Finite Group Databasebeta

← #665654

Subgroups — #665654

Order 512.

4190 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2512C211yesmaximal, characteristic, complemented
2C2×#2480C212yesmaximal, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4#15527C212yesmaximal, complemented
5#15308C212yesmaximal, complemented
6#15297C212yesmaximal, complemented
7#15297C212yesmaximal, complemented
8#15138C211yesmaximal, characteristic, complemented
9#15138C211yesmaximal, characteristic, complemented
10#15132C211yesmaximal, characteristic, complemented
11#15131C211yesmaximal, characteristic, complemented
12#14984C212yesmaximal, complemented
13#14917C212yesmaximal, complemented
14#14700C211yesmaximal, characteristic, complemented
15#14018C211yesmaximal, characteristic, complemented
16#13994C211yesmaximal, characteristic, complemented
17#13991C212yesmaximal, complemented
18#13977C211yesmaximal, characteristic, complemented
19#13920C211yesmaximal, characteristic, complemented
20#13902C211yesmaximal, characteristic
21#13902C211yesmaximal, characteristic
22C4×#390C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#126C2212yescomplemented
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29#2512—28no—
30#2480—216no—
31C2×#397C2212yes—
32C2×#397C2212yescomplemented
33C2×#397C2212yescomplemented
34C2×#397C2212yescomplemented
35C2×#396C2212yes—
36C2×#396C2212yescomplemented
37D4×C22⋊C4—28no—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#389C2211yescharacteristic, complemented
52C2×#388C2212yes—
53C2×#388C2211yescharacteristic
54C2×#388C2211yescharacteristic
55C2×#388C2212yescomplemented
56C2×#388C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#385C2212yescomplemented
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#384C2211yescharacteristic, complemented
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2212yescomplemented
68C2×#379C2212yes—
69C2×#379C2212yes—
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×C4×C4⋊C4C2211yescharacteristic, complemented
74C2×C4×C4⋊C4C2211yescharacteristic, complemented
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yescomplemented
79C2×C4×C22⋊C4C2212yescomplemented
80C2×C43C2211yescharacteristic, complemented
81#1443C2212yescomplemented
82#1442C2212yescomplemented
83#1442C2212yescomplemented
84#1441C2212yescomplemented
85#1441C2212yescomplemented
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yes—
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1437C2211yescharacteristic
106#1437C2211yescharacteristic
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1436C2211yescharacteristic, complemented
112#1436C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119#1434C2212yescomplemented
120#1434C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×D4—24no—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—42no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C24×C4C2312yes—
140C2×#126—28no—
141C2×#126—28no—
142C2×#126—44no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—42no—
148C2×C4×D4—42no—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C22⋊C4—28no—
164C22×C22⋊C4—28no—
165C22×C22⋊C4—44no—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208#397—28no—
209#397—28no—
210#397—28no—
211#397—28no—
212#396—28no—
213#396—28no—
214#390—24no—
215#390—24no—
216#390—24no—
217#390—24no—
218#390—24no—
219#390—24no—
220#390—24no—
221#390—42no—
222#390—42no—
223#390D418yes—
224#389—24no—
225#389—42no—
226#389—42no—
227#389—42no—
228#388—28no—
229#388—28no—
230#388—24no—
231#388—28no—
232#388—44no—
233#388D418yescomplemented
234#386—28no—
235#386—28no—
236#385—28no—
237#385—28no—
238#385—44no—
239#384—24no—
240#380—24no—
241#380—24no—
242#380—28no—
243#380—42no—
244#379—28no—
245#379—28no—
246#379—28no—
247#379—28no—
248#379—44no—
249C4×C4⋊C4—24no—
250C4×C4⋊C4—24no—
251C4×C22⋊C4—24no—
252C4×C22⋊C4—24no—
253C4×C22⋊C4—28no—
254C4×C22⋊C4—42no—
255C4×C22⋊C4—44no—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C43—42no—
293C25—24no—
294C25—24no—
295C25—24no—
296C25—24no—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—42no—
301C25—42no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25C2412yes—
309C25C2411yescharacteristic
310C25C2412yes—
311C22×D4—232no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—24no—
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—416no—
328C22×D4—416no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—416no—
332C22×D4—416no—
333C22×D4—416no—
334C22×D4—416no—
335C22×D4C2×D414yes—
336C22×D4#4114yes—
337C22×D4#4114yes—
