Finite Group Databasebeta

← #518689

Subgroups — #518689

Order 512.

5558 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2358C212yesmaximal, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#2275C211yesmaximal, characteristic, complemented
5#14312C211yesmaximal, characteristic, complemented
6#14311C211yesmaximal, characteristic, complemented
7#14275C211yesmaximal, characteristic, complemented
8#14228C211yesmaximal, characteristic, complemented
9#14227C211yesmaximal, characteristic, complemented
10#14176C211yesmaximal, characteristic, complemented
11#14175C211yesmaximal, characteristic, complemented
12#14100C212yesmaximal, complemented
13#14082C212yesmaximal, complemented
14#14036C212yesmaximal, complemented
15#14023C212yesmaximal, complemented
16#13971C212yesmaximal, complemented
17#13967C212yesmaximal, complemented
18#13960C211yesmaximal, characteristic, complemented
19C4×#394C211yesmaximal, characteristic, complemented
20C4×#392C211yesmaximal, characteristic, complemented
21C2×#1438C211yesmaximal, characteristic, complemented
22#13802C211yesmaximal, characteristic, complemented
23C22⋊C42C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C22×#121C2212yes—
26C22×#120C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yescomplemented
33C23×C22⋊C4C2212yes—
34C23×C22⋊C4C2212yes—
35C23×C22⋊C4C2212yes—
36#2408C4116yescomplemented
37C2×#394C2211yescharacteristic
38C2×#394C2211yescharacteristic
39C2×#392C2211yescharacteristic
40C2×#392C2211yescharacteristic
41#2358—216no—
42D4×C22⋊C4—28no—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yescomplemented
47C2×#388C2212yescomplemented
48C2×#388C2212yescomplemented
49C2×#388C2212yescomplemented
50C2×#388C2212yescomplemented
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#385C2212yes—
59C2×#385C2212yescomplemented
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#379C2212yes—
63C2×#379C2212yes—
64#2275—28no—
65C2×C4×C4⋊C4C2211yescharacteristic, complemented
66C2×C4×C4⋊C4C2211yescharacteristic, complemented
67C2×C4×C4⋊C4C2211yescharacteristic, complemented
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2211yescharacteristic, complemented
74C2×C4×C22⋊C4C2211yescharacteristic, complemented
75C2×C4×C22⋊C4C2211yescharacteristic, complemented
76C2×C4×C22⋊C4C2212yescomplemented
77C2×C4×C22⋊C4C2212yescomplemented
78C2×#376C2211yescharacteristic, complemented
79C22×#95C2211yescharacteristic
80C22×#95C2211yescharacteristic
81C22×#95C2211yescharacteristic, complemented
82#1444C2211yescharacteristic, complemented
83#1444C2211yescharacteristic, complemented
84#1442C2211yescharacteristic, complemented
85#1442C2211yescharacteristic, complemented
86#1441C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2211yescharacteristic, complemented
89#1441C2211yescharacteristic, complemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2211yescharacteristic, complemented
94#1439C2212yescomplemented
95#1439C2211yescharacteristic, complemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2211yescharacteristic
101#1438C2211yescharacteristic
102#1438C2211yescharacteristic
103#1438C2211yescharacteristic
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117#1434C2211yescharacteristic, complemented
118#1434C2211yescharacteristic, complemented
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—44no—
131C23×D4—44no—
132C23×D4C2×C418yescomplemented
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C24×C4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C2×#121—44no—
149C2×#121—44no—
150C2×#121C2×C4116yescomplemented
151C2×#120—28no—
152C2×#120—28no—
153C2×#120C2×C4116yescomplemented
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—28no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C2×C4×D4C2×C418yescomplemented
169C2×C4×D4D418yescomplemented
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—28no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#394C2×C418yescomplemented
229#394C2×C418yescomplemented
230#392C2×C418yescomplemented
231#392C2×C418yescomplemented
232#390—28no—
233#390—24no—
234#390—24no—
235#390C2×C4116yescomplemented
236#388—28no—
237#388—28no—
238#388—44no—
239#388—44no—
240#386—28no—
241#386—28no—
242#386—28no—
243#386—28no—
244#386—28no—
245#386—44no—
246#386—44no—
247#385—28no—
248#385—28no—
249#380—24no—
250#380C2×C418yescomplemented
251#379—28no—
252#379C2×C4116yescomplemented
253C4×C4⋊C4—24no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—24no—
256C4×C22⋊C4—28no—
257C4×C22⋊C4—24no—
