Finite Group Databasebeta

← #721549

Subgroups — #721549

Order 512.

4522 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2476C212yesmaximal, complemented
2C2×#2428C211yesmaximal, characteristic, complemented
3C2×#2424C212yesmaximal, complemented
4C2×#2342C211yesmaximal, characteristic, complemented
5#16984C211yesmaximal, characteristic, complemented
6#16502C211yesmaximal, characteristic, complemented
7#16363C211yesmaximal, characteristic, complemented
8#16363C211yesmaximal, characteristic, complemented
9#15776C212yesmaximal, complemented
10#15561C212yesmaximal, complemented
11#15340C212yesmaximal, complemented
12#15267C212yesmaximal, complemented
13#15124C211yesmaximal, characteristic, complemented
14#14977C212yesmaximal, complemented
15#14969C211yesmaximal, characteristic, complemented
16#14796C212yesmaximal, complemented
17#14716C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14321C211yesmaximal, characteristic, complemented
20#14228C211yesmaximal, characteristic, complemented
21#14189C211yesmaximal, characteristic, complemented
22C4×#392C211yesmaximal, characteristic, complemented
23#13788C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic, complemented
25C22×#121C2212yes—
26C22×#121C2212yes—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2212yes—
30C22×#120C2212yes—
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic, complemented
33C22×#117C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2476—216no—
37#2428—28no—
38#2424—216no—
39C2×#399C2212yescomplemented
40C2×#399C2212yescomplemented
41C2×#398C2212yescomplemented
42C2×#396C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yescomplemented
48C2×#394C2212yescomplemented
49C2×#392C2211yescharacteristic
50C2×#392C2211yescharacteristic
51C2×#392C2212yes—
52C2×#392C2211yescharacteristic
53C2×#392C2211yescharacteristic
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yes—
57#2342—28no—
58C2×#390C2212yes—
59C2×#390C2212yes—
60C2×#390C2212yes—
61C2×#390C2212yescomplemented
62C2×#390C2211yescharacteristic, complemented
63C2×#389C2211yescharacteristic, complemented
64C2×#388C2211yescharacteristic
65C2×#388C2211yescharacteristic
66C2×#388C2211yescharacteristic
67C2×#388C2211yescharacteristic
68C2×#388C2212yes—
69C2×#388C2212yescomplemented
70C2×#388C2212yescomplemented
71C2×#387C2212yescomplemented
72C2×#386C2212yes—
73C2×#386C2212yes—
74C2×#386C2212yes—
75C2×#386C2212yes—
76C2×#386C2212yescomplemented
77C2×#385C2211yescharacteristic
78C2×#385C2211yescharacteristic
79C2×#385C2212yes—
80C2×#385C2212yescomplemented
81C2×#381C2211yescharacteristic
82C2×#380C2211yescharacteristic
83C2×#379C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87C2×C4×C22⋊C4C2212yescomplemented
88#1445C2212yescomplemented
89#1445C2212yescomplemented
90#1444C2211yescharacteristic, complemented
91#1444C2211yescharacteristic, complemented
92#1444C2211yescharacteristic, complemented
93#1444C2211yescharacteristic, complemented
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2211yescharacteristic
99#1439C2212yes—
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2211yescharacteristic, complemented
111#1438C2212yescomplemented
112#1438C2211yescharacteristic, complemented
113#1438C2211yescharacteristic, complemented
114#1438C2211yescharacteristic, complemented
115#1438C2212yescomplemented
116#1437C2212yes—
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122#1434C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C2×#127—24no—
144C2×#127—44no—
145C2×#121—24no—
146C2×#121—24no—
147C2×#121—28no—
148C2×#121—28no—
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—44no—
152C2×#121—44no—
153C2×#121—44no—
154C2×#121—44no—
155C2×#120—28no—
156C2×#120—28no—
157C2×#120—44no—
158C2×#120—44no—
159C2×#120—44no—
160C2×#120—44no—
161C2×C4×D4—28no—
162C2×C4×D4—24no—
163C2×C4×D4—44no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×#117—24no—
167C2×#117—28no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—28no—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#399—44no—
229#399—44no—
230#398—28no—
231#396—28no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—28no—
238#392—28no—
239#392—24no—
240#392—24no—
241#392—24no—
242#392—24no—
243#392—28no—
244#392—44no—
245#392—44no—
246#390—28no—
247#390—28no—
248#390—24no—
249#390—44no—
250#390—44no—
251#389—24no—
252#388—24no—
253#388—24no—
254#388—28no—
255#388—24no—
256#388—24no—
257#388—28no—
258#388D4116yescomplemented
259#387—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—28no—
264#386—28no—
265#385—24no—
266#385—24no—
267#385—28no—
268#385—28no—
269#381—24no—
270#380—24no—
271#379—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—24no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4D418yescomplemented
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C25—22no—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—22no—
309C25—22no—
310C25—42no—
311C25—41no—
312C25—41no—
313C25—42no—
314C25—42no—
315C25C2412yes—
316C25C2411yescharacteristic
317C25C2412yes—
318C25C2411yescharacteristic
319C25C2411yescharacteristic
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
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—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
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×C4—41no—
411C23×C4—41no—
412C23×C4C2×D414yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431#127—416no—
432#121—416no—
433#121—416no—
434#121—432no—
435#121—432no—
436#120—432no—
437#120—432no—
438C4×D4—432no—
439C4×D4—416no—
440#117—416no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4C2×D418yes—
471C2×C22⋊C4—232no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
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—22no—
512C2×C22⋊C4—22no—
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—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
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—416no—
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—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4C2×D418yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D418yes—
