Finite Group Databasebeta

← #515774

Subgroups — #515774

Order 512.

4340 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic
2C2×#2324C211yesmaximal, characteristic, complemented
3C2×#2324C211yesmaximal, characteristic, complemented
4C2×C4×#127C211yesmaximal, characteristic, complemented
5C2×#2275C211yesmaximal, characteristic, complemented
6#14228C212yesmaximal, complemented
7#14201C212yesmaximal, complemented
8#14187C212yesmaximal, complemented
9#14185C212yesmaximal, complemented
10#14141C211yesmaximal, characteristic, complemented
11#14076C212yesmaximal, complemented
12#14025C211yesmaximal, characteristic, complemented
13#14023C212yesmaximal, complemented
14#14005C211yesmaximal, characteristic, complemented
15#13998C211yesmaximal, characteristic, complemented
16#13998C212yesmaximal, complemented
17#13975C212yesmaximal, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13920C211yesmaximal, characteristic, complemented
20#13876C211yesmaximal, characteristic, complemented
21#13785C211yesmaximal, characteristic, complemented
22C4×#389C211yesmaximal, characteristic, complemented
23#13761C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2212yes—
34C22×#117C2211yescharacteristic
35#2428C4116yescomplemented
36C2×#394C2212yes—
37C2×#392C2212yes—
38#2324—28no—
39#2324—28no—
40C4×#127—28no—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2212yes—
56C2×#389C2211yescharacteristic
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#385C2212yes—
68C2×#385C2212yes—
69C2×#384C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2212yes—
73#2275—28no—
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2212yes—
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×#376C2211yescharacteristic
85C22×#95C2212yes—
86C2×C43C2211yescharacteristic
87#1444C2212yes—
88#1442C2212yes—
89#1441C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2211yescharacteristic
104#1437C2212yes—
105#1437C2211yescharacteristic
106#1437C2211yescharacteristic
107#1437C2212yes—
108#1437C2211yescharacteristic
109#1436C2212yes—
110#1436C2211yescharacteristic
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116#1436C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2212yes—
127C4×#95C2211yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#127—24no—
140C2×#127—24no—
141C2×#127C2×C418yes—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—24no—
146C2×#121—44no—
147C2×#121—44no—
148C2×#121C2×C418yescomplemented
149C2×#121C2×C418yescomplemented
150C2×#121C2×C4116yescomplemented
151C2×C4×D4—24no—
152C2×C4×D4—28no—
153C2×C4×D4—28no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—44no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C2×C4×D4C2×C418yescomplemented
168C2×C4×D4D418yescomplemented
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—24no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#394C2×C4116yescomplemented
227#392C2×C4116yescomplemented
228#390—24no—
229#390—24no—
230#390—24no—
231#390—24no—
232#390—28no—
233#390—28no—
234#390—28no—
235#390—28no—
236#390—24no—
237#390—44no—
238#390C2×C418yescomplemented
239#389—24no—
240#389—24no—
241#389—24no—
242#389—44no—
243#389C2×C418yescomplemented
244#388—28no—
245#388—28no—
246#388—44no—
247#388—44no—
248#386—28no—
249#386—28no—
250#386—44no—
251#386—44no—
252#386—44no—
253#386C2×C4116yescomplemented
254#385—28no—
255#385—28no—
256#384—24no—
257#380—24no—
258#380—24no—
259#380—44no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—24no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4—44no—
264C4×C4⋊C4D418yescomplemented
265C4×C22⋊C4—28no—
266C4×C22⋊C4—28no—
267C4×C22⋊C4—24no—
268C4×C22⋊C4—28no—
269C4×C22⋊C4C2×C418yescomplemented
270#376—24no—
271C2×#95—28no—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2312yes—
306C43—24no—
307C25C2411yescharacteristic
308C25C2412yes—
309C25C2412yes—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4C22×C414yes—
345C22×D4C22×C418yes—
346C22×D4C22×C418yes—
347C22×D4C22×C414yes—
348C22×D4C22×C418yes—
349C22×D4C22×C418yes—
350C22×D4C2×D414yes—
351C22×D4#4114yes—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—42no—
