Finite Group Databasebeta

← #647749

Subgroups — #647749

Order 512.

5202 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic, complemented
2C2×#2342C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5#15967C212yesmaximal, complemented
6#15345C212yesmaximal, complemented
7#15345C212yesmaximal, complemented
8#15343C212yesmaximal, complemented
9#15014C211yesmaximal, characteristic, complemented
10#14919C211yesmaximal, characteristic, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14777C212yesmaximal, complemented
13#14737C212yesmaximal, complemented
14#14734C211yesmaximal, characteristic, complemented
15#14693C211yesmaximal, characteristic, complemented
16#14140C212yesmaximal, complemented
17#14128C211yesmaximal, characteristic, complemented
18#14040C211yesmaximal, characteristic, complemented
19#14019C212yesmaximal, complemented
20#13991C211yesmaximal, characteristic, complemented
21#13869C211yesmaximal, characteristic, complemented
22#13867C211yesmaximal, characteristic
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2212yescomplemented
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33#2482—28no—
34C2×#399C2212yescomplemented
35C2×#399C2212yescomplemented
36C2×#397C2212yescomplemented
37#2342—28no—
38C2×#388C2211yescharacteristic, complemented
39C2×#388C2211yescharacteristic, complemented
40C2×#388C2211yescharacteristic, complemented
41C2×#388C2211yescharacteristic, complemented
42C2×#388C2212yescomplemented
43C2×#388C2212yescomplemented
44C2×#388C2212yescomplemented
45C2×#386—28no—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#385—28no—
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic, complemented
62C2×#385C2211yescharacteristic, complemented
63C2×#385C2212yescomplemented
64C2×#385C2212yescomplemented
65C2×#385C2212yescomplemented
66C2×#385C2212yescomplemented
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#381C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic, complemented
79C2×C4×C22⋊C4C2211yescharacteristic, complemented
80C22×#95C2211yescharacteristic
81C22×#95C2211yescharacteristic
82C22×#95C2212yescomplemented
83#1445C2212yescomplemented
84#1445C2212yescomplemented
85#1445C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1443C2212yescomplemented
89#1443C2212yescomplemented
90#1443C2212yescomplemented
91#1442C2212yescomplemented
92#1442C2212yescomplemented
93#1442C2212yescomplemented
94#1442C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1440C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1437C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1434C2212yescomplemented
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C24×C4—24no—
137C24×C4—24no—
138C24×C4—44no—
139C24×C4—42no—
140C24×C4—44no—
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C2×#117—24no—
152C2×#117—24no—
153C2×#117—42no—
154C22×C4⋊C4—28no—
155C22×C4⋊C4—44no—
156C22×C4⋊C4—44no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—24no—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—44no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4D418yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218#399—28no—
219#399—44no—
220#397—28no—
221#388—28no—
222#388—24no—
223#388—24no—
224#388—24no—
225#388—24no—
226#388—28no—
227#388—44no—
228#386—28no—
229#386—28no—
230#386—28no—
231#386—28no—
232#386—28no—
233#386—28no—
234#386—44no—
235#386—44no—
236#385—24no—
237#385—24no—
238#385—28no—
239#385—24no—
240#385—24no—
241#385—24no—
242#385—24no—
243#385—28no—
244#385—44no—
245#385—42no—
246#385—44no—
247#385D418yescomplemented
248#381—24no—
249#381—24no—
250#381—24no—
251#380—24no—
252#379—24no—
253#379—24no—
254#379—24no—
255#379—24no—
256#379—24no—
257#379—42no—
258C4×C22⋊C4—24no—
259C4×C22⋊C4—24no—
260C4×C22⋊C4—24no—
261C2×#95—24no—
262C2×#95—24no—
263C2×#95—28no—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C25—22no—
303C25—22no—
304C25—24no—
305C25—22no—
306C25—24no—
307C25—22no—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25C2×D414yes—
322C25#4114yes—
323C25#4114yes—
324C25C2412yes—
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C22×D4—232no—
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—42no—
341C22×D4—42no—
342C22×D4—432no—
343C22×D4—432no—
344C22×D4—416no—
345C22×D4—416no—
346C22×D4#4118yes—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—41no—
398C23×C4—41no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—416no—
403C23×C4—416no—
404C23×C4—432no—
405C23×C4—416no—
406C23×C4—432no—
407C23×C4C2×D414yes—
408C23×C4C2×D414yes—
409C23×C4C2×D414yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429#117—416no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—432no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4C2×D418yescomplemented
459C2×C22⋊C4—232no—
460C2×C22⋊C4—232no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
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—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
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—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—416no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—416no—
538C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
553C2×C22⋊C4C2×D414yes—
554C2×C22⋊C4C2×D414yes—
555C2×C22⋊C4C2×D414yes—
556C2×C22⋊C4C2×D414yes—
557C2×C22⋊C4C2×D414yes—
558C2×C22⋊C4#4114yes—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—41no—
566C2×C42—41no—
567C2×C42—42no—
568C2×C42—42no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95C2×D418yescomplemented
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—22no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—28no—
618C24—28no—
619C24—28no—
620C24—28no—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—216no—
625C24—216no—
626C24—28no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—22no—
