Finite Group Databasebeta

← #674164

Subgroups — #674164

Order 512.

3670 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2536C212yesmaximal, complemented
4C2×#2365C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic
6#15408C214yesmaximal, complemented
7#15380C214yesmaximal, complemented
8#15236C212yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15137C212yesmaximal, complemented
11#15126C212yesmaximal
12#14141C212yesmaximal, complemented
13#13969C212yesmaximal, complemented
14#13911C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C23×C42C2211yescharacteristic
27#2857—28no—
28#2542—28no—
29#2536—216no—
30C2×#399C2214yes—
31C2×#398C2214yes—
32C2×#394C2214yes—
33#2365—28no—
34C4×#121—28no—
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#388C2214yes—
45C2×#388C2212yes—
46C2×#388C2214yes—
47C2×#387C2214yes—
48C2×#386C2212yes—
49C2×#384C2211yescharacteristic
50C2×#384C2212yes—
51C2×#382C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65#1444C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1437C2214yes—
78#1436C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85#1434C2212yes—
86C22⋊#95C2212yes—
87C4×#95C2212yes—
88C23×Q8C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8D418yescomplemented
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×C4×Q8—28no—
111C2×C4×Q8—28no—
112C2×C4×Q8—44no—
113C2×C4×D4—28no—
114C2×C4×D4—24no—
115C2×C4×D4—28no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—44no—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2314yes—
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159#399—216no—
160#398—216no—
161#394—216no—
162#391—28no—
163#391—28no—
164#390—28no—
165#390—28no—
166#390—24no—
167#389—28no—
168#389—28no—
169#389—28no—
170#389—24no—
171#388—216no—
172#388—216no—
173#388—28no—
174#387—216no—
175#386—28no—
176#384—28no—
177#384—24no—
178#382—28no—
179#380—28no—
180#380—28no—
181#380—28no—
182#380—24no—
183#380—24no—
184#380—44no—
185#380D418yescomplemented
186C4×C4⋊C4—28no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4D418yes—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C25C2412yes—
214C25C2411yescharacteristic
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8C2×D418yes—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4#4114yes—
236C23×C4—22no—
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—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—41no—
261C23×C4—41no—
262C23×C4C2×D414yes—
263C23×C4#4114yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2414yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C4⋊Q8—232no—
280C22⋊Q8—432no—
281C22⋊Q8—432no—
282C22⋊Q8—432no—
283#121—232no—
284C4×Q8—432no—
285C4×D4—432no—
286C4×D4—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
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—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D418yes—
335C2×C4⋊C4C2×D418yes—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4#4114yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4C2×D418yes—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—28no—
377C2×C42—28no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—44no—
394C2×C42—416no—
395C2×C42C2×D418yes—
396C2×C42C2×D414yes—
397C2×C42C2×D414yes—
398C2×C42#4114yes—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—24no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95C2×D418yes—
419#95C2×D418yes—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24C2×#4112yes—
449C242−1+412yes—
450C24C2511yescharacteristic
451C2×Q8—216no—
452C2×Q8—216no—
453C2×Q8—216no—
454C2×Q8—48no—
455C2×Q8—48no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×D4—216no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
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—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4C22×D414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D418yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C22×C42−1+412yes—
604C22×C42−1+412yes—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—416no—
614C4⋊C4—416no—
615C4⋊C4—416no—
616C4⋊C4—416no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—416no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—88no—
634C42—216no—
635C42—416no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—48no—
640C42—48no—
641C42#121116yes—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23#54714yes—
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C22×#4111yescharacteristic
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C22×#4111yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×2−1+411yescharacteristic
722C23C2×2−1+411yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23C2×2−1+411yescharacteristic
725C23#58511yescharacteristic
726C23#58511yescharacteristic
727Q8—432no—
728D4—432no—
729D4—416no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—416no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—816no—
824C2×C4C2×#12114yes—
825C2×C4C2×#12114yes—
826C2×C4C2×#12114yes—
827C2×C4#52514yes—
828C2×C4#53214yes—
829C2×C4#53614yes—
830C2×C4#54014yes—
831C2×C4D4214yes—
832C2×C4D4214yes—
833C2×C4#54614yes—
834C2×C4#54814yes—
835C2×C4#54814yes—
836C2×C4#55014yes—
837C2×C4#55214yes—
838C2×C4#55214yes—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22C22×#12111yescharacteristic
870C22C2×#52511yescharacteristic
871C22C2×#53211yescharacteristic
872C22C2×#53611yescharacteristic
873C22C2×#54011yescharacteristic
874C22C2×D4211yescharacteristic
875C22C2×D4211yescharacteristic
876C22C2×#54611yescharacteristic
877C22C2×#54711yescharacteristic
878C22C2×#54811yescharacteristic
879C22C2×#54811yescharacteristic
880C22C2×#55011yescharacteristic
881C22D4×#4111yescharacteristic
882C22C2×#55211yescharacteristic
883C22C2×#55211yescharacteristic
884C22#347511yescharacteristic
885C22#348211yescharacteristic
886C22#348611yescharacteristic
887C22#348711yescharacteristic
888C22#348911yescharacteristic
889C22#348911yescharacteristic
890C22#349511yescharacteristic
891C22#349511yescharacteristic
892C22#349711yescharacteristic
893C22#349911yescharacteristic
894C22#350611yescharacteristic
895C22#351111yescharacteristic
896C22#351411yescharacteristic
897C22#351511yescharacteristic
898C22#352011yescharacteristic
899C22#352311yescharacteristic
900C22#354711yescharacteristic
901C22#355011yescharacteristic
902C22#355211yescharacteristic
903C22#355411yescharacteristic
904C4—24no—
905C4—44no—
906C4—44no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—48no—
911C4—44no—
912C4—44no—
913C4—44no—
914C4—82no—
915C4—82no—
916C4—84no—
917C4#242818yes—
918C4#253618yescomplemented
919C2—44no—
920C2—84no—
921C2C2×#242811yescharacteristic
922C2C2×#253611yescharacteristic
923C2#3566111yescharacteristic
924C2#3610011yescharacteristic
925C2#3618611yescharacteristic
926C2#3627211yescharacteristic
927C2#3650411yescharacteristic
928C2#3893011yescharacteristic
929C2#3913911yescharacteristic
930C2#3934311yescharacteristic
931C2#3948111yescharacteristic
932C2#5903411yescharacteristic
933C2#5904211yescharacteristic
934C2#5908011yescharacteristic
935C2#5912511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2857C2semidirect
2. C2×#2542C2semidirect
3. C2×#2536C2semidirect
4. C2×#2365C2semidirect
6. #15408C2semidirect
7. #15380C2semidirect
8. #15236C2semidirect
9. #15177C2semidirect
10. #15137C2semidirect
12. #14141C2semidirect
13. #13969C2semidirect
14. #13911C2semidirect
15. #13906C2semidirect
16. #13876C2semidirect
17. C4×#380C2semidirect
97. C2×C4⋊Q8D4semidirect
185. #380D4semidirect
918. C4#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25422
C2×#25362
C2×#23652
C2×C4×#1212
#154082
#153802
#152362
#151772
#151372
#151262
#141412
#139692
#139112
#139062
#138762
C4×#3802