Finite Group Databasebeta

← #874298

Subgroups — #874298

Order 512.

3064 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×#2504C211yesmaximal, characteristic, complemented
2C2×#2420C211yesmaximal, characteristic, complemented
3#16386C214yesmaximal, complemented
4#15419C214yesmaximal, complemented
5#15285C214yesmaximal, complemented
6#15244C211yesmaximal, characteristic, complemented
7#15231C211yesmaximal, characteristic, complemented
8#15224C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15134C211yesmaximal, characteristic, complemented
11#15124C211yesmaximal, characteristic
12#14713C211yesmaximal, characteristic, complemented
13#14689C211yesmaximal, characteristic, complemented
14#14519C214yesmaximal, complemented
15#14137C211yesmaximal, characteristic, complemented
16#14025C211yesmaximal, characteristic, complemented
17#13941C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2504—28no—
26#2420—28no—
27C2×#397C2212yes—
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#396C2214yes—
31C2×#394C2212yes—
32C2×#392C2214yes—
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2214yes—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2214yes—
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#388C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#386C2214yes—
51C2×#385C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#381C2212yes—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C43C2211yescharacteristic
65#1444C2214yes—
66#1442C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2212yes—
80#1436C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87#1434C2214yes—
88#1434C2214yes—
89#1434C2212yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C23×D4C2314yes—
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×#127—24no—
102C2×#127—24no—
103C2×#127—42no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—42no—
108C2×#121—42no—
109C2×#121—42no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—42no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#397—28no—
156#397—28no—
157#397—28no—
158#396—48no—
159#394—28no—
160#392—216no—
161#390—24no—
162#390—24no—
163#390—24no—
164#390—48no—
165#390—42no—
166#390—42no—
167#390—42no—
168#390—42no—
169#390—42no—
170#390—42no—
171#390—48no—
172#389—24no—
173#388—28no—
174#386—28no—
175#386—28no—
176#386—28no—
177#386—48no—
178#386—48no—
179#385—48no—
180#384—42no—
181#384—42no—
182#382—24no—
183#382—24no—
184#382—24no—
185#382—42no—
186#381—28no—
187#380—24no—
188C4×C4⋊C4—42no—
189C4×C22⋊C4—24no—
190C4×C22⋊C4—42no—
191C4×C22⋊C4D418yescomplemented
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C43—24no—
217C25C2412yes—
218C25C2412yes—
219C25C2411yescharacteristic
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—28no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4#4114yes—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4C2×D414yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284#127—416no—
285#121—416no—
286#121—416no—
287C4×D4—416no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
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—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—416no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
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—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
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⋊C4—44no—
369C2×C22⋊C4C2×D414yes—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4#4118yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—42no—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42#4114yes—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—24no—
410#95—28no—
411#95—44no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95C2×D414yes—
419#95C2×D414yes—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—24no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—22no—
440C24—24no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—22no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24C22×D412yes—
451C24C2×#4114yes—
452C24C2×#4114yes—
453C24C2511yescharacteristic
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—416no—
458C2×D4—416no—
459C2×D4—416no—
460C2×D4—48no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—416no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—88no—
479C2×D4—88no—
480C2×D4—88no—
481C2×D4—84no—
482C2×D4—88no—
483C2×D4—88no—
484C2×D4—88no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
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—24no—
562C22×C4—24no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—84no—
571C22×C4—88no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—88no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)14yes—
589C22×C4H(5,𝔽2)14yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C42−1+412yes—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—88no—
603C4⋊C4—84no—
604C4⋊C4—88no—
605C22⋊C4—28no—
606C22⋊C4—216no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—88no—
619C22⋊C4—88no—
620C22⋊C4—88no—
621C22⋊C4—88no—
622C22⋊C4—84no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C42—28no—
626C42—28no—
627C42—28no—
628C42—48no—
629C42—44no—
630C42—44no—
631C42—48no—
632C42—44no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—28no—
649C23—28no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—44no—
666C23—44no—
667C23—42no—
668C23—42no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23#53214yes—
702C23C23×D411yescharacteristic
703C23C22×#4112yes—
704C23C22×#4111yescharacteristic
705C23C22×#4111yescharacteristic
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)12yes—
710C23C2×H(5,𝔽2)12yes—
711C23C2×2−1+411yescharacteristic
712C23#58512yes—
713D4—416no—
714D4—832no—
715D4—816no—
716D4—816no—
717D4—88no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
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—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—416no—
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—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—816no—
804C2×C4—816no—
805C2×C4#53514yes—
806C2×C4#53914yes—
807C2×C4#54014yes—
808C2×C4#54614yes—
809C2×C4#54714yes—
810C2×C4#55114yes—
811C2×C4#55318yes—
812C2×C4#56214yes—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—42no—
817C22—44no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—48no—
827C22—44no—
828C22—48no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—84no—
833C22—84no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—84no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—84no—
843C22—84no—
844C22—84no—
845C22—82no—
846C22C2×#53211yescharacteristic
847C22C2×#53511yescharacteristic
848C22#344911yescharacteristic
849C22C2×#53911yescharacteristic
850C22C2×#54011yescharacteristic
851C22C2×#54611yescharacteristic
852C22C2×#54711yescharacteristic
853C22C2×#55111yescharacteristic
854C22C2×#55312yes—
855C22#348112yes—
856C22#349412yes—
857C22#349811yescharacteristic
858C22#349811yescharacteristic
859C22#351112yes—
860C22#351312yes—
861C22#351412yes—
862C22#351412yes—
863C22#351912yes—
864C22C2×#56211yescharacteristic
865C22#354312yes—
866C22#354312yes—
867C22#354612yes—
868C22#354712yes—
869C4—28no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4#270618yes—
885C2—44no—
886C2—84no—
887C2—162no—
888C2#3513111yescharacteristic
889C2#3618211yescharacteristic
890C2#3636211yescharacteristic
891C2#3730211yescharacteristic
892C2#3786911yescharacteristic
893C2#3894511yescharacteristic
894C2#3914812yes—
895C2#4015212yes—
896C2#4604212yes—
897C2C2×#270611yescharacteristic
898C2#5920812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15124C2
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×#2504C2semidirect
2. C2×#2420C2semidirect
3. #16386C2semidirect
4. #15419C2semidirect
5. #15285C2semidirect
6. #15244C2semidirect
7. #15231C2semidirect
8. #15224C2semidirect
9. #15219C2semidirect
10. #15134C2semidirect
12. #14713C2semidirect
13. #14689C2semidirect
14. #14519C2semidirect
15. #14137C2semidirect
16. #14025C2semidirect
17. #13941C2semidirect
18. #13880C2semidirect
19. C4×#388C2semidirect
191. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25042
C2×#24202
#163862
#154192
#152852
#152442
#152312
#152242
#152192
#151342
#151242
#147132
#146892
#145192
#141372
#140252
#139412
#138802
C4×#3882