Finite Group Databasebeta

← #845345

Subgroups — #845345

Order 512.

4755 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2849C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×#2486C211yesmaximal, characteristic, complemented
5C2×#2424C211yesmaximal, characteristic
6C22×#385C211yesmaximal, characteristic, complemented
7#16271C212yesmaximal, complemented
8#16269C212yesmaximal, complemented
9#15392C212yesmaximal, complemented
10#15377C212yesmaximal, complemented
11#15358C212yesmaximal, complemented
12#15327C212yesmaximal, complemented
13#15073C211yesmaximal, characteristic, complemented
14#15069C211yesmaximal, characteristic, complemented
15#14927C211yesmaximal, characteristic, complemented
16#14926C211yesmaximal, characteristic, complemented
17#14911C211yesmaximal, characteristic, complemented
18#14911C211yesmaximal, characteristic, complemented
19#14405C212yesmaximal, complemented
20#14361C212yesmaximal, complemented
21#13972C211yesmaximal, characteristic, complemented
22#13968C211yesmaximal, characteristic, complemented
23#13873C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#120C2211yescharacteristic
34C22×#120C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40#2849—28no—
41#2849—28no—
42#2501—28no—
43#2486—28no—
44#2424—28no—
45C2×#399C2212yescomplemented
46C2×#399C2212yescomplemented
47C2×#398C2212yescomplemented
48C2×#397C2212yescomplemented
49C2×#396C2211yescharacteristic
50C2×#394C2211yescharacteristic
51C2×#394C2211yescharacteristic
52C2×#392C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2212yescomplemented
55C2×#389C2212yescomplemented
56C2×#388C2212yes—
57C2×#388C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#385—28no—
67C2×#385C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#385C2212yes—
72C2×#385C2212yes—
73C2×#385C2211yescharacteristic
74C2×#385C2212yes—
75C2×#385C2212yes—
76C2×#384C2212yescomplemented
77C2×#381C2211yescharacteristic
78C2×#381C2211yescharacteristic
79C2×#381C2211yescharacteristic
80C2×#381C2211yescharacteristic
81C2×#381C2211yescharacteristic
82C2×#381C2211yescharacteristic
83C2×#380C2211yescharacteristic
84C2×#380C2212yescomplemented
85C2×#379C2211yescharacteristic
86C2×#379C2211yescharacteristic
87C2×C4×C22⋊C4C2211yescharacteristic
88C22×#95C2211yescharacteristic
89C22×#95C2211yescharacteristic
90#1444C2212yescomplemented
91#1444C2212yescomplemented
92#1444C2212yescomplemented
93#1443C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1442C2212yescomplemented
97#1442C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1440C2212yes—
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yes—
119#1438C2212yescomplemented
120#1437C2212yes—
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123#1434C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—24no—
140C24×C4—42no—
141C24×C4—42no—
142C24×C4—42no—
143C24×C4—42no—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C2×#123—24no—
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—24no—
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—42no—
162C2×#123—42no—
163C2×#123—42no—
164C2×#123—42no—
165C2×#123—42no—
166C2×#123—42no—
167C2×#123—42no—
168C2×#123—42no—
169C2×#123—42no—
170C2×#123D418yescomplemented
171C2×#121—24no—
172C2×#121—24no—
173C2×#121—24no—
174C2×#121—28no—
175C2×#121—42no—
176C2×#120—24no—
177C2×#120—24no—
178C2×#120—24no—
179C2×#120—24no—
180C2×#120—42no—
181C2×#120—42no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—42no—
185C22×C4⋊C4—24no—
186C22×C4⋊C4—24no—
187C22×C4⋊C4—24no—
188C22×C4⋊C4—24no—
189C22×C4⋊C4—42no—
190C22×C4⋊C4—42no—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C22⋊C4—28no—
207C22×C22⋊C4—24no—
208C22×C22⋊C4—42no—
209C22×C22⋊C4—42no—
210C22×C22⋊C4D418yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#399—28no—
247#399—28no—
248#398—28no—
249#397—28no—
250#396—24no—
251#394—24no—
252#394—24no—
253#392—24no—
254#390—24no—
255#390—28no—
256#389—28no—
257#388—24no—
258#388—28no—
259#386—24no—
260#386—28no—
261#386—28no—
262#386—24no—
263#386—28no—
264#386—28no—
265#386—42no—
266#386—42no—
267#385—24no—
268#385—28no—
269#385—28no—
270#385—28no—
