Finite Group Databasebeta

← #875322

Subgroups — #875322

Order 512.

2766 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2417C211yesmaximal, characteristic
3#16825C214yesmaximal, complemented
4#15817C214yesmaximal, complemented
5#15488C214yesmaximal, complemented
6#15197C211yesmaximal, characteristic, complemented
7#15195C211yesmaximal, characteristic, complemented
8#15185C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15178C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14513C214yesmaximal
15#14139C211yesmaximal, characteristic, complemented
16#14024C211yesmaximal, characteristic, complemented
17#13976C211yesmaximal, characteristic, complemented
18#13924C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2538—28no—
30#2417—28no—
31C2×#398C2212yes—
32C2×#396C2212yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56#1445C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1444C2214yes—
60#1444C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1437C2212yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2212yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C22⋊#95C2214yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—42no—
102C2×C4⋊Q8—42no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C2×C4×Q8—42no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4D418yes—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C42—42no—
155C22×C42—42no—
156C22×C42—42no—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164#398—28no—
165#396—28no—
166#396—28no—
167#396—28no—
168#391—24no—
169#391—24no—
170#391—42no—
171#391—42no—
172#391—42no—
173#391—42no—
174#391—42no—
175#390—28no—
176#389—28no—
177#389—24no—
178#386—28no—
179#386Q8116yescomplemented
180#384—24no—
181#384—42no—
182#380—24no—
183#380—24no—
184#380—24no—
185#380—28no—
186C4×C22⋊C4—42no—
187C4×C22⋊C4—42no—
188C4×C22⋊C4—42no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×Q8—22no—
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—22no—
231C22×Q8#4114yes—
232C22×D4—41no—
233C22×D4—41no—
234C22×D4—42no—
235C22×D4C2×D414yes—
236C22×D4C2×Q818yes—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
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—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2×Q818yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C4⋊Q8—416no—
281C22⋊Q8—416no—
282C22⋊Q8—416no—
283C22⋊Q8—416no—
284C22⋊Q8—416no—
285C4×Q8—416no—
286C4×D4—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—416no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4#4114yes—
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—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4C2×D414yes—
368C2×C22⋊C4C2×D414yes—
369C2×C22⋊C4C2×Q818yes—
370C2×C22⋊C4C2×Q818yes—
371C2×C22⋊C4C2×Q818yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
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×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—416no—
393C2×C42C2×D414yes—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—42no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95C2×Q818yes—
420#95C2×Q818yes—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×Q814yes—
442C24C22×Q814yes—
443C24C2511yescharacteristic
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4C4⋊Q8116yescomplemented
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
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—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—88no—
572C22×C4—84no—
573C22×C4—88no—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×Q814yes—
580C22×C4C22×Q814yes—
581C22×C4C22×Q814yes—
582C22×C4C22×Q814yes—
583C22×C4C22×Q814yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C4⋊C4—28no—
593C4⋊C4—44no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—416no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C4⋊C4—88no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C42—28no—
623C42—48no—
624C42—48no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
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—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C2×C4⋊Q814yes—
674C23C2×C4⋊Q814yes—
675C23C23×D411yescharacteristic
676C23C23×Q812yes—
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23#58512yes—
684C23#58512yes—
685C23#58512yes—
686Q8—416no—
687Q8—88no—
688D4—416no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—432no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
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—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
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—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—816no—
788C2×C4C2×C4⋊Q814yes—
789C2×C4#53414yes—
790C2×C4#53814yes—
791C2×C4#54014yes—
792C2×C4#54614yes—
793C2×C4#54614yes—
794C2×C4#55314yes—
795C2×C4#56014yes—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—44no—
803C22—44no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22C22×C4⋊Q811yescharacteristic
819C22C2×#53411yescharacteristic
820C22#344911yescharacteristic
821C22C2×#53811yescharacteristic
822C22C2×#54011yescharacteristic
823C22C2×#54611yescharacteristic
824C22C2×#54611yescharacteristic
825C22C2×#55311yescharacteristic
826C22Q8×#4112yes—
827C22Q8×#4112yes—
828C22#350011yescharacteristic
829C22#350011yescharacteristic
830C22#350112yes—
831C22#350112yes—
832C22#350112yes—
833C22#350112yes—
834C22#352112yes—
835C22#352412yes—
836C22C2×#56011yescharacteristic
837C22#353912yes—
838C22#353912yes—
839C22#354012yes—
840C22#355112yes—
841C4—24no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4#268818yes—
858C2—44no—
859C2—44no—
860C2#3501111yescharacteristic
861C2#3627611yescharacteristic
862C2#3627611yescharacteristic
863C2#3741811yescharacteristic
864C2#3809311yescharacteristic
865C2#3809411yescharacteristic
866C2#3966412yes—
867C2#3966612yes—
868C2#4549312yes—
869C2C2×#268811yescharacteristic
870C2#5939312yes—
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. #16825C2semidirect
4. #15817C2semidirect
5. #15488C2semidirect
6. #15197C2semidirect
7. #15195C2semidirect
8. #15185C2semidirect
9. #15182C2semidirect
10. #15178C2semidirect
11. #15178C2semidirect
12. #14702C2semidirect
13. #14702C2semidirect
15. #14139C2semidirect
16. #14024C2semidirect
17. #13976C2semidirect
18. #13924C2semidirect
179. #386Q8semidirect
462. C2×D4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24172
#168252
#158172
#154882
#151972
#151952
#151852
#151822
#151782
#147022
#145132
#141392
#140242
#139762
#139242
C4×#3862