Finite Group Databasebeta

← #532749

Subgroups — #532749

Order 512.

4118 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic
2C2×#2363C212yesmaximal, complemented
3C2×#2361C211yesmaximal, characteristic, complemented
4C2×#2293C211yesmaximal, characteristic, complemented
5#14563C212yesmaximal, complemented
6#14520C212yesmaximal, complemented
7#14195C212yesmaximal, complemented
8#14187C212yesmaximal, complemented
9#14154C211yesmaximal, characteristic, complemented
10#14145C212yesmaximal, complemented
11#14141C211yesmaximal, characteristic, complemented
12#14137C211yesmaximal, characteristic, complemented
13#14100C212yesmaximal, complemented
14#14064C212yesmaximal, complemented
15#14046C211yesmaximal, characteristic, complemented
16#14025C211yesmaximal, characteristic, complemented
17#13998C211yesmaximal, characteristic, complemented
18#13998C211yesmaximal, characteristic, complemented
19#13821C211yesmaximal, characteristic, complemented
20#13820C211yesmaximal, characteristic, complemented
21C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
22C4×#390C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32C23×C4⋊C4C2211yescharacteristic
33#2428C4116yescomplemented
34C2×#394C2212yes—
35C2×#392C2212yes—
36#2363—216no—
37#2361—28no—
38#2293—28no—
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2212yes—
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388C2211yescharacteristic
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#388C2211yescharacteristic
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#385C2212yes—
69C2×#380C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2212yes—
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2212yes—
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C43C2211yescharacteristic
86#1442C2212yes—
87#1441C2212yes—
88#1440C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1438C2212yes—
95#1438C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2211yescharacteristic
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2211yescharacteristic
108#1437C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2211yescharacteristic
114#1436C2212yes—
115#1436C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120#1434C2211yescharacteristic
121#1434C2212yes—
122#1434C2211yescharacteristic
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C2×#127—42no—
138C2×#127—42no—
139C2×#127C2×C418yescomplemented
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—28no—
143C2×#121—28no—
144C2×#121—42no—
145C2×#121—42no—
146C2×#121C2×C418yes—
147C2×#121C2×C4116yescomplemented
148C2×#121C2×C418yescomplemented
149C2×C4×D4—24no—
150C2×C4×D4—28no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—28no—
154C2×C4×D4—24no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×C4×D4C2×C418yescomplemented
158C2×#117—28no—
159C2×#117—28no—
160C2×#117—44no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—42no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2312yes—
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219#394C2×C4116yescomplemented
220#392C2×C4116yescomplemented
221#390—24no—
222#390—28no—
223#390—24no—
224#390—24no—
225#390—24no—
226#390—24no—
227#390—28no—
228#390—28no—
229#390—24no—
230#390—42no—
231#390—44no—
232#390C2×C418yescomplemented
233#389—28no—
234#389—24no—
235#389—42no—
236#389C2×C418yescomplemented
237#389D418yescomplemented
238#388—28no—
239#388—24no—
240#388—28no—
241#388—28no—
242#388—28no—
243#388D418yescomplemented
244#386—28no—
245#386—28no—
246#386—28no—
247#386—44no—
248#386—44no—
249#386C2×C4116yescomplemented
250#385—28no—
251#380—24no—
252C4×C4⋊C4—24no—
253C4×C4⋊C4—24no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—28no—
256C4×C4⋊C4—42no—
257C4×C4⋊C4—42no—
258C4×C4⋊C4—42no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—28no—
264C4×C22⋊C4—44no—
265C4×C22⋊C4—42no—
266C4×C22⋊C4C2×C418yescomplemented
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C43—24no—
302C25C2412yes—
303C25C2412yes—
304C25C2411yescharacteristic
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—24no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—42no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4C22×C414yes—
342C22×D4C22×C414yes—
343C22×D4C22×C418yes—
