Finite Group Databasebeta

← #4933565

Subgroups — #4933565

Order 512.

2518 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2734C211yesmaximal, characteristic, complemented
2C2×#2731C211yesmaximal, characteristic
3C2×#2545C211yesmaximal, characteristic
4C2×#2379C211yesmaximal, characteristic
5#16565C212yesmaximal, complemented
6#16518C212yesmaximal, complemented
7#16295C212yesmaximal, complemented
8#15823C212yesmaximal, complemented
9#15803C212yesmaximal
10#15590C212yesmaximal, complemented
11#15436C212yesmaximal, complemented
12#15426C212yesmaximal, complemented
13#15311C212yesmaximal
14#15075C212yesmaximal, complemented
15#14988C212yesmaximal, complemented
16#14972C212yesmaximal, complemented
17#14450C211yesmaximal, characteristic, complemented
18#14024C211yesmaximal, characteristic, complemented
19#13978C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25#2734—28no—
26#2731—28no—
27#2545—28no—
28C2×#398C2212yes—
29C2×#397C2212yes—
30C2×#396C2212yes—
31C2×#396C2212yes—
32C2×#396C2212yes—
33C2×#395C2212yes—
34C2×#395C2212yes—
35C2×#394C2212yes—
36C2×#393C2212yes—
37#2379—28no—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2211yescharacteristic
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#387C2212yes—
54C2×#387C2212yes—
55C2×#387C2212yes—
56C2×#386C2212yes—
57C2×#385C2212yes—
58C2×#385C2212yes—
59C2×#382C2212yes—
60C2×#382C2211yescharacteristic
61C2×#380C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63#1446C2212yes—
64#1445C2212yes—
65#1445C2212yes—
66#1444C2212yes—
67#1443C2212yes—
68#1443C2212yes—
69#1443C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1441C2212yes—
81#1441C2212yes—
82#1441C2212yes—
83#1441C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105#1434C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C4×#95C2211yescharacteristic
110C4×#95C2211yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×Q8C2311yescharacteristic
113C23×Q8C2311yescharacteristic
114C23×D4C2311yescharacteristic
115C24×C4C2312yes—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—42no—
126C2×#124—42no—
127C2×#124D418yes—
128C2×C4×Q8—24no—
129C2×C4×Q8—42no—
130C2×C4×Q8—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
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×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#398—28no—
172#397—44no—
173#396—28no—
174#396—28no—
175#396—28no—
176#395—28no—
177#395—28no—
178#394—28no—
179#393—28no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—42no—
184#391—42no—
185#391D418yes—
186#390—24no—
187#389—28no—
188#389—42no—
189#388—28no—
190#388—28no—
191#388—28no—
192#388—28no—
193#388—28no—
194#388—28no—
195#387—28no—
196#387—28no—
197#387—28no—
198#386—28no—
199#385—28no—
200#385—28no—
201#382—28no—
202#382—42no—
203#380—44no—
204C4×C4⋊C4—24no—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C25C2412yes—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—41no—
255C22×Q8—41no—
256C22×Q8—41no—
257C22×Q8—41no—
258C22×Q8—41no—
259C22×Q8—41no—
260C22×Q8—41no—
261C22×Q8—41no—
262C22×Q8—41no—
263C22×Q8—41no—
264C22×Q8—41no—
265C22×Q8—41no—
266C22×Q8C2×D414yes—
267C22×Q8C2×D414yes—
268C22×Q8#4114yes—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—41no—
272C22×D4—41no—
273C22×D4—41no—
274C22×D4—41no—
275C22×D4C2×D414yes—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C4⋊Q8—416no—
302C4⋊Q8—416no—
303#124—232no—
304#124—416no—
305C4×Q8—416no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
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—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
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—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
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—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×D414yes—
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—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
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—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
398C2×C22⋊C4C2×D418yes—
399C2×C42—22no—
400C2×C42—22no—
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—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—41no—
417C2×C42—41no—
418C2×C42—41no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—41no—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
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—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95C2×D418yes—
467#95C2×D418yes—
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—22no—
482C24C22×D414yes—
483C24C2511yescharacteristic
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—82no—
497C2×Q8—82no—
498C2×Q8—82no—
499C2×Q8—82no—
500C2×Q8—82no—
501C2×Q8—82no—
502C2×Q8—82no—
503C2×Q8—82no—
504C2×Q8#121116yes—
505C2×D4—28no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—82no—
511C2×D4—82no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
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—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—21no—
567C22×C4—21no—
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—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
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—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—48no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4112yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+414yes—
636C22×C42−1+414yes—
637C4⋊C4—216no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C22⋊C4—216no—
656C22⋊C4—216no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—84no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C22⋊C4—84no—
667C22⋊C4—84no—
668C42—28no—
669C42—28no—
670C42—44no—
671C42—44no—
672C42—44no—
673C42—44no—
674C42—44no—
675C42—82no—
676C42—82no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C22×#4111yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+412yes—
718C23C2×2−1+412yes—
719C23#58511yescharacteristic
720C23#58511yescharacteristic
721C23#58512yes—
722C23#58512yes—
723Q8—416no—
724Q8—88no—
725Q8—88no—
726D4—88no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
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—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
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—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—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
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—816no—
843C2×C4C2×#12114yes—
844C2×C4C2×#12114yes—
845C2×C4C2×#12114yes—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22C22×#12111yescharacteristic
862C22#348411yescharacteristic
863C22#348511yescharacteristic
864C22#348612yes—
865C22#348912yes—
866C22#348912yes—
867C22#349611yescharacteristic
868C22#349611yescharacteristic
869C22#350012yes—
870C22#350511yescharacteristic
871C22#350511yescharacteristic
872C22#351612yes—
873C22#351612yes—
874C22#352911yescharacteristic
875C22#354411yescharacteristic
876C22#354511yescharacteristic
877C22#354712yes—
878C22#355011yescharacteristic
879C22#355512yes—
880C22#355912yes—
881C22#356512yes—
882C22#356512yes—
883C22#356812yes—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—82no—
901C4—82no—
902C2—84no—
903C2#3535811yescharacteristic
904C2#3573712yes—
905C2#4622811yescharacteristic
906C2#4623711yescharacteristic
907C2#4626911yescharacteristic
908C2#4956712yes—
909C2#5002912yes—
910C2#5141412yes—
911C2#5153111yescharacteristic
912C2#5188211yescharacteristic
913C2#5207911yescharacteristic
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×#2734C2semidirect
5. #16565C2semidirect
6. #16518C2semidirect
7. #16295C2semidirect
8. #15823C2semidirect
10. #15590C2semidirect
11. #15436C2semidirect
12. #15426C2semidirect
14. #15075C2semidirect
15. #14988C2semidirect
16. #14972C2semidirect
17. #14450C2semidirect
18. #14024C2semidirect
19. #13978C2semidirect

Maximal subgroups

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

subgroupindex
C2×#27342
C2×#27312
C2×#25452
C2×#23792
#165652
#165182
#162952
#158232
#158032
#155902
#154362
#154262
#153112
#150752
#149882
#149722
#144502
#140242
#139782