Finite Group Databasebeta

← #674394

Subgroups — #674394

Order 512.

3930 conjugacy classes of subgroups.

The subgroup lattice has 951 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×#2417C212yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic
6#15439C214yesmaximal, complemented
7#15294C214yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15137C212yesmaximal, complemented
11#15131C212yesmaximal, complemented
12#14155C211yesmaximal, characteristic, complemented
13#14151C211yesmaximal, characteristic, complemented
14#14139C212yesmaximal, complemented
15#13970C212yesmaximal
16#13920C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2212yes—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27C23×C42C2211yescharacteristic
28#2857—28no—
29#2542—28no—
30#2417—216no—
31C2×#399C2214yes—
32C2×#398C2214yes—
33C2×#396C2214yes—
34D4×C4⋊C4—28no—
35C4×#121—28no—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#388C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#384C2212yes—
52C2×#384C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2214yes—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65#1445C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83#1434C2212yes—
84C22⋊#95C2214yes—
85C22⋊#95C2214yes—
86C22⋊#95C2212yes—
87C4×#95C2212yes—
88C23×Q8C2312yes—
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—24no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×C22⋊Q8—44no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121Q818yescomplemented
111C2×C4×D4—28no—
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—28no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—44no—
118C2×C4×D4—44no—
119C2×C4×D4D418yes—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—44no—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#399—216no—
163#398—216no—
164#396—216no—
165#391—28no—
166#391—28no—
167#391—44no—
168#390—28no—
169#390—24no—
170#389—28no—
171#389—28no—
172#389—28no—
173#389—28no—
174#389—24no—
175#389—44no—
176#388—28no—
177#386—216no—
178#386—28no—
179#385—216no—
180#384—28no—
181#384D418yescomplemented
182#380—28no—
183#380—28no—
184#380—28no—
185#380—24no—
186#380—24no—
187#380—216no—
188#380D418yescomplemented
189C4×C4⋊C4—24no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—44no—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4C2×D414yes—
235C22×D4C2×Q818yes—
236C22×D4C2×Q814yes—
237C22×D4#4114yes—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—28no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—28no—
263C23×C4—28no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4C2×D414yes—
271C23×C4C2×D418yes—
272C23×C4C2×Q814yes—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2414yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C4⋊Q8—416no—
289C22⋊Q8—432no—
290C22⋊Q8—432no—
291C22⋊Q8—432no—
292#121—232no—
293C4×D4—232no—
294C4×D4—432no—
295C4×D4—432no—
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—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—432no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D418yes—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D418yes—
349C2×C4⋊C4C2×Q814yes—
350C2×C4⋊C4#4114yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4C2×D418yes—
382C2×C22⋊C4C2×D418yes—
383C2×C22⋊C4C2×Q818yes—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—416no—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42#4114yes—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—44no—
421#95—42no—
422#95—42no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95C2×D418yes—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24C22×D414yes—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C22×Q812yes—
455C24C2×#4114yes—
456C242−1+412yes—
457C24C2511yescharacteristic
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—48no—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4C22⋊Q8116yescomplemented
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—28no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—216no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—216no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—416no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—88no—
590C22×C4—88no—
591C22×C4—88no—
592C22×C4—88no—
593C22×C4C22×D414yes—
594C22×C4C22×D418yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×Q812yes—
606C22×C4C22×Q814yes—
607C22×C4C22×Q812yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C42−1+412yes—