271#385—28no—
272#385—28no—
273#385—28no—
274#385—28no—
275#385—28no—
276#384—28no—
277#381—24no—
278#381—24no—
279#381—24no—
280#381—24no—
281#381—42no—
282#381D418yescomplemented
283#380—24no—
284#380—28no—
285#379—24no—
286#379—24no—
287C4×C22⋊C4—24no—
288C2×#95—24no—
289C2×#95—24no—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—24no—
323C25—22no—
324C25—22no—
325C25—24no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—42no—
331C25—42no—
332C25C2×D414yes—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C25C2411yescharacteristic
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4—41no—
370C22×D4—41no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4C2×D414yes—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
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—24no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4—24no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—416no—
425C23×C4—41no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—416no—
430C23×C4—416no—
431C23×C4—416no—
432C23×C4—416no—
433C23×C4—416no—
434C23×C4—416no—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4C2×D414yes—
438C23×C4C2×D414yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457#123—416no—
458#123—416no—
459#123—416no—
460#123—416no—
461#123—416no—
462#123—416no—
463#121—416no—
464#121—416no—
465#120—416no—
466#120—416no—
467C4×D4—416no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—416no—
510C2×C4⋊C4—416no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4C2×D418yes—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—232no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
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—24no—
566C2×C22⋊C4—22no—
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—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
600C2×C22⋊C4C2×D414yes—
601C2×C22⋊C4C2×D414yes—
602C2×C22⋊C4C2×D414yes—
603C2×C22⋊C4C2×D414yes—
604C2×C22⋊C4C2×D414yes—
605C2×C22⋊C4C2×D418yes—
606C2×C22⋊C4C2×D414yes—
607C2×C22⋊C4#4118yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—24no—
611C2×C42—24no—
612C2×C42—41no—
613C2×C42—42no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—24no—
633#95—24no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95C2×D418yes—
645#95C2×D418yes—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—216no—
651C24—216no—
652C24—28no—
653C24—28no—
654C24—28no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—28no—
674C24—28no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—44no—
697C24—44no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C2×#4114yes—
719C24H(5,𝔽2)12yes—
720C24H(5,𝔽2)12yes—
721C24H(5,𝔽2)12yes—
722C24H(5,𝔽2)12yes—
723C242−1+414yes—
724C24C2511yescharacteristic
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—82no—
755C2×D4—84no—
756C2×D4—82no—
757C2×D4—82no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—82no—
761C2×D4—82no—
762C2×D4—84no—
763C2×D4—84no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—21no—
779C22×C4—21no—
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—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
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—28no—
825C22×C4—28no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—4128no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—82no—
914C22×C4—84no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D414yes—
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C22×D414yes—
923C22×C4C22×D414yes—
924C22×C4C22×D414yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C2×#4114yes—
929C22×C4C2×#4114yes—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—82no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—82no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4#123116yescomplemented
978C42—48no—
979C42—44no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—232no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—416no—
1030C23—416no—
1031C23—432no—
1032C23—432no—
1033C23—432no—
1034C23—432no—
1035C23—416no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—42no—
1062C23—41no—