574C2×C22⋊C4#4114yes—
575C2×C22⋊C4#4114yes—
576C2×C42—22no—
577C2×C42—24no—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42C2×D414yes—
588C2×C42C2×D418yes—
589C2×C42C2×D414yes—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95C2×D414yes—
615#95C2×D414yes—
616#95C2×D418yes—
617#95C2×D418yes—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—28no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—21no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—48no—
676C24—48no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—48no—
682C24—48no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—82no—
688C24—82no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24C22×D414yes—
698C24C22×D412yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24H(5,𝔽2)14yes—
702C24H(5,𝔽2)12yes—
703C24H(5,𝔽2)12yes—
704C24C2511yescharacteristic
705C2×D4—216no—
706C2×D4—28no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
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—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—21no—
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—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
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—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—84no—
875C22×C4—82no—
876C22×C4—82no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4C22×D412yes—
884C22×C4C22×D414yes—
885C22×C4C22×D412yes—
886C22×C4C22×D414yes—
887C22×C4C22×D414yes—
888C22×C4C22×D414yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D414yes—
893C22×C4C22×D412yes—
894C22×C4C22×D414yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4H(5,𝔽2)14yes—
900C4⋊C4—28no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—82no—
909C4⋊C4—82no—
910C4⋊C4—84no—
911C4⋊C4—84no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—48no—
941C22⋊C4—82no—
942C22⋊C4—84no—
943C22⋊C4—82no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4#127116yes—
949C42—44no—
950C42—48no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—84no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—416no—
992C23—416no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—41no—
999C23—41no—
1000C23—42no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—41no—
1033C23—41no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—41no—
1043C23—41no—
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—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—88no—
1095C23—88no—
1096C23—816no—
1097C23—88no—
1098C23—816no—
1099C23—816no—
1100C23—88no—
1101C23—816no—
1102C23—88no—
1103C23C2×#12714yes—
1104C23#54014yes—
1105C23C23×D411yescharacteristic
1106C23C23×D412yes—
1107C23C22×#4111yescharacteristic
1108C23C22×#4111yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)12yes—
1112C23C2×H(5,𝔽2)12yes—
1113C23#58512yes—
1114C23#58511yescharacteristic
1115C23#58511yescharacteristic
1116D4—416no—
1117D4—432no—
1118D4—816no—
1119D4—88no—
1120D4—816no—
1121D4—816no—
1122D4—816no—
1123D4—816no—
1124D4—816no—
1125D4—816no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—416no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
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—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—88no—
1227C2×C4—816no—
1228C2×C4—88no—
1229C2×C4—88no—
1230C2×C4#52514yes—
1231C2×C4C2×#12714yes—
1232C2×C4C2×#12714yes—
1233C22—24no—
1234C22—24no—
1235C22—28no—
1236C22—24no—
1237C22—24no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—42no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—42no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—832no—
1268C22—81no—
1269C22—82no—
1270C22—81no—
1271C22—81no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—81no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22C2×#52511yescharacteristic
1298C22C22×#12711yescharacteristic
1299C22#344911yescharacteristic
1300C22C2×#54011yescharacteristic
1301C22#345511yescharacteristic
1302C22D4×#4112yes—
1303C22D4×#4112yes—
1304C22#348411yescharacteristic
1305C22#348411yescharacteristic
1306C22#348412yes—
1307C22#348412yes—
1308C22#348811yescharacteristic
1309C22#348812yes—
1310C22#348812yes—
1311C22#348811yescharacteristic
1312C22#349411yescharacteristic
1313C22#349411yescharacteristic
1314C22#351912yes—
1315C22#351912yes—
1316C22#353412yes—
1317C22#354212yes—
1318C22#354512yes—
1319C22#356212yes—
1320C4—24no—
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—82no—
1338C2—44no—
1339C2—44no—
1340C2—84no—
1341C2—82no—
1342C2—162no—
1343C2#3493611yescharacteristic
1344C2#3526111yescharacteristic
1345C2#3535511yescharacteristic
1346C2#3592111yescharacteristic
1347C2#3592111yescharacteristic
1348C2#3772212yes—
1349C2#3773712yes—
1350C2#4060111yescharacteristic
1351C2#4198911yescharacteristic
1352C2#4310712yes—
1353C2#4443312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2476C2semidirect
2. C2×#2428C2semidirect
3. C2×#2424C2semidirect
4. C2×#2342C2semidirect
5. #16984C2semidirect
6. #16502C2semidirect
7. #16363C2semidirect
8. #16363C2semidirect
9. #15776C2semidirect
10. #15561C2semidirect
11. #15340C2semidirect
12. #15267C2semidirect
13. #15124C2semidirect
14. #14977C2semidirect
15. #14969C2semidirect
16. #14796C2semidirect
17. #14716C2semidirect
18. #14716C2semidirect
19. #14321C2semidirect
20. #14228C2semidirect
21. #14189C2semidirect
22. C4×#392C2semidirect
23. #13788C2semidirect
24. C22×#127C22semidirect
32. C22×C4×D4C22semidirect
39. C2×#399C22semidirect
40. C2×#399C22semidirect
41. C2×#398C22semidirect
47. C2×#394C22semidirect
48. C2×#394C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
63. C2×#389C22semidirect
69. C2×#388C22semidirect
70. C2×#388C22semidirect
71. C2×#387C22semidirect
76. C2×#386C22semidirect
80. C2×#385C22semidirect
87. C2×C4×C22⋊C4C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
258. #388D4semidirect
275. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24762
C2×#24282
C2×#24242
C2×#23422
#169842
#165022
#163632
#157762
#155612
#153402
#152672
#151242
#149772
#149692
#147962
#147162
#143212
#142282
#141892
C4×#3922
#137882