Finite Group Databasebeta

← #1393457

Subgroups — #1393457

Order 512.

4914 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2418C212yesmaximal, complemented
3C2×#2618C211yesmaximal, characteristic, complemented
4C22×#394C211yesmaximal, characteristic, complemented
5C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
6#17069C211yesmaximal, characteristic, complemented
7#16811C211yesmaximal, characteristic, complemented
8#16549C212yesmaximal, complemented
9#16514C212yesmaximal, complemented
10#16501C211yesmaximal, characteristic, complemented
11#16282C212yesmaximal, complemented
12#16261C211yesmaximal, characteristic, complemented
13#16256C212yesmaximal, complemented
14#15163C211yesmaximal, characteristic, complemented
15#14821C211yesmaximal, characteristic, complemented
16#14766C211yesmaximal, characteristic, complemented
17#14726C212yesmaximal, complemented
18#14726C212yesmaximal, complemented
19#14724C211yesmaximal, characteristic, complemented
20#14719C211yesmaximal, characteristic, complemented
21#14312C211yesmaximal, characteristic, complemented
22#13967C212yesmaximal, complemented
23#13899C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2212yescomplemented
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#120C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic, complemented
34C23×C22⋊C4C2212yes—
35C23×C22⋊C4C2212yes—
36#2618—28no—
37#2418—216no—
38#2408—28no—
39C2×#399C2212yescomplemented
40C2×#398C2211yescharacteristic, complemented
41C2×#398C2211yescharacteristic, complemented
42C2×#398C2211yescharacteristic, complemented
43C2×#397C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#396C2212yescomplemented
46C2×#396C2212yescomplemented
47C2×#396C2212yescomplemented
48C2×#394—28no—
49C2×#394C2211yescharacteristic
50C2×#394C2212yes—
51C2×#394C2211yescharacteristic
52C2×#394C2212yes—
53C2×#394C2211yescharacteristic
54C2×#394C2211yescharacteristic
55C2×#394C2212yes—
56C2×#394C2211yescharacteristic
57C2×#394C2212yes—
58C2×#394C2211yescharacteristic
59C2×#394C2212yescomplemented
60C2×#394C2212yescomplemented
61C2×#392C2212yes—
62D4×C4⋊C4—28no—
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#389C2211yescharacteristic, complemented
66C2×#389C2211yescharacteristic, complemented
67C2×#388C2212yescomplemented
68C2×#388C2212yescomplemented
69C2×#386C2212yes—
70C2×#386C2212yescomplemented
71C2×#386C2212yescomplemented
72C2×#386C2212yescomplemented
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2212yes—
76C2×#385C2212yes—
77C2×#385C2211yescharacteristic, complemented
78C2×#385C2211yescharacteristic, complemented
79C2×#384C2211yescharacteristic, complemented
80C2×#380C2211yescharacteristic
81C2×#380C2212yes—
82C2×#380C2211yescharacteristic
83C2×#380C2211yescharacteristic, complemented
84C2×#380C2211yescharacteristic, complemented
85C2×#379C2212yes—
86C2×#379C2212yes—
87C2×#379C2212yes—
88C2×C4×C4⋊C4C2211yescharacteristic, complemented
89C22×#95C2211yescharacteristic
90#1445C2211yescharacteristic, complemented
91#1444C2211yescharacteristic, complemented
92#1442C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2211yescharacteristic, complemented
95#1441C2211yescharacteristic, complemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2211yescharacteristic, complemented
99#1441C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1438C2211yescharacteristic
116#1438C2211yescharacteristic
117#1438C2212yes—
118#1438C2212yescomplemented
119#1438C2212yescomplemented
120#1437C2212yescomplemented
121#1437C2212yescomplemented
122C4⋊#95C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2211yescharacteristic, complemented
128C26C2312yes—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#123—28no—
148C2×#123—28no—
149C2×#123—44no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121—44no—
154C2×#121—42no—
155C2×#120—28no—
156C2×#120—28no—
157C2×#120—28no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—44no—
162C2×C4×D4—44no—
163C2×C4×D4D418yes—
164C2×C4×D4D418yescomplemented
165C22×C4⋊C4—24no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—24no—
169C22×C4⋊C4—42no—
170C22×C4⋊C4—42no—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C22⋊C4—28no—
193C22×C22⋊C4—28no—
194C22×C22⋊C4—28no—
195C22×C22⋊C4—44no—
