Finite Group Databasebeta

← #946655

Subgroups — #946655

Order 512.

2888 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3#17188C214yesmaximal, complemented
4#16319C214yesmaximal, complemented
5#16285C214yesmaximal, complemented
6#15277C214yesmaximal, complemented
7#15234C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#15134C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic, complemented
13#14276C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14137C211yesmaximal, characteristic, complemented
16#13924C211yesmaximal, characteristic, complemented
17#13881C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13847C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2487—28no—
27#2416—28no—
28C2×#400C2212yes—
29C2×#399C2212yes—
30C2×#397C2214yes—
31C2×#396C2212yes—
32C2×#396C2214yes—
33C2×#394C2212yes—
34C2×#394C2214yes—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#385C2212yes—
47C2×#385C2214yes—
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×#376C2211yescharacteristic
62#1445C2212yes—
63#1445C2214yes—
64#1445C2214yes—
65#1444C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2212yes—
81#1438C2214yes—
82#1438C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×#121—28no—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—48no—
106C2×#121—42no—
107C2×#121—42no—
108C2×#121—42no—
109C2×C4×D4—42no—
110C2×C4×D4—42no—
111C2×C4×D4D418yes—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#400—28no—
158#399—28no—
159#397—48no—
160#396—28no—
161#396—48no—
162#394—28no—
163#394—48no—
164#390—24no—
165#390—24no—
166#390—42no—
167#390—42no—
168#390—42no—
169#389—24no—
170#389—24no—
171#389—24no—
172#386—28no—
173#386—28no—
174#386—48no—
175#385—28no—
176#385—48no—
177#384—24no—
178#384—42no—
179#382—42no—
180#382—42no—
181#380—24no—
182#380—24no—
183#380—24no—
184#380—24no—
185C4×C4⋊C4—42no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—42no—
189C4×C22⋊C4—42no—
190#376—42no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—41no—
233C22×D4—41no—
234C22×D4—42no—
235C22×D4—44no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—44no—
239C22×D4C2×D414yes—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280#121—416no—
281#121—416no—
282#121—432no—
283C4×D4—416no—
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—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—416no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4#4114yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
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—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
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—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42C2×D414yes—
393C2×C42#4114yes—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—24no—
447C24C22×D412yes—
448C24C22×D412yes—
449C24H(5,𝔽2)14yes—
450C242−1+414yes—
451C24C2511yescharacteristic
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—44no—
455C2×D4—48no—
456C2×D4—416no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—84no—
471C2×D4—88no—
472C2×D4—88no—
473C2×D4—88no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
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—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—48no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—88no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4H(5,𝔽2)14yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C42−1+412yes—
592C4⋊C4—28no—
593C4⋊C4—44no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—84no—
605C4⋊C4—84no—
606C4⋊C4—88no—
607C4⋊C4—88no—
608C22⋊C4—216no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—88no—
620C22⋊C4—84no—
621C22⋊C4—88no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C42—28no—
627C42—28no—
628C42—44no—
629C42—44no—
630C42—44no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23#53514yes—
699C23#53614yes—
700C23C23×D411yescharacteristic
701C23C22×#4111yescharacteristic
702C23C22×#4111yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)12yes—
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×H(5,𝔽2)12yes—
708C23C2×2−1+412yes—
709C23C2×2−1+411yescharacteristic
710C23#58512yes—
711D4—416no—
712D4—816no—
713D4—816no—
714D4—88no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—416no—
759C2×C4—416no—
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—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—816no—
805C2×C4—816no—
806C2×C4#53414yes—
807C2×C4#54014yes—
808C2×C4#54214yes—
809C2×C4#54614yes—
810C2×C4#54714yes—
811C2×C4#55314yes—
812C2×C4#56214yes—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—84no—
837C22—82no—
838C22—84no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—84no—
844C22—82no—
845C22—82no—
846C22C2×#53411yescharacteristic
847C22C2×#53511yescharacteristic
848C22C2×#53611yescharacteristic
849C22C2×#54011yescharacteristic
850C22C2×#54211yescharacteristic
851C22C2×#54611yescharacteristic
852C22C2×#54711yescharacteristic
853C22C2×#55311yescharacteristic
854C22#349212yes—
855C22#349412yes—
856C22#349811yescharacteristic
857C22#350011yescharacteristic
858C22#351612yes—
859C22#351912yes—
860C22C2×#56211yescharacteristic
861C22#353612yes—
862C22#353612yes—
863C22#353712yes—
864C22#354112yes—
865C22#354212yes—
866C22#354612yes—
867C22#355212yes—
868C22#355912yes—
869C4—44no—
870C4—44no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—44no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4#270118yes—
885C2—44no—
886C2—44no—
887C2—162no—
888C2#3730011yescharacteristic
889C2#3745111yescharacteristic
890C2#3786211yescharacteristic
891C2#3786411yescharacteristic
892C2#3808011yescharacteristic
893C2#3808311yescharacteristic
894C2#4250812yes—
895C2#4261312yes—
896C2#4537312yes—
897C2C2×#270111yescharacteristic
898C2#5296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2487C2semidirect
3. #17188C2semidirect
4. #16319C2semidirect
5. #16285C2semidirect
6. #15277C2semidirect
7. #15234C2semidirect
8. #15219C2semidirect
9. #15219C2semidirect
10. #15150C2semidirect
11. #15134C2semidirect
12. #15130C2semidirect
13. #14276C2semidirect
14. #14260C2semidirect
15. #14137C2semidirect
16. #13924C2semidirect
17. #13881C2semidirect
18. #13880C2semidirect
19. #13847C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#24162
#171882
#163192
#162852
#152772
#152342
#152192
#151502
#151342
#151302
#142762
#142602
#141372
#139242
#138812
#138802
#138472