Finite Group Databasebeta

← #372492

Subgroups — #372492

Order 512.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2491C211yesmaximal, characteristic
2C2×#1990C211yesmaximal, characteristic, complemented
3C2×#1893C211yesmaximal, characteristic
4C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
5#13876C211yesmaximal, characteristic, complemented
6#11384C211yesmaximal, characteristic, complemented
7#11199C211yesmaximal, characteristic, complemented
8#11049C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10925C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10721C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×#124—21no—
19C22×#121C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2491—24no—
28#2491C418yescomplemented
29C2×#394—21no—
30C2×#393—21no—
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#388—21no—
34C2×#388—21no—
35C2×#384C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42#1990—24no—
43#1893—24no—
44C8×C22⋊C4—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1442—21no—
60#1439—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8—21no—
65C23×D4—21no—
66C23×D4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—41no—
83C2×C4⋊Q8—41no—
84C2×C4⋊Q8C2×C414yes—
85C2×#124—28no—
86C2×#124—44no—
87C2×#124—44no—
88C2×#121—22no—
89C2×#121—22no—
90C2×#121—22no—
91C2×#121—41no—
92C2×#121—41no—
93C2×#121C2×C414yes—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4D411yescharacteristic
114C22×C42—21no—
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—41no—
127C2×#102—41no—
128C2×#102—41no—
129C2×#102—41no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C4×C8—22no—
134C2×C4×C8—22no—
135C2×C4×C8—22no—
136C2×C4×C8—22no—
137C2×C4×C8—41no—
138C2×C4×C8—41no—
139#394—28no—
140#393—28no—
141#390—22no—
142#390—22no—
143#390C2×C414yes—
144#390C2×C414yes—
145#388—28no—
146#388—44no—
147#384—22no—
148#384—41no—
149#380—22no—
150#380—22no—
151#380—22no—
152#380—41no—
153#380—41no—
154#380C2×C414yes—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—22no—
157C4×C4⋊C4—41no—
158C4×C4⋊C4C2×C414yes—
159C4×C22⋊C4C2×C414yes—
160C4×C22⋊C4D414yes—
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×#95—21no—
170C2×#95D411yescharacteristic
171C2×#95D411yescharacteristic
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—41no—
182#340—41no—
183#340D414yes—
184#336—22no—
185#336—22no—
186C25—21no—
187C25C2×D411yescharacteristic
188C22×Q8—24no—
189C22×Q8—42no—
190C22×Q8—42no—
191C22×Q8—42no—
192C22×Q8—42no—
193C22×Q8—81no—
194C22×Q8—81no—
195C22×D4—24no—
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—21no—
209C22×D4—42no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—81no—
214C22×D4—81no—
215C22×D4C22×C412yes—
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×C4—21no—
235C23×C4C22×C412yes—
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2411yescharacteristic
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—28no—
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—44no—
267C22×C8—44no—
268C22×C8—44no—
269C22×C8—44no—
270C22×C8—44no—
271C22×C8—44no—
272C22×C8C2×D412yes—
273C22×C8#4112yes—
274C22×C8#4112yes—
275C22×C8#4112yes—
276C22×C8#4112yes—
277C22×C8#4112yes—
278C4⋊Q8—28no—
279C4⋊Q8—44no—
280C4⋊Q8—44no—
281C4⋊Q8—44no—
282#124—432no—
283#121—28no—
284#121—44no—
285#121—44no—
286#121—44no—
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—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—24no—
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—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
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—81no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C22×C412yes—
333C2×C4⋊C4C22×C412yes—
334C2×C4⋊C4C2×D412yes—
335C2×C4⋊C4C2×D412yes—
336C2×C4⋊C4#4112yes—
337C2×C4⋊C4#4112yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
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—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4C22⋊C414yes—
365C2×C22⋊C4C22⋊C414yes—
366C2×C22⋊C4D814yes—
367C2×C22⋊C4SD1614yes—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—24no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—81no—
382C2×C42C22×C412yes—
383C2×C42C22×C412yes—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386#102—44no—
387#102—44no—
388#102—44no—
389#102—44no—
390C22⋊C8—28no—
391C4×C8—44no—
392C4×C8—44no—
393#95—24no—
394#95—24no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—81no—
402#95C22⋊C414yes—
403#95C22⋊C414yes—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
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—
430C24—41no—
431C24C2×C22⋊C412yes—
432C24C2×D812yes—
433C24C2×SD1612yes—
434C24C22×D411yescharacteristic
435C2×Q8—48no—
436C2×Q8—48no—
437C2×Q8—84no—
438C2×Q8—84no—
439C2×Q8—84no—
440C2×Q8—84no—
441C2×Q8—84no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—48no—