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×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4C22×C414yes—
385C23×C4C22×C418yes—
386C23×C4C2×D418yes—
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407#127—232no—
408#121—232no—
409#121—232no—
410#121—432no—
411C4×D4—232no—
412C4×D4—232no—
413C4×D4—232no—
414C4×D4—432no—
415C4×D4—432no—
416C4×D4—416no—
417#117—416no—
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—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
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⋊C4C22×C414yes—
454C2×C4⋊C4C22×C418yes—
455C2×C4⋊C4C22×C414yes—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4C2×D414yes—
458C2×C4⋊C4C2×D414yes—
459C2×C4⋊C4#4114yes—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
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—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—24no—
482C2×C22⋊C4—24no—
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—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
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—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
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—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⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4C22×C418yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C418yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C2×D418yes—
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—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—41no—
566C2×C42—41no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42C22×C414yes—
574C2×C42C22×C414yes—
575C2×C42C2×D418yes—
576C2×C42C2×D414yes—
577C2×C42C2×D414yes—
578C2×C42#4114yes—
579C2×C42#4114yes—
580#95—22no—
581#95—24no—
582#95—24no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—41no—
604#95—41no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95C22×C414yes—
611#95C22×C414yes—
612#95C22×C418yes—
613#95C2×D418yes—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24C23×C414yes—
655C24C23×C412yes—
656C24C23×C414yes—
657C24C22×D414yes—
658C24C2×#4114yes—
659C24C2511yescharacteristic
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—216no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—216no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—84no—
694C2×D4—84no—
695C2×D4—84no—
696C2×D4—84no—
697C2×D4—84no—
698C2×D4—84no—
699C2×D4—84no—
700C2×D4—84no—
701C2×D4C4×D4116yes—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—216no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—216no—
787C22×C4—216no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—48no—
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×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C23×C412yes—
848C22×C4C23×C414yes—
849C22×C4C23×C414yes—
850C22×C4C23×C412yes—
851C22×C4C23×C412yes—
852C22×C4C23×C412yes—
853C22×C4C22×D414yes—
854C22×C4C22×D414yes—
855C22×C4C22×D414yes—
856C22×C4C22×D412yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4114yes—
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C4H(5,𝔽2)12yes—
873C22×C4H(5,𝔽2)12yes—
874C22×C4H(5,𝔽2)12yes—
875C22×C4H(5,𝔽2)12yes—
876C22×C42−1+412yes—
877C4⋊C4—28no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—84no—
889C4⋊C4—84no—
890C4⋊C4C4×D4116yescomplemented
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—216no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—216no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C42—28no—
918C42—28no—
919C42—28no—
920C42—28no—
921C42—28no—
922C42—48no—
923C42—44no—
924C42—44no—
925C42—44no—
926C42—44no—
927C42—84no—
928C42—84no—
929C42—84no—
930C42#121116yescomplemented
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—41no—
980C23—42no—
981C23—41no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—41no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23C2×C4×D418yes—
1036C23C24×C411yescharacteristic
1037C23C23×D411yescharacteristic
1038C23C23×D411yescharacteristic
1039C23C22×#4111yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C2×H(5,𝔽2)11yescharacteristic