344C22×D4C22×C418yes—
345C22×D4C22×C418yes—
346C22×D4C22×C418yes—
347C23×C4—22no—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4C22×C414yes—
374C23×C4C22×C418yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2412yes—
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395#127—416no—
396#121—232no—
397#121—264no—
398#121—416no—
399C4×D4—232no—
400C4×D4—416no—
401C4×D4—432no—
402#117—432no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—416no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4C22×C414yes—
434C2×C4⋊C4C22×C418yes—
435C2×C4⋊C4C22×C414yes—
436C2×C4⋊C4C2×D414yes—
437C2×C4⋊C4C2×D418yes—
438C2×C4⋊C4C2×D414yes—
439C2×C4⋊C4C2×D414yes—
440C2×C4⋊C4#4114yes—
441C2×C4⋊C4#4114yes—
442C2×C4⋊C4#4114yes—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
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—22no—
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—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
514C2×C22⋊C4C22×C418yes—
515C2×C22⋊C4C22×C418yes—
516C2×C22⋊C4C22×C418yes—
517C2×C22⋊C4C22×C414yes—
518C2×C22⋊C4C22×C418yes—
519C2×C22⋊C4C22×C414yes—
520C2×C22⋊C4C2×D414yes—
521C2×C22⋊C4C2×D414yes—
522C2×C22⋊C4C2×D414yes—
523C2×C22⋊C4#4114yes—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—24no—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—24no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—24no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—42no—
559C2×C42—41no—
560C2×C42—41no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42C22×C414yes—
566C2×C42C22×C414yes—
567C2×C42C2×D414yes—
568C2×C42C2×D414yes—
569#95—24no—
570#95—22no—
571#95—24no—
572#95—24no—
573#95—22no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—22no—
584#95—41no—
585#95—41no—
586#95—41no—
587#95—42no—
588#95—41no—
589#95—41no—
590#95—42no—
591#95—41no—
592#95—41no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95C22×C414yes—
598#95C22×C414yes—
599#95C22×C418yes—
600#95C2×D414yes—
601#95C2×D418yes—
602#95C2×D414yes—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24C23×C414yes—
644C24C23×C414yes—
645C24C23×C412yes—
646C24C22×D412yes—
647C24C2×#4112yes—
648C24C2511yescharacteristic
649C2×D4—216no—
650C2×D4—216no—
651C2×D4—28no—
652C2×D4—216no—
653C2×D4—28no—
654C2×D4—216no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—84no—
680C2×D4—84no—
681C2×D4—84no—
682C2×D4—84no—
683C2×D4—84no—
684C2×D4—84no—
685C2×D4—84no—
686C2×D4—84no—
687C2×D4—84no—
688C2×D4—84no—
689C2×D4—84no—
690C2×D4—84no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—216no—
780C22×C4—216no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—48no—
821C22×C4—84no—
822C22×C4—84no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4C23×C412yes—
829C22×C4C23×C412yes—
830C22×C4C23×C412yes—
831C22×C4C23×C414yes—
832C22×C4C23×C412yes—
833C22×C4C23×C412yes—
834C22×C4C23×C414yes—
835C22×C4C23×C412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C22×D414yes—
840C22×C4C22×D412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D414yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C2×#4114yes—
848C22×C4C2×#4114yes—
849C22×C4C2×#4112yes—
850C22×C4C2×#4114yes—
851C22×C4C2×#4112yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2×#4112yes—
855C22×C4H(5,𝔽2)12yes—
856C22×C4H(5,𝔽2)12yes—
857C22×C4H(5,𝔽2)12yes—
858C22×C4H(5,𝔽2)12yes—
859C4⋊C4—216no—
860C4⋊C4—28no—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—84no—
871C4⋊C4C4×D4116yes—
872C22⋊C4—216no—
873C22⋊C4—216no—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C22⋊C4—84no—
898C22⋊C4C4×D4116yescomplemented
899C42—28no—
900C42—28no—
901C42—28no—
902C42—28no—
903C42—44no—
904C42—48no—
905C42—44no—
906C42—48no—
907C42—48no—
908C42—44no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—84no—
913C42—84no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—42no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23C2×C4×D414yes—
1019C23C24×C411yescharacteristic
1020C23C23×D411yescharacteristic
1021C23C23×D411yescharacteristic
1022C23C22×#4111yescharacteristic
1023C23C22×#4111yescharacteristic
1024C23C22×#4111yescharacteristic
1025C23C22×#4111yescharacteristic
1026C23C2×H(5,𝔽2)11yescharacteristic
1027C23C2×H(5,𝔽2)11yescharacteristic
1028C23C2×H(5,𝔽2)11yescharacteristic
