Finite Group Databasebeta

← #759739

Subgroups — #759739

Order 512.

5888 conjugacy classes of subgroups.

The subgroup lattice has 1425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2534C211yesmaximal, characteristic, complemented
2C2×#2412C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C2×C4×#120C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7#16513C212yesmaximal, complemented
8#16512C212yesmaximal, complemented
9#15002C212yesmaximal, complemented
10#14935C211yesmaximal, characteristic, complemented
11#14927C211yesmaximal, characteristic, complemented
12#14732C212yesmaximal, complemented
13#14729C212yesmaximal, complemented
14#14726C211yesmaximal, characteristic, complemented
15#14725C211yesmaximal, characteristic, complemented
16#14719C212yesmaximal, complemented
17#14149C211yesmaximal, characteristic, complemented
18#14023C212yesmaximal, complemented
19#13999C212yesmaximal, complemented
20#13960C211yesmaximal, characteristic, complemented
21#13903C211yesmaximal, characteristic, complemented
22#13869C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2212yes—
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic, complemented
32C22×C4×D4C2211yescharacteristic, complemented
33C23×C4⋊C4C2212yescomplemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39#2534—28no—
40#2412—28no—
41#2410—28no—
42C2×#397C2212yescomplemented
43C2×#396C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#394C2212yes—
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#394C2212yescomplemented
49C2×#392C2212yes—
50C4×#120—28no—
51C2×#388C2212yescomplemented
52C2×#386—28no—
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2212yes—
57C2×#386C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yescomplemented
64C2×#386C2212yescomplemented
65C2×#386C2211yescharacteristic, complemented
66C2×#386C2211yescharacteristic, complemented
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic, complemented
71C2×#385C2211yescharacteristic, complemented
72C2×#381C2211yescharacteristic
73C2×#381C2211yescharacteristic
74C2×#381C2211yescharacteristic
75C2×#380—28no—
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2212yescomplemented
81C2×#380C2212yescomplemented
82C2×#380C2212yescomplemented
83C2×#379C2211yescharacteristic
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86C2×#379C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic, complemented
89C2×C4×C22⋊C4C2211yescharacteristic, complemented
90C22×#95C2211yescharacteristic
91C22×#95C2211yescharacteristic
92C22×#95C2212yescomplemented
93#1443C2212yescomplemented
94#1442C2212yescomplemented
95#1441C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1440C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1434C2212yescomplemented
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—28no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—44no—
145C24×C4—44no—
146C24×C4D418yescomplemented
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—42no—
162C2×#121—28no—
163C2×#121—28no—
164C2×#121—44no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—24no—
169C2×#120—42no—
170C2×#120D418yes—
171C2×C4×D4—24no—
172C2×C4×D4—24no—
173C2×C4×D4—24no—
174C2×C4×D4—24no—
175C2×C4×D4—24no—
176C2×C4×D4—44no—
177C2×C4×D4—44no—
178C22×C4⋊C4—28no—
179C22×C4⋊C4—44no—
180C22×C4⋊C4—44no—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—24no—
202C22×C22⋊C4—44no—
203C22×C22⋊C4—42no—
204C22×C22⋊C4—42no—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242#397—28no—
243#396—28no—
244#396—44no—
245#394—28no—
246#394—28no—
247#394—28no—
248#394—44no—
249#392—28no—
250#388—28no—
251#386—24no—
252#386—24no—
253#386—28no—
254#386—28no—
255#386—28no—
256#386—28no—
257#386—28no—
258#386—28no—
259#386—24no—
260#386—24no—
261#386—24no—
262#386—28no—
263#386—28no—
264#386—44no—
