Finite Group Databasebeta

← #571030

Subgroups — #571030

Order 512.

5220 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2403C211yesmaximal, characteristic
2C2×#2375C211yesmaximal, characteristic, complemented
3C2×#2308C211yesmaximal, characteristic, complemented
4#14534C212yesmaximal, complemented
5#14534C212yesmaximal, complemented
6#14401C211yesmaximal, characteristic, complemented
7#14374C212yesmaximal, complemented
8#14365C212yesmaximal, complemented
9#14357C212yesmaximal, complemented
10#14357C211yesmaximal, characteristic, complemented
11#14311C212yesmaximal, complemented
12#14228C212yesmaximal, complemented
13#14007C212yesmaximal, complemented
14#13995C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13988C212yesmaximal, complemented
17#13902C211yesmaximal, characteristic, complemented
18#13902C212yesmaximal, complemented
19#13824C211yesmaximal, characteristic, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C22×#120C2211yescharacteristic
23C22×#120C2212yes—
24C22×#120C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic, complemented
26C23×C22⋊C4C2211yescharacteristic, complemented
27#2403C4116yescomplemented
28C2×#392C2212yes—
29C2×#392C2212yes—
30#2375—28no—
31#2308—28no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yescomplemented
37C2×#390C2212yescomplemented
38C2×#390C2211yescharacteristic, complemented
39C2×#390C2212yescomplemented
40C2×#390C2211yescharacteristic, complemented
41C2×#390C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#388C2212yescomplemented
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#386C2211yescharacteristic
47C2×#386C2212yes—
48C2×#386C2211yescharacteristic
49C2×#386C2212yes—
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#386C2211yescharacteristic, complemented
55C2×#386C2211yescharacteristic, complemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#385C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#381C2212yescomplemented
62C2×#380C2211yescharacteristic, complemented
63C2×#380C2212yescomplemented
64C2×#379C2212yes—
65C2×#379C2212yes—
66C2×#379C2211yescharacteristic
67C2×#379C2212yescomplemented
68C2×#379C2212yescomplemented
69C2×#379C2212yescomplemented
70C2×C4×C22⋊C4C2212yescomplemented
71C2×C4×C22⋊C4C2212yescomplemented
72C2×C4×C22⋊C4C2211yescharacteristic, complemented
73C2×C4×C22⋊C4C2212yescomplemented
74#1444C2212yescomplemented
75#1442C2212yescomplemented
76#1440C2212yescomplemented
77#1440C2212yescomplemented
78#1440C2212yescomplemented
79#1440C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yescomplemented
92#1438C2212yescomplemented
93#1438C2212yescomplemented
94#1438C2212yescomplemented
95#1438C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107#1436C2212yescomplemented
108#1434C2212yescomplemented
109C4×#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C26C2311yescharacteristic
113C23×D4—24no—
114C23×D4—24no—
115C23×D4—44no—
116C23×D4—44no—
117C23×D4—42no—
118C23×D4—42no—
119C23×D4—42no—
120C23×D4—42no—
121C23×D4—42no—
122C23×D4—42no—
123C23×D4C2×C418yes—
124C23×D4C2×C418yescomplemented
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2312yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C2×#120—24no—
139C2×#120—24no—
140C2×#120—44no—
141C2×#120—44no—
142C2×#120—42no—
143C2×#120—42no—
144C2×#120C2×C4116yes—
145C2×#120C2×C418yescomplemented
146C2×#120C2×C418yescomplemented
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—42no—
156C22×C22⋊C4—42no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4—42no—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2312yes—
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2312yes—
200#392C2×C4116yescomplemented
201#392C2×C4116yescomplemented
202#390—24no—
203#390—24no—
204#390—28no—
205#390—44no—
206#390—44no—
207#390—44no—
208#390—44no—
209#390—44no—
210#390—42no—
211#390—42no—
212#388—28no—
213#388—28no—
214#388—28no—
215#388—44no—
216#386—24no—
217#386—24no—
218#386—28no—
219#386—28no—
220#386—24no—
221#386—28no—
222#386—44no—
223#386—44no—
224#386—44no—
225#386C2×C418yescomplemented
226#386C2×C418yescomplemented
227#386C2×C4116yescomplemented
228#386D418yescomplemented
229#385—44no—
230#385—44no—
231#381—28no—
232#380—44no—
233#380—42no—
234#379—28no—
235#379—28no—
236#379—44no—
237#379—44no—
238#379—44no—
239#379C2×C418yescomplemented
240C4×C22⋊C4—44no—
241C4×C22⋊C4—44no—
242C4×C22⋊C4—44no—
243C4×C22⋊C4—42no—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—22no—
272C25—22no—
273C25—22no—
274C25—22no—
275C25—22no—
276C25—22no—
