Finite Group Databasebeta

← #533225

Subgroups — #533225

Order 512.

4174 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×#2537C211yesmaximal, characteristic
2C2×#2364C212yesmaximal, complemented
3C2×#2361C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#14517C212yesmaximal, complemented
6#14417C212yesmaximal, complemented
7#14190C212yesmaximal, complemented
8#14181C212yesmaximal, complemented
9#14173C212yesmaximal, complemented
10#14108C212yesmaximal, complemented
11#14049C211yesmaximal, characteristic, complemented
12#14029C211yesmaximal, characteristic, complemented
13#14028C212yesmaximal, complemented
14#13994C211yesmaximal, characteristic, complemented
15#13974C211yesmaximal, characteristic, complemented
16#13970C211yesmaximal, characteristic, complemented
17#13970C211yesmaximal, characteristic, complemented
18#13872C211yesmaximal, characteristic, complemented
19#13820C211yesmaximal, characteristic, complemented
20D4×#95C211yesmaximal, characteristic, complemented
21C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
22C4×#380C211yesmaximal, characteristic, complemented
23C4×#386C211yesmaximal, characteristic, complemented
24C22×#121C2212yes—
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×D4C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2537C4116yescomplemented
36C2×#394C2212yes—
37C2×#394C2212yes—
38#2364—216no—
39#2361—28no—
40C4×#121—28no—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#387C2212yes—
51C2×#387C2212yes—
52C2×#386C2212yes—
53C2×#386C2211yescharacteristic
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2211yescharacteristic
59C2×#385C2212yes—
60C2×#384C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2212yes—
74C2×C4×C22⋊C4C2212yes—
75C2×C4×C22⋊C4C2212yes—
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C22×#95C2212yes—
79#1445C2212yes—
80#1445C2212yes—
81#1445C2212yes—
82#1443C2212yes—
83#1442C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1439C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1437C2212yes—
94#1437C2211yescharacteristic
95#1437C2212yes—
96#1437C2211yescharacteristic
97#1436C2211yescharacteristic
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2211yescharacteristic
106C4⋊#95C2211yescharacteristic
107C4⋊#95C2211yescharacteristic
108C4⋊#95C2211yescharacteristic
109C4⋊#95C2211yescharacteristic
110C4⋊#95C2211yescharacteristic
111#1434C2212yes—
112#1434C2212yes—
113C22⋊#95C2212yes—
114C22⋊#95C2212yes—
115C22⋊#95C2212yes—
116C22⋊#95C2212yes—
117C22⋊#95C2212yes—
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C4×#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C23×D4C2312yes—
128C23×D4C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#121—24no—
140C2×#121—28no—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—28no—
145C2×#121C2×C418yescomplemented
146C2×#121C2×C418yescomplemented
147C2×#121C2×C4116yescomplemented
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—28no—
151C2×C4×D4—24no—
152C2×C4×D4—28no—
153C2×C4×D4—28no—
154C2×C4×D4—28no—
155C2×C4×D4—24no—
156C2×C4×D4—44no—
157C2×C4×D4—42no—
158C2×C4×D4—42no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C2×C4×D4—42no—
162C2×C4×D4—42no—
163C2×C4×D4—44no—
164C2×C4×D4C2×C418yescomplemented
165C2×C4×D4C2×C418yescomplemented
166C22×C4⋊C4—24no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—42no—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C42—24no—
205C22×C42—24no—
206C22×C42—42no—
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218#394C2×C4116yescomplemented
219#394C2×C4116yescomplemented
220#390—24no—
221#390D418yescomplemented
222#389—24no—
223#389—24no—
224#388—28no—
225#388—28no—
226#388—28no—
227#388—28no—
228#387—28no—
229#387—28no—
230#387—44no—
231#386—28no—
232#386—24no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—28no—
237#386D418yescomplemented
238#385—28no—
239#384C2×C418yescomplemented
240#380—24no—
241#380—24no—
242#380—42no—
243#380C2×C418yescomplemented
244#380C2×C418yescomplemented
245#380C2×C4116yescomplemented
246C4×C4⋊C4—24no—
247C4×C4⋊C4—24no—
248C4×C4⋊C4—42no—
249C4×C4⋊C4—42no—
250C4×C22⋊C4—28no—
251C4×C22⋊C4—28no—
252C4×C22⋊C4—28no—
253C4×C22⋊C4—24no—
254C4×C22⋊C4—24no—
255C4×C22⋊C4—28no—
256C4×C22⋊C4—42no—
257C2×#95—28no—
258C2×#95C2311yescharacteristic
259C2×#95C2312yes—
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C25C2412yes—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—41no—
315C22×D4—41no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—41no—
319C22×D4—41no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4C22×C418yes—
