Finite Group Databasebeta

← #387975

Subgroups — #387975

Order 512.

1736 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×#2501C211yesmaximal, characteristic
2C2×#1923C211yesmaximal, characteristic, complemented
3#13876C211yesmaximal, characteristic, complemented
4#11373C211yesmaximal, characteristic, complemented
5#11357C211yesmaximal, characteristic, complemented
6#11076C211yesmaximal, characteristic, complemented
7#11049C211yesmaximal, characteristic, complemented
8#10969C211yesmaximal, characteristic
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10841C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#123—21no—
17C22×#123—21no—
18C22×#121C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28#2501—24no—
29#2501C418yescomplemented
30C2×#399—21no—
31C2×#399—21no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#388—21no—
35C2×#384C2211yescharacteristic
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42#1923—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1442—21no—
58#1439—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×#123—28no—
71C2×#123—28no—
72C2×#123—44no—
73C2×#123—44no—
74C2×#123—44no—
75C2×#123—44no—
76C2×#121—22no—
77C2×#121—41no—
78C2×#121—41no—
79C2×#121—41no—
80C2×#121—41no—
81C2×#121C2×C414yes—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4—41no—
93C22×C4⋊C4—41no—
94C22×C4⋊C4C2×C414yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
110C22×C22⋊C4D411yescharacteristic
111C22×C42—21no—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—41no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102—41no—
127C2×#102—41no—
128C2×#102—41no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8—41no—
135C2×C4×C8—22no—
136C2×C4×C8—22no—
137C2×C4×C8—41no—
138#399—28no—
139#399—28no—
140#390—22no—
141#390—22no—
142#390C2×C414yes—
143#390C2×C414yes—
144#388—44no—
145#384—22no—
146#384—22no—
147#384—22no—
148#384—41no—
149#384C2×C414yes—
150#384C2×C414yes—
151#380—22no—
152#380—22no—
153#380—41no—
154#380—41no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—41no—
157C4×C22⋊C4C2×C414yes—
158C4×C22⋊C4D414yes—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95D411yescharacteristic
167C2×#95D411yescharacteristic
168#340—41no—
169#340—41no—
170#340—41no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340—41no—
180#336—22no—
181#336—22no—
182C25—21no—
183C25C2×D411yescharacteristic
184C22×D4—24no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—42no—
199C22×D4—42no—
200C22×D4—42no—
201C22×D4—42no—
202C22×D4—42no—
203C22×D4—42no—
204C22×D4C22×C412yes—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—24no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4C22×C412yes—
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D412yes—
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2411yescharacteristic
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
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#4112yes—
266C22×C8#4112yes—
267#123—432no—
268#123—432no—
269#121—44no—
270#121—44no—
271#121—44no—
272#121—44no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
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—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
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—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—81no—
334C2×C4⋊C4—81no—
335C2×C4⋊C4C22×C412yes—
336C2×C4⋊C4C22×C412yes—
337C2×C4⋊C4C22×C412yes—
338C2×C4⋊C4#4112yes—
339C2×C4⋊C4#4112yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
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—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4C22⋊C414yes—
364C2×C22⋊C4C22⋊C414yes—
365C2×C22⋊C4D814yes—
366C2×C22⋊C4SD1614yes—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—81no—
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—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—81no—
397#95C22⋊C414yes—
398#95C22⋊C414yes—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24C2×C22⋊C412yes—
427C24C2×D812yes—
428C24C2×SD1612yes—
429C24C22×D411yescharacteristic
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
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—84no—
462C2×D4—84no—
463C2×D4—84no—
464C2×D4—84no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
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—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—48no—
523C22×C4—48no—
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—48no—
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—84no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4—84no—
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C22⋊C412yes—
577C22×C4C2×C22⋊C412yes—
578C22×C4C2×D812yes—
579C22×C4C2×D812yes—
580C22×C4C2×SD1612yes—
581C22×C4C2×SD1612yes—
582C22×C4AGL(1,ℤ/8)12yes—
583C22×C4AGL(1,ℤ/8)12yes—
584C22×C4C23×C411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C4H(5,𝔽2)11yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C4H(5,𝔽2)11yescharacteristic
594C22×C4H(5,𝔽2)11yescharacteristic
595C22×C4H(5,𝔽2)11yescharacteristic
596C22×C42−1+411yescharacteristic
597C22×C42−1+411yescharacteristic
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—41no—
605C2×C8—41no—
