Finite Group Databasebeta

← #515758

Subgroups — #515758

Order 512.

4080 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×#2324C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic, complemented
5C2×#2275C211yesmaximal, characteristic, complemented
6#14205C212yesmaximal, complemented
7#14199C212yesmaximal, complemented
8#14185C212yesmaximal, complemented
9#14182C212yesmaximal, complemented
10#14151C211yesmaximal, characteristic, complemented
11#14108C212yesmaximal, complemented
12#14100C212yesmaximal, complemented
13#14047C212yesmaximal, complemented
14#14023C212yesmaximal, complemented
15#13994C211yesmaximal, characteristic, complemented
16#13993C211yesmaximal, characteristic, complemented
17#13970C211yesmaximal, characteristic, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13941C211yesmaximal, characteristic, complemented
20#13905C211yesmaximal, characteristic, complemented
21#13779C211yesmaximal, characteristic, complemented
22#13777C211yesmaximal, characteristic, complemented
23C4×#380C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×#117C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2537C4116yescomplemented
35C2×#394C2212yes—
36C2×#394C2212yes—
37#2324—28no—
38C4×#121—28no—
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45#2290—28no—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2211yescharacteristic
49C2×#388C2211yescharacteristic
50C2×#388C2212yes—
51C2×#387C2211yescharacteristic
52C2×#387C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#385C2212yes—
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C2×#382C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2212yes—
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71#2275—28no—
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2212yes—
85C2×#376C2211yescharacteristic
86C22×#95C2212yes—
87#1445C2212yes—
88#1443C2212yes—
89#1442C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113C4⋊#95C2212yes—
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120#1434C2212yes—
121#1434C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C4×#95C2212yes—
128C23×D4C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121—44no—
144C2×#121—44no—
145C2×#121C2×C418yes—
146C2×#121C2×C418yescomplemented
147C2×#121C2×C4116yescomplemented
148C2×C4×D4—24no—
149C2×C4×D4—28no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—44no—
159C2×C4×D4—44no—
160C2×C4×D4C2×C418yescomplemented
161C2×C4×D4C2×C418yescomplemented
162C2×C4×D4D418yescomplemented
163C2×#117—24no—
164C2×#117—24no—
165C2×#117—24no—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C42—24no—
206C22×C42—24no—
207C22×C42—24no—
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220#394C2×C4116yescomplemented
221#394C2×C4116yescomplemented
222#390—24no—
223#390—24no—
224#390—28no—
225#389—24no—
226#389—24no—
227#389—44no—
228#388—28no—
229#388—28no—
230#388—24no—
231#388—24no—
232#388—44no—
233#387—24no—
234#387—24no—
235#386—28no—
236#386—28no—
237#386—24no—
238#386—24no—
239#386—44no—
240#386—44no—
241#385—28no—
242#385—24no—
243#385—24no—
244#384C2×C418yescomplemented
245#382—24no—
246#380—24no—
247#380—24no—
248#380—24no—
249#380—24no—
250#380C2×C4116yescomplemented
251#380C2×C418yescomplemented
252#380C2×C418yescomplemented
253C4×C4⋊C4—24no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—24no—
256C4×C4⋊C4—24no—
257C4×C4⋊C4—24no—
258C4×C4⋊C4—24no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—24no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—28no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—44no—
266#376D418yescomplemented
267C2×#95—28no—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
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×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25C2411yescharacteristic
306C25C2412yes—
307C25C2411yescharacteristic
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—42no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—42no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4C22×C414yes—