258C4×C22⋊C4—24no—
259C4×C22⋊C4—24no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—44no—
264C4×C22⋊C4—44no—
265C4×C22⋊C4D418yescomplemented
266#376—24no—
267C2×#95—24no—
268C2×#95—24no—
269C2×#95—24no—
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—24no—
311C25—24no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25C22×C418yes—
319C25C2412yes—
320C25C2411yescharacteristic
321C25C2412yes—
322C25C2411yescharacteristic
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—232no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—432no—
355C22×D4—416no—
356C22×D4—416no—
357C22×D4—432no—
358C22×D4C22×C414yes—
359C22×D4C22×C418yes—
360C22×D4C22×C418yes—
361C22×D4C22×C414yes—
362C22×D4C22×C418yes—
363C22×D4C22×C414yes—
364C22×D4C2×D414yes—
365C22×D4#4114yes—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4C22×C414yes—
411C23×C4C22×C414yes—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4C2×D414yescomplemented
415C23×C4#4114yes—
416C23×C4#4114yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436#121—432no—
437#120—264no—
438C4×D4—232no—
439C4×D4—232no—
440C4×D4—232no—
441C4×D4—432no—
442C4×D4—416no—
443C4×D4—416no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C418yes—
465C2×C4⋊C4C2×D414yescomplemented
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
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—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—432no—
520C2×C22⋊C4—432no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—432no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4C22×C414yes—
546C2×C22⋊C4C22×C414yes—
547C2×C22⋊C4C22×C418yes—
548C2×C22⋊C4C22×C418yes—
549C2×C22⋊C4C22×C418yes—
550C2×C22⋊C4C22×C418yes—
551C2×C22⋊C4C22×C418yes—
552C2×C22⋊C4C22×C418yes—
553C2×C22⋊C4C22×C418yes—
554C2×C22⋊C4C2×D414yes—
555C2×C22⋊C4C2×D414yes—
556C2×C22⋊C4C2×D414yes—
557C2×C22⋊C4C2×D414yescomplemented
558C2×C22⋊C4#4114yes—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—24no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—24no—
573C2×C42—42no—
574C2×C42—42no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42C22×C414yes—
583C2×C42C2×D414yes—
584C2×C42C2×D414yes—
585C2×C42C2×D414yescomplemented
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—22no—
602#95—24no—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95C22×C414yes—
617#95C22×C414yes—
618#95C2×D414yes—
619#95C2×D414yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—216no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—216no—
660C24—216no—
661C24—216no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24C23×C414yes—
694C24C23×C412yes—
695C24C23×C414yes—
696C24C23×C412yes—
697C24C22×D412yes—
698C24C22×D412yes—
699C24C22×D412yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24C2×#4112yes—
704C24C2×#4112yes—
705C24H(5,𝔽2)14yes—
706C24H(5,𝔽2)14yes—
707C24C2511yescharacteristic
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—216no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—4128no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4C4×D4116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
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—22no—
792C22×C4—22no—
793C22×C4—22no—
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—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—82no—
856C22×C4—84no—
857C22×C4—82no—
858C22×C4—82no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—82no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—82no—
868C22×C4—84no—
869C22×C4—82no—
870C22×C4—82no—
871C22×C4—82no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—82no—
876C22×C4—82no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4C4×D4116yescomplemented
881C22×C4C23×C414yes—
882C22×C4C23×C414yes—
883C22×C4C23×C412yes—
884C22×C4C23×C412yes—
885C22×C4C23×C412yes—
886C22×C4C23×C412yes—
887C22×C4C23×C412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4C2×#4112yes—
902C22×C4C2×#4112yes—
903C22×C4C2×#4112yes—
904C22×C4C2×#4112yes—
905C22×C4C2×#4112yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—84no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—28no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4#121116yescomplemented
945C42—28no—
946C42—28no—
947C42—28no—
948C42—44no—
949C42—44no—
950C42—48no—
951C42—82no—
952C42—84no—
953C42—82no—
954C42—82no—
955C42—82no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—432no—
1010C23—432no—
1011C23—432no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—432no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—816no—