1029C23C2×H(5,𝔽2)11yescharacteristic
1030C23#58511yescharacteristic
1031C23#58511yescharacteristic
1032C23#58511yescharacteristic
1033C23#58511yescharacteristic
1034D4—432no—
1035D4—416no—
1036D4—416no—
1037D4—816no—
1038D4—816no—
1039D4—816no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
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—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—432no—
1101C2×C4—42no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—416no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—816no—
1172C2×C4—816no—
1173C2×C4C2×C4×D414yes—
1174C2×C4C2×C4×D418yes—
1175C2×C4C2×C4×D414yes—
1176C2×C4C2×C4×D414yes—
1177C2×C4C4×#4114yes—
1178C2×C4#51814yes—
1179C2×C4D4214yes—
1180C2×C4#54614yes—
1181C2×C4#55014yes—
1182C2×C4#55314yes—
1183C2×C4#55514yes—
1184C22—24no—
1185C22—24no—
1186C22—24no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—82no—
1214C22—82no—
1215C22—82no—
1216C22—82no—
1217C22—82no—
1218C22—82no—
1219C22—82no—
1220C22—82no—
1221C22—82no—
1222C22—82no—
1223C22—82no—
1224C22—82no—
1225C22—82no—
1226C22—82no—
1227C22—82no—
1228C22—82no—
1229C22C22×C4×D411yescharacteristic
1230C22C22×C4×D411yescharacteristic
1231C22C2×C4×#4111yescharacteristic
1232C22C2×#51811yescharacteristic
1233C22#342811yescharacteristic
1234C22C4×H(5,𝔽2)11yescharacteristic
1235C22C4×H(5,𝔽2)11yescharacteristic
1236C22C2×D4211yescharacteristic
1237C22C2×#54611yescharacteristic
1238C22C2×#55011yescharacteristic
1239C22D4×#4111yescharacteristic
1240C22D4×#4111yescharacteristic
1241C22D4×#4111yescharacteristic
1242C22D4×#4111yescharacteristic
1243C22C2×#55311yescharacteristic
1244C22C2×#55511yescharacteristic
1245C22#348011yescharacteristic
1246C22#348011yescharacteristic
1247C22#348111yescharacteristic
1248C22#348711yescharacteristic
1249C22#348811yescharacteristic
1250C22#349611yescharacteristic
1251C22#349811yescharacteristic
1252C22#351311yescharacteristic
1253C22#351411yescharacteristic
1254C22#351711yescharacteristic
1255C22#351711yescharacteristic
1256C22#351911yescharacteristic
1257C22#351911yescharacteristic
1258C22#352411yescharacteristic
1259C22#352411yescharacteristic
1260C22#354611yescharacteristic
1261C22#355111yescharacteristic
1262C22#355811yescharacteristic
1263C22#356211yescharacteristic
1264C4—24no—
1265C4—24no—
1266C4—28no—
1267C4—24no—
1268C4—44no—
1269C4—44no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—44no—
1277C4—44no—
1278C4—42no—
1279C4—42no—
1280C4—81no—
1281C4—82no—
1282C4—81no—
1283C4#236318yescomplemented
1284C2—44no—
1285C2—84no—
1286C2—84no—
1287C2C2×#236311yescharacteristic
1288C2#3414111yescharacteristic
1289C2C4×D4211yescharacteristic
1290C2#3428711yescharacteristic
1291C2#3429511yescharacteristic
1292C2#3431011yescharacteristic
1293C2#3449511yescharacteristic
1294C2#5905111yescharacteristic
1295C2#5905811yescharacteristic
1296C2#5909511yescharacteristic
1297C2#5910411yescharacteristic
1298C2#5969311yescharacteristic
1299C2#5970011yescharacteristic
1300C2#5975011yescharacteristic
1301C2#5984111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2428C2
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×#2363C2semidirect
3. C2×#2361C2semidirect
4. C2×#2293C2semidirect
5. #14563C2semidirect
6. #14520C2semidirect
7. #14195C2semidirect
8. #14187C2semidirect
9. #14154C2semidirect
10. #14145C2semidirect
11. #14141C2semidirect
12. #14137C2semidirect
13. #14100C2semidirect
14. #14064C2semidirect
15. #14046C2semidirect
16. #14025C2semidirect
17. #13998C2semidirect
18. #13998C2semidirect
19. #13821C2semidirect
20. #13820C2semidirect
21. C22⋊C4×C4⋊C4C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
33. #2428C4semidirect
139. C2×#127C2×C4semidirect
147. C2×#121C2×C4semidirect
148. C2×#121C2×C4semidirect
157. C2×C4×D4C2×C4semidirect
219. #394C2×C4semidirect
220. #392C2×C4semidirect
232. #390C2×C4semidirect
236. #389C2×C4semidirect
237. #389D4semidirect
243. #388D4semidirect
249. #386C2×C4semidirect
266. C4×C22⋊C4C2×C4semidirect
898. C22⋊C4C4×D4semidirect
1283. C4#2363semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#23632
C2×#23612
C2×#22932
#145632
#145202
#141952
#141872
#141542
#141452
#141412
#141372
#141002
#140642
#140462
#140252
#139982
#138212
#138202
C22⋊C4×C4⋊C42
C4×#3902
C4×#3882