Finite Group Databasebeta

← #526185

Subgroups — #526185

Order 512.

4050 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic, complemented
3C2×#2324C212yesmaximal, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#14698C211yesmaximal, characteristic, complemented
6#14563C212yesmaximal, complemented
7#14521C212yesmaximal, complemented
8#14410C212yesmaximal, complemented
9#14361C212yesmaximal, complemented
10#14299C212yesmaximal, complemented
11#14201C212yesmaximal, complemented
12#14154C211yesmaximal, characteristic, complemented
13#14064C212yesmaximal, complemented
14#14046C211yesmaximal, characteristic, complemented
15#14025C211yesmaximal, characteristic, complemented
16#14018C211yesmaximal, characteristic, complemented
17#14001C211yesmaximal, characteristic, complemented
18#13998C211yesmaximal, characteristic, complemented
19#13998C211yesmaximal, characteristic, complemented
20#13920C211yesmaximal, characteristic, complemented
21#13876C211yesmaximal, characteristic, complemented
22#13821C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32C23×C42C2211yescharacteristic
33#2428C4116yescomplemented
34C2×#394C2212yes—
35C2×#392C2212yes—
36#2354—28no—
37#2324—216no—
38C4×#121—28no—
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2212yes—
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388C2212yes—
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#388C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#385C2212yes—
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#384C2211yescharacteristic
72C2×#380C2212yes—
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2212yes—
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86#1442C2212yes—
87#1442C2212yes—
88#1441C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2211yescharacteristic
111#1436C2212yes—
112#1436C2211yescharacteristic
113#1436C2212yes—
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120#1434C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2311yescharacteristic
138C2×#127—42no—
139C2×#127—42no—
140C2×#127C2×C418yescomplemented
141C2×#121—24no—
142C2×#121—24no—
143C2×#121—28no—
144C2×#121—28no—
145C2×#121—42no—
146C2×#121—42no—
147C2×#121C2×C418yes—
148C2×#121C2×C4116yescomplemented
149C2×#121C2×C418yescomplemented
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—42no—
157C2×C4×D4—44no—
158C2×C4×D4C2×C418yescomplemented
159C2×#117—28no—
160C2×#117—28no—
161C2×#117—44no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
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×C42—24no—
205C22×C42—42no—
206C22×C42—42no—
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2312yes—
219#394C2×C4116yescomplemented
220#392C2×C4116yescomplemented
221#390—28no—
222#390—24no—
223#390—24no—
224#390—28no—
225#390—28no—
226#390—24no—
227#390—42no—
228#390—42no—
229#390—42no—
230#390—42no—
231#390—44no—
232#390C2×C418yescomplemented
233#389—28no—
234#389—24no—
235#389—24no—
236#389—42no—
237#389C2×C418yescomplemented
238#388—28no—
239#388—28no—
240#388—28no—
241#388—28no—
242#388—28no—
243#388—44no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—44no—
248#386—44no—
249#386C2×C4116yescomplemented
250#385—28no—
251#385—24no—
252#385D418yescomplemented
253#384—24no—
254#380—24no—
255#380—28no—
256#380—28no—
257#380—42no—
258C4×C4⋊C4—24no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—28no—
261C4×C4⋊C4—42no—
262C4×C4⋊C4—42no—
263C4×C4⋊C4—42no—
264C4×C4⋊C4D418yescomplemented
265C4×C22⋊C4—28no—
266C4×C22⋊C4—42no—
267C4×C22⋊C4C2×C418yescomplemented
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
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—24no—
315C22×D4—22no—
316C22×D4—24no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
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—24no—
348C23×C4—24no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—41no—
372C23×C4—41no—
373C23×C4—41no—
374C23×C4—41no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4C22×C414yes—
380C23×C4C22×C418yes—
381C23×C4C2×D414yes—
