Finite Group Databasebeta

← #386176

Subgroups — #386176

Order 512.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2491C211yesmaximal, characteristic
2C2×#1990C211yesmaximal, characteristic, complemented
3C2×#1923C211yesmaximal, characteristic, complemented
4C2×#1875C211yesmaximal, characteristic
5#13879C211yesmaximal, characteristic, complemented
6#11384C211yesmaximal, characteristic, complemented
7#11200C211yesmaximal, characteristic, complemented
8#11076C211yesmaximal, characteristic, complemented
9#11051C211yesmaximal, characteristic, complemented
10#11049C211yesmaximal, characteristic, complemented
11#10969C211yesmaximal, characteristic
12#10925C211yesmaximal, characteristic, complemented
13#10850C211yesmaximal, characteristic, complemented
14#10807C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic, complemented
16C22×C4⋊Q8C2211yescharacteristic
17C22×#124—21no—
18C22×#121C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28#2491—24no—
29#2491C418yescomplemented
30C2×#394—21no—
31C2×#393—21no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#388—21no—
35C2×#384C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1990—24no—
42#1923—24no—
43#1875—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1439—21no—
59#1439—21no—
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8—21no—
65C23×D4—21no—
66C23×D4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8—41no—
76C2×C4⋊Q8—41no—
77C2×C4⋊Q8C2×C414yes—
78C2×#124—28no—
79C2×#124—44no—
80C2×#124—44no—
81C2×#121—22no—
82C2×#121—22no—
83C2×#121—22no—
84C2×#121—41no—
85C2×#121—41no—
86C2×#121C2×C414yes—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—41no—
90C2×#117—41no—
91C2×#117—41no—
92C2×#117—41no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4D411yescharacteristic
112C22×C22⋊C4D411yescharacteristic
113C22×C42—21no—
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—41no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102—41no—
127C2×#102—41no—
128C2×#102—41no—
129C2×#102—41no—
130C2×#102—41no—
131C2×#102—41no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8—41no—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141#394—28no—
142#393—28no—
143#390—22no—
144#390—22no—
145#390C2×C414yes—
146#390C2×C414yes—
147#388—28no—
148#384—22no—
149#384—41no—
150#382—22no—
151#382—41no—
152#380—22no—
153#380—41no—
154#380—41no—
155#380C2×C414yes—
156C4×C4⋊C4—22no—
157C4×C4⋊C4C2×C414yes—
158C4×C22⋊C4C2×C414yes—
159C4×C22⋊C4D414yes—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95D411yescharacteristic
170C2×#95D411yescharacteristic
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340D414yes—
183#336—22no—
184#336—22no—
185C25—21no—
186C25C2×D411yescharacteristic
187C22×Q8—24no—
188C22×Q8—42no—
189C22×Q8—42no—
190C22×Q8—42no—
191C22×Q8—42no—
192C22×Q8—81no—
193C22×Q8—81no—
194C22×D4—24no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—42no—
209C22×D4—42no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4—81no—
213C22×D4—81no—
214C22×D4C22×C412yes—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
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×C4C22×C412yes—
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2411yescharacteristic
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8C2×D412yes—
269C22×C8#4112yes—
270C4⋊Q8—28no—
271C4⋊Q8—44no—
272C4⋊Q8—44no—
273C4⋊Q8—44no—
274#124—432no—
275#121—28no—
276#121—44no—
277#121—44no—
278#121—44no—
279#117—44no—
280#117—44no—
281#117—44no—
282#117—44no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4C22×C412yes—
328C2×C4⋊C4C22×C412yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C2×D412yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4#4112yes—
333C2×C4⋊C4#4112yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—81no—
359C2×C22⋊C4—81no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4C22⋊C414yes—
363C2×C22⋊C4C22⋊C414yes—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—24no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42C22×C412yes—
379C2×C42C22×C412yes—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C4⋊C8—44no—
383#102—44no—
384#102—44no—
385#102—44no—
386#102—44no—
387C22⋊C8—44no—
388C22⋊C8—44no—
389C4×C8—44no—
390#95—24no—
391#95—24no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—81no—
398#95—81no—
399#95C22⋊C414yes—
400#95C22⋊C414yes—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24C2×C22⋊C412yes—
431C24C22×D411yescharacteristic
432C2×Q8—48no—
433C2×Q8—48no—
434C2×Q8—84no—
435C2×Q8—84no—
436C2×Q8—84no—
437C2×Q8—84no—
438C2×Q8—84no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—84no—
470C2×D4—84no—
471C2×D4—84no—
472C2×D4—84no—
473C2×D4—84no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4C2×C22⋊C412yes—
578C22×C4C2×C22⋊C412yes—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C412yes—
582C22×C4#13512yes—
583C22×C4#13512yes—
584C22×C4AGL(1,ℤ/8)12yes—
