Finite Group Databasebeta

← #356513

Subgroups — #356513

Order 512.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic, complemented
5C22×#340C211yesmaximal, characteristic, complemented
6#10850C211yesmaximal, characteristic, complemented
7#10849C211yesmaximal, characteristic, complemented
8#10843C211yesmaximal, characteristic, complemented
9#10731C211yesmaximal, characteristic, complemented
10#10730C211yesmaximal, characteristic, complemented
11#10730C211yesmaximal, characteristic, complemented
12#10730C211yesmaximal, characteristic, complemented
13#10722C211yesmaximal, characteristic, complemented
14#10721C211yesmaximal, characteristic, complemented
15#10703C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4—21no—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C2×#435—24no—
25C2×#435—24no—
26C2×#435C418yescomplemented
27C22×C4⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31#2352—24no—
32#2352C418yescomplemented
33D4×C4⋊C4—24no—
34D4×C4⋊C4C418yescomplemented
35C2×#389—21no—
36C2×#388—21no—
37C2×#387—21no—
38C2×#386—21no—
39C2×#385—21no—
40C2×#385—21no—
41C2×#384C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4—21no—
50#1736—24no—
51C2×#340—24no—
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62C2×#340C2211yescharacteristic
63C2×#340C2211yescharacteristic
64C2×#340C2211yescharacteristic
65C2×#340C2211yescharacteristic
66C2×#340C2211yescharacteristic
67C2×#340C2211yescharacteristic
68C23×D4D411yescharacteristic
69C24×C4—21no—
70C24×C4—21no—
71C24×C4—21no—
72C24×C4C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—41no—
79C22×M16—41no—
80C22×M16C2×C414yescomplemented
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—22no—
85C23×C8—41no—
86C23×C8—41no—
87C23×C8C2×C414yescomplemented
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C2×C4×D4—28no—
93C2×C4×D4—44no—
94C2×C4×D4—44no—
95C2×C4×D4C2×C414yes—
96C2×C4×D4C2×C414yes—
97C2×C4×D4C2×C414yes—
98C2×C4×D4D414yes—
99C2×C4×D4D414yes—
100C2×C4×D4Q814yes—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—41no—
105C2×#117—41no—
106C2×#117C2×C414yescomplemented
107C22×C4⋊C4—22no—
108C22×C4⋊C4—22no—
109C22×C4⋊C4—22no—
110C22×C4⋊C4—22no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4—22no—
113C22×C4⋊C4—22no—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—41no—
122C22×C4⋊C4—41no—
123C22×C4⋊C4—41no—
124C22×C4⋊C4—41no—
125C22×C4⋊C4—41no—
126C22×C4⋊C4—41no—
127C22×C4⋊C4C2×C414yes—
128C22×C4⋊C4C2×C414yescomplemented
129C22×C4⋊C4C2×C414yescomplemented
130C22×C4⋊C4D411yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4D411yescharacteristic
145C22×C22⋊C4D411yescharacteristic
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150#435—232no—
151C2×C4⋊C8—22no—
152C2×C4⋊C8—22no—
153C2×C4⋊C8C2×C414yescomplemented
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8C2×C414yescomplemented
159C2×C22⋊C8C2×C414yescomplemented
160C2×#97—22no—
161C2×#97—22no—
162C2×#97C2×C414yescomplemented
163#389—28no—
164#388—28no—
165#387—28no—
166#386—28no—
167#385—28no—
168#385—28no—
169#384—22no—
170#384C2×C414yescomplemented
171#382—22no—
172#382C2×C414yescomplemented
173#380—22no—
174#380—22no—
175#380—22no—
176#380—22no—
177#380C2×C414yes—
178#380C2×C414yescomplemented
