Finite Group Databasebeta

← #647780

Subgroups — #647780

Order 512.

4538 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×C4×#123C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic, complemented
5#15956C212yesmaximal, complemented
6#15373C212yesmaximal, complemented
7#15295C212yesmaximal, complemented
8#15284C212yesmaximal, complemented
9#14927C211yesmaximal, characteristic, complemented
10#14918C211yesmaximal, characteristic, complemented
11#14778C212yesmaximal, complemented
12#14777C211yesmaximal, characteristic, complemented
13#14739C212yesmaximal, complemented
14#14727C211yesmaximal, characteristic, complemented
15#14706C211yesmaximal, characteristic, complemented
16#14118C212yesmaximal, complemented
17#14020C211yesmaximal, characteristic, complemented
18#14016C211yesmaximal, characteristic, complemented
19#13968C211yesmaximal, characteristic, complemented
20#13873C212yesmaximal, complemented
21#13873C211yesmaximal, characteristic, complemented
22#13872C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic, complemented
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic, complemented
35#2405—28no—
36C2×#399C2212yescomplemented
37C2×#397C2212yescomplemented
38C2×#394C2212yes—
39C2×#394C2212yes—
40D4×C22⋊C4—28no—
41C4×#123—28no—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#388—28no—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yescomplemented
49C2×#388C2212yescomplemented
50C2×#388C2212yescomplemented
51C2×#387C2212yescomplemented
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#385C2212yes—
63C2×#385C2211yescharacteristic, complemented
64C2×#385C2211yescharacteristic, complemented
65C2×#381C2211yescharacteristic, complemented
66C2×#381C2211yescharacteristic, complemented
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic, complemented
69C2×#380C2212yescomplemented
70C2×#379C2211yescharacteristic
71C2×#379C2212yes—
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2212yes—
76C2×C4×C4⋊C4C2212yescomplemented
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yescomplemented
79C2×C4×C22⋊C4C2211yescharacteristic, complemented
80C22×#95C2211yescharacteristic, complemented
81C22×#95C2211yescharacteristic, complemented
82#1445C2212yescomplemented
83#1444C2212yescomplemented
84#1443C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1438C2212yes—
107#1438C2212yes—
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116C4⋊#95C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2212yes—
119C22⋊#95C2211yescharacteristic, complemented
120C22⋊#95C2211yescharacteristic, complemented
121C22⋊#95C2211yescharacteristic, complemented
122C22⋊#95C2211yescharacteristic, complemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2211yescharacteristic, complemented
126C22⋊#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—42no—
154C2×#123D418yes—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—44no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—28no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—28no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4D418yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C42—24no—
218C22×C42—24no—
219C22×C42—42no—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225#399—44no—
226#397—44no—
227#394—28no—
228#394—28no—
229#390—24no—
230#390—24no—
231#388—28no—
232#388—28no—
233#388—28no—
234#388—28no—
235#388—28no—
236#388—28no—
237#387—28no—
238#386—24no—
239#386—24no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—24no—
247#386—42no—
248#385—28no—
249#385—24no—
250#385—42no—
251#381—24no—
252#381—42no—
253#380—24no—
254#380—44no—
255#380—42no—
256#379—24no—
257#379—24no—
258#379—24no—
259#379—28no—
260#379—44no—
261#379—42no—
262C4×C4⋊C4—28no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—24no—
266C2×#95—24no—
267C2×#95—24no—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
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—24no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—24no—
314C25—22no—
315C25—42no—
316C25—41no—
317C25—41no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25C2×D414yes—
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—232no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
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—41no—
351C22×D4—41no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—416no—
355C22×D4—416no—
356C22×D4—416no—
357C22×D4—416no—
358C22×D4—416no—
359C22×D4—416no—
360C22×D4C2×D414yes—
361C22×D4#4114yes—
362C22×D4#4114yes—
363C22×D4#4114yes—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
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—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—41no—
401C23×C4—41no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—41no—
405C23×C4—41no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431#123—232no—
432#123—416no—
433C4×D4—416no—
434C4×D4—416no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—416no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4C2×D418yes—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—232no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
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—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—416no—
533C2×C22⋊C4—416no—
534C2×C22⋊C4—416no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
557C2×C22⋊C4C2×D414yes—
558C2×C22⋊C4C2×D414yes—
559C2×C22⋊C4C2×D414yes—
560C2×C22⋊C4C2×D418yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4#4118yes—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—24no—
568C2×C42—24no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—22no—
572C2×C42—24no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—416no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—22no—
