Finite Group Databasebeta

← #526104

Subgroups — #526104

Order 512.

4238 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#2325C212yesmaximal, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#14698C211yesmaximal, characteristic, complemented
6#14572C212yesmaximal, complemented
7#14523C212yesmaximal, complemented
8#14391C212yesmaximal, complemented
9#14361C212yesmaximal, complemented
10#14299C212yesmaximal, complemented
11#14173C212yesmaximal, complemented
12#14133C211yesmaximal, characteristic, complemented
13#14042C211yesmaximal, characteristic, complemented
14#14025C211yesmaximal, characteristic, complemented
15#14018C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13999C212yesmaximal, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13906C211yesmaximal, characteristic, complemented
21#13876C211yesmaximal, characteristic, complemented
22D4×#95C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2428C4116yescomplemented
36C2×#394C2212yes—
37C2×#392C2212yes—
38#2366—28no—
39#2325—216no—
40C4×#121—28no—
41C2×#390C2212yes—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#387C2212yes—
55C2×#387C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#385C2212yes—
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#384C2211yescharacteristic
70C2×#380C2212yes—
71C2×#380C2211yescharacteristic
72C2×#380C2212yes—
73C2×#380C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2212yes—
82#1443C2212yes—
83#1443C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1441C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2211yescharacteristic
105#1436C2211yescharacteristic
106#1436C2211yescharacteristic
107#1436C2211yescharacteristic
108C4⋊#95C2211yescharacteristic
109C4⋊#95C2211yescharacteristic
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116#1434C2212yes—
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C2×#127—24no—
141C2×#127—24no—
142C2×#127C2×C418yescomplemented
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—28no—
146C2×#121—28no—
147C2×#121—42no—
148C2×#121—42no—
149C2×#121C2×C4116yescomplemented
150C2×#121C2×C418yescomplemented
151C2×#121C2×C418yescomplemented
152C2×C4×D4—24no—
153C2×C4×D4—28no—
154C2×C4×D4—28no—
155C2×C4×D4—28no—
156C2×C4×D4—28no—
157C2×C4×D4—24no—
158C2×C4×D4—42no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C2×C4×D4—42no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C2×C4×D4C2×C418yescomplemented
169C2×C4×D4D418yescomplemented
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C42—24no—
209C22×C42—42no—
210C22×C42—42no—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221#394C2×C4116yescomplemented
222#392C2×C4116yescomplemented
223#390—24no—
224#390—24no—
225#390—28no—
226#390—24no—
227#390—42no—
228#390—42no—
229#390C2×C418yescomplemented
230#389—24no—
231#389C2×C418yescomplemented
232#388—28no—
233#388—28no—
234#388—28no—
235#388—44no—
236#387—28no—
237#387—28no—
238#386—28no—
239#386—28no—
240#386—28no—
241#386—28no—
242#386—28no—
243#386—28no—
244#386—28no—
245#386—44no—
246#386—44no—
247#386C2×C4116yescomplemented
248#385—28no—
249#385—24no—
250#385D418yescomplemented
251#384—42no—
252#380—28no—
253#380—24no—
254#380—44no—
255#380—42no—
256C4×C4⋊C4—24no—
257C4×C4⋊C4—24no—
258C4×C4⋊C4—24no—
259C4×C4⋊C4—42no—
260C4×C22⋊C4—28no—
261C4×C22⋊C4—42no—
262C4×C22⋊C4C2×C418yescomplemented
263C2×#95—28no—
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C25C2412yes—
303C25C2412yes—
304C25C2411yescharacteristic
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
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×D4C22×C414yes—
340C22×D4C22×C418yes—
341C22×D4C22×C418yes—
342C22×D4C22×C414yes—
343C22×D4C22×C418yes—
344C22×D4C22×C418yes—
345C22×D4C2×D414yes—
346C22×D4#4114yes—
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—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—41no—
372C23×C4—41no—
373C23×C4—41no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4C22×C414yes—