618C22×C42−1+412yes—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—216no—
623C4⋊C4—28no—
624C4⋊C4—216no—
625C4⋊C4—28no—
626C4⋊C4—48no—
627C4⋊C4—416no—
628C4⋊C4—48no—
629C4⋊C4—416no—
630C4⋊C4—416no—
631C4⋊C4—416no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—88no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—416no—
645C22⋊C4—416no—
646C22⋊C4—416no—
647C22⋊C4—416no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—48no—
652C42—48no—
653C42—48no—
654C42#121116yes—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—41no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23C2×C22⋊Q818yes—
724C23D4×Q814yes—
725C23C23×D411yescharacteristic
726C23C23×D411yescharacteristic
727C23C23×D411yescharacteristic
728C23C23×Q811yescharacteristic
729C23C22×#4111yescharacteristic
730C23C22×#4111yescharacteristic
731C23C22×#4111yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)11yescharacteristic
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×2−1+411yescharacteristic
736C23C2×2−1+411yescharacteristic
737C23C2×2−1+411yescharacteristic
738C23#58511yescharacteristic
739C23#58511yescharacteristic
740Q8—816no—
741D4—232no—
742D4—432no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—416no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—416no—
814C2×C4—432no—
815C2×C4—416no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—832no—
838C2×C4C2×#12114yes—
839C2×C4C2×#12114yes—
840C2×C4C2×#12114yes—
841C2×C4C2×C22⋊Q814yes—
842C2×C4#53214yes—
843C2×C4#53714yes—
844C2×C4#54014yes—
845C2×C4D4214yes—
846C2×C4D4214yes—
847C2×C4#54614yes—
848C2×C4#54614yes—
849C2×C4D4×Q814yes—
850C2×C4#55014yes—
851C2×C4#55214yes—
852C2×C4#55414yes—
853C22—28no—
854C22—28no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—28no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22—42no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—42no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—42no—
883C22C22×#12111yescharacteristic
884C22C22×C22⋊Q811yescharacteristic
885C22C2×#53211yescharacteristic
886C22C2×#53711yescharacteristic
887C22C2×#54011yescharacteristic
888C22C2×D4211yescharacteristic
889C22C2×D4211yescharacteristic
890C22C2×#54611yescharacteristic
891C22C2×#54611yescharacteristic
892C22C2×D4×Q811yescharacteristic
893C22C2×D4×Q811yescharacteristic
894C22C2×#55011yescharacteristic
895C22D4×#4111yescharacteristic
896C22C2×#55211yescharacteristic
897C22C2×#55411yescharacteristic
898C22Q8×#4111yescharacteristic
899C22#348211yescharacteristic
900C22#348511yescharacteristic
901C22#348611yescharacteristic
902C22#348911yescharacteristic
903C22#348911yescharacteristic
904C22#349511yescharacteristic
905C22#349511yescharacteristic
906C22#349611yescharacteristic
907C22#349911yescharacteristic
908C22#350111yescharacteristic
909C22#350311yescharacteristic
910C22#351411yescharacteristic
911C22#351511yescharacteristic
912C22#352011yescharacteristic
913C22#352011yescharacteristic
914C22#354611yescharacteristic
915C22#354711yescharacteristic
916C22#354811yescharacteristic
917C22#355211yescharacteristic
918C4—24no—
919C4—42no—
920C4—44no—
921C4—42no—
922C4—42no—
923C4—48no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4—84no—
929C4—82no—
930C4—82no—
931C4#241718yescomplemented
932C4#242818yes—
933C2—48no—
934C2—44no—
935C2C2×#242811yescharacteristic
936C2C2×#241711yescharacteristic
937C2#3563311yescharacteristic
938C2D4×C22⋊Q811yescharacteristic
939C2#3627211yescharacteristic
940C2#3627411yescharacteristic
941C2#3656111yescharacteristic
942C2#3890811yescharacteristic
943C2#3893011yescharacteristic
944C2#3934011yescharacteristic
945C2#3960611yescharacteristic
946C2#5903511yescharacteristic
947C2#5904011yescharacteristic
948C2#5905211yescharacteristic
949C2#5912711yescharacteristic
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×#2417C2semidirect
4. C2×D4×C4⋊C4C2semidirect
6. #15439C2semidirect
7. #15294C2semidirect
8. #15179C2semidirect
9. #15177C2semidirect
10. #15137C2semidirect
11. #15131C2semidirect
12. #14155C2semidirect
13. #14151C2semidirect
14. #14139C2semidirect
16. #13920C2semidirect
17. C4×#380C2semidirect
110. C2×#121Q8semidirect
181. #384D4semidirect
188. #380D4semidirect
478. C2×D4C22⋊Q8semidirect
931. C4#2417semidirect

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×#24172
C2×D4×C4⋊C42
C2×C4×#1212
#154392
#152942
#151792
#151772
#151372
#151312
#141552
#141512
#141392
#139702
#139202
C4×#3802