196C22×C22⋊C4—44no—
197C22×C22⋊C4—44no—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2312yes—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#399—28no—
234#398—24no—
235#398—24no—
236#398—42no—
237#397—28no—
238#396—28no—
239#396—28no—
240#396—44no—
241#396—44no—
242#394—24no—
243#394—24no—
244#394—24no—
245#394—28no—
246#394—28no—
247#394—28no—
248#394—28no—
249#394—28no—
250#394—24no—
251#394—42no—
252#394—44no—
253#394D418yescomplemented
254#392—28no—
255#390—24no—
256#390—24no—
257#389—24no—
258#389—24no—
259#388—28no—
260#388—28no—
261#386—28no—
262#386—28no—
263#386—28no—
264#386—44no—
265#385—24no—
266#385—24no—
267#385—28no—
268#385—24no—
269#385—24no—
270#385—44no—
271#384—24no—
272#380—24no—
273#380—24no—
274#380—24no—
275#380—28no—
276#380—24no—
277#379—28no—
278#379—28no—
279#379—44no—
280C4×C4⋊C4—24no—
281C2×#95—24no—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C25—24no—
312C25—24no—
313C25—24no—
314C25—24no—
315C25—24no—
316C25—24no—
317C25—24no—
318C25—24no—
319C25—24no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25C2412yes—
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—416no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—416no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—416no—
365C22×D4—432no—
366C22×D4—432no—
367C22×D4C2×D414yes—
368C22×D4C2×D414yes—
369C22×D4C2×D414yes—
370C22×D4#4114yes—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—41no—
402C23×C4—41no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4C2×D414yes—
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2×D414yescomplemented
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431#123—432no—
432#121—416no—
433#121—416no—
434#120—432no—
435C4×D4—232no—
436C4×D4—416no—
437C4×D4—416no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
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—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—416no—
474C2×C4⋊C4—416no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4C2×D414yes—
496C2×C4⋊C4C2×D414yes—
497C2×C4⋊C4C2×D414yescomplemented
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
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—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—432no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—432no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4C2×D418yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D418yes—
590C2×C22⋊C4C2×D414yes—
591C2×C22⋊C4C2×D414yescomplemented
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—42no—
596C2×C42—42no—
597C2×C42C2×D414yes—
598C2×C42C2×D414yescomplemented
599#95—24no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—22no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—22no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95C2×D414yes—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—216no—
643C24—22no—
644C24—22no—
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—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24C22×D414yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C22×D412yes—
710C24C2×#4112yes—
711C24C2×#4112yes—
712C24H(5,𝔽2)14yes—
713C24H(5,𝔽2)14yes—
714C242−1+414yes—
715C24C2511yescharacteristic
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—4128no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4#121116yes—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
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—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—82no—
884C22×C4—82no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D414yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C2×#4112yes—
905C22×C4H(5,𝔽2)12yes—
906C22×C4H(5,𝔽2)12yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—82no—
923C4⋊C4—84no—
924C4⋊C4—82no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C4⋊C4—84no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—216no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C42—28no—
961C42—44no—
962C42—44no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—22no—
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—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
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—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—816no—