277C25—22no—
278C25—22no—
279C25—22no—
280C25—42no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—41no—
285C25—41no—
286C25—41no—
287C25—41no—
288C25—42no—
289C25—42no—
290C25—41no—
291C25—41no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25C22×C414yes—
299C25C22×C414yes—
300C25C22×C414yes—
301C25C2412yes—
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C25C2411yescharacteristic
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—232no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—432no—
329C22×D4—416no—
330C22×D4—41no—
331C22×D4—42no—
332C22×D4—41no—
333C22×D4—42no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—416no—
357C22×D4—416no—
358C22×D4—416no—
359C22×D4—416no—
360C22×D4—416no—
361C22×D4—416no—
362C22×D4—416no—
363C22×D4—432no—
364C22×D4—416no—
365C22×D4C22×C418yes—
366C22×D4C22×C414yes—
367C22×D4C22×C414yes—
368C22×D4C22×C418yes—
369C22×D4C22×C418yes—
370C22×D4C22×C414yes—
371C22×D4C22×C418yes—
372C22×D4C22×C414yes—
373C22×D4C2×D414yes—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—41no—
388C23×C4—41no—
389C23×C4—41no—
390C23×C4—42no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4C22×C414yes—
402C23×C4C22×C414yes—
403C23×C4C2×D414yescomplemented
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417#120—232no—
418#120—432no—
419#120—416no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—42no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—416no—
497C2×C22⋊C4—416no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C22×C414yes—
538C2×C22⋊C4C22×C418yes—
539C2×C22⋊C4C22×C418yes—
540C2×C22⋊C4C22×C414yes—
541C2×C22⋊C4C22×C418yes—
542C2×C22⋊C4C22×C418yes—
543C2×C22⋊C4C2×D418yes—
544C2×C22⋊C4C2×D414yescomplemented
545C2×C42—24no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—41no—
553C2×C42—41no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42—42no—
558C2×C42—41no—
559C2×C42—42no—
560C2×C42—41no—
561C2×C42—42no—
562C2×C42—42no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95C22×C418yes—
585#95C22×C418yes—
586#95C2×D418yescomplemented
587C24—28no—
588C24—28no—
589C24—28no—
590C24—28no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—28no—
624C24—28no—
625C24—28no—
626C24—22no—
627C24—21no—
628C24—22no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—48no—
654C24—44no—
655C24—48no—
656C24—44no—
657C24—48no—
658C24—44no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—48no—
668C24—44no—
669C24—44no—
670C24—48no—
671C24—44no—
672C24—82no—
673C24—82no—
674C24—82no—
675C24—82no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—82no—
689C24—84no—
690C24—82no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—82no—
696C24—82no—
697C24—84no—
698C24—82no—
699C24—82no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—82no—
708C24—84no—
709C24—82no—
710C24—84no—
711C24—84no—
712C24C23×C414yes—
713C24C23×C412yes—
714C24C23×C412yes—
715C24C23×C412yes—
716C24C23×C412yes—
717C24C23×C412yes—
718C24C22×D412yes—
719C24C22×D412yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24H(5,𝔽2)12yes—
723C24H(5,𝔽2)12yes—
724C24H(5,𝔽2)12yes—
725C24H(5,𝔽2)12yes—
726C24C2511yescharacteristic
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—216no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—216no—
734C2×D4—28no—
735C2×D4—216no—
736C2×D4—216no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—4128no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—4128no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—84no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4C4×D4116yes—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—28no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—216no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—82no—
891C22×C4—84no—
892C22×C4—82no—
893C22×C4C23×C412yes—
894C22×C4C23×C414yes—
895C22×C4C23×C414yes—
896C22×C4C23×C412yes—
897C22×C4C23×C414yes—
898C22×C4C22×D414yes—
899C22×C4C22×D414yes—
900C22×C4C22×D412yes—
901C22×C4C2×#4112yes—
902C22×C4H(5,𝔽2)14yes—
903C22×C4H(5,𝔽2)14yes—
904C22×C4H(5,𝔽2)14yes—
905C4⋊C4—82no—
906C4⋊C4—82no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C4⋊C4—84no—
910C4⋊C4—84no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C42—82no—
947C42—82no—
948C42—84no—
949C42—84no—
950C42—84no—
951C42—84no—
952C23—232no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—416no—
1016C23—416no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—416no—
1056C23—42no—
1057C23—42no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—41no—
1097C23—42no—