265#385—24no—
266#385—24no—
267#385—24no—
268#385—24no—
269#385—24no—
270#381—24no—
271#381—24no—
272#381—42no—
273#380—24no—
274#380—28no—
275#380—28no—
276#380—24no—
277#380—24no—
278#380—28no—
279#380D418yescomplemented
280#379—24no—
281#379—24no—
282#379—24no—
283#379—42no—
284C4×C22⋊C4—24no—
285C4×C22⋊C4—24no—
286C4×C22⋊C4—24no—
287C2×#95—24no—
288C2×#95—24no—
289C2×#95—28no—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2311yescharacteristic
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—22no—
323C25—22no—
324C25—24no—
325C25—22no—
326C25—24no—
327C25—22no—
328C25—22no—
329C25—24no—
330C25—22no—
331C25—22no—
332C25—22no—
333C25—22no—
334C25—22no—
335C25—22no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25—42no—
341C25C2×D414yes—
342C25C2×D414yes—
343C25#4114yes—
344C25C2411yescharacteristic
345C25C2412yes—
346C25C2411yescharacteristic
347C25C2411yescharacteristic
348C25C2411yescharacteristic
349C22×D4—232no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—22no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—24no—
373C22×D4—24no—
374C22×D4—24no—
375C22×D4—24no—
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—432no—
385C22×D4—432no—
386C22×D4—416no—
387C22×D4—416no—
388C22×D4C2×D414yes—
389C22×D4C2×D414yes—
390C22×D4C2×D414yes—
391C22×D4#4118yes—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—232no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—416no—
434C23×C4—416no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—432no—
454C23×C4—432no—
455C23×C4C2×D414yes—
456C23×C4C2×D414yes—
457C23×C4C2×D414yes—
458C23×C4C2×D414yes—
459C23×C4C2×D414yes—
460C23×C4C2×D414yes—
461C23×C4C2×D414yes—
462C23×C4#4114yes—
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481#123—416no—
482#121—432no—
483#120—232no—
484#120—416no—
485C4×D4—416no—
486C4×D4—416no—
487C4×D4—416no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—42no—
513C2×C4⋊C4—432no—
514C2×C4⋊C4—42no—
515C2×C4⋊C4—42no—
516C2×C4⋊C4C2×D418yescomplemented
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—416no—
586C2×C22⋊C4—416no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—416no—
600C2×C22⋊C4—416no—
601C2×C22⋊C4—416no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4C2×D414yes—
614C2×C22⋊C4C2×D414yes—
615C2×C22⋊C4C2×D414yes—
616C2×C22⋊C4C2×D414yes—
617C2×C22⋊C4C2×D414yes—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—42no—
624C2×C42—42no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—24no—
639#95—24no—
640#95—24no—
641#95—24no—
642#95—24no—
643#95—24no—
644#95—24no—
645#95—24no—
646#95—24no—
647#95—24no—
648#95—42no—
649#95—42no—
650#95—42no—
651#95—42no—
652#95—42no—
653#95—42no—
654#95—42no—
655#95—42no—
656#95C2×D418yescomplemented
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—28no—
668C24—28no—
669C24—28no—
670C24—28no—
671C24—28no—
672C24—216no—
673C24—28no—
674C24—28no—
675C24—216no—
676C24—28no—
677C24—21no—
678C24—21no—
679C24—22no—
680C24—21no—
681C24—22no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—28no—
686C24—22no—
687C24—22no—
688C24—21no—
689C24—21no—
690C24—22no—
691C24—22no—
692C24—21no—
693C24—22no—
694C24—21no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—21no—
703C24—22no—
704C24—22no—
705C24—21no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—44no—
711C24—44no—
712C24—48no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—44no—
729C24—44no—
730C24—44no—
731C24—44no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24—44no—
737C24—44no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24—84no—
742C24—84no—
743C24—84no—
744C24#121116yes—
745C24C22×D412yes—
746C24C22×D412yes—
747C24C22×D412yes—
748C24C22×D412yes—
749C24C22×D412yes—
750C24C22×D412yes—
751C24C22×D412yes—
752C24C22×D412yes—
753C24C2×#4114yes—
754C24C2×#4112yes—
