Finite Group Databasebeta

← #515759

Subgroups — #515759

Order 512.

4032 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2324C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic, complemented
5C2×#2275C211yesmaximal, characteristic, complemented
6#14209C212yesmaximal, complemented
7#14207C212yesmaximal, complemented
8#14202C212yesmaximal, complemented
9#14187C212yesmaximal, complemented
10#14150C211yesmaximal, characteristic, complemented
11#14012C212yesmaximal, complemented
12#13999C212yesmaximal, complemented
13#13994C211yesmaximal, characteristic, complemented
14#13993C211yesmaximal, characteristic, complemented
15#13988C212yesmaximal, complemented
16#13975C212yesmaximal, complemented
17#13970C211yesmaximal, characteristic, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13906C211yesmaximal, characteristic, complemented
20#13906C211yesmaximal, characteristic, complemented
21#13779C211yesmaximal, characteristic, complemented
22#13777C211yesmaximal, characteristic, complemented
23C4×#380C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×#117C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2535C4116yescomplemented
34C2×#397C2212yes—
35C2×#392C2212yes—
36#2324—28no—
37C4×#121—28no—
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2212yes—
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44#2290—28no—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2211yescharacteristic
48C2×#388C2211yescharacteristic
49C2×#388C2212yes—
50C2×#387C2211yescharacteristic
51C2×#387C2211yescharacteristic
52C2×#386C2212yes—
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#385C2212yes—
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#382C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2212yes—
70C2×#380C2212yes—
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73#2275—28no—
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2212yes—
86C2×C4×C22⋊C4C2212yes—
87C2×#376C2211yescharacteristic
88C22×#95C2212yes—
89#1444C2212yes—
90#1443C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1440C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2212yes—
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122#1434C2212yes—
123#1434C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C4×#95C2212yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121C2×C418yes—
144C2×#121C2×C418yescomplemented
145C2×C4×D4—24no—
146C2×C4×D4—28no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—44no—
156C2×C4×D4—44no—
157C2×C4×D4C2×C418yescomplemented
158C2×C4×D4C2×C418yescomplemented
159C2×C4×D4D418yescomplemented
160C2×#117—24no—
161C2×#117—24no—
162C2×#117—24no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C42—24no—
203C22×C42—24no—
204C22×C42—24no—
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217#397C2×C4116yescomplemented
218#392C2×C4116yescomplemented
219#390—24no—
220#390—24no—
221#390—28no—
222#390—44no—
223#389—24no—
224#389—24no—
225#388—28no—
226#388—28no—
227#388—24no—
228#388—24no—
229#388—44no—
230#387—24no—
231#387—24no—
232#386—28no—
233#386—28no—
234#386—24no—
235#386—24no—
236#386—44no—
237#386—44no—
238#386C2×C4116yescomplemented
239#386C2×C4116yescomplemented
240#385—28no—
241#385—24no—
242#385—24no—
243#384—24no—
244#382C2×C418yescomplemented
245#380—24no—
246#380—24no—
247#380—24no—
248#380—24no—
249#380—44no—
250#380—44no—
251#380C2×C418yescomplemented
252#380C2×C418yescomplemented
253C4×C4⋊C4—24no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—24no—
256C4×C4⋊C4—24no—
257C4×C4⋊C4—24no—
258C4×C4⋊C4—24no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—24no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—28no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—44no—
266#376D418yescomplemented
267C2×#95—28no—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25C2411yescharacteristic
306C25C2412yes—
307C25C2411yescharacteristic