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402#127—416no—
403#121—232no—
404#121—264no—
405#121—416no—
406C4×D4—232no—
407C4×D4—432no—
408C4×D4—416no—
409#117—432no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
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—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4C22×C414yes—
451C2×C4⋊C4C22×C418yes—
452C2×C4⋊C4C22×C414yes—
453C2×C4⋊C4C2×D414yes—
454C2×C4⋊C4C2×D414yes—
455C2×C4⋊C4C2×D414yes—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4#4114yes—
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—22no—
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—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—41no—
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—41no—
499C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C2×D414yes—
534C2×C22⋊C4C2×D414yes—
535C2×C22⋊C4#4114yes—
536C2×C42—24no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—24no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42—416no—
560C2×C42—42no—
561C2×C42—41no—
562C2×C42—41no—
563C2×C42—41no—
564C2×C42—41no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42C22×C414yes—
570C2×C42C22×C414yes—
571C2×C42C2×D418yes—
572C2×C42C2×D414yes—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—22no—
586#95—24no—
587#95—22no—
588#95—42no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—42no—
594#95—41no—
595#95—41no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95C22×C414yes—
602#95C22×C414yes—
603#95C22×C418yes—
604#95C2×D414yes—
605#95C2×D418yes—
606#95C2×D414yes—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
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—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24C23×C414yes—
648C24C23×C414yes—
649C24C23×C412yes—
650C24C22×D412yes—
651C24C2×#4112yes—
652C24C2511yescharacteristic
653C2×D4—216no—
654C2×D4—216no—
655C2×D4—28no—
656C2×D4—216no—
657C2×D4—28no—
658C2×D4—216no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—28no—
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—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—84no—
684C2×D4—84no—
685C2×D4—84no—
686C2×D4—84no—
687C2×D4—84no—
688C2×D4—84no—
689C2×D4—84no—
690C2×D4—84no—
691C2×D4—84no—
692C2×D4—84no—
693C2×D4—84no—
694C2×D4—84no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—216no—
772C22×C4—216no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—48no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4C23×C412yes—
842C22×C4C23×C412yes—
843C22×C4C23×C412yes—
844C22×C4C23×C414yes—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C23×C414yes—
848C22×C4C23×C412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D414yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D414yes—
856C22×C4C22×D412yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4114yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4H(5,𝔽2)12yes—
865C22×C4H(5,𝔽2)12yes—
866C22×C4H(5,𝔽2)12yes—
867C22×C4H(5,𝔽2)12yes—
868C22×C4H(5,𝔽2)12yes—
869C22×C42−1+412yes—
870C4⋊C4—216no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—84no—
884C4⋊C4—84no—
885C4⋊C4C4×D4116yes—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4C4×D4116yescomplemented
912C42—28no—
913C42—28no—
914C42—28no—
915C42—216no—
916C42—48no—
917C42—44no—
918C42—44no—
919C42—44no—
920C42—44no—
921C42—44no—
922C42—84no—
923C42—84no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
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—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23C2×C4×D414yes—
1029C23C24×C411yescharacteristic
1030C23C23×D411yescharacteristic
1031C23C23×D411yescharacteristic
1032C23C22×#4111yescharacteristic
1033C23C22×#4111yescharacteristic
1034C23C2×H(5,𝔽2)11yescharacteristic
1035C23C2×H(5,𝔽2)11yescharacteristic
1036C23C2×H(5,𝔽2)11yescharacteristic
1037C23C2×H(5,𝔽2)11yescharacteristic
1038C23C2×H(5,𝔽2)11yescharacteristic
1039C23C2×2−1+411yescharacteristic
1040C23#58511yescharacteristic
1041C23#58511yescharacteristic
1042C23#58511yescharacteristic