1098C23—41no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—88no—
1106C23—88no—
1107C23—88no—
1108C23—88no—
1109C23—816no—
1110C23—88no—
1111C23—816no—
1112C23—88no—
1113C23—88no—
1114C23—88no—
1115C23—816no—
1116C23—88no—
1117C23—816no—
1118C23—816no—
1119C23—88no—
1120C23—816no—
1121C23—88no—
1122C23—88no—
1123C23—88no—
1124C23—816no—
1125C23—88no—
1126C23—816no—
1127C23—88no—
1128C23—88no—
1129C23—88no—
1130C23—816no—
1131C23C2×C4×D414yes—
1132C23C2×C4×D414yes—
1133C23#51814yes—
1134C23#51814yes—
1135C23C24×C411yescharacteristic
1136C23C23×D411yescharacteristic
1137C23C22×#4111yescharacteristic
1138C23C2×H(5,𝔽2)11yescharacteristic
1139C23C2×H(5,𝔽2)11yescharacteristic
1140C23C2×H(5,𝔽2)11yescharacteristic
1141C23C2×H(5,𝔽2)11yescharacteristic
1142C23C2×H(5,𝔽2)12yes—
1143C23C2×H(5,𝔽2)12yes—
1144C23C2×H(5,𝔽2)12yes—
1145C23#58512yes—
1146D4—416no—
1147D4—432no—
1148D4—416no—
1149D4—432no—
1150D4—416no—
1151D4—416no—
1152D4—816no—
1153D4—816no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—416no—
1185C2×C4—416no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—88no—
1246C2×C4—816no—
1247C2×C4—88no—
1248C2×C4C2×C4×D414yes—
1249C2×C4#51818yes—
1250C22—28no—
1251C22—28no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—28no—
1259C22—44no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—832no—
1307C22—832no—
1308C22—832no—
1309C22—81no—
1310C22—82no—
1311C22—82no—
1312C22—82no—
1313C22—82no—
1314C22—81no—
1315C22—82no—
1316C22—82no—
1317C22—81no—
1318C22—82no—
1319C22—81no—
1320C22—82no—
1321C22—82no—
1322C22—82no—
1323C22C22×C4×D411yescharacteristic
1324C22C2×#51812yes—
1325C22C2×#51811yescharacteristic
1326C22C2×#51811yescharacteristic
1327C22C4×H(5,𝔽2)12yes—
1328C22#348411yescharacteristic
1329C22#348411yescharacteristic
1330C22#349011yescharacteristic
1331C22#349011yescharacteristic
1332C22#349612yes—
1333C22#349812yes—
1334C22#351412yes—
1335C22#351912yes—
1336C22#353211yescharacteristic
1337C22#353212yes—
1338C22#353211yescharacteristic
1339C22#353412yes—
1340C22#353712yes—
1341C22#354212yes—
1342C22#354311yescharacteristic
1343C22#354312yes—
1344C22#354511yescharacteristic
1345C22#355812yes—
1346C4—28no—
1347C4—24no—
1348C4—44no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—44no—
1353C4—44no—
1354C4—82no—
1355C4—82no—
1356C4—82no—
1357C4—82no—
1358C4—82no—
1359C2—44no—
1360C2—44no—
1361C2—44no—
1362C2—44no—
1363C2—84no—
1364C2—82no—
1365C2#3419811yescharacteristic
1366C2#3431012yes—
1367C2#3435611yescharacteristic
1368C2#3440811yescharacteristic
1369C2#3447112yes—
1370C2#4784811yescharacteristic
1371C2#4785312yes—
1372C2#4814311yescharacteristic
1373C2#4814912yes—
1374C2#4892211yescharacteristic
1375C2#5064611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2403C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2375C2semidirect
3. C2×#2308C2semidirect
4. #14534C2semidirect
5. #14534C2semidirect
6. #14401C2semidirect
7. #14374C2semidirect
8. #14365C2semidirect
9. #14357C2semidirect
10. #14357C2semidirect
11. #14311C2semidirect
12. #14228C2semidirect
13. #14007C2semidirect
14. #13995C2semidirect
15. #13995C2semidirect
16. #13988C2semidirect
17. #13902C2semidirect
18. #13902C2semidirect
19. #13824C2semidirect
25. C23×C22⋊C4C22semidirect
26. C23×C22⋊C4C22semidirect
27. #2403C4semidirect
36. C2×#390C22semidirect
37. C2×#390C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
40. C2×#390C22semidirect
41. C2×#390C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#385C22semidirect
60. C2×#385C22semidirect
61. C2×#381C22semidirect
62. C2×#380C22semidirect
63. C2×#380C22semidirect
67. C2×#379C22semidirect
68. C2×#379C22semidirect
69. C2×#379C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. #1444C22semidirect
75. #1442C22semidirect
76. #1440C22semidirect
77. #1440C22semidirect
78. #1440C22semidirect
79. #1440C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1438C22semidirect
94. #1438C22semidirect
95. #1438C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. #1434C22semidirect
109. C4×#95C22semidirect
124. C23×D4C2×C4semidirect
145. C2×#120C2×C4semidirect
146. C2×#120C2×C4semidirect
200. #392C2×C4semidirect
201. #392C2×C4semidirect
225. #386C2×C4semidirect
226. #386C2×C4semidirect
227. #386C2×C4semidirect
228. #386D4semidirect
239. #379C2×C4semidirect
403. C23×C4C2×D4semidirect
544. C2×C22⋊C4C2×D4semidirect
586. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24032
C2×#23752
C2×#23082
#145342
#144012
#143742
#143652
#143572
#143112
#142282
#140072
#139952
#139882
#139022
#138242