Finite Group Databasebeta

← #687700

Subgroups — #687700

Order 512.

3930 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5#16269C214yesmaximal, complemented
6#15292C214yesmaximal, complemented
7#15269C214yesmaximal, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15199C211yesmaximal, characteristic, complemented
10#15136C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14721C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14139C211yesmaximal, characteristic, complemented
15#14002C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#123C2214yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2501—28no—
30#2407—28no—
31C2×#399C2214yes—
32C2×#397C2214yes—
33C2×#394C2212yes—
34C2×#394C2214yes—
35C2×#392C2212yes—
36D4×C4⋊C4—28no—
37#2311—28no—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2212yes—
49C2×#386C2214yes—
50C2×#386C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#385C2214yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2214yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2214yes—
76#1440C2212yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2214yes—
80#1439C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2212yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C2×#123—216no—
113C2×#123—48no—
114C2×#123—48no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—42no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4—28no—
124C2×C4×D4—48no—
125C2×C4×D4D418yes—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—42no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—42no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174#399—216no—
175#397—48no—
176#394—28no—
177#394—48no—
178#392—28no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—42no—
184#390—24no—
185#390—24no—
186#390—24no—
187#390—42no—
188#390D418yescomplemented
189#389—28no—
190#386—216no—
191#386—28no—
192#385—28no—
193#385—28no—
194#385—28no—
195#385—48no—
196#384—24no—
197#384—24no—
198#384—24no—
199#384—42no—
200#382—42no—
201#380—24no—
202#380—24no—
203#380—24no—
204#380—216no—
205C4×C4⋊C4—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—42no—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C2×#41—232no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C2×#41—416no—
240C2×#41—416no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8#4114yes—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—28no—
258C22×D4—22no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—24no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4C2×D414yes—
271C22×D4C2×D414yes—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—28no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4#4114yes—
302C23×C4#4114yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319#123—464no—
320C22⋊Q8—416no—
321#121—416no—
322C4×D4—232no—
323C4×D4—432no—
324#117—416no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4—416no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4C2×D414yes—
418C2×C22⋊C4C2×D4116yes—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—44no—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—28no—
442#95—28no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—28no—
447#95—28no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—42no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—24no—
480C24—24no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—24no—
485C24C22×D414yes—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24H(5,𝔽2)14yes—
491C24C2511yescharacteristic
492#41—4128no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×D4—216no—
501C2×D4—216no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—216no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—416no—
517C2×D4—48no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—84no—
523C2×D4—88no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—216no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—416no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—88no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4—88no—
630C22×C4—88no—
631C22×C4#123116yescomplemented
632C22×C4C22×D412yes—
633C22×C4C22×D414yes—
634C22×C4C22×D412yes—
635C22×C4C22×D414yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4H(5,𝔽2)14yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C4H(5,𝔽2)12yes—
649C22×C42−1+414yes—
650C22×C42−1+414yes—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—416no—
658C4⋊C4—48no—
659C4⋊C4—416no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—84no—
666C4⋊C4—88no—
667C22⋊C4—216no—
668C22⋊C4—216no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—416no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—416no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—84no—
681C22⋊C4—88no—
682C22⋊C4—88no—
683C22⋊C4—84no—
684C42—28no—
685C42—28no—
686C42—48no—
687C42—44no—
688C42—44no—
689C42—44no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—28no—
720C23—28no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—42no—
749C23—42no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23C2×#12314yes—
758C23#53514yes—
759C23C23×D411yescharacteristic
760C23C23×D411yescharacteristic
761C23C22×#4111yescharacteristic
762C23C22×#4111yescharacteristic
763C23C22×#4111yescharacteristic
764C23C2×H(5,𝔽2)12yes—
765C23C2×H(5,𝔽2)11yescharacteristic
766C23C2×H(5,𝔽2)11yescharacteristic
767C23C2×H(5,𝔽2)12yes—
768C23C2×2−1+412yes—
769C23C2×2−1+412yes—
770Q8—416no—
771D4—232no—
772D4—432no—
773D4—416no—
774D4—816no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—232no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—432no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—416no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—42no—
865C2×C4—816no—
866C2×C4—816no—
867C2×C4C2×#12314yes—
868C2×C4C2×#12314yes—
869C2×C4#52514yes—
870C2×C4#53614yes—
871C2×C4#53814yes—
872C2×C4D4214yes—
873C2×C4#54614yes—
874C2×C4#54614yes—
875C2×C4#55114yes—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—44no—
883C22—44no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—48no—
900C22—44no—
901C22—48no—
902C22—44no—
903C22—84no—
904C22—82no—
905C22—84no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22C22×#12311yescharacteristic
910C22C2×#52511yescharacteristic
911C22C2×#53511yescharacteristic
912C22C2×#53611yescharacteristic
913C22C2×#53811yescharacteristic
914C22C2×D4211yescharacteristic
915C22C2×#54611yescharacteristic
916C22C2×#54611yescharacteristic
917C22C2×#55111yescharacteristic
918C22#348412yes—
919C22#349212yes—
920C22#349212yes—
921C22#349212yes—
922C22#349811yescharacteristic
923C22#349912yes—
924C22#349911yescharacteristic
925C22#351112yes—
926C22#352212yes—
927C22#352212yes—
928C22#353612yes—
929C22#354312yes—
930C22#354812yes—
931C22#355212yes—
932C4—24no—
933C4—24no—
934C4—44no—
935C4—44no—
936C4—44no—
937C4—42no—
938C4—44no—
939C4—44no—
940C4—42no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4#241818yes—
948C2—44no—
949C2—44no—
950C2—84no—
951C2C2×#241811yescharacteristic
952C2#3522711yescharacteristic
953C2#3553011yescharacteristic
954C2#3569312yes—
955C2#3767411yescharacteristic
956C2#3807911yescharacteristic
957C2#3895211yescharacteristic
958C2#3936011yescharacteristic
959C2#4250412yes—
960C2#4486912yes—
961C2#4492012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2501C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. C2×#2311C2semidirect
5. #16269C2semidirect
6. #15292C2semidirect
7. #15269C2semidirect
8. #15236C2semidirect
9. #15199C2semidirect
10. #15136C2semidirect
11. #15130C2semidirect
12. #14721C2semidirect
13. #14340C2semidirect
14. #14139C2semidirect
15. #14002C2semidirect
16. #14000C2semidirect
17. #13937C2semidirect
18. #13880C2semidirect
19. #13839C2semidirect
188. #390D4semidirect
631. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24072
C2×D4×C4⋊C42
C2×#23112
#162692
#152922
#152692
#152362
#151992
#151362
#151302
#147212
#143402
#141392
#140022
#140002
#139372
#138802
#138392