331C22×D4C22×C418yes—
332C22×D4C22×C414yes—
333C22×D4C22×C418yes—
334C22×D4C2×D414yes—
335C22×D4#4114yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—24no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4C22×C414yes—
382C23×C4C22×C414yes—
383C23×C4C22×C418yes—
384C23×C4C2×D418yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#121—232no—
406#121—232no—
407#121—432no—
408C4×D4—232no—
409C4×D4—232no—
410C4×D4—232no—
411C4×D4—232no—
412C4×D4—432no—
413#117—416no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
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⋊C4C22×C414yes—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C22×C414yes—
457C2×C4⋊C4C22×C414yes—
458C2×C4⋊C4C22×C418yes—
459C2×C4⋊C4C22×C418yes—
460C2×C4⋊C4C2×D414yes—
461C2×C4⋊C4#4114yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—41no—
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—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4C22×C414yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C414yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C2×D418yes—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—24no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—416no—
553C2×C42—42no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42C22×C414yes—
562C2×C42C2×D414yes—
563C2×C42C2×D414yes—
564C2×C42C2×D414yes—
565C2×C42C2×D414yes—
566C2×C42#4114yes—
567C2×C42#4114yes—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—22no—
573#95—22no—
574#95—24no—
575#95—22no—
576#95—22no—
577#95—24no—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—42no—
589#95—42no—
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#95C22×C418yes—
600#95C22×C418yes—
601#95C2×D414yes—
602#95C2×D414yes—
603#95C2×D414yes—
604#95C2×D414yes—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C23×C412yes—
644C24C23×C414yes—
645C24C23×C412yes—
646C24C22×D414yes—
647C24C2×#4114yes—
648C24H(5,𝔽2)12yes—
649C24H(5,𝔽2)12yes—
650C24C2511yescharacteristic
651C2×D4—216no—
652C2×D4—28no—
653C2×D4—216no—
654C2×D4—216no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—84no—
675C2×D4—84no—
676C2×D4—84no—
677C2×D4—84no—
678C2×D4C4×D4116yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—216no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—216no—
771C22×C4—216no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4—84no—
831C22×C4—84no—
832C22×C4—84no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4C23×C412yes—
839C22×C4C23×C412yes—
840C22×C4C23×C414yes—
841C22×C4C23×C414yes—
842C22×C4C23×C414yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D414yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C2×#4114yes—
858C22×C4C2×#4112yes—
859C22×C4C2×#4112yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C4C2×#4112yes—
866C22×C4H(5,𝔽2)12yes—
867C22×C42−1+412yes—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—84no—
884C22⋊C4—216no—
885C22⋊C4—216no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—216no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C42—28no—
908C42—48no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—44no—
913C42—84no—
914C42—84no—
915C42—84no—
916C42—84no—
917C42C4×D4116yescomplemented
918C42#121116yescomplemented
919C23—22no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—22no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—41no—
972C23—41no—
973C23—42no—
974C23—42no—
975C23—41no—
976C23—42no—
977C23—41no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—41no—
984C23—41no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C2×C4×D418yes—
1023C23#51814yes—
1024C23C24×C411yescharacteristic
1025C23C23×D411yescharacteristic
1026C23C23×D411yescharacteristic
1027C23C22×#4111yescharacteristic
1028C23C22×#4111yescharacteristic
1029C23C22×#4111yescharacteristic
1030C23C22×#4111yescharacteristic
1031C23C2×H(5,𝔽2)11yescharacteristic
1032C23C2×H(5,𝔽2)11yescharacteristic
1033C23C2×H(5,𝔽2)11yescharacteristic
1034C23C2×2−1+411yescharacteristic
1035C23#58511yescharacteristic
