Finite Group Databasebeta

← #945760

Subgroups — #945760

Order 512.

3178 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2426C211yesmaximal, characteristic
4C2×#2429C211yesmaximal, characteristic, complemented
5C2×#2621C211yesmaximal, characteristic, complemented
6C2×#2620C211yesmaximal, characteristic
7#17096C214yesmaximal, complemented
8#16330C214yesmaximal, complemented
9#16330C214yesmaximal, complemented
10#15348C214yesmaximal, complemented
11#15243C211yesmaximal, characteristic, complemented
12#15243C211yesmaximal, characteristic, complemented
13#15222C211yesmaximal, characteristic, complemented
14#15215C211yesmaximal, characteristic
15#15184C211yesmaximal, characteristic, complemented
16#15178C211yesmaximal, characteristic, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2621—28no—
34#2620—28no—
35#2546—28no—
36#2545—28no—
37#2429—28no—
38#2426—28no—
39C2×#398C2214yes—
40C2×#398C2214yes—
41C2×#398C2212yes—
42C2×#397C2214yes—
43C2×#396C2214yes—
44C2×#396C2214yes—
45C2×#396C2212yes—
46C2×#396C2212yes—
47C2×#394C2214yes—
48C2×#394C2212yes—
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2212yes—
60C2×#389C2211yescharacteristic
61C2×#389C2214yes—
62C2×#389C2211yescharacteristic
63C2×#389C2212yes—
64C2×#388C2214yes—
65C2×#388C2212yes—
66C2×#388C2212yes—
67C2×#384C2211yescharacteristic
68C2×#382C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73#1444C2212yes—
74#1444C2214yes—
75#1444C2214yes—
76#1442C2212yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1439C2214yes—
90#1438C2214yes—
91#1436C2214yes—
92#1436C2214yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C23×D4C2312yes—
102C24×C4C2311yescharacteristic
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—42no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—42no—
117C2×#124—42no—
118C2×#124—42no—
119C2×#124—42no—
120C2×#124—42no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×#121—24no—
131C2×#121—24no—
132C2×#121—42no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—42no—
138C2×C4×Q8—42no—
139C2×#117—24no—
140C2×#117—24no—
141C2×#117—42no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2314yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2312yes—
180C22×C42C2312yes—
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185#398—216no—
186#398—28no—
187#398—216no—
188#397—216no—
189#396—28no—
190#396—216no—
191#396—28no—
192#396—216no—
193#394—28no—
194#394—216no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—42no—
199#391—42no—
200#391D418yes—
201#391D418yescomplemented
202#390—24no—
203#390—28no—
204#390—24no—
205#390—24no—
206#389—24no—
207#389—24no—
208#389—28no—
209#389—216no—
210#388—28no—
211#388—28no—
212#388—216no—
213#384—24no—
214#382—24no—
215C4×C4⋊C4—24no—
216C4×C4⋊C4—24no—
217C4×C22⋊C4—42no—
218C4×C22⋊C4D418yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C2×#95C2314yes—
238C2×#95C2311yescharacteristic
239C2×#95C2314yes—
240C2×#95C2311yescharacteristic
241C25C2412yes—
242C25C2411yescharacteristic
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8C2×D414yes—
263C22×Q8C2×D414yes—
264C22×D4—24no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—42no—
274C22×D4—44no—
275C22×D4—44no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4C2×D414yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C4⋊Q8—416no—
301C4⋊Q8—416no—
302C4⋊Q8—416no—
303#124—416no—
304#124—416no—
305#124—416no—
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308C22⋊Q8—416no—
309#121—416no—
310C4×Q8—416no—
311C4×Q8—416no—
312#117—416no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
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—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
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—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4C2×D414yes—