755C24C2×#4112yes—
756C24C2×#4112yes—
757C24C2×#4112yes—
758C24C2×#4114yes—
759C24H(5,𝔽2)14yes—
760C24H(5,𝔽2)12yes—
761C242−1+412yes—
762C24C2511yescharacteristic
763C2×D4—216no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—216no—
768C2×D4—28no—
769C2×D4—216no—
770C2×D4—216no—
771C2×D4—28no—
772C2×D4—216no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—4128no—
784C2×D4—48no—
785C2×D4—44no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—48no—
791C2×D4—44no—
792C2×D4—48no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—84no—
802C22×C4—216no—
803C22×C4—216no—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
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—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—4128no—
924C22×C4—48no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—48no—
944C22×C4—48no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—84no—
950C22×C4—84no—
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#121116yescomplemented
960C22×C4C22×D412yes—
961C22×C4C22×D412yes—
962C22×C4C22×D412yes—
963C22×C4C22×D412yes—
964C22×C4C22×D414yes—
965C22×C4C22×D414yes—
966C22×C4C22×D412yes—
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C22×D412yes—
970C22×C4C22×D412yes—
971C22×C4C2×#4114yes—
972C22×C4C2×#4112yes—
973C22×C4C2×#4112yes—
974C22×C4H(5,𝔽2)14yes—
975C4⋊C4—48no—
976C4⋊C4—48no—
977C4⋊C4—48no—
978C4⋊C4—48no—
979C4⋊C4—48no—
980C4⋊C4—48no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—84no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—48no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—44no—
1012C22⋊C4—48no—
1013C22⋊C4—44no—
1014C22⋊C4—84no—
1015C22⋊C4—84no—
1016C22⋊C4—84no—
1017C22⋊C4—84no—
1018C22⋊C4—84no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—22no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—22no—
1057C23—22no—
1058C23—232no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—24no—
1065C23—22no—
1066C23—22no—
1067C23—24no—
1068C23—22no—
1069C23—24no—
1070C23—24no—
1071C23—232no—
1072C23—22no—
1073C23—24no—
1074C23—22no—
1075C23—24no—
1076C23—24no—
1077C23—22no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—416no—
1085C23—416no—
1086C23—416no—
1087C23—416no—
1088C23—432no—
1089C23—432no—
1090C23—416no—
1091C23—432no—
1092C23—432no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—41no—
1106C23—42no—
1107C23—41no—
1108C23—42no—
1109C23—41no—
1110C23—41no—
1111C23—42no—
1112C23—41no—
1113C23—42no—
1114C23—41no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—41no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—41no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—816no—
1151C23—816no—
1152C23—816no—
1153C23—816no—
1154C23—88no—
1155C23—88no—
1156C23—88no—
1157C23—88no—
1158C23C2×#12114yes—
1159C23C2×#12114yes—
1160C23C2×#12114yes—
1161C23C2×#12114yes—
1162C23#52514yes—
1163C23#53414yes—
1164C23#53714yes—
1165C23D4214yes—
1166C23#54618yes—
1167C23#54714yes—
1168C23#54814yes—
1169C23#55118yes—
1170C23#55314yes—
1171C23C23×D411yescharacteristic
1172C23C23×D411yescharacteristic
1173C23C23×D411yescharacteristic
1174C23C22×#4111yescharacteristic
1175C23C22×#4111yescharacteristic
1176C23C22×#4112yes—
1177C23C2×H(5,𝔽2)12yes—
1178C23C2×H(5,𝔽2)12yes—
1179C23C2×H(5,𝔽2)11yescharacteristic
1180C23C2×2−1+411yescharacteristic
1181C23#58512yes—
1182D4—416no—
1183D4—432no—
1184D4—416no—
1185D4—416no—
1186D4—432no—
1187D4—816no—
1188C2×C4—232no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—416no—
1221C2×C4—416no—
1222C2×C4—416no—
1223C2×C4—416no—
1224C2×C4—416no—
1225C2×C4—416no—
1226C2×C4—41no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—42no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—41no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—42no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—42no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—42no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—42no—
