Finite Group Databasebeta

← #719377

Subgroups — #719377

Order 512.

3576 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2536C211yesmaximal, characteristic, complemented
2C2×#2417C212yesmaximal, complemented
3C2×#2392C211yesmaximal, characteristic
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#2323C211yesmaximal, characteristic, complemented
6#17070C212yesmaximal, complemented
7#16821C212yesmaximal, complemented
8#15769C214yesmaximal, complemented
9#15303C214yesmaximal, complemented
10#15179C212yesmaximal, complemented
11#15129C212yesmaximal, complemented
12#15129C212yesmaximal, complemented
13#14806C212yesmaximal
14#14340C211yesmaximal, characteristic, complemented
15#13954C211yesmaximal, characteristic, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13907C212yesmaximal, complemented
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26#2536—28no—
27#2417—216no—
28#2392—28no—
29C2×#398C2212yes—
30C2×#398C2214yes—
31C2×#398C2211yescharacteristic
32C2×#397C2211yescharacteristic
33C2×#396C2214yes—
34C2×#396C2212yes—
35C2×#394C2211yescharacteristic
36C2×#394C2212yes—
37C2×#394C2212yes—
38C2×#394C2214yes—
39C2×#392C2211yescharacteristic
40D4×C4⋊C4—28no—
41#2323—28no—
42C2×#391C2211yescharacteristic
43C2×#391C2212yes—
44C2×#389C2212yes—
45C2×#389C2211yescharacteristic
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2214yes—
52C2×#387C2212yes—
53C2×#386C2214yes—
54C2×#385C2214yes—
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2214yes—
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1444C2214yes—
67#1442C2214yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2212yes—
76#1440C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2214yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2314yes—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—44no—
99C2×C22⋊Q8D418yescomplemented
100C2×C4×Q8—24no—
101C2×C4×Q8—24no—
102C2×C4×Q8—24no—
103C2×C4×D4—28no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—28no—
107C2×C4×D4—24no—
108C2×C4×D4—44no—
109C2×C4×D4—48no—
110C2×C4×D4D418yes—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C22×C4⋊C4—28no—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—28no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154#398—24no—
155#398—216no—
156#398—28no—
157#397—24no—
158#396—28no—
159#396—216no—
160#394—24no—
161#394—28no—
162#394—28no—
163#394—48no—
164#392—24no—
165#391—28no—
166#391—24no—
167#389—24no—
168#389—28no—
169#389—28no—
170#389—28no—
171#389—44no—
172#388—216no—
173#388—28no—
174#388—28no—
175#387—28no—
176#386—216no—
177#385—216no—
178#384—24no—
179#382—24no—
180#380—28no—
181#380—28no—
182#380—24no—
183#380—28no—
184#380—216no—
185#380—48no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4D418yescomplemented
188C4×C22⋊C4—28no—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C25C2411yescharacteristic
212C25C2412yes—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8C2×D414yes—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4C2×D414yes—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4C2×D414yes—
252C23×C4C2×D418yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2414yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C22⋊Q8—232no—
269C22⋊Q8—432no—
270C4×Q8—416no—
271C4×D4—232no—
272C4×D4—432no—
273C4×D4—432no—
274#117—416no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
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—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—432no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D418yes—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4#4114yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4C2×D418yes—
367C2×C22⋊C4C2×D418yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—44no—
378C2×C42C2×D418yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42#4114yes—
382#95—24no—
383#95—24no—
384#95—22no—
385#95—22no—
386#95—28no—
387#95—28no—
388#95—24no—
389#95—28no—
390#95—28no—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95C2×D418yes—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24C22×D412yes—
427C24C22×D414yes—
