Finite Group Databasebeta

← #946451

Subgroups — #946451

Order 512.

2856 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic, complemented
2C2×#2504C211yesmaximal, characteristic
3C2×#2426C211yesmaximal, characteristic
4C2×#2440C211yesmaximal, characteristic, complemented
5#17129C214yesmaximal, complemented
6#16295C214yesmaximal, complemented
7#16273C214yesmaximal, complemented
8#15280C214yesmaximal, complemented
9#15242C211yesmaximal, characteristic, complemented
10#15226C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic
12#15182C211yesmaximal, characteristic, complemented
13#15144C211yesmaximal, characteristic, complemented
14#15134C211yesmaximal, characteristic, complemented
15#14277C211yesmaximal, characteristic, complemented
16#14273C211yesmaximal, characteristic, complemented
17#14139C211yesmaximal, characteristic, complemented
18#13978C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2212yes—
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2568—28no—
28#2504—28no—
29#2440—28no—
30#2426—28no—
31C2×#400C2214yes—
32C2×#398C2212yes—
33C2×#397C2214yes—
34C2×#396C2212yes—
35C2×#396C2214yes—
36C2×#395C2212yes—
37C2×#394C2212yes—
38C2×#393C2214yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2214yes—
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2212yes—
54C2×#386C2214yes—
55C2×#385C2212yes—
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1445C2214yes—
68#1444C2214yes—
69#1443C2212yes—
70#1442C2212yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2212yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1438C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—42no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—42no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—48no—
111C2×C22⋊Q8—42no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—42no—
115C2×C4×Q8—24no—
116C2×C4×Q8—24no—
117C2×C4×Q8—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#400—216no—
161#398—28no—
162#397—216no—
163#396—28no—
164#396—48no—
165#395—28no—
166#394—28no—
167#393—48no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—216no—
172#391—42no—
173#390—24no—
174#390—28no—
175#390—24no—
176#390—24no—
177#390—42no—
178#390—42no—
179#389—24no—
180#389—24no—
181#389—24no—
182#388—28no—
183#386—216no—
184#385—28no—
185#384—24no—
186#384—42no—
187#382—24no—
188#382—24no—
189#382D418yes—
190#380—24no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—42no—
194C4×C22⋊C4D418yes—
195#376—42no—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2314yes—
222C25C2412yes—
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—28no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—42no—
234C22×Q8—44no—
235C22×Q8#4114yes—
236C22×D4—24no—
237C22×D4—28no—
238C22×D4—22no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4—44no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4C2×D414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C4⋊Q8—416no—
278#124—416no—
279C22⋊Q8—432no—
280C22⋊Q8—416no—
281#121—416no—
282C4×Q8—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—416no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4C2×D414yes—
369C2×C22⋊C4C2×D414yes—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42C2×D414yes—
389C2×C42C2×D414yes—
390C2×C42C2×D414yes—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—28no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—44no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95C2×D414yes—
415#95C2×D414yes—
416#95C2×D4116yes—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24C22×D412yes—
438C242−1+414yes—
439C24C2511yescharacteristic
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—48no—
444C2×Q8—416no—
445C2×Q8—48no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—84no—
451C2×Q8—88no—
452C2×D4—48no—
453C2×D4—416no—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—84no—
463C2×D4—88no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—88no—
556C22×C4—84no—
557C22×C4—88no—
558C22×C4C22×D414yes—
559C22×C4C22×D414yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)14yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C42−1+412yes—
574C22×C42−1+412yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—84no—
590C4⋊C4—84no—
591C4⋊C4—88no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—88no—
603C22⋊C4—88no—
604C22⋊C4—84no—
605C22⋊C4—88no—
606C22⋊C4—88no—
607C42—28no—
608C42—28no—
609C42—28no—
610C42—48no—
611C42—44no—
612C42—44no—
613C42—44no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—44no—
649C23—44no—
650C23—42no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23#53614yes—
660C23C23×D411yescharacteristic
661C23C23×D411yescharacteristic
662C23C22×#4111yescharacteristic
663C23C2×H(5,𝔽2)12yes—
664C23C2×H(5,𝔽2)11yescharacteristic
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23C2×2−1+411yescharacteristic
668C23C2×2−1+412yes—
669C23#58512yes—
670C23#58512yes—
671Q8—416no—
672Q8—816no—
673D4—816no—
674D4—88no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—416no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—816no—
768C2×C4#53514yes—
769C2×C4#53614yes—
770C2×C4#53714yes—
771C2×C4#53914yes—
772C2×C4D4214yes—
773C2×C4#54614yes—
774C2×C4#54814yes—
775C2×C4#56214yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—84no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—84no—
793C22—82no—
794C22—84no—
795C22—82no—
796C22—82no—
797C22—84no—
798C22C2×#53511yescharacteristic
799C22C2×#53611yescharacteristic
800C22C2×#53611yescharacteristic
801C22C2×#53711yescharacteristic
802C22C2×#53911yescharacteristic
803C22C2×D4211yescharacteristic
804C22C2×#54611yescharacteristic
805C22C2×#54811yescharacteristic
806C22#348812yes—
807C22#348912yes—
808C22#350011yescharacteristic
809C22#350011yescharacteristic
810C22#351612yes—
811C22#351712yes—
812C22C2×#56211yescharacteristic
813C22#354112yes—
814C22#354612yes—
815C22#355212yes—
816C22#355212yes—
817C22#355812yes—
818C22#356112yes—
819C22#356512yes—
820C22#356512yes—
821C4—24no—
822C4—42no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—42no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4#268118yes—
838C2—44no—
839C2—162no—
840C2#3742311yescharacteristic
841C2#3761511yescharacteristic
842C2#3767611yescharacteristic
843C2#3767711yescharacteristic
844C2#3808311yescharacteristic
845C2#3895611yescharacteristic
846C2#4283312yes—
847C2#4292812yes—
848C2#4531312yes—
849C2C2×#268111yescharacteristic
850C2#5297512yes—
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
1. C2×#2568C2semidirect
4. C2×#2440C2semidirect
5. #17129C2semidirect
6. #16295C2semidirect
7. #16273C2semidirect
8. #15280C2semidirect
9. #15242C2semidirect
10. #15226C2semidirect
12. #15182C2semidirect
13. #15144C2semidirect
14. #15134C2semidirect
15. #14277C2semidirect
16. #14273C2semidirect
17. #14139C2semidirect
18. #13978C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25682
C2×#25042
C2×#24262
C2×#24402
#171292
#162952
#162732
#152802
#152422
#152262
#152192
#151822
#151442
#151342
#142772
#142732
#141392
#139782
#138422