Finite Group Databasebeta

← #532459

Subgroups — #532459

Order 512.

4304 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2407C211yesmaximal, characteristic
2C2×#2363C211yesmaximal, characteristic, complemented
3C2×#2354C211yesmaximal, characteristic, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5C2×#2297C211yesmaximal, characteristic, complemented
6#14571C212yesmaximal, complemented
7#14519C212yesmaximal, complemented
8#14207C212yesmaximal, complemented
9#14182C212yesmaximal, complemented
10#14142C211yesmaximal, characteristic, complemented
11#14140C212yesmaximal, complemented
12#14138C211yesmaximal, characteristic, complemented
13#14129C211yesmaximal, characteristic, complemented
14#14007C212yesmaximal, complemented
15#14000C211yesmaximal, characteristic, complemented
16#13997C211yesmaximal, characteristic, complemented
17#13983C212yesmaximal, complemented
18#13977C211yesmaximal, characteristic, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13820C211yesmaximal, characteristic, complemented
21#13814C212yesmaximal, complemented
22C4×#380C211yesmaximal, characteristic, complemented
23C4×#386C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2407C4116yescomplemented
34C2×#394C2212yes—
35C2×#392C2212yes—
36#2363—28no—
37#2354—28no—
38#2339—28no—
39#2297—28no—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#385C2212yes—
65C2×#385C2212yes—
66C2×#385C2212yes—
67C2×#384C2211yescharacteristic
68C2×#381C2212yes—
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2212yes—
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2212yes—
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C22×#95C2212yes—
85#1445C2212yes—
86#1443C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2212yes—
99#1437C2211yescharacteristic
100#1437C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2211yescharacteristic
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2211yescharacteristic
112#1436C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C4×#95C2212yes—
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—42no—
133C22×#41—42no—
134C22×#41C2×C418yes—
135C23×Q8C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2312yes—
147C2×C22⋊Q8—42no—
148C2×C22⋊Q8—42no—
149C2×C22⋊Q8C2×C418yescomplemented
150C2×#121—24no—
151C2×#121—24no—
152C2×#121C2×C418yescomplemented
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C2×C4×D4C2×C418yescomplemented
162C2×#117—24no—
163C2×#117—24no—
164C2×#117—24no—
165C2×#117—24no—
166C2×#117—42no—
167C2×#117—42no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C42—24no—
204C22×C42—24no—
205C22×C42—42no—
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218#394C2×C4116yescomplemented
219#392C2×C4116yescomplemented
220#391—24no—
221#391—24no—
222#391—24no—
223#391—24no—
224#391C2×C418yescomplemented
225#390—24no—
226#390—28no—
227#390—28no—
228#390C2×C418yescomplemented
229#390D418yescomplemented
230#389—24no—
231#389—42no—
232#388—28no—
233#388—28no—
234#388—28no—
235#386—28no—
236#386—28no—
237#386—28no—
238#386—28no—
239#386—28no—
240#386—24no—
241#386—24no—
242#386—44no—
243#386C2×C4116yescomplemented
244#385—28no—
245#385—44no—
246#385C2×C4116yescomplemented
247#384—24no—
248#381—28no—
249#380—24no—
250#380C2×C418yescomplemented
251#380D418yescomplemented
252C4×C4⋊C4—24no—
253C4×C4⋊C4—24no—
254C4×C4⋊C4—28no—
255C4×C4⋊C4—42no—
256C4×C22⋊C4—24no—
257C4×C22⋊C4—28no—
258C4×C22⋊C4—28no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—44no—
263C4×C22⋊C4—42no—
264C2×#95—28no—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25C2411yescharacteristic
306C25C2412yes—
307C25C2411yescharacteristic
308C2×#41—232no—
309C2×#41—232no—
310C2×#41—416no—
311C2×#41—416no—
312C2×#41—416no—
313C2×#41—416no—
314C2×#41—416no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8C22×C414yes—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4C22×C414yes—
345C22×D4C22×C418yes—
346C22×D4C22×C414yes—
347C22×D4C22×C418yes—
348C22×D4C2×D414yes—
349C22×D4#4114yes—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—24no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4—41no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4C22×C414yes—
395C23×C4C22×C418yes—
396C23×C4C22×C414yes—
397C23×C4C2×D414yes—
398C23×C4#4114yes—
