Finite Group Databasebeta

← #663734

Subgroups — #663734

Order 512.

4194 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2480C212yesmaximal, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×C4×#126C211yesmaximal, characteristic, complemented
4#15795C212yesmaximal, complemented
5#15452C212yesmaximal, complemented
6#15297C212yesmaximal, complemented
7#15282C212yesmaximal, complemented
8#15147C211yesmaximal, characteristic, complemented
9#15134C211yesmaximal, characteristic, complemented
10#15132C211yesmaximal, characteristic, complemented
11#15132C211yesmaximal, characteristic, complemented
12#14924C212yesmaximal, complemented
13#14756C212yesmaximal, complemented
14#14700C211yesmaximal, characteristic, complemented
15#14022C211yesmaximal, characteristic, complemented
16#14018C211yesmaximal, characteristic, complemented
17#14018C211yesmaximal, characteristic, complemented
18#13906C211yesmaximal, characteristic, complemented
19#13902C211yesmaximal, characteristic
20#13902C211yesmaximal, characteristic
21#13876C211yesmaximal, characteristic, complemented
22#13873C212yesmaximal, complemented
23C4×#390C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#126C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29#2480—216no—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yescomplemented
33C2×#396C2212yescomplemented
34C2×#396C2212yescomplemented
35D4×C22⋊C4—28no—
36C4×#126—28no—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic, complemented
48C2×#389C2211yescharacteristic, complemented
49C2×#388C2211yescharacteristic
50C2×#388C2212yes—
51C2×#388C2211yescharacteristic
52C2×#388C2211yescharacteristic
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#388C2212yescomplemented
56C2×#387C2211yescharacteristic, complemented
57C2×#387C2211yescharacteristic, complemented
58C2×#387C2211yescharacteristic, complemented
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#384C2211yescharacteristic, complemented
64C2×#383C2211yescharacteristic, complemented
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2212yescomplemented
69C2×#380C2212yescomplemented
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×#379C2212yes—
74C2×#379C2212yes—
75C2×C4×C4⋊C4C2211yescharacteristic, complemented
76C2×C4×C4⋊C4C2211yescharacteristic, complemented
77C2×C4×C4⋊C4C2211yescharacteristic, complemented
78C2×C4×C4⋊C4C2211yescharacteristic, complemented
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yescomplemented
83C2×C4×C22⋊C4C2212yescomplemented
84C2×C43C2211yescharacteristic, complemented
85#1443C2212yescomplemented
86#1443C2212yescomplemented
87#1442C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1439C2212yes—
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120C4⋊#95C2211yescharacteristic, complemented
121C4⋊#95C2211yescharacteristic, complemented
122C4⋊#95C2211yescharacteristic, complemented
123C4⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
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—24no—
141C2×#126—24no—
142C2×#126D418yescomplemented
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⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4—28no—
166C22×C22⋊C4—28no—
167C22×C22⋊C4—28no—
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⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210#397—28no—
211#397—28no—
212#397—28no—
213#396—28no—
214#396—44no—
215#390—24no—
216#390—24no—
217#390—24no—
218#390—24no—
219#390—24no—
220#390—24no—
221#390—24no—
222#390—24no—
223#390—42no—
224#390—42no—
225#389—42no—
226#389—42no—
227#388—28no—
228#388—24no—
229#388—24no—
230#388—24no—
231#388—28no—
232#388—28no—
233#388—44no—
234#387—24no—
235#387—24no—
236#387—24no—
237#386—28no—
238#386—28no—
239#385—28no—
240#385—28no—
241#384—42no—
242#383—24no—
243#380—24no—
244#380—28no—
245#380—44no—
246#380—42no—
247#380—42no—
248#379—28no—
249#379—28no—
250#379—28no—
251#379—44no—
252#379—44no—
253C4×C4⋊C4—24no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—24no—
256C4×C4⋊C4—42no—
257C4×C22⋊C4—24no—
258C4×C22⋊C4—24no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—44no—
261C4×C22⋊C4D418yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C43—24no—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25C2412yes—
313C25C2411yescharacteristic