1076C23—816no—
1077C23—816no—
1078C23C2×C4×D414yes—
1079C23C2×C4×D414yes—
1080C23C2×C4×D414yes—
1081C23C4×#4114yes—
1082C23#51818yes—
1083C23C2×#12114yes—
1084C23#52514yes—
1085C23#52914yes—
1086C23#53214yes—
1087C23C24×C411yescharacteristic
1088C23C23×D411yescharacteristic
1089C23C23×D411yescharacteristic
1090C23C22×#4111yescharacteristic
1091C23C22×#4111yescharacteristic
1092C23C22×#4111yescharacteristic
1093C23C22×#4111yescharacteristic
1094C23C2×H(5,𝔽2)12yes—
1095C23C2×H(5,𝔽2)12yes—
1096C23C2×H(5,𝔽2)12yes—
1097C23#58512yes—
1098D4—232no—
1099D4—232no—
1100D4—432no—
1101D4—416no—
1102D4—432no—
1103D4—816no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4—816no—
1212C2×C4—816no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—88no—
1216C2×C4—816no—
1217C2×C4C2×C4×D414yes—
1218C2×C4C2×C4×D414yes—
1219C2×C4C2×C4×D414yes—
1220C2×C4C2×#12114yes—
1221C2×C4C2×#12114yes—
1222C22—28no—
1223C22—28no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—28no—
1231C22—28no—
1232C22—28no—
1233C22—24no—
1234C22—28no—
1235C22—28no—
1236C22—28no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—44no—
1247C22—44no—
1248C22—42no—
1249C22—42no—
1250C22—44no—
1251C22—42no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—864no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22C4×#12118yes—
1275C22C22×C4×D411yescharacteristic
1276C22C22×C4×D411yescharacteristic
1277C22C2×C4×#4111yescharacteristic
1278C22C2×#51812yes—
1279C22C4×H(5,𝔽2)12yes—
1280C22C22×#12111yescharacteristic
1281C22C2×#52511yescharacteristic
1282C22C2×#52911yescharacteristic
1283C22C2×#53211yescharacteristic
1284C22#348412yes—
1285C22#348411yescharacteristic
1286C22#348411yescharacteristic
1287C22#348812yes—
1288C22#349012yes—
1289C22#349012yes—
1290C22#349412yes—
1291C22#349412yes—
1292C22#349811yescharacteristic
1293C22#350011yescharacteristic
1294C22#351312yes—
1295C22#351312yes—
1296C22#351912yes—
1297C22#351912yes—
1298C4—24no—
1299C4—24no—
1300C4—24no—
1301C4—24no—
1302C4—24no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—82no—
1315C4—82no—
1316C4—82no—
1317C2—28no—
1318C2—44no—
1319C2—48no—
1320C2—84no—
1321C2C2×C4×#12111yescharacteristic
1322C2#3419811yescharacteristic
1323C2#3427511yescharacteristic
1324C2#3429012yes—
1325C2#3430212yes—
1326C2#3569111yescharacteristic
1327C2#3569211yescharacteristic
1328C2#3572811yescharacteristic
1329C2#3572911yescharacteristic
1330C2#3590412yes—
1331C2#3592212yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2408C2
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×#2358C2semidirect
3. C2×D4×C22⋊C4C2semidirect
4. C2×#2275C2semidirect
5. #14312C2semidirect
6. #14311C2semidirect
7. #14275C2semidirect
8. #14228C2semidirect
9. #14227C2semidirect
10. #14176C2semidirect
11. #14175C2semidirect
12. #14100C2semidirect
13. #14082C2semidirect
14. #14036C2semidirect
15. #14023C2semidirect
16. #13971C2semidirect
17. #13967C2semidirect
18. #13960C2semidirect
19. C4×#394C2semidirect
20. C4×#392C2semidirect
21. C2×#1438C2semidirect
22. #13802C2semidirect
23. C22⋊C42C2semidirect
32. C22×C4×D4C22semidirect
36. #2408C4semidirect
46. C2×#390C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
50. C2×#388C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
59. C2×#385C22semidirect
65. C2×C4×C4⋊C4C22semidirect
66. C2×C4×C4⋊C4C22semidirect
67. C2×C4×C4⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
75. C2×C4×C22⋊C4C22semidirect
76. C2×C4×C22⋊C4C22semidirect
77. C2×C4×C22⋊C4C22semidirect
78. C2×#376C22semidirect
81. C22×#95C22semidirect
82. #1444C22semidirect
83. #1444C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
118. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
132. C23×D4C2×C4semidirect
150. C2×#121C2×C4semidirect
153. C2×#120C2×C4semidirect
168. C2×C4×D4C2×C4semidirect
169. C2×C4×D4D4semidirect
228. #394C2×C4semidirect
229. #394C2×C4semidirect
230. #392C2×C4semidirect
231. #392C2×C4semidirect
235. #390C2×C4semidirect
250. #380C2×C4semidirect
252. #379C2×C4semidirect
265. C4×C22⋊C4D4semidirect
414. C23×C4C2×D4semidirect
465. C2×C4⋊C4C2×D4semidirect
557. C2×C22⋊C4C2×D4semidirect
585. C2×C42C2×D4semidirect
746. C2×D4C4×D4semidirect
880. C22×C4C4×D4semidirect
944. C22⋊C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#23582
C2×D4×C22⋊C42
C2×#22752
#143122
#143112
#142752
#142282
#142272
#141762
#141752
#141002
#140822
#140362
#140232
#139712
#139672
#139602
C4×#3942
C4×#3922
C2×#14382
#138022
C22⋊C422