635C24—28no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—44no—
651C24—44no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24#123116yes—
685C24C22×D412yes—
686C24C22×D412yes—
687C24C22×D412yes—
688C24C22×D412yes—
689C24C2×#4114yes—
690C24C2×#4112yes—
691C24C2×#4112yes—
692C24C2×#4112yes—
693C24C2×#4112yes—
694C24C2×#4112yes—
695C24C2×#4112yes—
696C24C2×#4112yes—
697C24C2×#4114yes—
698C24H(5,𝔽2)14yes—
699C24H(5,𝔽2)12yes—
700C242−1+412yes—
701C24C2511yescharacteristic
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—216no—
705C2×D4—216no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—4128no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C22×C4—216no—
718C22×C4—28no—
719C22×C4—216no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—28no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—4128no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—82no—
873C22×C4—82no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D414yes—
883C22×C4C22×D412yes—
884C22×C4C22×D414yes—
885C22×C4C22×D412yes—
886C22×C4C2×#4114yes—
887C22×C4C2×#4114yes—
888C22×C4H(5,𝔽2)14yes—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—82no—
896C4⋊C4—84no—
897C4⋊C4—82no—
898C4⋊C4—84no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—82no—
929C22⋊C4—82no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C42—44no—
933C42—44no—
934C42—82no—
935C42—82no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—232no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—232no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—416no—
994C23—416no—
995C23—416no—
996C23—432no—
997C23—416no—
998C23—432no—
999C23—416no—
1000C23—432no—
1001C23—432no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—816no—
1042C23—816no—
1043C23—816no—
1044C23—816no—
1045C23—88no—
1046C23—88no—
1047C23—88no—
1048C23—88no—
1049C23C2×#12314yes—
1050C23C2×#12314yes—
1051C23C2×#12314yes—
1052C23#52514yes—
1053C23#52514yes—
1054C23#53514yes—
1055C23#53914yes—
1056C23D4214yes—
1057C23#54714yes—
1058C23#54814yes—
1059C23#55118yes—
1060C23#55118yes—
1061C23#55314yes—
1062C23C23×D411yescharacteristic
1063C23C23×D411yescharacteristic
1064C23C22×#4111yescharacteristic
1065C23C22×#4111yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C22×#4112yes—
1068C23C2×H(5,𝔽2)12yes—
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)12yes—
1071C23C2×2−1+411yescharacteristic
1072C23#58512yes—
1073D4—432no—
1074D4—432no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—432no—
1107C2×C4—432no—
1108C2×C4—416no—
1109C2×C4—416no—
1110C2×C4—416no—
1111C2×C4—432no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—416no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
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—88no—
1196C2×C4—88no—
1197C2×C4—88no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—28no—
1206C22—28no—
1207C22—24no—
1208C22—24no—
1209C22—28no—
1210C22—28no—
1211C22—24no—
1212C22—24no—
1213C22—28no—
1214C22—28no—
1215C22—24no—
1216C22—28no—
1217C22—28no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—464no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—832no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22#244318yes—
1247C22#248218yescomplemented
1248C22C22×#12311yescharacteristic
1249C22C2×#52511yescharacteristic
1250C22C2×#52511yescharacteristic
1251C22C2×#53511yescharacteristic
1252C22C2×#53911yescharacteristic
1253C22C2×D4211yescharacteristic
1254C22C2×#54711yescharacteristic
1255C22C2×#54811yescharacteristic
1256C22D4×#4112yes—
1257C22C2×#55112yes—
1258C22C2×#55112yes—
1259C22C2×#55311yescharacteristic
1260C22#348112yes—
1261C22#348411yescharacteristic
1262C22#348412yes—
1263C22#348511yescharacteristic
1264C22#350512yes—
1265C22#350512yes—
1266C22#351312yes—
1267C22#351312yes—
1268C22#352012yes—
1269C22#353212yes—
1270C22#353512yes—
1271C4—42no—
1272C4—44no—
1273C4—44no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—82no—
1288C4—81no—
1289C4—82no—
1290C2—28no—
1291C2—28no—
1292C2—44no—
1293C2—84no—
1294C2C2×#244311yescharacteristic
1295C2C2×#248211yescharacteristic
1296C2#3535111yescharacteristic
1297C2#3609911yescharacteristic
1298C2#3622012yes—
1299C2#3631711yescharacteristic
1300C2#3764511yescharacteristic
1301C2#3803911yescharacteristic
1302C2#3810912yes—
1303C2#5913312yes—
1304C2#5985112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2482C2semidirect
2. C2×#2342C2semidirect
4. C22×#385C2semidirect
5. #15967C2semidirect
6. #15345C2semidirect
7. #15345C2semidirect
8. #15343C2semidirect
9. #15014C2semidirect
10. #14919C2semidirect
11. #14918C2semidirect
12. #14777C2semidirect
13. #14737C2semidirect
14. #14734C2semidirect
15. #14693C2semidirect
16. #14140C2semidirect
17. #14128C2semidirect
18. #14040C2semidirect
19. #14019C2semidirect
20. #13991C2semidirect
21. #13869C2semidirect
27. C23×C4⋊C4C22semidirect
34. C2×#399C22semidirect
35. C2×#399C22semidirect
36. C2×#397C22semidirect
38. C2×#388C22semidirect
39. C2×#388C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
64. C2×#385C22semidirect
65. C2×#385C22semidirect
66. C2×#385C22semidirect
78. C2×C4×C22⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
82. C22×#95C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1443C22semidirect
89. #1443C22semidirect
90. #1443C22semidirect
91. #1442C22semidirect
92. #1442C22semidirect
93. #1442C22semidirect
94. #1442C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
99. #1440C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
247. #385D4semidirect
458. C2×C4⋊C4C2×D4semidirect
606. #95C2×D4semidirect
1247. C22#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C2×#23422
C22×#3862
C22×#3852
#159672
#153452
#153432
#150142
#149192
#149182
#147772
#147372
#147342
#146932
#141402
#141282
#140402
#140192
#139912
#138692
#138672