399C23×C4C2412yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C22⋊Q8—416no—
420#121—232no—
421C4×D4—232no—
422C4×D4—416no—
423C4×D4—416no—
424#117—416no—
425#117—416no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
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—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C22×C414yes—
457C2×C4⋊C4C22×C414yes—
458C2×C4⋊C4C22×C418yes—
459C2×C4⋊C4C2×D414yes—
460C2×C4⋊C4C2×D414yes—
461C2×C4⋊C4C2×D414yes—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
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—22no—
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—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
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—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C414yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C2×D418yes—
529C2×C22⋊C4C2×D418yes—
530C2×C22⋊C4C2×D418yes—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—24no—
536C2×C42—24no—
537C2×C42—24no—
538C2×C42—24no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—24no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—416no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—41no—
560C2×C42—41no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42C22×C414yes—
567C2×C42C2×D414yes—
568#95—22no—
569#95—24no—
570#95—24no—
571#95—22no—
572#95—22no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
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—24no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—22no—
591#95—22no—
592#95—42no—
593#95—42no—
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#95C22×C418yes—
603#95C22×C418yes—
604#95C22×C418yes—
605#95C2×D418yes—
606#95#4114yescomplemented
607#95#4114yescomplemented
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24C23×C412yes—
647C24C23×C414yes—
648C24C23×C412yes—
649C24C22×D412yes—
650C24C22×D414yes—
651C24C2×#4114yes—
652C24C2×#4112yes—
653C24C2511yescharacteristic
654#41—4128no—
655C2×Q8—28no—
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×D4—28no—
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—216no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—44no—
674C2×D4—48no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—84no—
686C2×D4—84no—
687C2×D4—84no—
688C2×D4—84no—
689C2×D4C4×D4116yes—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
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—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—216no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
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—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—216no—
791C22×C4—28no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
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—44no—
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×C4C4×D4116yes—
850C22×C4C23×C414yes—
851C22×C4C23×C412yes—
852C22×C4C23×C414yes—
853C22×C4C23×C414yes—
854C22×C4C23×C412yes—
855C22×C4C23×C412yes—
856C22×C4C23×C412yes—
857C22×C4C23×C412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D414yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4H(5,𝔽2)12yes—
876C22×C4H(5,𝔽2)12yes—
877C22×C4H(5,𝔽2)12yes—
878C22×C42−1+412yes—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—84no—
889C4⋊C4—84no—
890C4⋊C4—84no—
891C22⋊C4—28no—
892C22⋊C4—216no—
893C22⋊C4—28no—
894C22⋊C4—216no—
895C22⋊C4—216no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—84no—
914C42—28no—
915C42—28no—
916C42—48no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42—48no—
921C42—44no—
922C42—44no—
923C42—44no—
924C42—84no—
925C42—84no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—22no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—41no—
973C23—42no—
974C23—42no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—42no—
986C23—41no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—41no—
994C23—42no—
995C23—41no—
996C23—42no—
997C23—41no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23C2×C4×D418yes—
1030C23C2×C4×D414yes—
1031C23C24×C411yescharacteristic
1032C23C23×D411yescharacteristic
1033C23C23×D411yescharacteristic
1034C23C22×#4111yescharacteristic
1035C23C22×#4111yescharacteristic
1036C23C22×#4111yescharacteristic
1037C23C22×#4111yescharacteristic
1038C23C2×H(5,𝔽2)11yescharacteristic