393C23×C4C22×C418yes—
394C23×C4C2×D418yes—
395C23×C4C2×D414yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416#127—232no—
417#121—232no—
418#121—264no—
419#121—416no—
420C4×D4—416no—
421C4×D4—416no—
422C4×D4—432no—
423C4×D4—416no—
424C4×D4—432no—
425C4×D4—416no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C418yes—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2×D414yes—
467C2×C4⋊C4C2×D414yes—
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—22no—
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—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—41no—
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—41no—
512C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
530C2×C22⋊C4C22×C418yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C418yes—
533C2×C22⋊C4C22×C414yes—
534C2×C22⋊C4C22×C418yes—
535C2×C22⋊C4C22×C414yes—
536C2×C22⋊C4C2×D418yes—
537C2×C22⋊C4C2×D414yes—
538C2×C22⋊C4C2×D414yes—
539C2×C22⋊C4#4114yes—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—22no—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—24no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—416no—
563C2×C42—42no—
564C2×C42—41no—
565C2×C42—41no—
566C2×C42—41no—
567C2×C42—41no—
568C2×C42C22×C414yes—
569C2×C42C22×C414yes—
570C2×C42C2×D414yes—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—22no—
577#95—24no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—22no—
589#95—22no—
590#95—42no—
591#95—41no—
592#95—42no—
593#95—41no—
594#95—42no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95C22×C414yes—
605#95C22×C414yes—
606#95C22×C418yes—
607#95C2×D414yes—
608#95C2×D414yes—
609C24—21no—
610C24—22no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—22no—
632C24—21no—
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×D414yes—
651C24C22×D412yes—
652C24C2×#4114yes—
653C24C2×#4112yes—
654C24C2511yescharacteristic
655C2×D4—216no—
656C2×D4—216no—
657C2×D4—216no—
658C2×D4—216no—
659C2×D4—216no—
660C2×D4—216no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—84no—
689C2×D4—84no—
690C2×D4—84no—
691C2×D4—84no—
692C2×D4—84no—
693C2×D4—84no—
694C2×D4—84no—
695C2×D4—84no—
696C2×D4C4×D4116yes—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—216no—
780C22×C4—216no—
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—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4C23×C412yes—
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C23×C414yes—
863C22×C4C23×C414yes—
864C22×C4C23×C412yes—
865C22×C4C23×C412yes—
866C22×C4C23×C412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D414yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C2×#4112yes—
878C22×C4C2×#4112yes—
879C22×C4C2×#4112yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C4H(5,𝔽2)12yes—
882C22×C4H(5,𝔽2)12yes—
883C22×C4H(5,𝔽2)12yes—
884C22×C4H(5,𝔽2)12yes—
885C22×C42−1+412yes—
886C4⋊C4—28no—
887C4⋊C4—216no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—84no—
899C4⋊C4—84no—
900C22⋊C4—216no—
901C22⋊C4—216no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4C4×D4116yescomplemented
924C42—28no—
925C42—28no—
926C42—28no—
927C42—48no—
928C42—44no—
929C42—44no—
930C42—44no—
931C42—44no—
932C42—44no—
933C42—48no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—22no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—24no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—41no—
994C23—42no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
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—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23C2×C4×D418yes—
1038C23C2×C4×D414yes—
1039C23C24×C411yescharacteristic
1040C23C23×D411yescharacteristic
1041C23C23×D411yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C22×#4111yescharacteristic
1044C23C2×H(5,𝔽2)11yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23C2×2−1+411yescharacteristic
1050C23#58511yescharacteristic
1051C23#58511yescharacteristic
1052C23#58511yescharacteristic
