Finite Group Databasebeta

← #554264

Subgroups — #554264

Order 512.

5184 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2318C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic, complemented
4#14694C211yesmaximal, characteristic, complemented
5#14693C211yesmaximal, characteristic, complemented
6#14536C212yesmaximal, complemented
7#14534C212yesmaximal, complemented
8#14523C212yesmaximal, complemented
9#14521C212yesmaximal, complemented
10#14379C212yesmaximal, complemented
11#14377C212yesmaximal, complemented
12#14363C212yesmaximal, complemented
13#14361C212yesmaximal, complemented
14#14262C211yesmaximal, characteristic, complemented
15#14255C211yesmaximal, characteristic, complemented
16#14149C211yesmaximal, characteristic, complemented
17#13995C211yesmaximal, characteristic, complemented
18#13995C211yesmaximal, characteristic, complemented
19#13971C211yesmaximal, characteristic, complemented
20#13971C211yesmaximal, characteristic, complemented
21#13960C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic, complemented
23#13778C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#121C2212yes—
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33#2408C4116yescomplemented
34C2×#394C2212yes—
35C2×#392C2212yes—
36#2318—28no—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2212yescomplemented
41C2×#390C2212yescomplemented
42C2×#388C2211yescharacteristic, complemented
43C2×#388C2211yescharacteristic, complemented
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#387C2211yescharacteristic, complemented
47C2×#387C2211yescharacteristic, complemented
48C2×#386—28no—
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2212yescomplemented
64C2×#385C2212yescomplemented
65C2×#383C2211yescharacteristic, complemented
66C2×#382C2211yescharacteristic, complemented
67C2×#381C2211yescharacteristic, complemented
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic, complemented
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81C22×#95C2211yescharacteristic
82#1441C2212yescomplemented
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1440C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yescomplemented
101#1438C2212yescomplemented
102#1438C2212yescomplemented
103#1438C2212yescomplemented
104#1437C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1436C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1434C2212yescomplemented
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C26C2311yescharacteristic
127C26C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—44no—
131C23×D4—44no—
132C23×D4C2×C418yes—
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C24×C4—24no—
139C24×C4—44no—
140C24×C4—42no—
141C24×C4—42no—
142C24×C4—44no—
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C2×#121—44no—
152C2×#121—44no—
153C2×#121C2×C4116yescomplemented
154C2×#120—42no—
155C2×#120—42no—
156C2×#120—42no—
157C2×#120—42no—
158C2×#120C2×C418yes—
159C2×#120C2×C418yescomplemented
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4C2×C418yescomplemented
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—44no—
176C22×C22⋊C4—44no—
177C22×C22⋊C4—42no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218#394C2×C4116yescomplemented
219#392C2×C4116yescomplemented
220#390—44no—
221#390—44no—
222#390—44no—
223#390—44no—
224#390C2×C4116yescomplemented
225#388—24no—
226#388—24no—
227#388—44no—
228#388—44no—
229#387—24no—
230#387—24no—
231#386—24no—
232#386—24no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—28no—
237#386—44no—
238#386—42no—
239#386—42no—
240#386—44no—
241#385—24no—
242#385—24no—
243#385—44no—
244#385—42no—
245#385—42no—
246#385—44no—
247#383—24no—
248#382—24no—
249#381—24no—
250#380—24no—
251#380—24no—
252#380C2×C418yescomplemented
253#379—42no—
254#379—42no—
255#379—42no—
256#379—42no—
257#379C2×C418yes—
258#379C2×C418yescomplemented
259C4×C22⋊C4—24no—
260C4×C22⋊C4—42no—
261C4×C22⋊C4—42no—
262C2×#95—24no—
263C2×#95D418yescomplemented
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C25—22no—
301C25—22no—
302C25—24no—
303C25—24no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25C22×C414yes—
321C25C22×C414yes—
322C25C2412yes—
323C25C2411yescharacteristic
324C25C2412yes—
325C25C2411yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—232no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—432no—
358C22×D4—416no—
359C22×D4—416no—
360C22×D4—432no—
361C22×D4C22×C414yes—
