Finite Group Databasebeta

← #674157

Subgroups — #674157

Order 512.

3746 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C212yesmaximal, complemented
2C2×#2422C212yesmaximal
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#15298C214yesmaximal, complemented
6#15269C214yesmaximal, complemented
7#15137C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14686C211yesmaximal, characteristic, complemented
12#14151C211yesmaximal, characteristic, complemented
13#14130C212yesmaximal, complemented
14#13916C212yesmaximal, complemented
15#13910C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×#123C2214yes—
19C22×#121C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24C23×C42C2211yescharacteristic
25#2486—216no—
26#2422—216no—
27C2×#398C2214yes—
28C2×#397C2214yes—
29C2×#397C2214yes—
30C2×#394C2214yes—
31D4×C4⋊C4—28no—
32C4×#121—28no—
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#388C2212yes—
42C2×#386C2212yes—
43C2×#385C2214yes—
44C2×#385C2214yes—
45C2×#384C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#381C2214yes—
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63#1444C2214yes—
64#1444C2214yes—
65#1443C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74C4⋊#95C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2212yes—
83#1434C2212yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2314yes—
94C2×#123—216no—
95C2×#123—216no—
96C2×#123—48no—
97C2×#121—24no—
98C2×#121—24no—
99C2×#121D418yes—
100C2×C4×D4—28no—
101C2×C4×D4—28no—
102C2×C4×D4—28no—
103C2×C4×D4—28no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—44no—
108C2×C4×D4D418yes—
109C22×C4⋊C4—28no—
110C22×C4⋊C4—28no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151#398—216no—
152#397—216no—
153#397—216no—
154#394—216no—
155#390—28no—
156#390—24no—
157#389—28no—
158#389—28no—
159#389—28no—
160#389—28no—
161#389—24no—
162#389—44no—
163#388—28no—
164#386—28no—
165#385—216no—
166#385—216no—
167#384—28no—
168#384—24no—
169#384—24no—
170#381—216no—
171#380—28no—
172#380—28no—
173#380—28no—
174#380—28no—
175#380—24no—
176#380—24no—
177#380—28no—
178#380—44no—
179#380D418yescomplemented
180C4×C4⋊C4—24no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4—24no—
183C4×C22⋊C4—28no—
184C4×C22⋊C4—28no—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C25C2412yes—
208C25C2411yescharacteristic
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4C2×D418yes—
220C22×D4C2×D414yes—
221C22×D4C2×D414yes—
222C22×D4#4114yes—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—41no—
251C23×C4—41no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C2×D418yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2414yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2414yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273#123—464no—
274#121—232no—
275C4×D4—232no—
276C4×D4—432no—
277C4×D4—432no—
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—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—432no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4#4114yes—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4C2×D418yes—
364C2×C22⋊C4C2×D418yes—
365C2×C22⋊C4C2×D418yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—416no—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387C2×C42#4114yes—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—24no—
405#95—42no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95C2×D418yes—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24C22×D414yes—
435C24C22×D414yes—
436C24C22×D412yes—
437C24C22×D412yes—
438C24C2×#4114yes—
439C24H(5,𝔽2)12yes—
440C24C2511yescharacteristic
441C2×D4—216no—
442C2×D4—216no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4#121116yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—28no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—28no—
509C22×C4—216no—
510C22×C4—28no—
511C22×C4—216no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4—416no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—416no—
567C22×C4—88no—
568C22×C4—88no—
569C22×C4—88no—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C42−1+412yes—
592C22×C42−1+412yes—
