Finite Group Databasebeta

← #617375

Subgroups — #617375

Order 512.

3260 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2621C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic
5C2×#2323C211yesmaximal, characteristic, complemented
6C2×#2296C211yesmaximal, characteristic, complemented
7#15620C214yesmaximal, complemented
8#15577C214yesmaximal, complemented
9#15447C214yesmaximal, complemented
10#15404C214yesmaximal, complemented
11#15237C211yesmaximal, characteristic, complemented
12#15222C211yesmaximal, characteristic, complemented
13#15217C211yesmaximal, characteristic, complemented
14#15180C211yesmaximal, characteristic, complemented
15#14702C211yesmaximal, characteristic, complemented
16#14257C211yesmaximal, characteristic
17#14153C211yesmaximal, characteristic, complemented
18#13926C211yesmaximal, characteristic, complemented
19#13911C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2850—28no—
31#2621—28no—
32#2620—28no—
33#2545—28no—
34C2×#398C2214yes—
35C2×#397C2214yes—
36C2×#396C2212yes—
37C2×#396C2214yes—
38C2×#396C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yes—
41#2323—28no—
42#2296—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2212yes—
55C2×#389C2212yes—
56C2×#389C2211yescharacteristic
57C2×#389C2212yes—
58C2×#388C2214yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#388C2214yes—
62C2×#387C2212yes—
63C2×#386C2214yes—
64C2×#385C2212yes—
65C2×#385C2212yes—
66C2×#384C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#382C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75#1443C2214yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1440C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1438C2214yes—
88#1437C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2214yes—
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C22⋊#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—42no—
106C2×#124—24no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—24no—
110C2×#124—24no—
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⋊Q8D418yes—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—42no—
129C2×#117D418yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—42no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176#398—216no—
177#397—216no—
178#396—28no—
179#396—28no—
180#396—216no—
181#394—28no—
182#394—28no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—42no—
190#390—24no—
191#390—24no—
192#390—24no—
193#390—42no—
194#389—28no—
195#389—28no—
196#389—24no—
197#389—28no—
198#388—216no—
199#388—28no—
200#388—28no—
201#388—216no—
202#387—28no—
203#386—216no—
204#385—28no—
205#385—28no—
206#384—24no—
207#382—24no—
208#382—24no—
209#380—24no—
210C4×C4⋊C4—24no—
211C4×C4⋊C4—24no—
212C4×C4⋊C4—24no—
213C4×C4⋊C4—24no—
214C4×C4⋊C4D418yescomplemented
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C25C2412yes—
238C25C2411yescharacteristic
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×Q8C2×D414yes—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—44no—
264C22×D4—44no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C4⋊Q8—416no—
297#124—416no—
298#124—416no—
299C22⋊Q8—232no—
300C22⋊Q8—416no—
301#121—416no—
302C4×Q8—416no—
303#117—232no—
304#117—416no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—22no—
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—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
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⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D418yes—
358C2×C4⋊C4C2×D418yes—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
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—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D414yes—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D418yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—416no—
420C2×C42—42no—
421C2×C42—44no—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426C2×C42C2×D414yes—
427C2×C42#4114yes—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95C2×D418yes—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—24no—
465C24—22no—
466C24—24no—
467C24—24no—
468C24—24no—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4112yes—
472C24C2511yescharacteristic
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
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×D4—416no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—84no—
497C2×D4—84no—
498C2×D4—88no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
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—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
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—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
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—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4#121116yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C42−1+414yes—
613C22×C42−1+412yes—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—216no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—416no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—84no—
631C4⋊C4—84no—
632C4⋊C4—84no—
633C22⋊C4—216no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—416no—
637C22⋊C4—416no—
638C22⋊C4—48no—
639C22⋊C4—416no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—88no—
648C42—28no—
649C42—28no—
650C42—28no—
651C42—48no—
652C42—48no—
653C42—44no—
654C42—44no—
655C42—84no—
656C42#121116yes—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23C2×#12114yes—
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C23×D411yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×2−1+411yescharacteristic
710C23C2×2−1+412yes—
711C23#58512yes—
712C23#58512yes—
713C23#58512yes—
714Q8—416no—
715Q8—88no—
716D4—816no—
717D4—88no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—232no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—432no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
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—42no—
783C2×C4—42no—
784C2×C4—44no—
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—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4C2×#12114yes—
812C2×C4C2×#12114yes—
813C2×C4C2×#12114yes—
814C2×C4C2×#12114yes—
815C2×C4C2×#12114yes—
816C2×C4#53714yes—
817C2×C4D4214yes—
818C2×C4#54714yes—
819C2×C4#54814yes—
820C2×C4#55314yes—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—82no—
833C22—82no—
834C22—84no—
835C22—82no—
836C22—84no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—84no—
841C22—84no—
842C22—82no—
843C22C22×#12111yescharacteristic
844C22C22×#12111yescharacteristic
845C22C2×#53711yescharacteristic
846C22#344912yes—
847C22#346112yes—
848C22C2×D4211yescharacteristic
849C22C2×#54711yescharacteristic
850C22C2×#54811yescharacteristic
851C22C2×#55311yescharacteristic
852C22#348712yes—
853C22#348912yes—
854C22#348912yes—
855C22#349911yescharacteristic
856C22#350011yescharacteristic
857C22#350011yescharacteristic
858C22#350011yescharacteristic
859C22#350712yes—
860C22#351012yes—
861C22#351212yes—
862C22#354012yes—
863C22#354112yes—
864C22#355512yes—
865C22#355712yes—
866C4—24no—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—44no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—44no—
875C4—42no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4#241618yes—
883C2—44no—
884C2—162no—
885C2C2×#241611yescharacteristic
886C2#3530811yescharacteristic
887C2#3532811yescharacteristic
888C2#3562111yescharacteristic
889C2#3567711yescharacteristic
890C2#3738911yescharacteristic
891C2#3742111yescharacteristic
892C2#3765912yes—
893C2#3779912yes—
894C2#3971912yes—
895C2#3982012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2545C2semidirect
3. C2×#2621C2semidirect
5. C2×#2323C2semidirect
6. C2×#2296C2semidirect
7. #15620C2semidirect
8. #15577C2semidirect
9. #15447C2semidirect
10. #15404C2semidirect
11. #15237C2semidirect
12. #15222C2semidirect
13. #15217C2semidirect
14. #15180C2semidirect
15. #14702C2semidirect
17. #14153C2semidirect
18. #13926C2semidirect
19. #13911C2semidirect
214. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#25452
C2×#26212
C2×#26202
C2×#23232
C2×#22962
#156202
#155772
#154472
#154042
#152372
#152222
#152172
#151802
#147022
#142572
#141532
#139262
#139112