Finite Group Databasebeta

← #2108949

Subgroups — #2108949

Order 512.

2921 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C212yesmaximal, complemented
2C2×#2474C212yesmaximal, complemented
3#17106C211yesmaximal, characteristic, complemented
4#16661C212yesmaximal, complemented
5#16548C212yesmaximal, complemented
6#16295C212yesmaximal, complemented
7#15978C212yesmaximal, complemented
8#15666C212yesmaximal, complemented
9#15649C211yesmaximal, characteristic, complemented
10#15446C212yesmaximal, complemented
11#15297C212yesmaximal, complemented
12#15283C211yesmaximal, characteristic
13#15259C211yesmaximal, characteristic
14#14892C212yesmaximal, complemented
15#14785C212yesmaximal, complemented
16#14537C211yesmaximal, characteristic, complemented
17#14384C212yesmaximal, complemented
18#14255C211yesmaximal, characteristic
19#14194C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×#120C2211yescharacteristic
22C22×#117C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24#2482—216no—
25#2474—216no—
26C2×#399C2212yes—
27C2×#399C2212yes—
28C2×#399C2211yescharacteristic
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2211yescharacteristic
33C2×#396C2212yes—
34C2×#396C2212yescomplemented
35C2×#395C2212yescomplemented
36C2×#394C2212yes—
37C2×#393C2211yescharacteristic
38C2×#393C2211yescharacteristic
39C2×#391C2212yescomplemented
40C2×#390C2211yescharacteristic
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yescomplemented
47C2×#388C2212yescomplemented
48C2×#388C2212yescomplemented
49C2×#387C2212yescomplemented
50C2×#386C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#381C2212yes—
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×#379C2211yescharacteristic
57C2×C4×C4⋊C4C2212yescomplemented
58#1445C2212yescomplemented
59#1445C2212yescomplemented
60#1444C2212yescomplemented
61#1443C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1440C2212yes—
71#1440C2211yescharacteristic
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2211yescharacteristic
76#1440C2212yes—
77#1440C2212yescomplemented
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1438C2211yescharacteristic
87#1438C2212yes—
88#1438C2212yes—
89#1438C2211yescharacteristic
90#1438C2211yescharacteristic
91#1438C2212yes—
92#1438C2212yes—
93#1438C2211yescharacteristic
94#1437C2211yescharacteristic
95#1437C2211yescharacteristic
96#1437C2211yescharacteristic
97#1437C2212yes—
98#1437C2212yes—
99#1437C2211yescharacteristic
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107C4⋊#95C2212yescomplemented
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C23×D4C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C23×D4C2311yescharacteristic
114C24×C4C2312yes—
115C2×#124—28no—
116C2×#124—42no—
117C2×#120—24no—
118C2×#120—42no—
119C2×#120—42no—
120C2×#117—28no—
121C2×#117—28no—
122C2×#117—44no—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4—28no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169#399—28no—
170#399—28no—
171#399—24no—
172#397—28no—
173#397—28no—
174#397—28no—
175#397—42no—
176#396—28no—
177#396—44no—
178#395—28no—
179#394—28no—
180#393—24no—
181#393—42no—
182#391—28no—
183#390—42no—
184#388—28no—
185#388—28no—
186#388—28no—
187#388—28no—
188#388—28no—
189#388—28no—
190#388—28no—
191#388—28no—
192#387—28no—
193#386—28no—
194#385—28no—
195#385D4116yescomplemented
196#381—28no—
197#379—28no—
198#379—28no—
199#379—42no—
200C4×C4⋊C4—28no—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—24no—
242C25—42no—
243C25—42no—
244C25—42no—
245C25—42no—
246C25—42no—
247C25C2411yescharacteristic
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×Q8—24no—
252C22×Q8—22no—
253C22×Q8—41no—
254C22×Q8—42no—
255C22×Q8—41no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—41no—
263C22×D4—41no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—42no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4C2×D418yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293#124—416no—
294#120—416no—
295#117—432no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4C2×D418yes—
328C2×C4⋊C4C2×D418yes—
329C2×C22⋊C4—24no—
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—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—416no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
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—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×D418yes—
408C2×C22⋊C4C2×D418yes—
409C2×C22⋊C4#4114yes—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—41no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—41no—
422C2×C42—42no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—22no—
439#95—22no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—41no—
454#95—42no—
455#95—42no—
456#95—41no—
