Finite Group Databasebeta

← #637045

Subgroups — #637045

Order 512.

4106 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C2×#2582C211yesmaximal, characteristic, complemented
3C2×#2538C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5#16659C214yesmaximal, complemented
6#16257C214yesmaximal, complemented
7#15218C212yesmaximal, complemented
8#15217C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15177C212yesmaximal, complemented
11#15129C212yesmaximal, complemented
12#15126C212yesmaximal
13#14686C211yesmaximal, characteristic, complemented
14#14264C212yesmaximal, complemented
15#14258C212yesmaximal, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13906C211yesmaximal, characteristic, complemented
18C2×#529—28no—
19C2×#529—28no—
20C2×#529—28no—
21C22×#126C2212yes—
22C22×#125C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#123C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×#121C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2212yes—
34C23×C42C2211yescharacteristic
35#2582—28no—
36#2538—28no—
37C2×#398C2214yes—
38C2×#396C2214yes—
39C2×#394C2214yes—
40C4×C22⋊Q8—28no—
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2212yes—
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2211yescharacteristic
51C2×#387C2212yes—
52C2×#385C2212yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65#1444C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97#529—2128no—
98C2×#126—28no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#125—24no—
102C2×#125—24no—
103C2×#125—24no—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#123—28no—
108C2×#123—28no—
109C2×#123—28no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—44no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8—24no—
127C2×C4×Q8D418yes—
128C2×C4×D4—28no—
129C2×C4×D4—28no—
130C2×C4×D4—28no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4D418yes—
134C2×#117—28no—
135C2×#117—28no—
136C2×#117—28no—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42D418yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179#398—216no—
180#396—216no—
181#394—48no—
182#391—28no—
183#391—28no—
184#391—24no—
185#391—44no—
186#390—28no—
187#390—44no—
188#389—28no—
189#389—28no—
190#389—28no—
191#389—24no—
192#387—28no—
193#385—28no—
194#384—24no—
195#384—24no—
196#380—28no—
197#380—24no—
198#380—28no—
199#380—44no—
200#380—44no—
201#380—44no—
202#380—44no—
203C4×C4⋊C4—28no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—28no—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C25C2412yes—
225C25C2411yescharacteristic
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8C2×D414yes—
239C22×Q8#4114yes—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4C2×D414yes—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4C2×D418yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2414yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297#126—264no—
298#125—232no—
299#124—232no—
300#123—264no—
301C22⋊Q8—232no—
302C22⋊Q8—232no—
303C22⋊Q8—432no—
304#121—232no—
305C4×Q8—232no—
306C4×Q8—416no—
307C4×D4—264no—
308C4×D4—232no—
309#117—264no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D418yes—
369C2×C4⋊C4#4114yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
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—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4C2×D418yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—232no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42C2×D414yes—
422C2×C42C2×D418yes—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426C2×C42C2×D414yes—
427C2×C42C2×D414yes—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C22×D414yes—
473C24C22×D412yes—
474C24H(5,𝔽2)12yes—
475C242−1+412yes—
476C24C2511yescharacteristic
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—216no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—216no—
567C22×C4—216no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4C22×D412yes—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C42−1+412yes—
635C22×C42−1+412yes—
636C22×C42−1+412yes—
637C22×C42−1+412yes—
638C4⋊C4—216no—
639C4⋊C4—216no—
640C4⋊C4—216no—