338C22×D4#4114yes—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4#4114yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380#126—432no—
381C4×D4—416no—
382C4×D4—416no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×D414yes—
424C2×C4⋊C4C2×D414yescomplemented
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
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—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—432no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—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⋊C4C2×D414yes—
514C2×C22⋊C4C2×D418yes—
515C2×C22⋊C4C2×D414yes—
516C2×C22⋊C4C2×D414yes—
517C2×C22⋊C4C2×D418yes—
518C2×C22⋊C4#4114yes—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—24no—
523C2×C42—24no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—24no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—41no—
543C2×C42—41no—
544C2×C42—41no—
545C2×C42—41no—
546C2×C42—41no—
547C2×C42—41no—
548C2×C42—41no—
549C2×C42—41no—
550C2×C42C2×D414yes—
551C2×C42C2×D414yescomplemented
552#95—22no—
553#95—22no—
554#95—24no—
555#95—24no—
556#95—22no—
557#95—24no—
558#95—22no—
559#95—24no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—22no—
566#95—22no—
567#95—24no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—24no—
572#95—41no—
573#95—41no—
574#95—41no—
575#95—42no—
576#95—42no—
577#95—41no—
578#95—42no—
579#95—42no—
580#95—41no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95C2×D414yescomplemented
587#95C2×D414yescomplemented
588C24—22no—
589C24—21no—
590C24—22no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—21no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—216no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—48no—
628C24—48no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—48no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—84no—
644C24—84no—
645C24—84no—
646C24—84no—
647C24—84no—
648C24—84no—
649C24—84no—
650C24—84no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24C22×D414yes—
662C24C22×D412yes—
663C24C2×#4114yes—
664C24C2×#4114yes—
665C24C2×#4114yes—
666C24C2×#4112yes—
667C24C2×#4112yes—
668C24C2511yescharacteristic
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—4128no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4#126116yescomplemented
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—22no—
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—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
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—22no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—48no—
814C22×C4—48no—
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—48no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4—84no—
831C22×C4C22×D412yes—
832C22×C4C22×D412yes—
833C22×C4C22×D412yes—
834C22×C4C22×D412yes—
835C22×C4C22×D412yes—
836C22×C4C22×D414yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C2×#4112yes—
842C22×C4C2×#4112yes—
843C22×C4C2×#4112yes—
844C22×C4C2×#4112yes—
845C22×C4C2×#4112yes—
846C22×C4C2×#4112yes—
847C22×C4C2×#4112yes—
848C22×C4H(5,𝔽2)12yes—
849C22×C4H(5,𝔽2)12yes—
850C22×C4H(5,𝔽2)12yes—
851C22×C4H(5,𝔽2)12yes—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—84no—
863C4⋊C4—84no—
864C4⋊C4—84no—
865C4⋊C4—84no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—216no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—84no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—84no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C42—28no—
898C42—44no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—48no—
905C42—44no—
906C42—44no—
907C42—44no—
908C23—22no—
909C23—24no—
910C23—24no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—432no—
952C23—432no—
953C23—41no—
954C23—42no—
955C23—41no—
956C23—42no—
957C23—42no—
958C23—41no—
959C23—41no—
960C23—42no—
961C23—42no—
962C23—42no—
963C23—42no—
964C23—41no—
965C23—42no—
966C23—42no—
967C23—41no—
968C23—42no—
969C23—42no—
970C23—41no—
971C23—42no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—41no—
980C23—41no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—41no—
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—816no—
1014C23—816no—
1015C23—816no—
1016C23—816no—
1017C23—816no—
1018C23—816no—
1019C23—816no—
1020C23—816no—
1021C23—816no—
1022C23—816no—
1023C23—816no—
1024C23—816no—
1025C23—816no—
1026C23C2×#12618yes—
1027C23#53214yes—
1028C23C23×D411yescharacteristic
1029C23C23×D411yescharacteristic
1030C23C22×#4111yescharacteristic
1031C23C22×#4111yescharacteristic
1032C23C22×#4111yescharacteristic
1033C23C22×#4111yescharacteristic