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—
626C4⋊C4—22no—
627C4⋊C4—22no—
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—48no—
637C4⋊C4—48no—
638C4⋊C4—41no—
639C4⋊C4—41no—
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—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—84no—
660C4⋊C4—84no—
661C22⋊C4—28no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—84no—
668C22⋊C4—84no—
669C22⋊C4#102116yescomplemented
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—84no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
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—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—81no—
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—
748C23C2×#10214yes—
749C23C22×C22⋊C411yescharacteristic
750C23#53511yescharacteristic
751C23#53511yescharacteristic
752C23#54611yescharacteristic
753C23#54611yescharacteristic
754C23#54711yescharacteristic
755C23#54711yescharacteristic
756C23C22×D811yescharacteristic
757C23C22×SD1611yescharacteristic
758C23C2×AGL(1,ℤ/8)11yescharacteristic
759C23C2×AGL(1,ℤ/8)11yescharacteristic
760C23#57711yescharacteristic
761C23#57711yescharacteristic
762C23#57811yescharacteristic
763C23#57811yescharacteristic
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—816no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773C2×C4—22no—
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—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
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—816no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
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×C4C2×#10214yes—
864C2×C4C2×#10214yes—
865C2×C4#41814yes—
866C2×C4C4×#4111yescharacteristic
867C2×C4C4×#4111yescharacteristic
868C2×C4#51811yescharacteristic
869C2×C4#51811yescharacteristic
870C2×C4#52011yescharacteristic
871C2×C4#52011yescharacteristic
872C2×C4#53511yescharacteristic
873C2×C4#53511yescharacteristic
874C2×C4#53811yescharacteristic
875C2×C4#53811yescharacteristic
876C2×C4#53911yescharacteristic
877C2×C4#53911yescharacteristic
878C2×C4#54011yescharacteristic
879C2×C4#54011yescharacteristic
880C2×C4#54211yescharacteristic
881C2×C4#54211yescharacteristic
882C2×C4#54611yescharacteristic
883C2×C4#54611yescharacteristic
884C2×C4#54711yescharacteristic
885C2×C4#54711yescharacteristic
886C2×C4#55111yescharacteristic
887C2×C4#55311yescharacteristic
888C2×C4#55311yescharacteristic
889C2×C4#55911yescharacteristic
890C2×C4#56011yescharacteristic
891C2×C4#56211yescharacteristic
892C2×C4#56211yescharacteristic
893C2×C4#56311yescharacteristic
894C8—42no—
895C8—42no—
896C8—81no—
897C8—81no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
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#230911yescharacteristic
929C22#233911yescharacteristic
930C22#233911yescharacteristic
931C22#270311yescharacteristic
932C22#270611yescharacteristic
933C22#271011yescharacteristic
934C22#271811yescharacteristic
935C22C22×#10211yescharacteristic
936C22C2×#41811yescharacteristic
937C22#289811yescharacteristic
938C22#289811yescharacteristic
939C22#320511yescharacteristic
940C22#320511yescharacteristic
941C22#320811yescharacteristic
942C22#320811yescharacteristic
943C22#322111yescharacteristic
944C22#322311yescharacteristic
945C22#322511yescharacteristic
946C22#322511yescharacteristic
947C22#329411yescharacteristic
948C22#329411yescharacteristic
949C22#329811yescharacteristic
950C22#329811yescharacteristic
951C22#330611yescharacteristic
952C22#330811yescharacteristic
953C22#333011yescharacteristic
954C22#333211yescharacteristic
955C22#333411yescharacteristic
956C22#333411yescharacteristic
957C22#333511yescharacteristic
958C22#333511yescharacteristic
959C22#334311yescharacteristic
960C22#334511yescharacteristic
961C22#335311yescharacteristic
962C22#335411yescharacteristic
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—82no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—161no—
974C4—161no—
975C4#233511yescharacteristic
976C4#233511yescharacteristic
977C4#237411yescharacteristic
978C4#237611yescharacteristic
979C4#270311yescharacteristic
980C4#270611yescharacteristic
981C4#271011yescharacteristic
982C4#271811yescharacteristic
983C2—44no—
984C2—162no—
985C2#1450611yescharacteristic
986C2#2180311yescharacteristic
987C2#2181411yescharacteristic
988C2#2248511yescharacteristic
989C2#2248511yescharacteristic
990C2#2249511yescharacteristic
991C2#2250011yescharacteristic
992C2#3183411yescharacteristic
993C2#3183611yescharacteristic
994C2#3193011yescharacteristic
995C2#3193211yescharacteristic
996C2#3204611yescharacteristic
997C2#3205011yescharacteristic
998C2#3227811yescharacteristic
999C2#3228211yescharacteristic
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×#1923C2semidirect
3. #13876C2semidirect
4. #11373C2semidirect
5. #11357C2semidirect
6. #11076C2semidirect
7. #11049C2semidirect
10. #10931C2semidirect
11. #10925C2semidirect
12. #10849C2semidirect
13. #10841C2semidirect
14. #10730C2semidirect
15. #10730C2semidirect
29. #2501C4semidirect
669. C22⋊C4#102semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#19232
#138762
#113732
#113572
#110762
#110492
#109692
#109312
#109252
#108492
#108412
#107302