1053C23#58511yescharacteristic
1054D4—232no—
1055D4—432no—
1056D4—432no—
1057D4—416no—
1058D4—816no—
1059D4—816no—
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—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—416no—
1112C2×C4—416no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—416no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—816no—
1194C2×C4—816no—
1195C2×C4—816no—
1196C2×C4—816no—
1197C2×C4C2×C4×D414yes—
1198C2×C4C2×C4×D414yes—
1199C2×C4C2×C4×D414yes—
1200C2×C4#51814yes—
1201C2×C4#52014yes—
1202C2×C4#53414yes—
1203C2×C4#53714yes—
1204C2×C4#53814yes—
1205C2×C4#53914yes—
1206C2×C4D4214yes—
1207C22—24no—
1208C22—28no—
1209C22—28no—
1210C22—24no—
1211C22—24no—
1212C22—28no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—44no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22C22×C4×D411yescharacteristic
1253C22C22×C4×D411yescharacteristic
1254C22C2×#51811yescharacteristic
1255C22C2×#52011yescharacteristic
1256C22#342811yescharacteristic
1257C22C4×H(5,𝔽2)11yescharacteristic
1258C22C4×H(5,𝔽2)11yescharacteristic
1259C22C2×#53411yescharacteristic
1260C22C2×#53711yescharacteristic
1261C22C2×#53811yescharacteristic
1262C22C2×#53911yescharacteristic
1263C22C2×D4211yescharacteristic
1264C22D4×#4111yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22#348111yescharacteristic
1267C22#348511yescharacteristic
1268C22#348811yescharacteristic
1269C22#349611yescharacteristic
1270C22#349611yescharacteristic
1271C22#349711yescharacteristic
1272C22#349811yescharacteristic
1273C22#350611yescharacteristic
1274C22#350711yescharacteristic
1275C22#351411yescharacteristic
1276C22#351411yescharacteristic
1277C22#351911yescharacteristic
1278C22#352111yescharacteristic
1279C22#353911yescharacteristic
1280C22#354211yescharacteristic
1281C22#354211yescharacteristic
1282C22#354211yescharacteristic
1283C22#354611yescharacteristic
1284C22#354811yescharacteristic
1285C22#355711yescharacteristic
1286C22#356211yescharacteristic
1287C4—24no—
1288C4—24no—
1289C4—24no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—44no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—82no—
1302C4—82no—
1303C4—81no—
1304C4—81no—
1305C4—82no—
1306C4#232518yescomplemented
1307C2—44no—
1308C2—48no—
1309C2—84no—
1310C2C2×#232511yescharacteristic
1311C2C4×D4211yescharacteristic
1312C2#3420611yescharacteristic
1313C2#3429211yescharacteristic
1314C2#3431011yescharacteristic
1315C2#3442311yescharacteristic
1316C2#3447711yescharacteristic
1317C2#3933811yescharacteristic
1318C2#3934111yescharacteristic
1319C2#3940111yescharacteristic
1320C2#3940911yescharacteristic
1321C2#3985711yescharacteristic
1322C2#3986111yescharacteristic
1323C2#4014511yescharacteristic
1324C2#4014911yescharacteristic
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×#2366C2semidirect
3. C2×#2325C2semidirect
4. C2×C4×#121C2semidirect
5. #14698C2semidirect
6. #14572C2semidirect
7. #14523C2semidirect
8. #14391C2semidirect
9. #14361C2semidirect
10. #14299C2semidirect
11. #14173C2semidirect
12. #14133C2semidirect
13. #14042C2semidirect
14. #14025C2semidirect
15. #14018C2semidirect
16. #14001C2semidirect
17. #13999C2semidirect
18. #13970C2semidirect
19. #13970C2semidirect
20. #13906C2semidirect
21. #13876C2semidirect
22. D4×#95C2semidirect
23. C4×#385C2semidirect
35. #2428C4semidirect
142. C2×#127C2×C4semidirect
149. C2×#121C2×C4semidirect
150. C2×#121C2×C4semidirect
151. C2×#121C2×C4semidirect
168. C2×C4×D4C2×C4semidirect
169. C2×C4×D4D4semidirect
221. #394C2×C4semidirect
222. #392C2×C4semidirect
229. #390C2×C4semidirect
231. #389C2×C4semidirect
247. #386C2×C4semidirect
250. #385D4semidirect
262. C4×C22⋊C4C2×C4semidirect
923. C22⋊C4C4×D4semidirect
1306. C4#2325semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#23662
C2×#23252
C2×C4×#1212
#146982
#145722
#145232
#143912
#143612
#142992
#141732
#141332
#140422
#140252
#140182
#140012
#139992
#139702
#139062
#138762
D4×#952
C4×#3852