314C25C2412yes—
315C22×D4—232no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—416no—
332C22×D4—416no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—416no—
336C22×D4—416no—
337C22×D4—416no—
338C22×D4—416no—
339C22×D4#4114yes—
340C22×D4#4114yes—
341C22×D4#4114yes—
342C22×D4#4114yes—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4C2×D414yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384#126—232no—
385C4×D4—416no—
386C4×D4—416no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
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—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4C2×D414yescomplemented
433C2×C4⋊C4C2×D414yescomplemented
434C2×C4⋊C4C2×D414yescomplemented
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
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—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—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—41no—
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—432no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4C2×D414yes—
524C2×C22⋊C4C2×D414yes—
525C2×C22⋊C4C2×D414yes—
526C2×C22⋊C4C2×D414yes—
527C2×C22⋊C4C2×D414yes—
528C2×C22⋊C4#4114yes—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
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—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—24no—
553C2×C42—41no—
554C2×C42—41no—
555C2×C42—41no—
556C2×C42—41no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42C2×D414yes—
560C2×C42C2×D414yes—
561C2×C42C2×D414yescomplemented
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—24no—
567#95—24no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95C2×D414yes—
595#95C2×D414yes—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—216no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24C22×D412yes—
670C24C22×D412yes—
671C24C2×#4114yes—
672C24C2×#4112yes—
673C24C2×#4114yes—
674C24C2×#4114yes—
675C24C2×#4114yes—
676C24C2511yescharacteristic
677C2×D4—216no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—4128no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4#126116yescomplemented
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—21no—
711C22×C4—21no—
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—21no—
721C22×C4—21no—
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—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
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—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—21no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
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—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—84no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4C22×D412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C2×#4112yes—
851C22×C4C2×#4112yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4H(5,𝔽2)12yes—
857C22×C4H(5,𝔽2)12yes—
858C22×C4H(5,𝔽2)12yes—
859C22×C4H(5,𝔽2)12yes—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—84no—
873C4⋊C4—84no—
874C4⋊C4—84no—
875C4⋊C4—84no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4#121116yes—
907C42—28no—
908C42—28no—
909C42—28no—
910C42—44no—
911C42—44no—
912C42—44no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—44no—
917C42—84no—
918C23—22no—
919C23—24no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—432no—
962C23—432no—
963C23—42no—
964C23—41no—
965C23—42no—
966C23—41no—
967C23—42no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—41no—
977C23—41no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—42no—
988C23—41no—
989C23—42no—
990C23—41no—
991C23—42no—
992C23—42no—
993C23—41no—
994C23—41no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—816no—
1024C23—816no—
1025C23—816no—
1026C23—816no—
1027C23—816no—
1028C23—816no—
1029C23—816no—
1030C23—816no—
1031C23—816no—
1032C23—816no—
1033C23—816no—
1034C23—816no—
1035C23—816no—
1036C23C2×#12114yes—
1037C23C2×#12618yes—
1038C23C23×D411yescharacteristic
1039C23C23×D411yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C22×#4111yescharacteristic
1044C23C22×#4111yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23#58511yescharacteristic
1050C23#58511yescharacteristic
1051C23#58511yescharacteristic
1052C23#58511yescharacteristic
1053D4—232no—