591#95—22no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—28no—
635C24—28no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—28no—
657C24—28no—
658C24—28no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—82no—
691C24—82no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24C22×D412yes—
701C24C22×D412yes—
702C24C22×D412yes—
703C24C22×D412yes—
704C24C22×D412yes—
705C24C2×#4112yes—
706C24C2×#4114yes—
707C24C2×#4112yes—
708C24C2×#4112yes—
709C24C2×#4112yes—
710C24C2×#4112yes—
711C24C2×#4112yes—
712C24H(5,𝔽2)12yes—
713C24H(5,𝔽2)12yes—
714C24C2511yescharacteristic
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—4128no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4#123116yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
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—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—82no—
883C22×C4—82no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4C22×D412yes—
891C22×C4C22×D414yes—
892C22×C4C22×D412yes—
893C22×C4C22×D414yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4C2×#4114yes—
900C22×C4C2×#4114yes—
901C22×C4C2×#4112yes—
902C22×C4H(5,𝔽2)14yes—
903C4⋊C4—216no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—84no—
911C4⋊C4—84no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—82no—
936C22⋊C4—82no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—82no—
941C22⋊C4—82no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4#123116yescomplemented
948C42—48no—
949C42—48no—
950C42—48no—
951C42—44no—
952C42—44no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—416no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—41no—
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—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—88no—
1066C23—88no—
1067C23—88no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—816no—
1077C23—816no—
1078C23—88no—
1079C23—816no—
1080C23—88no—
1081C23C2×#12314yes—
1082C23C2×#12314yes—
1083C23C2×#12314yes—
1084C23#52514yes—
1085C23#53814yes—
1086C23D4214yes—
1087C23#54614yes—
1088C23#54614yes—
1089C23#55114yes—
1090C23C23×D411yescharacteristic
1091C23C23×D411yescharacteristic
1092C23C22×#4111yescharacteristic
1093C23C22×#4111yescharacteristic
1094C23C22×#4112yes—
1095C23C22×#4111yescharacteristic
1096C23C2×H(5,𝔽2)11yescharacteristic
1097C23C2×H(5,𝔽2)11yescharacteristic
1098C23C2×H(5,𝔽2)12yes—
1099C23#58512yes—
1100C23#58512yes—
1101D4—232no—
1102D4—416no—
1103D4—416no—
1104D4—416no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—416no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—416no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—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—88no—
1218C2×C4—88no—
1219C2×C4—88no—
1220C2×C4—88no—
1221C2×C4C2×#12314yes—
1222C2×C4C2×#12314yes—
1223C2×C4C2×#12314yes—
1224C22—24no—
1225C22—28no—
1226C22—28no—
1227C22—24no—
1228C22—24no—
1229C22—28no—
1230C22—28no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—28no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—832no—
1269C22—832no—
1270C22—81no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—81no—
1276C22—82no—
1277C22—82no—
1278C22—81no—
1279C22—81no—
1280C22#241818yes—
1281C22C22×#12311yescharacteristic
1282C22C22×#12311yescharacteristic
1283C22C2×#52511yescharacteristic
1284C22#344911yescharacteristic
1285C22C2×#53811yescharacteristic
1286C22C2×D4211yescharacteristic
1287C22C2×#54611yescharacteristic
1288C22C2×#54611yescharacteristic
1289C22D4×#4112yes—
1290C22C2×#55111yescharacteristic
1291C22#347512yes—
1292C22#347512yes—
1293C22#348112yes—
1294C22#348411yescharacteristic
1295C22#348511yescharacteristic
1296C22#348812yes—
1297C22#351312yes—
1298C22#351412yes—
1299C22#351412yes—
1300C22#351912yes—
1301C22#352112yes—
1302C22#353412yes—
1303C22#356012yes—
1304C4—24no—
1305C4—24no—
1306C4—24no—
1307C4—44no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—82no—
1315C4—82no—
1316C4—82no—
1317C4—81no—
1318C4—82no—
1319C4—82no—
1320C4—81no—
1321C4—81no—
1322C2—28no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2—82no—
1327C2C2×#241811yescharacteristic
1328C2#3480911yescharacteristic
1329C2#3545111yescharacteristic
1330C2D4×#12311yescharacteristic
1331C2#3621612yes—
1332C2#3623611yescharacteristic
1333C2#3765211yescharacteristic
1334C2#3816812yes—
1335C2#3890111yescharacteristic
1336C2#5909112yes—
1337C2#5937212yes—
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
3. C2×C4×#123C2semidirect
4. C22×#388C2semidirect
5. #15956C2semidirect
6. #15373C2semidirect
7. #15295C2semidirect
8. #15284C2semidirect
9. #14927C2semidirect
10. #14918C2semidirect
11. #14778C2semidirect
12. #14777C2semidirect
13. #14739C2semidirect
14. #14727C2semidirect
15. #14706C2semidirect
16. #14118C2semidirect
17. #14020C2semidirect
18. #14016C2semidirect
19. #13968C2semidirect
20. #13873C2semidirect
21. #13873C2semidirect
22. #13872C2semidirect
29. C23×C4⋊C4C22semidirect
34. C23×C42C22semidirect
36. C2×#399C22semidirect
37. C2×#397C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
50. C2×#388C22semidirect
51. C2×#387C22semidirect
63. C2×#385C22semidirect
64. C2×#385C22semidirect
65. C2×#381C22semidirect
66. C2×#381C22semidirect
68. C2×#380C22semidirect
69. C2×#380C22semidirect
76. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C22⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C22×#95C22semidirect
81. C22×#95C22semidirect
82. #1445C22semidirect
83. #1444C22semidirect
84. #1443C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. C4⋊#95C22semidirect
117. #1434C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
947. C22⋊C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C2×D4×C22⋊C42
C2×C4×#1232
C22×#3882
#159562
#153732
#152952
#152842
#149272
#149182
#147782
#147772
#147392
#147272
#147062
#141182
#140202
#140162
#139682
#138732
#138722
#138672