1034C23C22×#4111yescharacteristic
1035C23C2×H(5,𝔽2)11yescharacteristic
1036C23C2×H(5,𝔽2)11yescharacteristic
1037C23C2×H(5,𝔽2)11yescharacteristic
1038C23C2×H(5,𝔽2)11yescharacteristic
1039C23#58511yescharacteristic
1040C23#58511yescharacteristic
1041C23#58511yescharacteristic
1042C23#58511yescharacteristic
1043D4—232no—
1044D4—432no—
1045D4—416no—
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—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
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—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—416no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—816no—
1180C2×C4—816no—
1181C2×C4#52514yes—
1182C2×C4C2×#12614yes—
1183C2×C4#53814yes—
1184C2×C4D4214yes—
1185C2×C4#54614yes—
1186C2×C4#54614yes—
1187C2×C4#55114yes—
1188C2×C4#55114yes—
1189C22—28no—
1190C22—28no—
1191C22—24no—
1192C22—28no—
1193C22—24no—
1194C22—24no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—44no—
1199C22—42no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—864no—
1227C22—82no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22C2×#52511yescharacteristic
1236C22C22×#12611yescharacteristic
1237C22C2×#53211yescharacteristic
1238C22C2×#53811yescharacteristic
1239C22#346011yescharacteristic
1240C22C2×D4211yescharacteristic
1241C22C2×#54611yescharacteristic
1242C22C2×#54611yescharacteristic
1243C22D4×#4111yescharacteristic
1244C22D4×#4111yescharacteristic
1245C22D4×#4111yescharacteristic
1246C22D4×#4111yescharacteristic
1247C22C2×#55111yescharacteristic
1248C22C2×#55111yescharacteristic
1249C22#347511yescharacteristic
1250C22#348111yescharacteristic
1251C22#348111yescharacteristic
1252C22#349411yescharacteristic
1253C22#349611yescharacteristic
1254C22#349611yescharacteristic
1255C22#349811yescharacteristic
1256C22#350011yescharacteristic
1257C22#350511yescharacteristic
1258C22#351011yescharacteristic
1259C22#351311yescharacteristic
1260C22#351411yescharacteristic
1261C22#351411yescharacteristic
1262C22#351911yescharacteristic
1263C22#352111yescharacteristic
1264C22#352111yescharacteristic
1265C22#352111yescharacteristic
1266C22#354211yescharacteristic
1267C22#354211yescharacteristic
1268C22#354611yescharacteristic
1269C22#356211yescharacteristic
1270C4—24no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—82no—
1283C4—81no—
1284C4—81no—
1285C4—82no—
1286C4—82no—
1287C4—82no—
1288C4—82no—
1289C4#248018yescomplemented
1290C2—48no—
1291C2—44no—
1292C2—84no—
1293C2C2×#248011yescharacteristic
1294C2#3468111yescharacteristic
1295C2#3561111yescharacteristic
1296C2D4×#12611yescharacteristic
1297C2#3624011yescharacteristic
1298C2#3626211yescharacteristic
1299C2#3626411yescharacteristic
1300C2#3825411yescharacteristic
1301C2#3904611yescharacteristic
1302C2#3940111yescharacteristic
1303C2#4016911yescharacteristic
1304C2#5941211yescharacteristic
1305C2#5941611yescharacteristic
1306C2#5980811yescharacteristic
1307C2#5981211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2512C2semidirect
2. C2×#2480C2semidirect
4. #15527C2semidirect
5. #15308C2semidirect
6. #15297C2semidirect
7. #15297C2semidirect
8. #15138C2semidirect
9. #15138C2semidirect
10. #15132C2semidirect
11. #15131C2semidirect
12. #14984C2semidirect
13. #14917C2semidirect
14. #14700C2semidirect
15. #14018C2semidirect
16. #13994C2semidirect
17. #13991C2semidirect
18. #13977C2semidirect
19. #13920C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
25. C22×#126C22semidirect
32. C2×#397C22semidirect
33. C2×#397C22semidirect
34. C2×#397C22semidirect
36. C2×#396C22semidirect
48. C2×#389C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
51. C2×#389C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
60. C2×#385C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#384C22semidirect
67. C2×#380C22semidirect
73. C2×C4×C4⋊C4C22semidirect
74. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C22⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C2×C43C22semidirect
81. #1443C22semidirect
82. #1442C22semidirect
83. #1442C22semidirect
84. #1441C22semidirect
85. #1441C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
233. #388D4semidirect
424. C2×C4⋊C4C2×D4semidirect
551. C2×C42C2×D4semidirect
586. #95C2×D4semidirect
587. #95C2×D4semidirect
690. C2×D4#126semidirect
1289. C4#2480semidirect

Maximal subgroups

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

subgroupindex
C2×#25122
C2×#24802
C2×D4×C22⋊C42
#155272
#153082
#152972
#151382
#151322
#151312
#149842
#149172
#147002
#140182
#139942
#139912
#139772
#139202
#139022
C4×#3902
C4×#3882