585C22×C4AGL(1,ℤ/8)12yes—
586C22×C4C23×C411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C4H(5,𝔽2)11yescharacteristic
594C22×C4H(5,𝔽2)11yescharacteristic
595C22×C4H(5,𝔽2)11yescharacteristic
596C22×C4H(5,𝔽2)11yescharacteristic
597C22×C42−1+411yescharacteristic
598C22×C42−1+411yescharacteristic
599C22×C42−1+411yescharacteristic
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—48no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C4⋊C4C4×D414yes—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—84no—
668C22⋊C4—84no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—48no—
678C42—48no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23C22×C22⋊C411yescharacteristic
750C23#53511yescharacteristic
751C23#53611yescharacteristic
752C23D4211yescharacteristic
753C23#54611yescharacteristic
754C23#54611yescharacteristic
755C23#54711yescharacteristic
756C23C2×#13511yescharacteristic
757C23C2×#13511yescharacteristic
758C23C2×AGL(1,ℤ/8)11yescharacteristic
759C23C2×AGL(1,ℤ/8)11yescharacteristic
760C23#57611yescharacteristic
761C23#57711yescharacteristic
762C23#57711yescharacteristic
763C23#57811yescharacteristic
764Q8—816no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—816no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4#41614yes—
865C2×C4#41814yes—
866C2×C4C2×C4×D411yescharacteristic
867C2×C4C4×#4111yescharacteristic
868C2×C4#51811yescharacteristic
869C2×C4#52011yescharacteristic
870C2×C4#52011yescharacteristic
871C2×C4#52011yescharacteristic
872C2×C4#53511yescharacteristic
873C2×C4#53611yescharacteristic
874C2×C4#53711yescharacteristic
875C2×C4#53711yescharacteristic
876C2×C4#53811yescharacteristic
877C2×C4#53811yescharacteristic
878C2×C4#54211yescharacteristic
879C2×C4#54211yescharacteristic
880C2×C4#54211yescharacteristic
881C2×C4#54211yescharacteristic
882C2×C4D4211yescharacteristic
883C2×C4#54611yescharacteristic
884C2×C4#54611yescharacteristic
885C2×C4#54611yescharacteristic
886C2×C4#54711yescharacteristic
887C2×C4#54811yescharacteristic
888C2×C4#55611yescharacteristic
889C2×C4#55911yescharacteristic
890C2×C4H(3,𝔽4)11yescharacteristic
891C2×C4#56211yescharacteristic
892C2×C4#56211yescharacteristic
893C2×C4#56311yescharacteristic
894C8—42no—
895C8—42no—
896C8—81no—
897C8—81no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—161no—
921C22—161no—
922C22—161no—
923C22—161no—
924C22—161no—
925C22—161no—
926C22—161no—
927C22—161no—
928C22#231111yescharacteristic
929C22D4×C22⋊C411yescharacteristic
930C22#233911yescharacteristic
931C22#267011yescharacteristic
932C22#267411yescharacteristic
933C22#270011yescharacteristic
934C22#271011yescharacteristic
935C22C2×#41611yescharacteristic
936C22C2×#41811yescharacteristic
937C22#289711yescharacteristic
938C22#289811yescharacteristic
939C22#320711yescharacteristic
940C22#320711yescharacteristic
941C22#322411yescharacteristic
942C22#322511yescharacteristic
943C22#322811yescharacteristic
944C22#322811yescharacteristic
945C22#324311yescharacteristic
946C22#324411yescharacteristic
947C22#326411yescharacteristic
948C22#326511yescharacteristic
949C22#328211yescharacteristic
950C22#328511yescharacteristic
951C22#330011yescharacteristic
952C22#330111yescharacteristic
953C22#330311yescharacteristic
954C22#330511yescharacteristic
955C22#331011yescharacteristic
956C22#331811yescharacteristic
957C22#333011yescharacteristic
958C22#333211yescharacteristic
959C22#334011yescharacteristic
960C22#334111yescharacteristic
961C22#335311yescharacteristic
962C22#335411yescharacteristic
963C4—24no—
964C4—24no—
965C4—42no—
966C4—44no—
967C4—42no—
968C4—42no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—161no—
974C4—161no—
975C4#232611yescharacteristic
976C4#233711yescharacteristic
977C4#236711yescharacteristic
978C4#237911yescharacteristic
979C4#267211yescharacteristic
980C4#267611yescharacteristic
981C4#271211yescharacteristic
982C4#271511yescharacteristic
983C2—82no—
984C2—162no—
985C2#1442111yescharacteristic
986C2#2186311yescharacteristic
987C2#2187111yescharacteristic
988C2#2241611yescharacteristic
989C2#2242311yescharacteristic
990C2#2248911yescharacteristic
991C2#2250011yescharacteristic
992C2#3052811yescharacteristic
993C2#3052911yescharacteristic
994C2#3077811yescharacteristic
995C2#3078011yescharacteristic
996C2#3173911yescharacteristic
997C2#3174111yescharacteristic
998C2#3205111yescharacteristic
999C2#3205311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1990C2semidirect
3. C2×#1923C2semidirect
5. #13879C2semidirect
6. #11384C2semidirect
7. #11200C2semidirect
8. #11076C2semidirect
9. #11051C2semidirect
10. #11049C2semidirect
12. #10925C2semidirect
13. #10850C2semidirect
14. #10807C2semidirect
15. #10731C2semidirect
29. #2491C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24912
C2×#19902
C2×#19232
C2×#18752
#138792
#113842
#112002
#110762
#110512
#110492
#109692
#109252
#108502
#108072
#107312