1036C23#58511yescharacteristic
1037C23#58511yescharacteristic
1038C23#58511yescharacteristic
1039D4—232no—
1040D4—416no—
1041D4—432no—
1042D4—816no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—416no—
1101C2×C4—416no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—416no—
1147C2×C4—416no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—816no—
1177C2×C4—816no—
1178C2×C4—816no—
1179C2×C4C2×C4×D414yes—
1180C2×C4C2×C4×D414yes—
1181C2×C4C2×C4×D414yes—
1182C2×C4C2×C4×D414yes—
1183C2×C4C4×#4114yes—
1184C2×C4C2×#12114yes—
1185C2×C4C2×#12114yes—
1186C2×C4C2×#12114yes—
1187C2×C4#52514yes—
1188C2×C4#52914yes—
1189C2×C4#53214yes—
1190C22—24no—
1191C22—28no—
1192C22—28no—
1193C22—24no—
1194C22—28no—
1195C22—24no—
1196C22—42no—
1197C22—44no—
1198C22—44no—
1199C22—42no—
1200C22—44no—
1201C22—42no—
1202C22—44no—
1203C22—42no—
1204C22—44no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22C22×C4×D411yescharacteristic
1236C22C22×C4×D411yescharacteristic
1237C22C2×C4×#4111yescharacteristic
1238C22C2×#51811yescharacteristic
1239C22#342811yescharacteristic
1240C22C4×H(5,𝔽2)11yescharacteristic
1241C22C4×2−1+411yescharacteristic
1242C22C22×#12111yescharacteristic
1243C22C2×#52511yescharacteristic
1244C22C2×#52911yescharacteristic
1245C22C2×#53211yescharacteristic
1246C22#348411yescharacteristic
1247C22#348511yescharacteristic
1248C22#348811yescharacteristic
1249C22#348811yescharacteristic
1250C22#348811yescharacteristic
1251C22#348811yescharacteristic
1252C22#348911yescharacteristic
1253C22#348911yescharacteristic
1254C22#349211yescharacteristic
1255C22#349311yescharacteristic
1256C22#349411yescharacteristic
1257C22#349411yescharacteristic
1258C22#349411yescharacteristic
1259C22#349411yescharacteristic
1260C22#351111yescharacteristic
1261C22#351211yescharacteristic
1262C22#351311yescharacteristic
1263C22#351311yescharacteristic
1264C22#351411yescharacteristic
1265C22#351511yescharacteristic
1266C22#351911yescharacteristic
1267C22#352111yescharacteristic
1268C22#352211yescharacteristic
1269C22#352411yescharacteristic
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—24no—
1274C4—44no—
1275C4—42no—
1276C4—44no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—82no—
1286C4—81no—
1287C4—81no—
1288C4—82no—
1289C4C4×#12118yes—
1290C2—44no—
1291C2—48no—
1292C2—82no—
1293C2C2×C4×#12111yescharacteristic
1294C2#3420411yescharacteristic
1295C2#3426711yescharacteristic
1296C2#3428911yescharacteristic
1297C2#3429011yescharacteristic
1298C2#3429811yescharacteristic
1299C2#3430611yescharacteristic
1300C2#3551411yescharacteristic
1301C2#3551811yescharacteristic
1302C2#3552011yescharacteristic
1303C2#3552211yescharacteristic
1304C2#3555111yescharacteristic
1305C2#3555211yescharacteristic
1306C2#3557011yescharacteristic
1307C2#3560711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2537C2
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×#2324C2semidirect
3. C2×C4×#121C2semidirect
4. C2×#2290C2semidirect
5. C2×#2275C2semidirect
6. #14205C2semidirect
7. #14199C2semidirect
8. #14185C2semidirect
9. #14182C2semidirect
10. #14151C2semidirect
11. #14108C2semidirect
12. #14100C2semidirect
13. #14047C2semidirect
14. #14023C2semidirect
15. #13994C2semidirect
16. #13993C2semidirect
17. #13970C2semidirect
18. #13970C2semidirect
19. #13941C2semidirect
20. #13905C2semidirect
21. #13779C2semidirect
22. #13777C2semidirect
23. C4×#380C2semidirect
34. #2537C4semidirect
146. C2×#121C2×C4semidirect
147. C2×#121C2×C4semidirect
160. C2×C4×D4C2×C4semidirect
161. C2×C4×D4C2×C4semidirect
162. C2×C4×D4D4semidirect
220. #394C2×C4semidirect
221. #394C2×C4semidirect
244. #384C2×C4semidirect
250. #380C2×C4semidirect
251. #380C2×C4semidirect
252. #380C2×C4semidirect
266. #376D4semidirect
917. C42C4×D4semidirect
918. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#23242
C2×C4×#1212
C2×#22902
C2×#22752
#142052
#141992
#141852
#141822
#141512
#141082
#141002
#140472
#140232
#139942
#139932
#139702
#139412
#139052
#137792
#137772
C4×#3802