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—42no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—42no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4C22×C414yes—
331C22×D4C22×C418yes—
332C22×D4C22×C414yes—
333C22×D4C22×C418yes—
334C22×D4C2×D414yes—
335C22×D4#4114yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—24no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4C22×C414yes—
382C23×C4C22×C414yes—
383C23×C4C22×C418yes—
384C23×C4C2×D418yes—
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#121—232no—
406#121—232no—
407C4×D4—232no—
408C4×D4—232no—
409C4×D4—232no—
410C4×D4—232no—
411C4×D4—432no—
412#117—416no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C22×C414yes—
457C2×C4⋊C4C22×C414yes—
458C2×C4⋊C4C22×C414yes—
459C2×C4⋊C4C2×D414yes—
460C2×C4⋊C4#4114yes—
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—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—41no—
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⋊C4C22×C414yes—
523C2×C22⋊C4C22×C414yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C2×D418yes—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—24no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—416no—
552C2×C42—42no—
553C2×C42—42no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42C22×C414yes—
561C2×C42C2×D414yes—
562C2×C42C2×D414yes—
563C2×C42C2×D414yes—
564C2×C42C2×D414yes—
565C2×C42#4114yes—
566C2×C42#4114yes—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—22no—
572#95—22no—
573#95—24no—
574#95—22no—
575#95—22no—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95C22×C418yes—
597#95C22×C418yes—
598#95C22×C418yes—
599#95C22×C418yes—
600#95C2×D414yes—
601#95C2×D414yes—
602#95C2×D414yes—
603#95C2×D414yes—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C23×C412yes—
643C24C23×C414yes—
644C24C23×C412yes—
645C24C22×D414yes—
646C24C2×#4114yes—
647C24H(5,𝔽2)12yes—
648C242−1+412yes—
649C24C2511yescharacteristic
650C2×D4—216no—
651C2×D4—28no—
652C2×D4—216no—
653C2×D4—216no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—44no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—84no—
674C2×D4—84no—
675C2×D4—84no—
676C2×D4—84no—
677C2×D4C4×D4116yes—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—216no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—216no—
770C22×C4—216no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4—84no—
831C22×C4—84no—
832C22×C4—84no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4C23×C414yes—
838C22×C4C23×C414yes—
839C22×C4C23×C412yes—
840C22×C4C23×C412yes—
841C22×C4C23×C414yes—
842C22×C4C23×C412yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D414yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C2×#4114yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4C2×#4112yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C4H(5,𝔽2)12yes—
866C22×C4H(5,𝔽2)12yes—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—84no—
881C4⋊C4—84no—
882C4⋊C4—84no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—216no—
886C22⋊C4—216no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C42—28no—
907C42—48no—
908C42—44no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—84no—
913C42—84no—
914C42—84no—
915C42—84no—
916C42C4×D4116yescomplemented
917C42#121116yes—
918C23—22no—
919C23—24no—
920C23—22no—
921C23—22no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—24no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—22no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—41no—
975C23—42no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23C2×C4×D418yes—
1022C23#52014yes—
1023C23C24×C411yescharacteristic
1024C23C23×D411yescharacteristic
1025C23C23×D411yescharacteristic
1026C23C22×#4111yescharacteristic
1027C23C22×#4111yescharacteristic
1028C23C22×#4111yescharacteristic
1029C23C22×#4111yescharacteristic
1030C23C2×H(5,𝔽2)11yescharacteristic
1031C23C2×H(5,𝔽2)11yescharacteristic
1032C23C2×H(5,𝔽2)11yescharacteristic
1033C23C2×2−1+411yescharacteristic
1034C23#58511yescharacteristic
1035C23#58511yescharacteristic