1077C23—816no—
1078C23—816no—
1079C23—816no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23C2×#12114yes—
1089C23C2×#12114yes—
1090C23#53414yes—
1091C23#53614yes—
1092C23#53718yes—
1093C23#53918yes—
1094C23C23×D411yescharacteristic
1095C23C23×D411yescharacteristic
1096C23C23×D411yescharacteristic
1097C23C22×#4111yescharacteristic
1098C23C2×H(5,𝔽2)12yes—
1099C23C2×H(5,𝔽2)11yescharacteristic
1100C23C2×H(5,𝔽2)11yescharacteristic
1101C23C2×H(5,𝔽2)12yes—
1102C23C2×2−1+412yes—
1103C23#58511yescharacteristic
1104C23#58512yes—
1105D4—232no—
1106D4—416no—
1107D4—416no—
1108D4—432no—
1109D4—816no—
1110D4—816no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—416no—
1148C2×C4—416no—
1149C2×C4—416no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—816no—
1227C2×C4—88no—
1228C2×C4C2×#12114yes—
1229C2×C4D4214yes—
1230C2×C4D4214yes—
1231C22—24no—
1232C22—28no—
1233C22—24no—
1234C22—28no—
1235C22—28no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—28no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—42no—
1251C22—44no—
1252C22—44no—
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—44no—
1266C22—864no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22#261818yescomplemented
1284C22C22×#12111yescharacteristic
1285C22C2×#53411yescharacteristic
1286C22C2×#53611yescharacteristic
1287C22C2×#53712yes—
1288C22C2×#53912yes—
1289C22C2×D4211yescharacteristic
1290C22C2×D4211yescharacteristic
1291C22D4×#4111yescharacteristic
1292C22#348412yes—
1293C22#348411yescharacteristic
1294C22#348812yes—
1295C22#348811yescharacteristic
1296C22#348912yes—
1297C22#349611yescharacteristic
1298C22#350011yescharacteristic
1299C22#351312yes—
1300C22#351911yescharacteristic
1301C22#353212yes—
1302C22#353312yes—
1303C22#353512yes—
1304C22#353612yes—
1305C22#354212yes—
1306C22#356112yes—
1307C4—24no—
1308C4—24no—
1309C4—24no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—81no—
1319C4—81no—
1320C4—82no—
1321C4—82no—
1322C4—82no—
1323C4—82no—
1324C4—81no—
1325C4—82no—
1326C2—28no—
1327C2—44no—
1328C2—84no—
1329C2—84no—
1330C2C2×#261811yescharacteristic
1331C2#3572811yescharacteristic
1332C2D4×#12111yescharacteristic
1333C2#3764411yescharacteristic
1334C2#3764812yes—
1335C2#3767611yescharacteristic
1336C2#3771212yes—
1337C2#4051412yes—
1338C2#4059211yescharacteristic
1339C2#4068812yes—
1340C2#4193311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2408C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2418C2semidirect
3. C2×#2618C2semidirect
4. C22×#394C2semidirect
5. C2×D4×C4⋊C4C2semidirect
6. #17069C2semidirect
7. #16811C2semidirect
8. #16549C2semidirect
9. #16514C2semidirect
10. #16501C2semidirect
11. #16282C2semidirect
12. #16261C2semidirect
13. #16256C2semidirect
14. #15163C2semidirect
15. #14821C2semidirect
16. #14766C2semidirect
17. #14726C2semidirect
18. #14726C2semidirect
19. #14724C2semidirect
20. #14719C2semidirect
21. #14312C2semidirect
22. #13967C2semidirect
23. #13899C2semidirect
25. C22×#123C22semidirect
33. C23×C4⋊C4C22semidirect
39. C2×#399C22semidirect
40. C2×#398C22semidirect
41. C2×#398C22semidirect
42. C2×#398C22semidirect
43. C2×#397C22semidirect
44. C2×#396C22semidirect
45. C2×#396C22semidirect
46. C2×#396C22semidirect
47. C2×#396C22semidirect
59. C2×#394C22semidirect
60. C2×#394C22semidirect
65. C2×#389C22semidirect
66. C2×#389C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
72. C2×#386C22semidirect
77. C2×#385C22semidirect
78. C2×#385C22semidirect
79. C2×#384C22semidirect
83. C2×#380C22semidirect
84. C2×#380C22semidirect
88. C2×C4×C4⋊C4C22semidirect
90. #1445C22semidirect
91. #1444C22semidirect
92. #1442C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
118. #1438C22semidirect
119. #1438C22semidirect
120. #1437C22semidirect
121. #1437C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
127. C22⋊#95C22semidirect
164. C2×C4×D4D4semidirect
253. #394D4semidirect
411. C23×C4C2×D4semidirect
497. C2×C4⋊C4C2×D4semidirect
591. C2×C22⋊C4C2×D4semidirect
598. C2×C42C2×D4semidirect
1283. C22#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#24182
C2×#26182
C22×#3942
C2×D4×C4⋊C42
#170692
#168112
#165492
#165142
#165012
#162822
#162612
#162562
#151632
#148212
#147662
#147262
#147242
#147192
#143122
#139672
#138992