Finite Group Databasebeta

← #523326

Subgroups — #523326

Order 512.

3980 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×#2535C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#2324C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5C2×#2290C211yesmaximal, characteristic, complemented
6#14697C211yesmaximal, characteristic, complemented
7#14541C212yesmaximal, complemented
8#14519C212yesmaximal, complemented
9#14397C212yesmaximal, complemented
10#14391C212yesmaximal, complemented
11#14277C211yesmaximal, characteristic, complemented
12#14264C211yesmaximal, characteristic, complemented
13#14189C212yesmaximal, complemented
14#14183C212yesmaximal, complemented
15#14019C212yesmaximal, complemented
16#14015C212yesmaximal, complemented
17#13974C211yesmaximal, characteristic, complemented
18#13973C211yesmaximal, characteristic, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13970C211yesmaximal, characteristic, complemented
21#13906C211yesmaximal, characteristic, complemented
22#13804C211yesmaximal, characteristic, complemented
23#13785C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2212yes—
33C23×C42C2211yescharacteristic
34#2535C4116yescomplemented
35C2×#397C2212yes—
36C2×#392C2212yes—
37D4×C4⋊C4—28no—
38#2324—28no—
39C4×#121—28no—
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48#2290—28no—
49C2×#388C2212yes—
50C2×#388C2211yescharacteristic
51C2×#388C2212yes—
52C2×#388C2211yescharacteristic
53C2×#388C2212yes—
54C2×#387C2211yescharacteristic
55C2×#387C2211yescharacteristic
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#385C2212yes—
65C2×#385C2211yescharacteristic
66C2×#385C2212yes—
67C2×#385C2212yes—
68C2×#385C2211yescharacteristic
69C2×#385C2212yes—
70C2×#384C2211yescharacteristic
71C2×#382C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×#376C2211yescharacteristic
87#1444C2212yes—
88#1444C2212yes—
89#1444C2212yes—
90#1443C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1440C2212yes—
96#1440C2212yes—
97#1440C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
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×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121C2×C418yes—
144C2×#121C2×C418yescomplemented
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—28no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×C4×D4—44no—
158C2×C4×D4C2×C418yescomplemented
159C2×C4×D4C2×C418yescomplemented
160C2×#117—24no—
161C2×#117—24no—
162C2×#117—42no—
163C22×C4⋊C4—28no—
164C22×C4⋊C4—44no—
165C22×C4⋊C4—44no—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C42—24no—
208C22×C42—24no—
209C22×C42—42no—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220#397C2×C4116yescomplemented
221#392C2×C4116yescomplemented
222#390—24no—
223#390—28no—
224#390—44no—
225#390D418yescomplemented
226#389—24no—
227#389—24no—
228#389—24no—
229#389—24no—
230#388—24no—
231#388—24no—
232#388—28no—
233#388—28no—
234#388—44no—
235#387—24no—
236#387—24no—
237#386—28no—
238#386—28no—
239#386—24no—
240#386—24no—
241#386—44no—
242#386—44no—
243#386C2×C4116yescomplemented
244#386C2×C4116yescomplemented
245#385—24no—
246#385—24no—
247#385—28no—
248#385—28no—
249#385—28no—
250#385—44no—
251#384—24no—
252#382C2×C418yescomplemented
253#380—24no—
254#380—28no—
255#380—24no—
256#380—42no—
257#380—42no—
258#380C2×C418yescomplemented
259#380C2×C418yescomplemented
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4D418yescomplemented
264C4×C22⋊C4—28no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4—24no—
267#376—24no—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
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×#95C2312yes—
302C2×#95C2312yes—
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—24no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—24no—
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—24no—
354C23×C4—22no—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—41no—
372C23×C4—41no—
373C23×C4—41no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4C22×C414yes—
383C23×C4C22×C414yes—
384C23×C4C22×C418yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#121—232no—
406#121—232no—
407C4×D4—232no—
408C4×D4—232no—
409C4×D4—416no—
410C4×D4—416no—
411C4×D4—432no—
412#117—416no—
413C2×C4⋊C4—22no—
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—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—432no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4C22×C414yes—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C414yes—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2×D414yes—
467C2×C4⋊C4C2×D414yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
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—24no—
488C2×C22⋊C4—24no—
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—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
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—42no—
521C2×C22⋊C4—42no—
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⋊C4C22×C414yes—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C418yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C418yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C22×C418yes—
535C2×C22⋊C4C2×D418yes—
536C2×C22⋊C4C2×D418yes—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—24no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—24no—
551C2×C42—22no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—416no—
555C2×C42—42no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42C22×C414yes—
563C2×C42C2×D414yes—
564C2×C42C2×D414yes—
565C2×C42C2×D414yes—
566C2×C42C2×D414yes—
567C2×C42#4114yes—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—24no—
576#95—22no—
577#95—22no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
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#95C22×C418yes—
602#95C22×C418yes—
603#95C2×D414yes—