1044C23C2×H(5,𝔽2)11yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×2−1+411yescharacteristic
1049C23#58511yescharacteristic
1050C23#58511yescharacteristic
1051D4—232no—
1052D4—432no—
1053D4—432no—
1054D4—416no—
1055D4—816no—
1056D4—816no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
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—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—416no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—816no—
1187C2×C4—816no—
1188C2×C4—816no—
1189C2×C4—816no—
1190C2×C4C2×C4×D418yes—
1191C2×C4C2×C4×D414yes—
1192C2×C4C2×C4×D414yes—
1193C2×C4C4×#4114yes—
1194C2×C4#51814yes—
1195C2×C4#52014yes—
1196C2×C4C2×#12114yes—
1197C2×C4C2×#12114yes—
1198C2×C4C2×#12114yes—
1199C2×C4#52514yes—
1200C2×C4#52914yes—
1201C2×C4#53214yes—
1202C22—28no—
1203C22—28no—
1204C22—28no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—81no—
1232C22—82no—
1233C22—82no—
1234C22—81no—
1235C22—81no—
1236C22—82no—
1237C22—81no—
1238C22—82no—
1239C22—81no—
1240C22—82no—
1241C22—81no—
1242C22—82no—
1243C22—81no—
1244C22—82no—
1245C22—81no—
1246C22—82no—
1247C22C22×C4×D411yescharacteristic
1248C22C22×C4×D411yescharacteristic
1249C22C2×C4×#4111yescharacteristic
1250C22C2×#51811yescharacteristic
1251C22C2×#52011yescharacteristic
1252C22C4×H(5,𝔽2)11yescharacteristic
1253C22C4×H(5,𝔽2)11yescharacteristic
1254C22C22×#12111yescharacteristic
1255C22C2×#52511yescharacteristic
1256C22C2×#52911yescharacteristic
1257C22C2×#53211yescharacteristic
1258C22#348411yescharacteristic
1259C22#348411yescharacteristic
1260C22#348811yescharacteristic
1261C22#348911yescharacteristic
1262C22#349411yescharacteristic
1263C22#349411yescharacteristic
1264C22#349611yescharacteristic
1265C22#349711yescharacteristic
1266C22#349811yescharacteristic
1267C22#349811yescharacteristic
1268C22#350811yescharacteristic
1269C22#350811yescharacteristic
1270C22#350811yescharacteristic
1271C22#351111yescharacteristic
1272C22#351111yescharacteristic
1273C22#351211yescharacteristic
1274C22#351311yescharacteristic
1275C22#351311yescharacteristic
1276C22#351411yescharacteristic
1277C22#351711yescharacteristic
1278C22#351911yescharacteristic
1279C22#351911yescharacteristic
1280C22#352011yescharacteristic
1281C22#352211yescharacteristic
1282C4—28no—
1283C4—24no—
1284C4—24no—
1285C4—24no—
1286C4—24no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—44no—
1296C4—42no—
1297C4—81no—
1298C4—82no—
1299C4—81no—
1300C4—82no—
1301C4C4×#12118yes—
1302C2—48no—
1303C2—82no—
1304C2—84no—
1305C2C2×C4×#12111yescharacteristic
1306C2#3422611yescharacteristic
1307C2#3428011yescharacteristic
1308C2#3428811yescharacteristic
1309C2#3429011yescharacteristic
1310C2#3431011yescharacteristic
1311C2#3431311yescharacteristic
1312C2#3552811yescharacteristic
1313C2#3553811yescharacteristic
1314C2#3553911yescharacteristic
1315C2#3555911yescharacteristic
1316C2#3556011yescharacteristic
1317C2#3556411yescharacteristic
1318C2#3557111yescharacteristic
1319C2#3560711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2428C2
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×#2324C2semidirect
4. C2×C4×#127C2semidirect
5. C2×#2275C2semidirect
6. #14228C2semidirect
7. #14201C2semidirect
8. #14187C2semidirect
9. #14185C2semidirect
10. #14141C2semidirect
11. #14076C2semidirect
12. #14025C2semidirect
13. #14023C2semidirect
14. #14005C2semidirect
15. #13998C2semidirect
16. #13998C2semidirect
17. #13975C2semidirect
18. #13970C2semidirect
19. #13920C2semidirect
20. #13876C2semidirect
21. #13785C2semidirect
22. C4×#389C2semidirect
23. #13761C2semidirect
35. #2428C4semidirect
148. C2×#121C2×C4semidirect
149. C2×#121C2×C4semidirect
150. C2×#121C2×C4semidirect
167. C2×C4×D4C2×C4semidirect
168. C2×C4×D4D4semidirect
226. #394C2×C4semidirect
227. #392C2×C4semidirect
238. #390C2×C4semidirect
243. #389C2×C4semidirect
253. #386C2×C4semidirect
264. C4×C4⋊C4D4semidirect
269. C4×C22⋊C4C2×C4semidirect
890. C4⋊C4C4×D4semidirect
930. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#23242
C2×C4×#1272
C2×#22752
#142282
#142012
#141872
#141852
#141412
#140762
#140252
#140232
#140052
#139982
#139752
#139702
#139202
#138762
#137852
C4×#3892
#137612