1297C2×C4—42no—
1298C2×C4—88no—
1299C2×C4—816no—
1300C2×C4—816no—
1301C2×C4—88no—
1302C2×C4—88no—
1303C2×C4C2×#12114yes—
1304C2×C4C2×#12114yes—
1305C2×C4#53414yes—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—24no—
1313C22—24no—
1314C22—28no—
1315C22—28no—
1316C22—28no—
1317C22—28no—
1318C22—24no—
1319C22—24no—
1320C22—24no—
1321C22—24no—
1322C22—28no—
1323C22—28no—
1324C22—28no—
1325C22—28no—
1326C22—24no—
1327C22—24no—
1328C22—24no—
1329C22—464no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—44no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—42no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—832no—
1351C22—81no—
1352C22—81no—
1353C22—82no—
1354C22—82no—
1355C22—81no—
1356C22—82no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—81no—
1361C22—82no—
1362C22—82no—
1363C22—82no—
1364C22—82no—
1365C22#241618yes—
1366C22#253418yescomplemented
1367C22C22×#12111yescharacteristic
1368C22C22×#12111yescharacteristic
1369C22C2×#52511yescharacteristic
1370C22C2×#53411yescharacteristic
1371C22C2×#53411yescharacteristic
1372C22C2×#53711yescharacteristic
1373C22#344911yescharacteristic
1374C22C2×D4211yescharacteristic
1375C22C2×#54612yes—
1376C22C2×#54711yescharacteristic
1377C22C2×#54811yescharacteristic
1378C22D4×#4112yes—
1379C22C2×#55112yes—
1380C22C2×#55311yescharacteristic
1381C22#347512yes—
1382C22#348412yes—
1383C22#349012yes—
1384C22#349612yes—
1385C22#350512yes—
1386C22#351912yes—
1387C22#352012yes—
1388C22#353412yes—
1389C22#353512yes—
1390C4—24no—
1391C4—24no—
1392C4—24no—
1393C4—44no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—44no—
1400C4—81no—
1401C4—81no—
1402C4—82no—
1403C4—81no—
1404C4—81no—
1405C4—82no—
1406C4—82no—
1407C4—82no—
1408C2—28no—
1409C2—28no—
1410C2—44no—
1411C2—82no—
1412C2—84no—
1413C2C2×#241611yescharacteristic
1414C2#3473711yescharacteristic
1415C2C2×#253411yescharacteristic
1416C2#3498111yescharacteristic
1417C2#3500011yescharacteristic
1418C2#3507711yescharacteristic
1419C2#3745211yescharacteristic
1420C2#5912312yes—
1421C2#5913312yes—
1422C2#5930112yes—
1423C2#5931112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2534C2semidirect
2. C2×#2412C2semidirect
4. C2×C4×#120C2semidirect
5. C22×#386C2semidirect
6. C22×#380C2semidirect
7. #16513C2semidirect
8. #16512C2semidirect
9. #15002C2semidirect
10. #14935C2semidirect
11. #14927C2semidirect
12. #14732C2semidirect
13. #14729C2semidirect
14. #14726C2semidirect
15. #14725C2semidirect
16. #14719C2semidirect
17. #14149C2semidirect
18. #14023C2semidirect
19. #13999C2semidirect
20. #13960C2semidirect
21. #13903C2semidirect
22. #13869C2semidirect
23. #13867C2semidirect
31. C22×C4×D4C22semidirect
32. C22×C4×D4C22semidirect
33. C23×C4⋊C4C22semidirect
42. C2×#397C22semidirect
43. C2×#396C22semidirect
44. C2×#396C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
48. C2×#394C22semidirect
51. C2×#388C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
80. C2×#380C22semidirect
81. C2×#380C22semidirect
82. C2×#380C22semidirect
88. C2×C4×C22⋊C4C22semidirect
89. C2×C4×C22⋊C4C22semidirect
92. C22×#95C22semidirect
93. #1443C22semidirect
94. #1442C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
105. #1440C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1434C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
146. C24×C4D4semidirect
279. #380D4semidirect
516. C2×C4⋊C4C2×D4semidirect
656. #95C2×D4semidirect
959. C22×C4#121semidirect
1366. C22#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#25342
C2×#24122
C2×#24102
C2×C4×#1202
C22×#3862
C22×#3802
#165132
#165122
#150022
#149352
#149272
#147322
#147292
#147262
#147252
#147192
#141492
#140232
#139992
#139602
#139032
#138692
#138672