323C22×D4C22×C418yes—
324C22×D4C22×C414yes—
325C22×D4C22×C414yes—
326C22×D4C2×D414yes—
327C22×D4C2×D414yes—
328C22×D4#4114yes—
329C22×D4#4114yes—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—42no—
368C23×C4—42no—
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×C4—42no—
382C23×C4C22×C414yes—
383C23×C4C22×C414yes—
384C23×C4C22×C418yes—
385C23×C4C2×D414yes—
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406#121—232no—
407#121—232no—
408#121—264no—
409C4×D4—416no—
410C4×D4—416no—
411C4×D4—416no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—416no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
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—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—416no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4C22×C414yes—
448C2×C4⋊C4C22×C418yes—
449C2×C4⋊C4C22×C414yes—
450C2×C4⋊C4C22×C414yes—
451C2×C4⋊C4C22×C414yes—
452C2×C4⋊C4C22×C418yes—
453C2×C4⋊C4C2×D414yes—
454C2×C4⋊C4#4114yes—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
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—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4C22×C418yes—
510C2×C22⋊C4C22×C418yes—
511C2×C22⋊C4C22×C418yes—
512C2×C22⋊C4C22×C418yes—
513C2×C22⋊C4C22×C418yes—
514C2×C22⋊C4C22×C414yes—
515C2×C22⋊C4C22×C414yes—
516C2×C22⋊C4C2×D414yes—
517C2×C22⋊C4C2×D418yes—
518C2×C22⋊C4C2×D414yes—
519C2×C22⋊C4C2×D418yes—
520C2×C22⋊C4C2×D414yes—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—24no—
528C2×C42—24no—
529C2×C42—24no—
530C2×C42—22no—
531C2×C42—24no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—24no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—416no—
545C2×C42—42no—
546C2×C42—41no—
547C2×C42—41no—
548C2×C42—42no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42C22×C414yes—
553C2×C42C2×D414yes—
554C2×C42#4114yes—
555#95—24no—
556#95—24no—
557#95—24no—
558#95—24no—
559#95—22no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—22no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—22no—
571#95—22no—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—41no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—41no—
583#95—42no—
584#95—41no—
585#95—41no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95C22×C418yes—
593#95C22×C418yes—
594#95C2×D414yes—
595#95C2×D414yes—
596C24—21no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—22no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—22no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24C23×C412yes—
633C24C23×C412yes—
634C24C23×C414yes—
635C24C22×D412yes—
636C24C22×D414yes—
637C24C22×D412yes—
638C24C2×#4114yes—
639C24C2×#4112yes—
640C24C2×#4112yes—
641C24C2511yescharacteristic
642C2×D4—216no—
643C2×D4—216no—
644C2×D4—216no—
645C2×D4—216no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—44no—
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×D4C4×D4116yes—
669C2×D4C4×D4116yescomplemented
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
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—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
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—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—216no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
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—48no—
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×C4—84no—
838C22×C4C23×C412yes—
839C22×C4C23×C412yes—
840C22×C4C23×C414yes—
841C22×C4C23×C414yes—
842C22×C4C23×C414yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D414yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C2×#4112yes—
856C22×C4C2×#4114yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4C2×#4112yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4H(5,𝔽2)12yes—
863C22×C4H(5,𝔽2)12yes—
864C22×C4H(5,𝔽2)12yes—
865C22×C42−1+412yes—
866C4⋊C4—216no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—48no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C42—28no—
902C42—28no—
903C42—28no—
904C42—44no—
905C42—44no—
906C42—48no—
907C42—48no—
908C42—44no—
909C42—44no—
910C42—84no—
911C42—84no—
912C23—22no—
913C23—22no—
914C23—24no—
915C23—22no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—24no—
921C23—24no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—41no—
1011C23—41no—
1012C23—42no—
1013C23—41no—
1014C23C2×C4×D418yes—
1015C23C2×C4×D414yes—
1016C23C2×C4×D414yes—
1017C23C24×C411yescharacteristic
1018C23C23×D411yescharacteristic
1019C23C23×D411yescharacteristic
1020C23C22×#4111yescharacteristic
1021C23C22×#4111yescharacteristic