428C24H(5,𝔽2)14yes—
429C242−1+414yes—
430C24C2511yescharacteristic
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—216no—
441C2×D4—216no—
442C2×D4—216no—
443C2×D4—28no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—216no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—28no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—24no—
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—22no—
515C22×C4—24no—
516C22×C4—24no—
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—22no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—416no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—44no—
537C22×C4—416no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4—88no—
541C22×C4C22×D414yes—
542C22×C4C22×D414yes—
543C22×C4C22×D412yes—
544C22×C4C22×D414yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D414yes—
548C22×C4C22×D414yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4114yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C42−1+414yes—
561C22×C42−1+412yes—
562C4⋊C4—28no—
563C4⋊C4—216no—
564C4⋊C4—28no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—416no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—48no—
576C4⋊C4—84no—
577C4⋊C4—88no—
578C4⋊C4—84no—
579C4⋊C4—88no—
580C4⋊C4#121116yes—
581C22⋊C4—216no—
582C22⋊C4—216no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—84no—
593C22⋊C4—88no—
594C42—48no—
595C42—44no—
596C42—48no—
597C42—48no—
598C42#121116yes—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#53718yes—
657C23C23×D411yescharacteristic
658C23C23×D411yescharacteristic
659C23C23×D411yescharacteristic
660C23C22×#4111yescharacteristic
661C23C22×#4111yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×H(5,𝔽2)12yes—
664C23C2×2−1+411yescharacteristic
665C23C2×2−1+412yes—
666C23C2×2−1+412yes—
667C23#58512yes—
668Q8—416no—
669D4—232no—
670D4—432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—432no—
717C2×C4—416no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—832no—
755C2×C4C2×#12114yes—
756C2×C4C2×#12114yes—
757C2×C4C2×#12118yes—
758C2×C4C2×#12114yes—
759C2×C4C2×#12114yes—
760C2×C4#53714yes—
761C2×C4D4214yes—
762C2×C4#54714yes—
763C2×C4#54714yes—
764C2×C4#55514yes—
765C22—28no—
766C22—28no—
767C22—28no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—42no—
785C22—81no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—82no—
790C22—81no—
791C22C22×#12111yescharacteristic
792C22C22×#12111yescharacteristic
793C22C2×#53712yes—
794C22C2×#53711yescharacteristic
795C22C2×D4211yescharacteristic
796C22C2×#54711yescharacteristic
797C22C2×#54711yescharacteristic
798C22C2×#55511yescharacteristic
799C22#348411yescharacteristic
800C22#348612yes—
801C22#348611yescharacteristic
802C22#348812yes—
803C22#348912yes—
804C22#349212yes—
805C22#349911yescharacteristic
806C22#350011yescharacteristic
807C22#350712yes—
808C22#351312yes—
809C22#352312yes—
810C22#353612yes—
811C22#354112yes—
812C22#354412yes—
813C22#356312yes—
814C4—24no—
815C4—28no—
816C4—24no—
817C4—44no—
818C4—44no—
819C4—42no—
820C4—44no—
821C4—44no—
822C4—82no—
823C4—84no—
824C4—81no—
825C4—84no—
826C4—81no—
827C4—82no—
828C4#253718yes—
829C2—48no—
830C2—82no—
831C2C2×#253711yescharacteristic
832C2#3522311yescharacteristic
833C2#3562111yescharacteristic
834C2#3570011yescharacteristic
835C2#3572811yescharacteristic
836C2#3764912yes—
837C2#3804312yes—
838C2#4242811yescharacteristic
839C2#4279011yescharacteristic
840C2#4492112yes—
841C2#4512212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
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×#2536C2semidirect
2. C2×#2417C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C2×#2323C2semidirect
6. #17070C2semidirect
7. #16821C2semidirect
8. #15769C2semidirect
9. #15303C2semidirect
10. #15179C2semidirect
11. #15129C2semidirect
12. #15129C2semidirect
14. #14340C2semidirect
15. #13954C2semidirect
16. #13926C2semidirect
17. #13907C2semidirect
99. C2×C22⋊Q8D4semidirect
187. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25362
C2×#24172
C2×#23922
C2×D4×C4⋊C42
C2×#23232
#170702
#168212
#157692
#153032
#151792
#151292
#148062
#143402
#139542
#139262
#139072