179#380C2×C414yescomplemented
180#380C2×C414yescomplemented
181C4×C4⋊C4—22no—
182C4×C4⋊C4—22no—
183C4×C4⋊C4C2×C414yescomplemented
184C4×C4⋊C4C2×C414yescomplemented
185C4×C22⋊C4—28no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194#340—22no—
195#340—22no—
196#340—22no—
197#340—22no—
198#340—22no—
199#340—22no—
200#340—22no—
201#340—22no—
202#340—22no—
203#340—41no—
204#340—41no—
205#340—41no—
206#340—41no—
207#340—41no—
208#340—41no—
209#340D414yescomplemented
210C25C2×D411yescharacteristic
211C25C2×D411yescharacteristic
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4C22⋊C414yes—
217C22×D4C22⋊C414yes—
218C22×D4C4⋊C414yes—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—81no—
259C23×C4—81no—
260C23×C4—81no—
261C23×C4—81no—
262C23×C4—81no—
263C23×C4—81no—
264C23×C4C22×C412yes—
265C23×C4C22×C412yes—
266C23×C4C22×C412yes—
267C23×C4C22×C412yes—
268C23×C4C22×C412yes—
269C23×C4C22×C412yes—
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D412yes—
278C23×C4C2×Q812yes—
279C23×C4C2×Q812yes—
280C23×C4C2411yescharacteristic
281C2×M16—28no—
282C2×M16—28no—
283C2×M16—44no—
284C2×M16—44no—
285C2×M16—44no—
286C2×M16—44no—
287C2×M16—44no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—28no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—28no—
312C22×C8—44no—
313C22×C8—44no—
314C22×C8—44no—
315C22×C8—44no—
316C22×C8—44no—
317C22×C8C22×C412yes—
318C22×C8C22×C412yes—
319C22×C8C22×C412yes—
320C22×C8C22×C412yes—
321C22×C8C2×D412yes—
322C22×C8#4112yes—
323C4×D4—432no—
324C4×D4C42116yes—
325C4×D4C22⋊C4116yes—
326C4×D4C4⋊C4116yes—
327C4×D4C4⋊C4116yes—
328#117—28no—
329#117—44no—
330#117—44no—
331#117—44no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—81no—
394C2×C4⋊C4—81no—
395C2×C4⋊C4C22⋊C414yes—
396C2×C4⋊C4C22⋊C414yes—
397C2×C4⋊C4C4⋊C414yes—
398C2×C4⋊C4C22×C412yes—
399C2×C4⋊C4C22×C412yes—
400C2×C4⋊C4C22×C412yes—
401C2×C4⋊C4C22×C412yes—
402C2×C4⋊C4C22×C412yes—
403C2×C4⋊C4C22×C412yes—
404C2×C4⋊C4C22×C412yes—
405C2×C4⋊C4C22×C412yes—
406C2×C4⋊C4C2×D412yes—
407C2×C4⋊C4C2×D412yes—
408C2×C4⋊C4#4112yes—
409C2×C4⋊C4#4112yes—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—81no—
424C2×C22⋊C4—81no—
425C2×C22⋊C4C22⋊C414yes—
426C2×C22⋊C4C22⋊C414yes—
427C2×C22⋊C4C22⋊C414yes—
428C2×C22⋊C4C22⋊C414yes—
429C2×C22⋊C4C4⋊C414yes—
430C2×C22⋊C4C4⋊C414yes—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—81no—
439C2×C42—81no—
440C2×C42C22×C412yes—
441C2×C42C22×C412yes—
442C2×C42C22×C412yes—
443C2×C42C2×D412yes—
444C2×C42C2×D412yes—
445C2×C42C2×Q812yes—
446C4⋊C8—28no—
447C22⋊C8—28no—
448C22⋊C8—28no—
449#97—28no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24C2×C22⋊C412yes—
479C24C2×C22⋊C412yes—
480C24C2×C22⋊C412yes—
481C24C2×C22⋊C412yes—
482C24C2×C4⋊C412yes—
483C24C2×C4⋊C412yes—
484C24AGL(1,ℤ/8)12yes—
485C24AGL(1,ℤ/8)12yes—
486C24#13712yes—
487C24#13712yes—
488C24C22×D411yescharacteristic
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4#95116yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—48no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4C2×C4214yes—
638C22×C4C2×C4214yes—
639C22×C4C2×C22⋊C414yes—
640C22×C4C2×C22⋊C414yes—
641C22×C4C2×C22⋊C412yes—
642C22×C4C2×C22⋊C412yes—
643C22×C4C2×C22⋊C412yes—
644C22×C4C2×C22⋊C412yes—
645C22×C4C2×C22⋊C412yes—