1036C23#58511yescharacteristic
1037C23#58511yescharacteristic
1038D4—232no—
1039D4—416no—
1040D4—432no—
1041D4—816no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—416no—
1100C2×C4—416no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—816no—
1176C2×C4—816no—
1177C2×C4—816no—
1178C2×C4C2×C4×D414yes—
1179C2×C4C2×C4×D414yes—
1180C2×C4C2×C4×D414yes—
1181C2×C4C2×C4×D414yes—
1182C2×C4C4×#4114yes—
1183C2×C4C2×#12114yes—
1184C2×C4C2×#12114yes—
1185C2×C4C2×#12114yes—
1186C2×C4#52514yes—
1187C2×C4#52914yes—
1188C2×C4#53214yes—
1189C22—24no—
1190C22—24no—
1191C22—28no—
1192C22—24no—
1193C22—28no—
1194C22—28no—
1195C22—44no—
1196C22—44no—
1197C22—42no—
1198C22—44no—
1199C22—42no—
1200C22—44no—
1201C22—42no—
1202C22—44no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—42no—
1214C22—44no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22C22×C4×D411yescharacteristic
1235C22C22×C4×D411yescharacteristic
1236C22C2×C4×#4111yescharacteristic
1237C22C2×#52011yescharacteristic
1238C22#342811yescharacteristic
1239C22C4×H(5,𝔽2)11yescharacteristic
1240C22C4×H(5,𝔽2)11yescharacteristic
1241C22C22×#12111yescharacteristic
1242C22C2×#52511yescharacteristic
1243C22C2×#52911yescharacteristic
1244C22C2×#53211yescharacteristic
1245C22#348411yescharacteristic
1246C22#348511yescharacteristic
1247C22#348811yescharacteristic
1248C22#348811yescharacteristic
1249C22#348811yescharacteristic
1250C22#348811yescharacteristic
1251C22#348911yescharacteristic
1252C22#348911yescharacteristic
1253C22#349211yescharacteristic
1254C22#349311yescharacteristic
1255C22#349411yescharacteristic
1256C22#349411yescharacteristic
1257C22#349411yescharacteristic
1258C22#349511yescharacteristic
1259C22#350811yescharacteristic
1260C22#351011yescharacteristic
1261C22#351311yescharacteristic
1262C22#351411yescharacteristic
1263C22#351611yescharacteristic
1264C22#351711yescharacteristic
1265C22#351911yescharacteristic
1266C22#352011yescharacteristic
1267C22#352111yescharacteristic
1268C22#352111yescharacteristic
1269C4—24no—
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—42no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—44no—
1278C4—42no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—44no—
1284C4—81no—
1285C4—81no—
1286C4—82no—
1287C4—82no—
1288C4C4×#12118yes—
1289C2—44no—
1290C2—48no—
1291C2—82no—
1292C2C2×C4×#12111yescharacteristic
1293C2#3420211yescharacteristic
1294C2#3426911yescharacteristic
1295C2#3428811yescharacteristic
1296C2#3429211yescharacteristic
1297C2#3430111yescharacteristic
1298C2#3430511yescharacteristic
1299C2#3551411yescharacteristic
1300C2#3551811yescharacteristic
1301C2#3552111yescharacteristic
1302C2#3552211yescharacteristic
1303C2#3555011yescharacteristic
1304C2#3555311yescharacteristic
1305C2#3557111yescharacteristic
1306C2#3563611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2535C2
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×#2324C2semidirect
3. C2×C4×#121C2semidirect
4. C2×#2290C2semidirect
5. C2×#2275C2semidirect
6. #14209C2semidirect
7. #14207C2semidirect
8. #14202C2semidirect
9. #14187C2semidirect
10. #14150C2semidirect
11. #14012C2semidirect
12. #13999C2semidirect
13. #13994C2semidirect
14. #13993C2semidirect
15. #13988C2semidirect
16. #13975C2semidirect
17. #13970C2semidirect
18. #13970C2semidirect
19. #13906C2semidirect
20. #13906C2semidirect
21. #13779C2semidirect
22. #13777C2semidirect
23. C4×#380C2semidirect
33. #2535C4semidirect
144. C2×#121C2×C4semidirect
157. C2×C4×D4C2×C4semidirect
158. C2×C4×D4C2×C4semidirect
159. C2×C4×D4D4semidirect
217. #397C2×C4semidirect
218. #392C2×C4semidirect
238. #386C2×C4semidirect
239. #386C2×C4semidirect
244. #382C2×C4semidirect
251. #380C2×C4semidirect
252. #380C2×C4semidirect
266. #376D4semidirect
916. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#23242
C2×C4×#1212
C2×#22902
C2×#22752
#142092
#142072
#142022
#141872
#141502
#140122
#139992
#139942
#139932
#139882
#139752
#139702
#139062
#137792
#137772
C4×#3802