Finite Group Databasebeta

← #4932166

Subgroups — #4932166

Order 512.

4652 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic, complemented
2C2×#2424C212yesmaximal, complemented
3C2×#2273C211yesmaximal, characteristic, complemented
4#15204C211yesmaximal, characteristic, complemented
5#15165C211yesmaximal, characteristic, complemented
6#15124C211yesmaximal, characteristic, complemented
7#15124C211yesmaximal, characteristic, complemented
8#14996C211yesmaximal, characteristic, complemented
9#14996C211yesmaximal, characteristic, complemented
10#14764C212yesmaximal, complemented
11#14754C212yesmaximal, complemented
12#14751C212yesmaximal, complemented
13#14716C211yesmaximal, characteristic, complemented
14#14716C212yesmaximal, complemented
15#14716C211yesmaximal, characteristic, complemented
16#14311C211yesmaximal, characteristic, complemented
17#14228C211yesmaximal, characteristic, complemented
18#14187C212yesmaximal, complemented
19#14175C211yesmaximal, characteristic, complemented
20#14100C212yesmaximal, complemented
21#14100C212yesmaximal, complemented
22#13948C211yesmaximal, characteristic, complemented
23C4×#392C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic, complemented
25C22×#121C2212yes—
26C22×#121C2212yes—
27C22×#121C2212yes—
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#120C2212yes—
31C22×#120C2212yes—
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic, complemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37#2428—28no—
38#2424—216no—
39C2×#396C2212yes—
40C2×#394C2212yes—
41C2×#394C2212yes—
42C2×#394C2212yescomplemented
43C2×#392C2211yescharacteristic
44C2×#392C2212yes—
45C2×#392C2211yescharacteristic
46C2×#392C2212yes—
47C2×#392C2211yescharacteristic
48C2×#392C2211yescharacteristic
49C2×#392C2212yes—
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic, complemented
52C2×#390C2212yescomplemented
53C2×#390C2212yescomplemented
54C2×#389C2211yescharacteristic, complemented
55C2×#388C2212yes—
56C2×#388C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#388C2212yescomplemented
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yescomplemented
66C2×#385C2212yes—
67#2273—28no—
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2212yescomplemented
81#1444C2211yescharacteristic, complemented
82#1444C2211yescharacteristic, complemented
83#1442C2211yescharacteristic, complemented
84#1442C2211yescharacteristic, complemented
85#1442C2212yescomplemented
86#1441C2212yescomplemented
87#1441C2212yescomplemented
88#1440C2212yescomplemented
89#1439C2211yescharacteristic
90#1439C2211yescharacteristic
91#1439C2211yescharacteristic
92#1439C2212yes—
93#1439C2211yescharacteristic
94#1439C2212yes—
95#1439C2212yescomplemented
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1438C2211yescharacteristic, complemented
107#1438C2211yescharacteristic, complemented
108#1438C2211yescharacteristic, complemented
109#1438C2211yescharacteristic, complemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C4×#95C2211yescharacteristic, complemented
126C26C2311yescharacteristic
127C23×D4C2312yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×#127—24no—
145C2×#127—44no—
146C2×#121—28no—
147C2×#121—24no—
148C2×#121—24no—
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—28no—
152C2×#121—28no—
153C2×#121—44no—
154C2×#121—44no—
155C2×#121—44no—
156C2×#121—44no—
157C2×#121—44no—
158C2×#121—44no—
159C2×#120—28no—
160C2×#120—28no—
161C2×#120—44no—
162C2×#120—44no—
163C2×#120—44no—
164C2×#120—44no—
165C2×C4×D4—28no—
166C2×C4×D4—24no—
167C2×C4×D4—44no—
168C2×C4×D4—44no—
169C2×C4×D4—44no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4D418yescomplemented
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#396—28no—
231#394—28no—
232#394—28no—
233#394—28no—
234#392—28no—
235#392—28no—
236#392—24no—
237#392—24no—
238#392—28no—
239#392—24no—
240#392—24no—
241#390—28no—
242#390—24no—
243#390—44no—
244#390—44no—
245#389—24no—
246#388—28no—
247#388—44no—
248#388—44no—
249#388—44no—
250#386—28no—
251#386—28no—
252#386—28no—
253#386—44no—
254#386—44no—
255#386—44no—
256#386—44no—
257#385—28no—
258C4×C22⋊C4—24no—
259C4×C22⋊C4—24no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—24no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4—24no—
267C4×C22⋊C4—24no—
268C4×C22⋊C4—24no—
269C4×C22⋊C4—44no—
270C4×C22⋊C4D418yescomplemented
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25C2×D414yes—
312C25C2412yes—
313C25C2412yes—
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
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—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
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—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
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×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2×D414yes—
419C23×C4#4114yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438#127—416no—
439#121—432no—
440#121—416no—
441#121—432no—
442#121—416no—
443#121—432no—
444#120—432no—
445#120—432no—
446C4×D4—432no—
447C4×D4—416no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
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×C22⋊C4—232no—
468C2×C22⋊C4—232no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—232no—
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—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—42no—
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⋊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—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⋊C4C2×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4#4114yes—
572C2×C22⋊C4#4114yes—
573C2×C22⋊C4#4114yes—
574C2×C22⋊C4#4114yes—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42—42no—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95C2×D414yes—
623#95C2×D414yes—
624C24—28no—
625C24—28no—
626C24—28no—
627C24—28no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—28no—
653C24—28no—
654C24—28no—
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—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—48no—
685C24—48no—
686C24—82no—