646C22×C4C2×C22⋊C412yes—
647C22×C4C2×C22⋊C412yes—
648C22×C4C2×C22⋊C412yes—
649C22×C4C2×C4⋊C414yes—
650C22×C4C2×C4⋊C414yes—
651C22×C4C2×C4⋊C414yes—
652C22×C4C2×C4⋊C414yes—
653C22×C4C2×C4⋊C412yes—
654C22×C4C2×C4⋊C412yes—
655C22×C4C2×C4⋊C412yes—
656C22×C4C2×C4⋊C412yes—
657C22×C4C23×C411yescharacteristic
658C22×C4C23×C411yescharacteristic
659C22×C4C23×C411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×Q811yescharacteristic
664C22×C4C2×#4111yescharacteristic
665C22×C4C2×#4111yescharacteristic
666C22×C4C2×#4111yescharacteristic
667C22×C4H(5,𝔽2)11yescharacteristic
668C22×C4H(5,𝔽2)11yescharacteristic
669C22×C4H(5,𝔽2)11yescharacteristic
670C22×C42−1+411yescharacteristic
671M16—416no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—416no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8C4×D414yescomplemented
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—41no—
730C4⋊C4—41no—
731C4⋊C4—41no—
732C4⋊C4—41no—
733C4⋊C4—41no—
734C4⋊C4—41no—
735C4⋊C4—84no—
736C4⋊C4#95116yes—
737C4⋊C4C4×D414yes—
738C4⋊C4C4×D414yescomplemented
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—84no—
744C22⋊C4#95116yes—
745C22⋊C4#95116yes—
746C42—48no—
747C42—48no—
748C42—84no—
749C42C2×C4214yes—
750C42C2×C22⋊C414yes—
751C42C2×C4⋊C414yes—
752C42C2×C4⋊C414yes—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23C2×#9514yes—
816C23C2×#9514yes—
817C23#41714yes—
818C23#41714yes—
819C23#41814yes—
820C23#41914yes—
821C23#42814yes—
822C23#42814yes—
823C23C22×C22⋊C411yescharacteristic
824C23C22×C22⋊C411yescharacteristic
825C23C22×C4⋊C411yescharacteristic
826C23D4211yescharacteristic
827C23#54611yescharacteristic
828C23#54611yescharacteristic
829C23#54711yescharacteristic
830C23C2×AGL(1,ℤ/8)11yescharacteristic
831C23C2×AGL(1,ℤ/8)11yescharacteristic
832C23C2×#13711yescharacteristic
833C23C2×#13711yescharacteristic
834C23#57611yescharacteristic
835C23#57711yescharacteristic
836C23#57711yescharacteristic
837C23#57811yescharacteristic
838D4—232no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—816no—
912C2×C4—816no—
913C2×C4—816no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4C2×#9514yes—
939C2×C4C2×#9514yes—
940C2×C4C2×#9514yes—
941C2×C4C2×#9514yes—
942C2×C4C22×C4211yescharacteristic
943C2×C4C22×C22⋊C411yescharacteristic
944C2×C4C22×C4⋊C411yescharacteristic
945C2×C4C22×C4⋊C411yescharacteristic
946C2×C4C2×C4×D411yescharacteristic
947C2×C4C2×C4×D411yescharacteristic
948C2×C4C2×C4×D411yescharacteristic
949C2×C4C4×#4111yescharacteristic
950C2×C4C4×#4111yescharacteristic
951C2×C4C4×#4111yescharacteristic
952C2×C4#51811yescharacteristic
953C2×C4#51811yescharacteristic
954C2×C4#51811yescharacteristic
955C2×C4#52011yescharacteristic
956C2×C4#52011yescharacteristic
957C2×C4#52011yescharacteristic
958C2×C4D4211yescharacteristic
959C2×C4D4211yescharacteristic
960C2×C4#54611yescharacteristic
961C2×C4#54611yescharacteristic
962C2×C4#54611yescharacteristic
963C2×C4#54611yescharacteristic
964C2×C4#54711yescharacteristic
965C2×C4#54711yescharacteristic
966C2×C4D4×Q811yescharacteristic
967C2×C4#55411yescharacteristic
968C2×C4#55411yescharacteristic
969C2×C4#55411yescharacteristic
970C8—24no—
971C8—42no—
972C8—42no—
973C8—42no—
