Finite Group Databasebeta

← #874739

Subgroups — #874739

Order 512.

2518 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2492C211yesmaximal, characteristic
2C2×#2502C211yesmaximal, characteristic
3#16828C214yesmaximal, complemented
4#15378C214yesmaximal
5#15333C214yesmaximal, complemented
6#15199C211yesmaximal, characteristic, complemented
7#15191C211yesmaximal, characteristic, complemented
8#15185C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic
10#15180C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic
12#14714C211yesmaximal, characteristic, complemented
13#14714C211yesmaximal, characteristic, complemented
14#14442C214yesmaximal
15#14139C211yesmaximal, characteristic
16#14000C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2502—28no—
26#2492—28no—
27C2×#400C2212yes—
28C2×#398C2212yes—
29C2×#398C2212yes—
30C2×#393C2212yes—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2212yes—
37C2×#391C2214yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#389C2214yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2214yes—
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C43C2211yescharacteristic
61#1446C2214yes—
62#1445C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1444C2214yes—
66#1444C2214yes—
67#1444C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1437C2212yes—
78#1436C2214yes—
79#1436C2212yes—
80C4⋊#95C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2214yes—
88C4⋊#95C2214yes—
89#1434C2212yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×Q8C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—42no—
102C2×C4⋊Q8—42no—
103C2×C4⋊Q8—42no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8—42no—
109C2×C22⋊Q8—42no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2312yes—
148#400—28no—
149#398—28no—
150#398—28no—
151#393—28no—
152#391—24no—
153#391—24no—
154#391—24no—
155#391—24no—
156#391—24no—
157#391—28no—
158#391—48no—
159#391—42no—
160#391—42no—
161#391—42no—
162#391—42no—
163#391—42no—
164#389—48no—
165#388—28no—
166#388Q8116yescomplemented
167#385—28no—
168#385—28no—
169#385—48no—
170#384—24no—
171#384—24no—
172#384—42no—
173#384—42no—
174#384—42no—
175#380—24no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—24no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4D418yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C43—42no—
213C25C2411yescharacteristic
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—24no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—28no—
231C22×Q8—42no—
232C22×Q8—44no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×D414yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C4⋊Q8—416no—
264C4⋊Q8—416no—
265C22⋊Q8—416no—
266C22⋊Q8—416no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
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—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—416no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C2×Q818yes—
320C2×C4⋊C4#4114yes—
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—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4C2×D414yes—
335C2×C22⋊C4C2×D414yes—
336C2×C22⋊C4C2×Q818yes—
337C2×C22⋊C4C2×Q818yes—
338C2×C22⋊C4C2×Q818yes—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—44no—
361C2×C42C2×D414yes—
362C2×C42C2×D414yes—
363C2×C42C2×Q818yes—
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—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—24no—
381#95—42no—
382#95—42no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95C2×D414yes—
393#95C2×D414yes—
394#95C2×Q818yes—
395#95C2×Q818yes—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24C22×D412yes—
406C24C22×Q814yes—
407C24C2511yescharacteristic
408C2×Q8—48no—
409C2×Q8—416no—
410C2×Q8—44no—
411C2×Q8—44no—
412C2×Q8—48no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—84no—
426C2×Q8—88no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
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—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—84no—
520C22×C4—84no—
521C22×C4—88no—
522C22×C4—88no—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×Q814yes—
530C22×C4C22×Q814yes—
531C22×C4C22×Q814yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q814yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)14yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C42−1+414yes—
544C22×C42−1+412yes—
545C4⋊C4—28no—
546C4⋊C4—216no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—416no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—84no—
558C4⋊C4—84no—
559C4⋊C4—84no—
560C4⋊C4—88no—
561C4⋊C4—84no—
562C4⋊C4—88no—
563C4⋊C4—88no—
564C22⋊C4—28no—
565C22⋊C4—216no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—84no—
570C22⋊C4C4⋊Q8116yescomplemented
571C42—28no—
572C42—28no—
573C42—28no—
574C42—48no—
575C42—48no—
576C42—44no—
577C42—44no—
578C42—44no—
579C42—84no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—24no—
585C23—24no—
586C23—22no—
587C23—22no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23C2×C4⋊Q814yes—
603C23C23×D411yescharacteristic
604C23C23×Q812yes—
605C23C22×#4111yescharacteristic
606C23C22×#4111yescharacteristic
607C23C2×H(5,𝔽2)11yescharacteristic
608C23C2×H(5,𝔽2)11yescharacteristic
609C23C2×H(5,𝔽2)11yescharacteristic
610C23C2×H(5,𝔽2)12yes—
611C23C2×2−1+412yes—
612C23C2×2−1+411yescharacteristic
613C23#58512yes—
614Q8—816no—
615Q8—88no—
616Q8—88no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—28no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—44no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
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—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—816no—
714C2×C4C2×C4⋊Q814yes—
715C2×C4C2×C4⋊Q814yes—
716C2×C4#53514yes—
717C2×C4#53614yes—
718C2×C4#53814yes—
719C2×C4#54214yes—
720C2×C4#54614yes—
721C2×C4#54714yes—
722C2×C4#55418yes—
723C2×C4#55914yes—
724C2×C4#56214yes—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22C22×C4⋊Q811yescharacteristic
737C22C2×#53511yescharacteristic
738C22C2×#53611yescharacteristic
739C22C2×#53811yescharacteristic
740C22C2×#54211yescharacteristic
741C22C2×#54611yescharacteristic
742C22C2×#54711yescharacteristic
743C22C2×#55412yes—
744C22Q8×#4112yes—
745C22C2×#55911yescharacteristic
746C22#349811yescharacteristic
747C22#350011yescharacteristic
748C22#350112yes—
749C22#350312yes—
750C22#350312yes—
751C22#350312yes—
752C22#350712yes—
753C22#352012yes—
754C22C2×#56211yescharacteristic
755C22#353612yes—
756C22#354612yes—
757C22#355512yes—
758C22#355812yes—
759C4—24no—
760C4—24no—
761C4—24no—
762C4—28no—
763C4—42no—
764C4—42no—
765C4—44no—
766C4—44no—
767C4—44no—
768C4—44no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4#271018yes—
777C2—44no—
778C2#3528111yescharacteristic
779C2#3618011yescharacteristic
780C2#3627611yescharacteristic
781C2#3730511yescharacteristic
782C2#3807811yescharacteristic
783C2#3949011yescharacteristic
784C2#3963212yes—
785C2#3966012yes—
786C2#4550112yes—
787C2C2×#271011yescharacteristic
788C2#5964212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16828C2semidirect
5. #15333C2semidirect
6. #15199C2semidirect
7. #15191C2semidirect
8. #15185C2semidirect
10. #15180C2semidirect
12. #14714C2semidirect
13. #14714C2semidirect
16. #14000C2semidirect
17. #13910C2semidirect
166. #388Q8semidirect
570. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24922
C2×#25022
#168282
#153782
#153332
#151992
#151912
#151852
#151822
#151802
#151782
#147142
#144422
#141392
#140002
#139102
#138802
C4×#3882