641C4⋊C4—216no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—28no—
646C4⋊C4—416no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—44no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—88no—
658C22⋊C4—216no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—216no—
663C22⋊C4—216no—
664C22⋊C4—416no—
665C22⋊C4—48no—
666C22⋊C4—88no—
667C22⋊C4—88no—
668C22⋊C4—88no—
669C22⋊C4—88no—
670C42—28no—
671C42—28no—
672C42—28no—
673C42—216no—
674C42—48no—
675C42—48no—
676C42#120116yes—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
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—42no—
746C23#53714yes—
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C23×D411yescharacteristic
750C23C22×#4111yescharacteristic
751C23C22×#4111yescharacteristic
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)11yescharacteristic
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×2−1+411yescharacteristic
756C23C2×2−1+411yescharacteristic
757C23C2×2−1+411yescharacteristic
758C23C2×2−1+411yescharacteristic
759C23C2×2−1+411yescharacteristic
760C23#58511yescharacteristic
761C23#58511yescharacteristic
762Q8—416no—
763Q8—416no—
764D4—432no—
765D4—416no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—416no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—416no—
830C2×C4—416no—
831C2×C4—432no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4C2×#12014yes—
861C2×C4C2×#12014yes—
862C2×C4C2×#12014yes—
863C2×C4#52514yes—
864C2×C4#53614yes—
865C2×C4#53614yes—
866C2×C4#53614yes—
867C2×C4#53714yes—
868C2×C4#53714yes—
869C2×C4#53714yes—
870C2×C4#53714yes—
871C2×C4#54614yes—
872C2×C4#54714yes—
873C2×C4#54814yes—
874C2×C4#55014yes—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22C22×#12011yescharacteristic
906C22C2×#52511yescharacteristic
907C22C2×#53611yescharacteristic
908C22C2×#53611yescharacteristic
909C22C2×#53611yescharacteristic
910C22C2×#53711yescharacteristic
911C22C2×#53711yescharacteristic
912C22C2×#53711yescharacteristic
913C22C2×#53711yescharacteristic
914C22C2×#53711yescharacteristic
915C22#344911yescharacteristic
916C22C2×#54611yescharacteristic
917C22C2×#54711yescharacteristic
918C22C2×#54811yescharacteristic
919C22C2×#55011yescharacteristic
920C22#348811yescharacteristic
921C22#348811yescharacteristic
922C22#348911yescharacteristic
923C22#348911yescharacteristic
924C22#351411yescharacteristic
925C22#351511yescharacteristic
926C22#351711yescharacteristic
927C22#351811yescharacteristic
928C22#352211yescharacteristic
929C22#352211yescharacteristic
930C22#352311yescharacteristic
931C22#352311yescharacteristic
932C22#354311yescharacteristic
933C22#354411yescharacteristic
934C22#355211yescharacteristic
935C22#355211yescharacteristic
936C22#355411yescharacteristic
937C22#355411yescharacteristic
938C22#355511yescharacteristic
939C22#355511yescharacteristic
940C4—24no—
941C4—42no—
942C4—44no—
943C4—44no—
944C4—42no—
945C4—44no—
946C4—44no—
947C4—42no—
948C4—44no—
949C4—82no—
950C4—84no—
951C4—82no—
952C4—84no—
953C4#240718yes—
954C4#261618yes—
955C2—44no—
956C2—84no—
957C2C2×#261611yescharacteristic
958C2C2×#240711yescharacteristic
959C2#3518911yescharacteristic
960C2#3524711yescharacteristic
961C2#3525111yescharacteristic
962C2#3762011yescharacteristic
963C2#3762211yescharacteristic
964C2#3890911yescharacteristic
965C2#3891111yescharacteristic
966C2#3892111yescharacteristic
967C2#3892311yescharacteristic
968C2#3912511yescharacteristic
969C2#3912711yescharacteristic
970C2#3913711yescharacteristic
971C2#3913911yescharacteristic
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
2. C2×#2582C2semidirect
3. C2×#2538C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. #16659C2semidirect
6. #16257C2semidirect
7. #15218C2semidirect
8. #15217C2semidirect
9. #15179C2semidirect
10. #15177C2semidirect
11. #15129C2semidirect
13. #14686C2semidirect
14. #14264C2semidirect
15. #14258C2semidirect
16. #13926C2semidirect
17. #13906C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#25822
C2×#25382
C2×C4×C22⋊Q82
#166592
#162572
#152182
#152172
#151792
#151772
#151292
#151262
#146862
#142642
#142582
#139262
#139062