362C22×D4C22×C418yes—
363C22×D4C22×C418yes—
364C22×D4C22×C418yes—
365C22×D4C22×C418yescomplemented
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
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—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—416no—
405C23×C4—416no—
406C23×C4—416no—
407C23×C4—432no—
408C23×C4—432no—
409C23×C4C22×C414yes—
410C23×C4C22×C414yescomplemented
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4#4114yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434#121—432no—
435#120—416no—
436#120—416no—
437C4×D4—232no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
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⋊C4—42no—
459C2×C4⋊C4C22×C414yescomplemented
460C2×C4⋊C4C22×C418yescomplemented
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
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—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—416no—
521C2×C22⋊C4—416no—
522C2×C22⋊C4—416no—
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—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
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⋊C4C22×C414yes—
553C2×C22⋊C4C22×C414yes—
554C2×C22⋊C4C22×C414yes—
555C2×C22⋊C4C22×C418yes—
556C2×C22⋊C4C22×C418yes—
557C2×C22⋊C4C22×C418yes—
558C2×C22⋊C4C22×C414yescomplemented
559C2×C22⋊C4C22×C418yescomplemented
560C2×C22⋊C4C22×C418yescomplemented
561C2×C22⋊C4C22×C418yescomplemented
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42C22×C414yescomplemented
575#95—24no—
576#95—24no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
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#95C22×C418yescomplemented
607#95C2×D414yes—
608#95C2×D414yes—
609#95C2×D414yes—
610#95C2×D414yes—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—216no—
618C24—28no—
619C24—216no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—28no—
633C24—28no—
634C24—28no—
635C24—21no—
636C24—22no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—28no—
660C24—28no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—44no—
673C24—44no—
674C24—48no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—48no—
679C24—44no—
680C24—48no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24C23×C414yes—
698C24C23×C412yes—
699C24C23×C414yes—
700C24C23×C412yes—
701C24C22×D412yes—
702C24C2×#4112yes—
703C24H(5,𝔽2)14yes—
704C24H(5,𝔽2)14yes—
705C24H(5,𝔽2)12yes—
706C24H(5,𝔽2)12yes—
707C24H(5,𝔽2)12yes—
708C242−1+412yes—
709C24C2511yescharacteristic
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—216no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—4128no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
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—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
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—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—4128no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—82no—
877C22×C4—82no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4C4×D4116yes—
884C22×C4C23×C414yes—
885C22×C4C23×C414yes—
886C22×C4C23×C412yes—
887C22×C4C23×C412yes—
888C22×C4C23×C412yes—
889C22×C4C23×C412yes—
890C22×C4C23×C412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4H(5,𝔽2)14yes—
900C4⋊C4—28no—
901C4⋊C4—48no—
902C4⋊C4—84no—
903C4⋊C4—82no—
904C4⋊C4—82no—
905C4⋊C4—82no—
906C4⋊C4—82no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—28no—
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—48no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—82no—
930C22⋊C4—82no—
931C22⋊C4—82no—
932C22⋊C4—82no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C42—28no—
944C42—82no—
945C42—82no—
946C42—84no—
947C42—84no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—232no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—432no—
996C23—432no—
997C23—416no—
998C23—416no—
999C23—416no—
1000C23—416no—
1001C23—432no—
1002C23—432no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
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—416no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—816no—
1071C23—816no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—816no—
1077C23—816no—
1078C23C2×C4×D414yes—
1079C23#51818yes—
1080C23#51814yes—
1081C23#52014yes—
1082C23#53514yes—
1083C23#53714yes—
1084C23#54014yes—
1085C23#54214yes—
1086C23C24×C411yescharacteristic
1087C23C23×D411yescharacteristic
1088C23C22×#4111yescharacteristic