1043C23#58511yescharacteristic
1044D4—432no—
1045D4—416no—
1046D4—416no—
1047D4—816no—
1048D4—816no—
1049D4—816no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—432no—
1105C2×C4—416no—
1106C2×C4—416no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
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—41no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
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—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—416no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—816no—
1184C2×C4C2×C4×D414yes—
1185C2×C4C2×C4×D418yes—
1186C2×C4C2×C4×D414yes—
1187C2×C4C2×C4×D414yes—
1188C2×C4#51814yes—
1189C2×C4#52014yes—
1190C2×C4#53514yes—
1191C2×C4#53714yes—
1192C2×C4#54014yes—
1193C2×C4#54214yes—
1194C2×C4D4214yes—
1195C22—24no—
1196C22—24no—
1197C22—24no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—82no—
1225C22—82no—
1226C22—82no—
1227C22—82no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22C22×C4×D411yescharacteristic
1241C22C22×C4×D411yescharacteristic
1242C22C2×#51811yescharacteristic
1243C22C2×#52011yescharacteristic
1244C22#342811yescharacteristic
1245C22C4×H(5,𝔽2)11yescharacteristic
1246C22C4×H(5,𝔽2)11yescharacteristic
1247C22C2×#53511yescharacteristic
1248C22C2×#53711yescharacteristic
1249C22C2×#54011yescharacteristic
1250C22C2×#54211yescharacteristic
1251C22C2×D4211yescharacteristic
1252C22D4×#4111yescharacteristic
1253C22D4×#4111yescharacteristic
1254C22#348111yescharacteristic
1255C22#348711yescharacteristic
1256C22#348811yescharacteristic
1257C22#349611yescharacteristic
1258C22#349611yescharacteristic
1259C22#349711yescharacteristic
1260C22#349811yescharacteristic
1261C22#350611yescharacteristic
1262C22#350711yescharacteristic
1263C22#351411yescharacteristic
1264C22#351711yescharacteristic
1265C22#351911yescharacteristic
1266C22#352411yescharacteristic
1267C22#354011yescharacteristic
1268C22#354211yescharacteristic
1269C22#354211yescharacteristic
1270C22#354211yescharacteristic
1271C22#354611yescharacteristic
1272C22#354811yescharacteristic
1273C22#355711yescharacteristic
1274C22#356211yescharacteristic
1275C4—24no—
1276C4—24no—
1277C4—28no—
1278C4—24no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—82no—
1290C4—82no—
1291C4—81no—
1292C4—82no—
1293C4—81no—
1294C4#232418yescomplemented
1295C2—44no—
1296C2—84no—
1297C2—84no—
1298C2C2×#232411yescharacteristic
1299C2C4×D4211yescharacteristic
1300C2#3420611yescharacteristic
1301C2#3429511yescharacteristic
1302C2#3431011yescharacteristic
1303C2#3442311yescharacteristic
1304C2#3447811yescharacteristic
1305C2#3933911yescharacteristic
1306C2#3934111yescharacteristic
1307C2#3940211yescharacteristic
1308C2#3941111yescharacteristic
1309C2#3988211yescharacteristic
1310C2#3988611yescharacteristic
1311C2#4017011yescharacteristic
1312C2#4017411yescharacteristic
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×#2354C2semidirect
3. C2×#2324C2semidirect
4. C2×C4×#121C2semidirect
5. #14698C2semidirect
6. #14563C2semidirect
7. #14521C2semidirect
8. #14410C2semidirect
9. #14361C2semidirect
10. #14299C2semidirect
11. #14201C2semidirect
12. #14154C2semidirect
13. #14064C2semidirect
14. #14046C2semidirect
15. #14025C2semidirect
16. #14018C2semidirect
17. #14001C2semidirect
18. #13998C2semidirect
19. #13998C2semidirect
20. #13920C2semidirect
21. #13876C2semidirect
22. #13821C2semidirect
23. C4×#385C2semidirect
33. #2428C4semidirect
140. C2×#127C2×C4semidirect
148. C2×#121C2×C4semidirect
149. C2×#121C2×C4semidirect
158. C2×C4×D4C2×C4semidirect
219. #394C2×C4semidirect
220. #392C2×C4semidirect
232. #390C2×C4semidirect
237. #389C2×C4semidirect
249. #386C2×C4semidirect
252. #385D4semidirect
264. C4×C4⋊C4D4semidirect
267. C4×C22⋊C4C2×C4semidirect
911. C22⋊C4C4×D4semidirect
1294. C4#2324semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#23542
C2×#23242
C2×C4×#1212
#146982
#145632
#145212
#144102
#143612
#142992
#142012
#141542
#140642
#140462
#140252
#140182
#140012
#139982
#139202
#138762
#138212
C4×#3852