604#95C2×D414yes—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—22no—
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—
649C242−1+412yes—
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—28no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—216no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
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—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4C23×C414yes—
842C22×C4C23×C414yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C414yes—
846C22×C4C23×C412yes—
847C22×C4C23×C412yes—
848C22×C4C23×C412yes—
849C22×C4C22×D414yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4H(5,𝔽2)12yes—
865C22×C4H(5,𝔽2)12yes—
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—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—84no—
885C4⋊C4—84no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C42—28no—
910C42—28no—
911C42—28no—
912C42—44no—
913C42—44no—
914C42—48no—
915C42—44no—
916C42—84no—
917C42—84no—
918C42C4×D4116yescomplemented
919C23—24no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—22no—
926C23—24no—
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—24no—
940C23—22no—
941C23—22no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—42no—
963C23—41no—
964C23—41no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—42no—
986C23—41no—
987C23—42no—
988C23—41no—
989C23—42no—
990C23—42no—
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#52014yes—
1024C23C24×C411yescharacteristic
1025C23C23×D411yescharacteristic
1026C23C23×D411yescharacteristic
1027C23C22×#4111yescharacteristic
1028C23C22×#4111yescharacteristic
1029C23C2×H(5,𝔽2)11yescharacteristic
1030C23C2×H(5,𝔽2)11yescharacteristic
1031C23C2×H(5,𝔽2)11yescharacteristic
1032C23C2×H(5,𝔽2)11yescharacteristic
1033C23C2×2−1+411yescharacteristic
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—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—416no—
1095C2×C4—432no—
1096C2×C4—416no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
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—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—416no—
1142C2×C4—416no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
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—816no—
1179C2×C4—816no—
1180C2×C4C2×C4×D414yes—
1181C2×C4C2×C4×D414yes—
1182C2×C4C2×C4×D414yes—
1183C2×C4C2×C4×D414yes—
1184C2×C4#52014yes—
1185C2×C4#53514yes—
1186C2×C4D4214yes—
1187C2×C4#54714yes—
1188C2×C4#54814yes—
1189C2×C4#55314yes—
1190C22—28no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—28no—
1195C22—28no—
1196C22—42no—
1197C22—44no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—44no—
1213C22—42no—
1214C22—44no—
1215C22—44no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—42no—
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×#52011yescharacteristic
1238C22C2×#52011yescharacteristic
1239C22#342811yescharacteristic
1240C22C4×H(5,𝔽2)11yescharacteristic
1241C22C4×H(5,𝔽2)11yescharacteristic
1242C22C2×#53511yescharacteristic
1243C22#344911yescharacteristic
1244C22#346011yescharacteristic
1245C22#346011yescharacteristic
1246C22C2×D4211yescharacteristic
1247C22C2×#54711yescharacteristic
1248C22C2×#54811yescharacteristic
1249C22C2×#55311yescharacteristic
1250C22#348411yescharacteristic
1251C22#348511yescharacteristic
1252C22#348811yescharacteristic
1253C22#348811yescharacteristic
1254C22#348911yescharacteristic
1255C22#348911yescharacteristic
1256C22#349411yescharacteristic
1257C22#349511yescharacteristic
1258C22#351311yescharacteristic
1259C22#351411yescharacteristic
1260C22#352011yescharacteristic
1261C22#352111yescharacteristic
1262C22#353711yescharacteristic
1263C22#353911yescharacteristic
1264C22#354111yescharacteristic
1265C22#354211yescharacteristic
1266C22#354711yescharacteristic
1267C22#355211yescharacteristic
1268C22#355911yescharacteristic
1269C22#356511yescharacteristic
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—44no—
1279C4—42no—
1280C4—42no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—82no—
1285C4—82no—
1286C4—82no—
1287C4—81no—
1288C4—81no—
1289C4#236118yes—
1290C2—48no—
1291C2—44no—
1292C2—82no—
1293C2C4×#53511yescharacteristic
1294C2C2×#236111yescharacteristic
1295C2#3420211yescharacteristic
1296C2#3428811yescharacteristic
1297C2#3429211yescharacteristic
1298C2#3446111yescharacteristic
1299C2#3446611yescharacteristic
1300C2#3765011yescharacteristic
1301C2#3765611yescharacteristic
1302C2#3776411yescharacteristic
1303C2#3776711yescharacteristic
1304C2#3911811yescharacteristic
1305C2#3912411yescharacteristic
1306C2#3925611yescharacteristic
1307C2#3926011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2535C2
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×D4×C4⋊C4C2semidirect
3. C2×#2324C2semidirect
4. C2×C4×#121C2semidirect
5. C2×#2290C2semidirect
6. #14697C2semidirect
7. #14541C2semidirect
8. #14519C2semidirect
9. #14397C2semidirect
10. #14391C2semidirect
11. #14277C2semidirect
12. #14264C2semidirect
13. #14189C2semidirect
14. #14183C2semidirect
15. #14019C2semidirect
16. #14015C2semidirect
17. #13974C2semidirect
18. #13973C2semidirect
19. #13970C2semidirect
20. #13970C2semidirect
21. #13906C2semidirect
22. #13804C2semidirect
23. #13785C2semidirect
34. #2535C4semidirect
144. C2×#121C2×C4semidirect
158. C2×C4×D4C2×C4semidirect
159. C2×C4×D4C2×C4semidirect
220. #397C2×C4semidirect
221. #392C2×C4semidirect
225. #390D4semidirect
243. #386C2×C4semidirect
244. #386C2×C4semidirect
252. #382C2×C4semidirect
258. #380C2×C4semidirect
259. #380C2×C4semidirect
263. C4×C4⋊C4D4semidirect
918. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×D4×C4⋊C42
C2×#23242
C2×C4×#1212
C2×#22902
#146972
#145412
#145192
#143972
#143912
#142772
#142642
#141892
#141832
#140192
#140152
#139742
#139732
#139702
#139062
#138042
#137852