1039C23C2×H(5,𝔽2)11yescharacteristic
1040C23C2×H(5,𝔽2)11yescharacteristic
1041C23C2×2−1+411yescharacteristic
1042C23#58511yescharacteristic
1043C23#58511yescharacteristic
1044C23#58511yescharacteristic
1045C23#58511yescharacteristic
1046Q8—416no—
1047D4—232no—
1048D4—416no—
1049D4—432no—
1050D4—816no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—232no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—432no—
1110C2×C4—416no—
1111C2×C4—416no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
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—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—416no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
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—41no—
1185C2×C4—42no—
1186C2×C4—816no—
1187C2×C4—816no—
1188C2×C4C2×C4×D414yes—
1189C2×C4C2×C4×D414yes—
1190C2×C4C2×C4×D414yes—
1191C2×C4C4×#4114yes—
1192C2×C4#51814yes—
1193C2×C4D4214yes—
1194C2×C4#54614yes—
1195C2×C4#54614yes—
1196C2×C4#54714yes—
1197C2×C4#55114yes—
1198C22—24no—
1199C22—28no—
1200C22—24no—
1201C22—28no—
1202C22—24no—
1203C22—28no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22C22×C4×D411yescharacteristic
1244C22C22×C4×D411yescharacteristic
1245C22C2×C4×#4111yescharacteristic
1246C22C2×#51811yescharacteristic
1247C22#342811yescharacteristic
1248C22C4×H(5,𝔽2)11yescharacteristic
1249C22C4×2−1+411yescharacteristic
1250C22C2×D4211yescharacteristic
1251C22C2×#54611yescharacteristic
1252C22C2×#54611yescharacteristic
1253C22C2×#54711yescharacteristic
1254C22D4×#4111yescharacteristic
1255C22D4×#4111yescharacteristic
1256C22D4×#4111yescharacteristic
1257C22C2×#55111yescharacteristic
1258C22#347511yescharacteristic
1259C22#347511yescharacteristic
1260C22#347511yescharacteristic
1261C22#348211yescharacteristic
1262C22#348511yescharacteristic
1263C22#348811yescharacteristic
1264C22#349211yescharacteristic
1265C22#349311yescharacteristic
1266C22#349611yescharacteristic
1267C22#349711yescharacteristic
1268C22#350611yescharacteristic
1269C22#350811yescharacteristic
1270C22#351411yescharacteristic
1271C22#351711yescharacteristic
1272C22#351911yescharacteristic
1273C22#352111yescharacteristic
1274C22#354011yescharacteristic
1275C22#354111yescharacteristic
1276C22#355411yescharacteristic
1277C22#356211yescharacteristic
1278C4—24no—
1279C4—24no—
1280C4—24no—
1281C4—44no—
1282C4—42no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—44no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—44no—
1292C4—44no—
1293C4—42no—
1294C4—81no—
1295C4—81no—
1296C4—82no—
1297C4#235818yes—
1298C2—44no—
1299C2—48no—
1300C2—82no—
1301C2C2×#235811yescharacteristic
1302C2#3413611yescharacteristic
1303C2C4×#54711yescharacteristic
1304C2#3427411yescharacteristic
1305C2#3429211yescharacteristic
1306C2#3433011yescharacteristic
1307C2#3447411yescharacteristic
1308C2#5901811yescharacteristic
1309C2#5902111yescharacteristic
1310C2#5906611yescharacteristic
1311C2#5912911yescharacteristic
1312C2#5927511yescharacteristic
1313C2#5928011yescharacteristic
1314C2#5956811yescharacteristic
1315C2#5981111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2407C2
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×#2354C2semidirect
4. C2×#2339C2semidirect
5. C2×#2297C2semidirect
6. #14571C2semidirect
7. #14519C2semidirect
8. #14207C2semidirect
9. #14182C2semidirect
10. #14142C2semidirect
11. #14140C2semidirect
12. #14138C2semidirect
13. #14129C2semidirect
14. #14007C2semidirect
15. #14000C2semidirect
16. #13997C2semidirect
17. #13983C2semidirect
18. #13977C2semidirect
19. #13970C2semidirect
20. #13820C2semidirect
21. #13814C2semidirect
22. C4×#380C2semidirect
23. C4×#386C2semidirect
33. #2407C4semidirect
149. C2×C22⋊Q8C2×C4semidirect
152. C2×#121C2×C4semidirect
161. C2×C4×D4C2×C4semidirect
218. #394C2×C4semidirect
219. #392C2×C4semidirect
224. #391C2×C4semidirect
228. #390C2×C4semidirect
229. #390D4semidirect
243. #386C2×C4semidirect
246. #385C2×C4semidirect
250. #380C2×C4semidirect
251. #380D4semidirect
606. #95#41semidirect
607. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24072
C2×#23632
C2×#23542
C2×#23392
C2×#22972
#145712
#145192
#142072
#141822
#141422
#141402
#141382
#141292
#140072
#140002
#139972
#139832
#139772
#139702
#138202
#138142
C4×#3802
C4×#3862