687C24—82no—
688C24—84no—
689C24—82no—
690C24—82no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24C22×D412yes—
701C24C22×D412yes—
702C24C22×D412yes—
703C24C22×D412yes—
704C24C2×#4112yes—
705C24C2×#4112yes—
706C24C2×#4112yes—
707C24C2×#4112yes—
708C24C2×#4112yes—
709C24H(5,𝔽2)14yes—
710C24C2511yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
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—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4—44no—
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—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—44no—
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—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
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—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
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—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—28no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—28no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—82no—
872C22×C4—84no—
873C22×C4—82no—
874C22×C4—82no—
875C22×C4—82no—
876C22×C4—84no—
877C22×C4—82no—
878C22×C4—82no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—82no—
891C22×C4—82no—
892C22×C4—84no—
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×C4C2×#4112yes—
904C22×C4C2×#4112yes—
905C22×C4C2×#4112yes—
906C22×C4C2×#4112yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2×#4112yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4C2×#4112yes—
913C22×C4H(5,𝔽2)14yes—
914C22×C4H(5,𝔽2)14yes—
915C22×C4H(5,𝔽2)14yes—
916C4⋊C4—28no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—84no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—216no—
928C22⋊C4—216no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
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—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4#121116yescomplemented
958C42—44no—
959C42—44no—
960C42—48no—
961C42—82no—
962C42—82no—
963C42—82no—
964C42—82no—
965C42—82no—
966C42—82no—
967C23—232no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—22no—
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—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
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—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—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—816no—
1105C23—88no—
1106C23—88no—
1107C23—816no—
1108C23—88no—
1109C23—816no—
1110C23—816no—
1111C23—88no—
1112C23—88no—
1113C23—88no—
1114C23C2×#12114yes—
1115C23#53214yes—
1116C23#53214yes—
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C22×#4111yescharacteristic
1121C23C22×#4111yescharacteristic
1122C23C22×#4111yescharacteristic
1123C23C22×#4111yescharacteristic
1124C23C2×H(5,𝔽2)12yes—
1125C23C2×H(5,𝔽2)12yes—
1126C23C2×H(5,𝔽2)12yes—
1127C23C2×H(5,𝔽2)12yes—
1128D4—416no—
1129D4—432no—
1130D4—816no—
1131D4—816no—
1132D4—88no—
1133D4—816no—
1134D4—816no—
1135D4—816no—
1136D4—816no—
1137D4—816no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
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—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—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—88no—
1237C2×C4—88no—
1238C2×C4—88no—
1239C2×C4—88no—
1240C2×C4—816no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4C2×#12114yes—
1244C2×C4C2×#12114yes—
1245C2×C4#52514yes—
1246C2×C4#52514yes—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—28no—
1251C22—24no—
1252C22—24no—
1253C22—28no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22—44no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—832no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22C22×#12111yescharacteristic
1312C22C2×#52511yescharacteristic
1313C22C2×#52511yescharacteristic
1314C22C2×#53211yescharacteristic
1315C22C2×#53211yescharacteristic
1316C22#344411yescharacteristic
1317C22#344411yescharacteristic
1318C22#348411yescharacteristic
1319C22#348411yescharacteristic
1320C22#348412yes—
1321C22#348412yes—
1322C22#349012yes—
1323C22#349811yescharacteristic
1324C22#349811yescharacteristic
1325C22#350812yes—
1326C22#351912yes—
1327C22#351912yes—
1328C22#351912yes—
1329C22#351912yes—
1330C22#351912yes—
1331C22#351912yes—
1332C22#351912yes—
1333C22#351912yes—
1334C4—24no—
1335C4—24no—
1336C4—24no—
1337C4—24no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—44no—
1345C4—42no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—82no—
1350C4—82no—
1351C4—82no—
1352C2—44no—
1353C2—44no—
1354C2—44no—
1355C2—84no—
1356C2—162no—
1357C2#3535511yescharacteristic
1358C2#3539512yes—
1359C2#3542212yes—
1360C2#3553711yescharacteristic
1361C2#3569111yescharacteristic
1362C2#3569111yescharacteristic
1363C2#3569211yescharacteristic
1364C2#3569412yes—
1365C2#3574111yescharacteristic
1366C2#3591812yes—
1367C2#3662411yescharacteristic
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×#2428C2semidirect
2. C2×#2424C2semidirect
3. C2×#2273C2semidirect
4. #15204C2semidirect
5. #15165C2semidirect
6. #15124C2semidirect
7. #15124C2semidirect
8. #14996C2semidirect
9. #14996C2semidirect
10. #14764C2semidirect
11. #14754C2semidirect
12. #14751C2semidirect
13. #14716C2semidirect
14. #14716C2semidirect
15. #14716C2semidirect
16. #14311C2semidirect
17. #14228C2semidirect
18. #14187C2semidirect
19. #14175C2semidirect
20. #14100C2semidirect
21. #14100C2semidirect
22. #13948C2semidirect
23. C4×#392C2semidirect
24. C22×#127C22semidirect
33. C22×C4×D4C22semidirect
42. C2×#394C22semidirect
51. C2×#390C22semidirect
52. C2×#390C22semidirect
53. C2×#390C22semidirect
54. C2×#389C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
65. C2×#386C22semidirect
80. C2×C4×C22⋊C4C22semidirect
81. #1444C22semidirect
82. #1444C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1440C22semidirect
95. #1439C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
185. C22×C22⋊C4D4semidirect
270. C4×C22⋊C4D4semidirect
957. C22⋊C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#24242
C2×#22732
#152042
#151652
#151242
#149962
#147642
#147542
#147512
#147162
#143112
#142282
#141872
#141752
#141002
#139482
C4×#3922