1022C23C22×#4111yescharacteristic
1023C23C22×#4111yescharacteristic
1024C23C2×H(5,𝔽2)11yescharacteristic
1025C23C2×H(5,𝔽2)11yescharacteristic
1026C23C2×H(5,𝔽2)11yescharacteristic
1027C23C2×2−1+411yescharacteristic
1028C23#58511yescharacteristic
1029C23#58511yescharacteristic
1030C23#58511yescharacteristic
1031C23#58511yescharacteristic
1032D4—232no—
1033D4—416no—
1034D4—432no—
1035D4—432no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
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—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—416no—
1091C2×C4—416no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—816no—
1171C2×C4—816no—
1172C2×C4—816no—
1173C2×C4—816no—
1174C2×C4C2×C4×D414yes—
1175C2×C4C2×C4×D414yes—
1176C2×C4C4×#4114yes—
1177C2×C4#51814yes—
1178C2×C4D4214yes—
1179C2×C4#54614yes—
1180C2×C4#54614yes—
1181C2×C4#54714yes—
1182C2×C4#55314yes—
1183C2×C4#55314yes—
1184C22—28no—
1185C22—28no—
1186C22—24no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—28no—
1193C22—42no—
1194C22—44no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—44no—
1199C22—44no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—44no—
1205C22—44no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—44no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—42no—
1220C22—42no—
1221C22—44no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22C22×C4×D411yescharacteristic
1230C22C22×C4×D411yescharacteristic
1231C22C2×C4×#4111yescharacteristic
1232C22C2×#51811yescharacteristic
1233C22#342811yescharacteristic
1234C22C4×H(5,𝔽2)11yescharacteristic
1235C22C4×2−1+411yescharacteristic
1236C22C2×D4211yescharacteristic
1237C22C2×#54611yescharacteristic
1238C22C2×#54611yescharacteristic
1239C22C2×#54711yescharacteristic
1240C22D4×#4111yescharacteristic
1241C22D4×#4111yescharacteristic
1242C22D4×#4111yescharacteristic
1243C22C2×#55311yescharacteristic
1244C22C2×#55311yescharacteristic
1245C22#347511yescharacteristic
1246C22#348111yescharacteristic
1247C22#348211yescharacteristic
1248C22#348511yescharacteristic
1249C22#348911yescharacteristic
1250C22#349311yescharacteristic
1251C22#349411yescharacteristic
1252C22#349611yescharacteristic
1253C22#349611yescharacteristic
1254C22#350511yescharacteristic
1255C22#350511yescharacteristic
1256C22#351411yescharacteristic
1257C22#351511yescharacteristic
1258C22#352111yescharacteristic
1259C22#352411yescharacteristic
1260C22#353611yescharacteristic
1261C22#353911yescharacteristic
1262C22#354611yescharacteristic
1263C22#354711yescharacteristic
1264C4—24no—
1265C4—24no—
1266C4—24no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—44no—
1272C4—44no—
1273C4—42no—
1274C4—42no—
1275C4—44no—
1276C4—42no—
1277C4—44no—
1278C4—44no—
1279C4—82no—
1280C4—81no—
1281C4—82no—
1282C4—81no—
1283C4#236418yescomplemented
1284C2—48no—
1285C2—44no—
1286C2—44no—
1287C2C2×#236411yescharacteristic
1288C2C4×D4211yescharacteristic
1289C2C4×#54711yescharacteristic
1290C2#3420511yescharacteristic
1291C2#3428911yescharacteristic
1292C2#3430611yescharacteristic
1293C2#3441011yescharacteristic
1294C2#5901511yescharacteristic
1295C2#5902011yescharacteristic
1296C2#5903511yescharacteristic
1297C2#5903711yescharacteristic
1298C2#5921311yescharacteristic
1299C2#5921511yescharacteristic
1300C2#5939211yescharacteristic
1301C2#5939711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2537C2
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×#2364C2semidirect
3. C2×#2361C2semidirect
4. C2×C4×#121C2semidirect
5. #14517C2semidirect
6. #14417C2semidirect
7. #14190C2semidirect
8. #14181C2semidirect
9. #14173C2semidirect
10. #14108C2semidirect
11. #14049C2semidirect
12. #14029C2semidirect
13. #14028C2semidirect
14. #13994C2semidirect
15. #13974C2semidirect
16. #13970C2semidirect
17. #13970C2semidirect
18. #13872C2semidirect
19. #13820C2semidirect
20. D4×#95C2semidirect
21. C22⋊C4×C4⋊C4C2semidirect
22. C4×#380C2semidirect
23. C4×#386C2semidirect
35. #2537C4semidirect
145. C2×#121C2×C4semidirect
146. C2×#121C2×C4semidirect
147. C2×#121C2×C4semidirect
164. C2×C4×D4C2×C4semidirect
165. C2×C4×D4C2×C4semidirect
218. #394C2×C4semidirect
219. #394C2×C4semidirect
221. #390D4semidirect
237. #386D4semidirect
239. #384C2×C4semidirect
243. #380C2×C4semidirect
244. #380C2×C4semidirect
245. #380C2×C4semidirect
669. C2×D4C4×D4semidirect
1283. C4#2364semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#23642
C2×#23612
C2×C4×#1212
#145172
#144172
#141902
#141812
#141732
#141082
#140492
#140292
#140282
#139942
#139742
#139702
#138722
#138202
D4×#952
C22⋊C4×C4⋊C42
C4×#3802
C4×#3862