Finite Group Databasebeta

← #945977

Subgroups — #945977

Order 512.

2326 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2485C211yesmaximal, characteristic
3#17194C214yesmaximal, complemented
4#16583C214yesmaximal, complemented
5#16573C214yesmaximal
6#16105C214yesmaximal, complemented
7#15242C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15233C211yesmaximal, characteristic, complemented
12#15197C211yesmaximal, characteristic, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14258C211yesmaximal, characteristic, complemented
15#14138C211yesmaximal, characteristic, complemented
16#13978C211yesmaximal, characteristic, complemented
17#13976C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2538—28no—
27#2485—28no—
28C2×#397C2212yes—
29C2×#396C2212yes—
30C2×#396C2212yes—
31C2×#394C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#390C2212yes—
37C2×#389C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#388C2212yes—
41C2×#387C2212yes—
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#382C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×#382C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55#1445C2214yes—
56#1444C2214yes—
57#1443C2214yes—
58#1443C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2212yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2212yes—
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1438C2212yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—42no—
102C2×C22⋊Q8—42no—
103C2×C4×Q8—24no—
104C2×C4×Q8—42no—
105C2×C4×Q8—42no—
106C2×C4×D4—42no—
107C2×C4×D4—42no—
108C2×C4×D4D418yes—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—42no—
112C2×#117—42no—
113C2×#117—42no—
114C2×#117—42no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153#397—28no—
154#396—28no—
155#396—28no—
156#394—28no—
157#391—24no—
158#391—24no—
159#391—42no—
160#391—42no—
161#390—28no—
162#389—28no—
163#389—24no—
164#389—24no—
165#388—28no—
166#387—28no—
167#384—24no—
168#384—42no—
169#382—42no—
170#382—42no—
171#382—42no—
172#380—24no—
173#380—24no—
174#380—24no—
175#380—24no—
176#380—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—42no—
179C4×C22⋊C4—42no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C25C2411yescharacteristic
210C25C2411yescharacteristic
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8#4114yes—
218C22×D4—24no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—42no—
222C22×D4C2×D414yes—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4C2×D414yes—
236C23×C4C2×D414yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C22⋊Q8—416no—
255C22⋊Q8—416no—
256C4×Q8—416no—
257C4×D4—416no—
258#117—416no—
259#117—416no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4C2×D414yes—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4C2×D414yes—
343C2×C22⋊C4C2×D414yes—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42C2×D414yes—
364C2×C42#4114yes—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—24no—
376#95—24no—
377#95—44no—
378#95—42no—
379#95—42no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—42no—
388#95—42no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24C22×D412yes—
415C24C22×D412yes—
416C24C2511yescharacteristic
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×D4—28no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C42−1+414yes—
543C22×C42−1+412yes—
544C4⋊C4—44no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—84no—
559C4⋊C4—84no—
560C4⋊C4—88no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—84no—
572C22⋊C4—84no—
573C22⋊C4—84no—
574C22⋊C4—84no—
575C42—28no—
576C42—28no—
577C42—48no—
578C42—48no—
579C42—44no—
580C42—44no—
581C42—44no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23C23×D411yescharacteristic
629C23C22×#4111yescharacteristic
630C23C22×#4111yescharacteristic
631C23C2×H(5,𝔽2)11yescharacteristic
632C23C2×H(5,𝔽2)11yescharacteristic
633C23C2×H(5,𝔽2)11yescharacteristic
634C23C2×2−1+412yes—
635C23C2×2−1+411yescharacteristic
636C23#58512yes—
637C23#58512yes—
638C23#58512yes—
639Q8—416no—
640D4—416no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—416no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4#53414yes—
737C2×C4#53614yes—
738C2×C4#53814yes—
739C2×C4#53914yes—
740C2×C4#54614yes—
741C2×C4#54714yes—
742C2×C4#55314yes—
743C2×C4#56214yes—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22C2×#53411yescharacteristic
767C22C2×#53611yescharacteristic
768C22#344911yescharacteristic
769C22C2×#53811yescharacteristic
770C22C2×#53911yescharacteristic
771C22C2×#54611yescharacteristic
772C22C2×#54711yescharacteristic
773C22C2×#55311yescharacteristic
774C22#349312yes—
775C22#350011yescharacteristic
776C22#350011yescharacteristic
777C22#350712yes—
778C22#351812yes—
779C22#352412yes—
780C22C2×#56211yescharacteristic
781C22#353912yes—
782C22#353912yes—
783C22#354112yes—
784C22#354112yes—
785C22#354712yes—
786C22#355112yes—
787C22#355512yes—
788C22#356512yes—
789C4—24no—
790C4—42no—
791C4—44no—
792C4—42no—
793C4—42no—
794C4—44no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#270818yes—
806C2—82no—
807C2—82no—
808C2#3741811yescharacteristic
809C2#3744911yescharacteristic
810C2#3787011yescharacteristic
811C2#3809311yescharacteristic
812C2#3895811yescharacteristic
813C2#3949011yescharacteristic
814C2#4265312yes—
815C2#4289612yes—
816C2#4526212yes—
817C2C2×#270811yescharacteristic
818C2#5305212yes—
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
3. #17194C2semidirect
4. #16583C2semidirect
6. #16105C2semidirect
7. #15242C2semidirect
8. #15236C2semidirect
9. #15236C2semidirect
10. #15233C2semidirect
11. #15233C2semidirect
12. #15197C2semidirect
13. #14340C2semidirect
14. #14258C2semidirect
15. #14138C2semidirect
16. #13978C2semidirect
17. #13976C2semidirect
18. #13879C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24852
#171942
#165832
#165732
#161052
#152422
#152362
#152332
#151972
#143402
#142582
#141382
#139782
#139762
#138792
#138392