457#95—42no—
458#95C2×D418yes—
459#95C2×D418yes—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—28no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—48no—
494C24—48no—
495C24—44no—
496C24—48no—
497C24—48no—
498C24—44no—
499C24—84no—
500C24—84no—
501C24—84no—
502C24—84no—
503C24—82no—
504C24—82no—
505C24—84no—
506C24—82no—
507C24—84no—
508C24—82no—
509C24—84no—
510C24—84no—
511C24—84no—
512C24—84no—
513C24C22×D414yes—
514C24C2×#4112yes—
515C24H(5,𝔽2)12yes—
516C24H(5,𝔽2)12yes—
517C24C2511yescharacteristic
518C2×Q8—44no—
519C2×Q8—48no—
520C2×Q8—84no—
521C2×Q8—82no—
522C2×Q8—82no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—48no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—84no—
530C2×D4—84no—
531C2×D4—82no—
532C2×D4—82no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4—84no—
536C2×D4—84no—
537C2×D4—84no—
538C22×C4—216no—
539C22×C4—22no—
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—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
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—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—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4C22×D414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D414yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—84no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C4⋊C4—82no—
654C4⋊C4—84no—
655C22⋊C4—216no—
656C22⋊C4—48no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—48no—
660C22⋊C4—44no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—84no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—84no—
683C42—48no—
684C42—48no—
685C42—44no—
686C42—48no—
687C42—82no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—416no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—42no—
762C23—41no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—816no—
773C23—88no—
774C23—88no—
775C23—816no—
776C23—816no—
777C23—816no—
778C23—816no—
779C23—816no—
780C23D4214yes—
781C23C23×D412yes—
782C23C22×#4111yescharacteristic
783C23C2×H(5,𝔽2)11yescharacteristic
784C23C2×H(5,𝔽2)11yescharacteristic
785C23#58512yes—
786C23#58512yes—
787C23#58512yes—
788C23#58512yes—
789C23#58512yes—
790Q8—88no—
791D4—88no—
792D4—88no—
793D4—88no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—432no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
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—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
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—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C22—28no—
895C22—24no—
896C22—44no—
897C22—42no—
898C22—44no—
899C22—42no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—44no—
912C22—44no—
913C22—832no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—81no—
925C22—81no—
926C22—82no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22#344912yes—
932C22C2×D4211yescharacteristic
933C22D4×#4112yes—
934C22#348512yes—
935C22#348512yes—
936C22#348712yes—
937C22#348812yes—
938C22#349011yescharacteristic
939C22#351011yescharacteristic
940C22#351011yescharacteristic
941C22#352112yes—
942C22#353312yes—
943C22#353312yes—
944C22#353311yescharacteristic
945C22#353311yescharacteristic
946C22#354511yescharacteristic
947C22#354512yes—
948C22#356612yes—
949C22#356612yes—
950C22#356612yes—
951C22#356812yes—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—42no—
956C4—42no—
957C4—44no—
958C4—44no—
959C4—44no—
960C4—82no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—81no—
966C4—82no—
967C2—44no—
968C2—82no—
969C2—82no—
970C2—161no—
971C2#3765512yes—
972C2#3987012yes—
973C2#4142312yes—
974C2#4354512yes—
975C2#4703511yescharacteristic
976C2#4894911yescharacteristic
977C2#5189112yes—
978C2#5759212yes—
979C2#5899211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2482C2semidirect
2. C2×#2474C2semidirect
3. #17106C2semidirect
4. #16661C2semidirect
5. #16548C2semidirect
6. #16295C2semidirect
7. #15978C2semidirect
8. #15666C2semidirect
9. #15649C2semidirect
10. #15446C2semidirect
11. #15297C2semidirect
14. #14892C2semidirect
15. #14785C2semidirect
16. #14537C2semidirect
17. #14384C2semidirect
19. #14194C2semidirect
34. C2×#396C22semidirect
35. C2×#395C22semidirect
39. C2×#391C22semidirect
46. C2×#388C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
49. C2×#387C22semidirect
57. C2×C4×C4⋊C4C22semidirect
58. #1445C22semidirect
59. #1445C22semidirect
60. #1444C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
77. #1440C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. C4⋊#95C22semidirect
195. #385D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C2×#24742
#171062
#166612
#165482
#162952
#159782
#156662
#156492
#154462
#152972
#152832
#152592
#148922
#147852
#145372
#143842
#142552
#141942