411C2×C22⋊C4C2×D414yes—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42C2×D414yes—
433C2×C42C2×D414yes—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436#95—24no—
437#95—24no—
438#95—28no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—24no—
444#95—28no—
445#95—24no—
446#95—44no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—44no—
451#95—42no—
452#95—44no—
453#95—44no—
454#95C2×D414yes—
455#95C2×D414yes—
456#95C2×D4116yes—
457#95C2×D4116yes—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—24no—
475C24—24no—
476C24—22no—
477C24—24no—
478C24—24no—
479C24C22×D412yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—88no—
512C2×D4—84no—
513C2×D4—88no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
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—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4C22×D412yes—
605C22×C4C22×D414yes—
606C22×C4C22×D414yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C42−1+414yes—
622C22×C42−1+414yes—
623C22×C42−1+412yes—
624C4⋊C4—216no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—48no—
637C4⋊C4—416no—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—84no—
642C4⋊C4—88no—
643C22⋊C4—28no—
644C22⋊C4—44no—
645C22⋊C4—416no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—416no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—416no—
656C22⋊C4—48no—
657C22⋊C4—84no—
658C22⋊C4—88no—
659C42—28no—
660C42—28no—
661C42—28no—
662C42—28no—
663C42—48no—
664C42—48no—
665C42—44no—
666C42—44no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C23×D411yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×2−1+412yes—
720C23C2×2−1+411yescharacteristic
721C23C2×2−1+412yes—
722C23#58512yes—
723C23#58512yes—
724Q8—416no—
725Q8—416no—
726Q8—88no—
727D4—816no—
728D4—88no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—416no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4#53614yes—
826C2×C4#53714yes—
827C2×C4#53714yes—
828C2×C4#53714yes—
829C2×C4D4214yes—
830C2×C4D4214yes—
831C2×C4D4214yes—
832C2×C4#56014yes—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—84no—
848C22—82no—
849C22—84no—
850C22—84no—
851C22—82no—
852C22—82no—
853C22—84no—
854C22—82no—
855C22C2×#53611yescharacteristic
856C22C2×#53711yescharacteristic
857C22C2×#53711yescharacteristic
858C22C2×#53711yescharacteristic
859C22#344911yescharacteristic
860C22C2×D4211yescharacteristic
861C22C2×D4211yescharacteristic
862C22C2×D4211yescharacteristic
863C22#348612yes—
864C22#348912yes—
865C22#349712yes—
866C22#349911yescharacteristic
867C22#350011yescharacteristic
868C22#350012yes—
869C22C2×#56011yescharacteristic
870C22#354112yes—
871C22#354712yes—
872C22#355212yes—
873C22#355412yes—
874C22#355412yes—
875C22#355512yes—
876C22#355512yes—
877C22#356212yes—
878C4—24no—
879C4—42no—
880C4—44no—
881C4—42no—
882C4—44no—
883C4—44no—
884C4—42no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—42no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4#267518yes—
895C2—82no—
896C2—162no—
897C2#3738911yescharacteristic
898C2#3763311yescharacteristic
899C2#3767511yescharacteristic
900C2#3768011yescharacteristic
901C2#3935711yescharacteristic
902C2#3936311yescharacteristic
903C2#4279512yes—
904C2#4280212yes—
905C2#4524512yes—
906C2C2×#267511yescharacteristic
907C2#5304712yes—
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×#2546C2semidirect
2. C2×#2545C2semidirect
4. C2×#2429C2semidirect
5. C2×#2621C2semidirect
7. #17096C2semidirect
8. #16330C2semidirect
9. #16330C2semidirect
10. #15348C2semidirect
11. #15243C2semidirect
12. #15243C2semidirect
13. #15222C2semidirect
15. #15184C2semidirect
16. #15178C2semidirect
17. #13978C2semidirect
18. #13976C2semidirect
19. #13844C2semidirect
201. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#25452
C2×#24262
C2×#24292
C2×#26212
C2×#26202
#170962
#163302
#153482
#152432
#152222
#152152
#151842
#151782
#139782
#139762
#138442