1054D4—432no—
1055D4—416no—
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—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—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—416no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—816no—
1189C2×C4—816no—
1190C2×C4C2×#12114yes—
1191C2×C4C2×#12114yes—
1192C2×C4#52514yes—
1193C2×C4C2×#12614yes—
1194C2×C4#53814yes—
1195C2×C4#54614yes—
1196C2×C4#54614yes—
1197C2×C4#55114yes—
1198C2×C4#55114yes—
1199C22—28no—
1200C22—28no—
1201C22—24no—
1202C22—28no—
1203C22—24no—
1204C22—24no—
1205C22—42no—
1206C22—44no—
1207C22—44no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—864no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22C22×#12111yescharacteristic
1246C22C2×#52511yescharacteristic
1247C22C22×#12611yescharacteristic
1248C22#344911yescharacteristic
1249C22C2×#53811yescharacteristic
1250C22C2×#54611yescharacteristic
1251C22C2×#54611yescharacteristic
1252C22D4×#4111yescharacteristic
1253C22D4×#4111yescharacteristic
1254C22D4×#4111yescharacteristic
1255C22D4×#4111yescharacteristic
1256C22C2×#55111yescharacteristic
1257C22C2×#55111yescharacteristic
1258C22#347511yescharacteristic
1259C22#347511yescharacteristic
1260C22#348111yescharacteristic
1261C22#348111yescharacteristic
1262C22#348811yescharacteristic
1263C22#348811yescharacteristic
1264C22#349811yescharacteristic
1265C22#349811yescharacteristic
1266C22#351311yescharacteristic
1267C22#351311yescharacteristic
1268C22#351411yescharacteristic
1269C22#351411yescharacteristic
1270C22#351411yescharacteristic
1271C22#351411yescharacteristic
1272C22#351911yescharacteristic
1273C22#352111yescharacteristic
1274C22#352111yescharacteristic
1275C22#352111yescharacteristic
1276C22#354611yescharacteristic
1277C22#355811yescharacteristic
1278C22#356211yescharacteristic
1279C22#356211yescharacteristic
1280C4—24no—
1281C4—24no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—82no—
1292C4—82no—
1293C4—81no—
1294C4—82no—
1295C4—82no—
1296C4—81no—
1297C4—82no—
1298C4—82no—
1299C4#248018yescomplemented
1300C2—48no—
1301C2—44no—
1302C2—84no—
1303C2C2×#248011yescharacteristic
1304C2#3493511yescharacteristic
1305C2#3552211yescharacteristic
1306C2D4×#12611yescharacteristic
1307C2#3624011yescharacteristic
1308C2#3625811yescharacteristic
1309C2#3625811yescharacteristic
1310C2#3803411yescharacteristic
1311C2#3890211yescharacteristic
1312C2#3903411yescharacteristic
1313C2#3940511yescharacteristic
1314C2#5947611yescharacteristic
1315C2#5947611yescharacteristic
1316C2#5948411yescharacteristic
1317C2#5948811yescharacteristic
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×#2480C2semidirect
3. C2×C4×#126C2semidirect
4. #15795C2semidirect
5. #15452C2semidirect
6. #15297C2semidirect
7. #15282C2semidirect
8. #15147C2semidirect
9. #15134C2semidirect
10. #15132C2semidirect
11. #15132C2semidirect
12. #14924C2semidirect
13. #14756C2semidirect
14. #14700C2semidirect
15. #14022C2semidirect
16. #14018C2semidirect
17. #14018C2semidirect
18. #13906C2semidirect
21. #13876C2semidirect
22. #13873C2semidirect
23. C4×#390C2semidirect
32. C2×#397C22semidirect
33. C2×#396C22semidirect
34. C2×#396C22semidirect
47. C2×#389C22semidirect
48. C2×#389C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#387C22semidirect
57. C2×#387C22semidirect
58. C2×#387C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#384C22semidirect
64. C2×#383C22semidirect
68. C2×#380C22semidirect
69. C2×#380C22semidirect
75. C2×C4×C4⋊C4C22semidirect
76. C2×C4×C4⋊C4C22semidirect
77. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C4⋊C4C22semidirect
82. C2×C4×C22⋊C4C22semidirect
83. C2×C4×C22⋊C4C22semidirect
84. C2×C43C22semidirect
85. #1443C22semidirect
86. #1443C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. C4⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
142. C2×#126D4semidirect
432. C2×C4⋊C4C2×D4semidirect
433. C2×C4⋊C4C2×D4semidirect
434. C2×C4⋊C4C2×D4semidirect
561. C2×C42C2×D4semidirect
698. C2×D4#126semidirect
1299. C4#2480semidirect

Maximal subgroups

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

subgroupindex
C2×#24802
C2×D4×C22⋊C42
C2×C4×#1262
#157952
#154522
#152972
#152822
#151472
#151342
#151322
#149242
#147562
#147002
#140222
#140182
#139062
#139022
#138762
#138732
C4×#3902