974C22—24no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—24no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22#173618yescomplemented
1004C22C22×#9511yescharacteristic
1005C22D4×C22⋊C411yescharacteristic
1006C22D4×C22⋊C411yescharacteristic
1007C22#233911yescharacteristic
1008C22#233911yescharacteristic
1009C22D4×C4⋊C411yescharacteristic
1010C22#234911yescharacteristic
1011C22C2×#41811yescharacteristic
1012C22C2×#41911yescharacteristic
1013C22C2×#41711yescharacteristic
1014C22C2×#41711yescharacteristic
1015C22#289711yescharacteristic
1016C22#289711yescharacteristic
1017C22#289811yescharacteristic
1018C22#289811yescharacteristic
1019C22C2×#42811yescharacteristic
1020C22C2×#42811yescharacteristic
1021C22#291211yescharacteristic
1022C22#291311yescharacteristic
1023C22#326411yescharacteristic
1024C22#326511yescharacteristic
1025C22#326611yescharacteristic
1026C22#327011yescharacteristic
1027C22#330611yescharacteristic
1028C22#330811yescharacteristic
1029C22#331011yescharacteristic
1030C22#331211yescharacteristic
1031C22#331411yescharacteristic
1032C22#331611yescharacteristic
1033C22#331811yescharacteristic
1034C22#332011yescharacteristic
1035C22#334311yescharacteristic
1036C22#334411yescharacteristic
1037C22#334511yescharacteristic
1038C22#334611yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—44no—
1044C4—44no—
1045C4—82no—
1046C4—82no—
1047C4—82no—
1048C4—82no—
1049C4—82no—
1050C4—82no—
1051C4C42×D411yescharacteristic
1052C4#227511yescharacteristic
1053C4D4×C22⋊C411yescharacteristic
1054C4#233911yescharacteristic
1055C4D4×C4⋊C411yescharacteristic
1056C4D4×C4⋊C411yescharacteristic
1057C4#234911yescharacteristic
1058C4#234911yescharacteristic
1059C2—28no—
1060C2—44no—
1061C2D4×#9511yescharacteristic
1062C2C2×#173611yescharacteristic
1063C2#2034811yescharacteristic
1064C2#2241911yescharacteristic
1065C2#2242111yescharacteristic
1066C2#2242311yescharacteristic
1067C2#2242511yescharacteristic
1068C2#2249111yescharacteristic
1069C2#2249311yescharacteristic
1070C2#2249511yescharacteristic
1071C2#2249711yescharacteristic
1072C2#2265911yescharacteristic
1073C2#2266111yescharacteristic
1074C2#2270911yescharacteristic
1075C2#2271111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1736C2semidirect
5. C22×#340C2semidirect
6. #10850C2semidirect
7. #10849C2semidirect
8. #10843C2semidirect
9. #10731C2semidirect
10. #10730C2semidirect
11. #10730C2semidirect
12. #10730C2semidirect
13. #10722C2semidirect
14. #10721C2semidirect
15. #10703C2semidirect
26. C2×#435C4semidirect
32. #2352C4semidirect
34. D4×C4⋊C4C4semidirect
80. C22×M16C2×C4semidirect
87. C23×C8C2×C4semidirect
106. C2×#117C2×C4semidirect
128. C22×C4⋊C4C2×C4semidirect
129. C22×C4⋊C4C2×C4semidirect
153. C2×C4⋊C8C2×C4semidirect
158. C2×C22⋊C8C2×C4semidirect
159. C2×C22⋊C8C2×C4semidirect
162. C2×#97C2×C4semidirect
170. #384C2×C4semidirect
172. #382C2×C4semidirect
178. #380C2×C4semidirect
179. #380C2×C4semidirect
180. #380C2×C4semidirect
183. C4×C4⋊C4C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect
209. #340D4semidirect
700. C2×C8C4×D4semidirect
738. C4⋊C4C4×D4semidirect
1003. C22#1736semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×#23522
C2×D4×C4⋊C42
C2×#17362
C22×#3402
#108502
#108492
#108432
#107312
#107302
#107222
#107212
#107032