1063C23—41no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—42no—
1083C23—42no—
1084C23—41no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23C2×#12314yes—
1098C23#53414yes—
1099C23#53514yes—
1100C23#53514yes—
1101C23#53614yes—
1102C23D4214yes—
1103C23D4214yes—
1104C23D4214yes—
1105C23#56014yes—
1106C23C23×D411yescharacteristic
1107C23C23×D411yescharacteristic
1108C23C23×D411yescharacteristic
1109C23C22×#4112yes—
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23C2×H(5,𝔽2)11yescharacteristic
1113C23C2×H(5,𝔽2)11yescharacteristic
1114C23C2×2−1+412yes—
1115C23#58512yes—
1116C23#58512yes—
1117D4—416no—
1118D4—88no—
1119D4—88no—
1120D4—88no—
1121D4—88no—
1122D4—88no—
1123D4—88no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—416no—
1158C2×C4—416no—
1159C2×C4—432no—
1160C2×C4—432no—
1161C2×C4—41no—
1162C2×C4—416no—
1163C2×C4—416no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
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—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—41no—
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—41no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—88no—
1239C2×C4—88no—
1240C2×C4—88no—
1241C2×C4C2×#12314yes—
1242C2×C4C2×#12314yes—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—28no—
1247C22—24no—
1248C22—28no—
1249C22—28no—
1250C22—28no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—464no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—42no—
1279C22—44no—
1280C22—42no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—82no—
1285C22—82no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—81no—
1297C22—81no—
1298C22#266918yes—
1299C22C22×#12311yescharacteristic
1300C22C2×#53411yescharacteristic
1301C22C2×#53511yescharacteristic
1302C22C2×#53511yescharacteristic
1303C22C2×#53611yescharacteristic
1304C22C2×D4211yescharacteristic
1305C22C2×D4211yescharacteristic
1306C22C2×D4211yescharacteristic
1307C22D4×#4112yes—
1308C22D4×#4112yes—
1309C22#348511yescharacteristic
1310C22#348511yescharacteristic
1311C22#348912yes—
1312C22#348912yes—
1313C22#349212yes—
1314C22#349212yes—
1315C22#351312yes—
1316C22#351312yes—
1317C22C2×#56011yescharacteristic
1318C22#353312yes—
1319C22#353312yes—
1320C22#353512yes—
1321C22#353512yes—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—82no—
1335C4—82no—
1336C4—82no—
1337C4—81no—
1338C4—82no—
1339C4—81no—
1340C2—28no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2—161no—
1345C2#3522711yescharacteristic
1346C2D4×#12311yescharacteristic
1347C2D4×#12311yescharacteristic
1348C2#3695611yescharacteristic
1349C2#3764711yescharacteristic
1350C2#3764711yescharacteristic
1351C2#3836512yes—
1352C2#3836712yes—
1353C2#4553812yes—
1354C2C2×#266911yescharacteristic
1355C2#5899312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2424C2
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×#2849C2semidirect
2. C2×#2849C2semidirect
3. C2×#2501C2semidirect
4. C2×#2486C2semidirect
6. C22×#385C2semidirect
7. #16271C2semidirect
8. #16269C2semidirect
9. #15392C2semidirect
10. #15377C2semidirect
11. #15358C2semidirect
12. #15327C2semidirect
13. #15073C2semidirect
14. #15069C2semidirect
15. #14927C2semidirect
16. #14926C2semidirect
17. #14911C2semidirect
18. #14911C2semidirect
19. #14405C2semidirect
20. #14361C2semidirect
21. #13972C2semidirect
22. #13968C2semidirect
23. #13873C2semidirect
45. C2×#399C22semidirect
46. C2×#399C22semidirect
47. C2×#398C22semidirect
48. C2×#397C22semidirect
54. C2×#390C22semidirect
55. C2×#389C22semidirect
76. C2×#384C22semidirect
84. C2×#380C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1443C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1442C22semidirect
97. #1442C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
119. #1438C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1434C22semidirect
128. C22⋊#95C22semidirect
170. C2×#123D4semidirect
282. #381D4semidirect
977. C22⋊C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#25012
C2×#24862
C2×#24242
C22×#3852
#162712
#162692
#153922
#153772
#153582
#153272
#150732
#150692
#149272
#149262
#149112
#144052
#143612
#139722
#139682
#138732