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23C2×H(5,𝔽2)12yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)11yescharacteristic
1094C23C2×H(5,𝔽2)12yes—
1095C23C2×2−1+411yescharacteristic
1096C23#58512yes—
1097D4—432no—
1098D4—432no—
1099D4—416no—
1100D4—816no—
1101D4—816no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—432no—
1142C2×C4—432no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
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—42no—
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—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
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—88no—
1215C2×C4—88no—
1216C2×C4—88no—
1217C2×C4C2×C4×D414yes—
1218C2×C4C2×C4×D414yes—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—28no—
1225C22—28no—
1226C22—28no—
1227C22—28no—
1228C22—24no—
1229C22—28no—
1230C22—28no—
1231C22—28no—
1232C22—464no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—42no—
1246C22—44no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—42no—
1256C22—44no—
1257C22—832no—
1258C22—81no—
1259C22—82no—
1260C22—81no—
1261C22—82no—
1262C22—81no—
1263C22—82no—
1264C22—81no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22#232418yes—
1273C22C22×C4×D411yescharacteristic
1274C22C2×#51811yescharacteristic
1275C22C2×#51812yes—
1276C22C2×#52011yescharacteristic
1277C22C4×H(5,𝔽2)12yes—
1278C22C2×#53511yescharacteristic
1279C22C2×#53711yescharacteristic
1280C22C2×#54011yescharacteristic
1281C22C2×#54211yescharacteristic
1282C22#348411yescharacteristic
1283C22#348411yescharacteristic
1284C22#348411yescharacteristic
1285C22#348711yescharacteristic
1286C22#349012yes—
1287C22#350612yes—
1288C22#353212yes—
1289C22#353212yes—
1290C22#353412yes—
1291C22#353412yes—
1292C22#353412yes—
1293C22#353512yes—
1294C22#353612yes—
1295C22#353712yes—
1296C4—24no—
1297C4—24no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—81no—
1309C4—82no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—82no—
1314C4—82no—
1315C2—28no—
1316C2—48no—
1317C2—82no—
1318C2—84no—
1319C2C2×#232411yescharacteristic
1320C2#3419811yescharacteristic
1321C2#3426511yescharacteristic
1322C2#3445612yes—
1323C2#3446812yes—
1324C2#3670311yescharacteristic
1325C2#3670611yescharacteristic
1326C2#3672211yescharacteristic
1327C2#3679312yes—
1328C2#3679412yes—
1329C2#3718511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2408C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2318C2semidirect
3. C22×#386C2semidirect
4. #14694C2semidirect
5. #14693C2semidirect
6. #14536C2semidirect
7. #14534C2semidirect
8. #14523C2semidirect
9. #14521C2semidirect
10. #14379C2semidirect
11. #14377C2semidirect
12. #14363C2semidirect
13. #14361C2semidirect
14. #14262C2semidirect
15. #14255C2semidirect
16. #14149C2semidirect
17. #13995C2semidirect
18. #13995C2semidirect
19. #13971C2semidirect
20. #13971C2semidirect
21. #13960C2semidirect
22. #13902C2semidirect
23. #13778C2semidirect
33. #2408C4semidirect
40. C2×#390C22semidirect
41. C2×#390C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#387C22semidirect
47. C2×#387C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
63. C2×#385C22semidirect
64. C2×#385C22semidirect
65. C2×#383C22semidirect
66. C2×#382C22semidirect
67. C2×#381C22semidirect
70. C2×#380C22semidirect
82. #1441C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1440C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
100. #1438C22semidirect
101. #1438C22semidirect
102. #1438C22semidirect
103. #1438C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1436C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1434C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
153. C2×#121C2×C4semidirect
159. C2×#120C2×C4semidirect
162. C2×C4×D4C2×C4semidirect
218. #394C2×C4semidirect
219. #392C2×C4semidirect
224. #390C2×C4semidirect
252. #380C2×C4semidirect
258. #379C2×C4semidirect
263. C2×#95D4semidirect
365. C22×D4C22×C4semidirect
410. C23×C4C22×C4semidirect
459. C2×C4⋊C4C22×C4semidirect
460. C2×C4⋊C4C22×C4semidirect
558. C2×C22⋊C4C22×C4semidirect
559. C2×C22⋊C4C22×C4semidirect
560. C2×C22⋊C4C22×C4semidirect
561. C2×C22⋊C4C22×C4semidirect
574. C2×C42C22×C4semidirect
606. #95C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#23182
C22×#3862
#146942
#146932
#145362
#145342
#145232
#145212
#143792
#143772
#143632
#143612
#142622
#142552
#141492
#139952
#139712
#139602
#139022
#137782