C22×C4—88no—
612C22×C4C22×D412yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×Q814yes—
622C22×C4C22×Q814yes—
623C22×C4C22×Q814yes—
624C22×C4C22×Q814yes—
625C22×C4C22×Q814yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4112yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C42−1+414yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—416no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—416no—
647C4⋊C4—48no—
648C4⋊C4—416no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—88no—
652C4⋊C4—84no—
653C22⋊C4—216no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—84no—
665C42—28no—
666C42—28no—
667C42—48no—
668C42—48no—
669C42—44no—
670C42—44no—
671C42—44no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
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—
716C23C2×C4⋊Q814yes—
717C23C2×C4⋊Q814yes—
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C23×Q812yes—
721C23C22×#4111yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×2−1+412yes—
727C23#58512yes—
728C23#58512yes—
729Q8—88no—
730Q8—88no—
731Q8—88no—
732D4—416no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
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—28no—
767C2×C4—432no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—416no—
800C2×C4—416no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
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—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—816no—
833C2×C4C2×C4⋊Q814yes—
834C2×C4#53414yes—
835C2×C4#53514yes—
836C2×C4#54014yes—
837C2×C4D4214yes—
838C2×C4#54614yes—
839C2×C4D4×Q818yes—
840C2×C4#55014yes—
841C2×C4#56014yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22C22×C4⋊Q811yescharacteristic
865C22C2×#53411yescharacteristic
866C22C2×#53511yescharacteristic
867C22#344911yescharacteristic
868C22C2×#54011yescharacteristic
869C22C2×D4211yescharacteristic
870C22C2×#54611yescharacteristic
871C22C2×D4×Q812yes—
872C22C2×#55011yescharacteristic
873C22Q8×#4112yes—
874C22#348512yes—
875C22#349911yescharacteristic
876C22#350011yescharacteristic
877C22#350112yes—
878C22#350112yes—
879C22#350112yes—
880C22#350312yes—
881C22#351512yes—
882C22C2×#56011yescharacteristic
883C22#354112yes—
884C22#354112yes—
885C22#354712yes—
886C22#356212yes—
887C4—28no—
888C4—24no—
889C4—42no—
890C4—44no—
891C4—44no—
892C4—42no—
893C4—42no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#267318yes—
904C2—44no—
905C2—44no—
906C2#3501111yescharacteristic
907C2D4×C4⋊Q811yescharacteristic
908C2#3627611yescharacteristic
909C2#3738811yescharacteristic
910C2#3768211yescharacteristic
911C2#3808811yescharacteristic
912C2#3959412yes—
913C2#3965612yes—
914C2#4549712yes—
915C2C2×#267311yescharacteristic
916C2#5905212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2857C2semidirect
3. C2×#2502C2semidirect
5. #16521C2semidirect
6. #15766C2semidirect
7. #15292C2semidirect
8. #15190C2semidirect
9. #15188C2semidirect
10. #15182C2semidirect
11. #15178C2semidirect
12. #15178C2semidirect
13. #15178C2semidirect
14. #14702C2semidirect
16. #14139C2semidirect
17. #14048C2semidirect
18. #14000C2semidirect
196. #386Q8semidirect
200. #384D4semidirect
501. C2×D4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25422
C2×#25022
C2×#24172
#165212
#157662
#152922
#151902
#151882
#151822
#151782
#147022
#144072
#141392
#140482
#140002
C4×#3862