593C22×C42−1+412yes—
594C22×C42−1+412yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—416no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—416no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—48no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—88no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C42—48no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—48no—
629C42—48no—
630C42#123116yescomplemented
631C23—22no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23C2×#12118yes—
700C23D4214yes—
701C23C23×D411yescharacteristic
702C23C23×D411yescharacteristic
703C23C23×D411yescharacteristic
704C23C22×#4111yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×2−1+411yescharacteristic
711C23C2×2−1+411yescharacteristic
712C23C2×2−1+411yescharacteristic
713C23C2×2−1+411yescharacteristic
714C23#58511yescharacteristic
715C23#58511yescharacteristic
716D4—232no—
717D4—432no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—416no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—432no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—832no—
813C2×C4C2×#12114yes—
814C2×C4C2×#12314yes—
815C2×C4C2×#12314yes—
816C2×C4C2×#12314yes—
817C2×C4#53214yes—
818C2×C4#53614yes—
819C2×C4#54214yes—
820C2×C4D4214yes—
821C2×C4#54714yes—
822C2×C4#54714yes—
823C2×C4#54714yes—
824C2×C4#54714yes—
825C2×C4#55214yes—
826C2×C4#55214yes—
827C2×C4#55314yes—
828C22—24no—
829C22—28no—
830C22—24no—
831C22—28no—
832C22—28no—
833C22—24no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—42no—
845C22—42no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—42no—
856C22—44no—
857C22—42no—
858C22C22×#12111yescharacteristic
859C22C22×#12311yescharacteristic
860C22C2×#53211yescharacteristic
861C22C2×#53611yescharacteristic
862C22C2×#54211yescharacteristic
863C22C2×D4211yescharacteristic
864C22C2×D4211yescharacteristic
865C22C2×#54711yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54711yescharacteristic
868C22C2×#54711yescharacteristic
869C22D4×#4111yescharacteristic
870C22D4×#4111yescharacteristic
871C22C2×#55211yescharacteristic
872C22C2×#55211yescharacteristic
873C22C2×#55311yescharacteristic
874C22#348211yescharacteristic
875C22#348811yescharacteristic
876C22#348911yescharacteristic
877C22#349211yescharacteristic
878C22#349311yescharacteristic
879C22#349411yescharacteristic
880C22#349511yescharacteristic
881C22#349611yescharacteristic
882C22#349711yescharacteristic
883C22#349911yescharacteristic
884C22#349911yescharacteristic
885C22#351511yescharacteristic
886C22#351511yescharacteristic
887C22#351911yescharacteristic
888C22#352211yescharacteristic
889C22#354411yescharacteristic
890C22#354711yescharacteristic
891C22#355011yescharacteristic
892C22#355511yescharacteristic
893C4—24no—
894C4—44no—
895C4—44no—
896C4—42no—
897C4—44no—
898C4—42no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—84no—
903C4—82no—
904C4—82no—
905C4—84no—
906C4#242218yescomplemented
907C4#248618yescomplemented
908C2—44no—
909C2—48no—
910C2C2×#242211yescharacteristic
911C2C2×#248611yescharacteristic
912C2#3551611yescharacteristic
913C2D4×#12111yescharacteristic
914C2#3612611yescharacteristic
915C2#3625911yescharacteristic
916C2#3627211yescharacteristic
917C2#3892111yescharacteristic
918C2#3893211yescharacteristic
919C2#3934311yescharacteristic
920C2#3935011yescharacteristic
921C2#5921311yescharacteristic
922C2#5921911yescharacteristic
923C2#5925811yescharacteristic
924C2#5931311yescharacteristic
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×#2486C2semidirect
3. C2×D4×C4⋊C4C2semidirect
5. #15298C2semidirect
6. #15269C2semidirect
7. #15137C2semidirect
8. #15132C2semidirect
9. #15132C2semidirect
10. #15129C2semidirect
11. #14686C2semidirect
12. #14151C2semidirect
13. #14130C2semidirect
14. #13916C2semidirect
15. #13910C2semidirect
16. #13906C2semidirect
17. C4×#380C2semidirect
179. #380D4semidirect
630. C42#123semidirect
906. C4#2422semidirect
907. C4#2486semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24222
C2×D4×C4⋊C42
C2×C4×#1212
#152982
#152692
#151372
#151322
#151292
#146862
#141512
#141302
#139162
#139102
#139062
C4×#3802