449C2×D4—48no—
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—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—84no—
473C2×D4—84no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
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—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
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—22no—
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×C4—41no—
578C22×C4C2×C22⋊C412yes—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C412yes—
582C22×C4C2×C22⋊C412yes—
583C22×C4C2×D812yes—
584C22×C4C2×D812yes—
585C22×C4C2×SD1612yes—
586C22×C4C2×SD1612yes—
587C22×C4#13512yes—
588C22×C4#13512yes—
589C22×C4C23×C411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4H(5,𝔽2)11yescharacteristic
600C22×C4H(5,𝔽2)11yescharacteristic
601C22×C4H(5,𝔽2)11yescharacteristic
602C22×C42−1+411yescharacteristic
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—416no—
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—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8#12414yescomplemented
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—48no—
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—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—84no—
661C4⋊C4—84no—
662C4⋊C4C4×D414yes—
663C22⋊C4—28no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—84no—
672C22⋊C4#102116yescomplemented
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—48no—
682C42—84no—
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—22no—
698C23—22no—
699C23—22no—
700C23—22no—
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—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
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—
749C23—81no—
750C23—81no—
751C23—81no—
752C23C2×#10214yes—
753C23C22×C22⋊C411yescharacteristic
754C23#53211yescharacteristic
755C23#53211yescharacteristic
756C23D4211yescharacteristic
757C23#54611yescharacteristic
758C23#54611yescharacteristic
759C23#54711yescharacteristic
760C23C22×D811yescharacteristic
761C23C22×SD1611yescharacteristic
762C23C2×#13511yescharacteristic
763C23C2×#13511yescharacteristic
764C23#57611yescharacteristic
765C23#57711yescharacteristic
766C23#57711yescharacteristic
767C23#57811yescharacteristic
768Q8—816no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—816no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
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—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
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—42no—
835C2×C4—42no—
836C2×C4—42no—
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—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4C2×#10214yes—
868C2×C4C2×#10214yes—
869C2×C4#41614yes—
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C4×#4111yescharacteristic
872C2×C4C4×#4111yescharacteristic
873C2×C4C4×#4111yescharacteristic
874C2×C4#51811yescharacteristic
875C2×C4#52011yescharacteristic
876C2×C4#52511yescharacteristic
877C2×C4#52511yescharacteristic
878C2×C4C2×#12411yescharacteristic
879C2×C4#52911yescharacteristic
880C2×C4#52911yescharacteristic
881C2×C4#53211yescharacteristic
882C2×C4#53811yescharacteristic
883C2×C4#53811yescharacteristic
884C2×C4#54211yescharacteristic
885C2×C4#54211yescharacteristic
886C2×C4D4211yescharacteristic
887C2×C4#54611yescharacteristic
888C2×C4#54611yescharacteristic
889C2×C4#54611yescharacteristic
890C2×C4#54711yescharacteristic
891C2×C4#54811yescharacteristic
892C2×C4#55111yescharacteristic
893C2×C4#55111yescharacteristic
894C2×C4#55511yescharacteristic
895C2×C4#55511yescharacteristic
896C2×C4#55611yescharacteristic
897C2×C4#55911yescharacteristic
898C8—24no—
899C8—42no—
900C8—42no—
901C8—42no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—161no—
925C22—161no—
926C22—161no—
927C22—161no—
928C22—161no—
929C22—161no—
930C22—161no—
931C22—161no—
932C22#229711yescharacteristic
933C22D4×C22⋊C411yescharacteristic
934C22#233911yescharacteristic
935C22#249111yescharacteristic
936C22#252111yescharacteristic
937C22#255511yescharacteristic
938C22#255711yescharacteristic
939C22C22×#10211yescharacteristic
940C22C2×#41611yescharacteristic
941C22#289711yescharacteristic
942C22#289811yescharacteristic
943C22#316711yescharacteristic
944C22#316711yescharacteristic
945C22#316911yescharacteristic
946C22#316911yescharacteristic
947C22#317311yescharacteristic
948C22#317511yescharacteristic
949C22#317811yescharacteristic
950C22#317911yescharacteristic
951C22D4×D811yescharacteristic
952C22D4×SD1611yescharacteristic
953C22#328211yescharacteristic
954C22#328511yescharacteristic
955C22#329411yescharacteristic
956C22#329411yescharacteristic
957C22#329511yescharacteristic
958C22#329811yescharacteristic
959C22#330011yescharacteristic
960C22#330111yescharacteristic
961C22#330311yescharacteristic
962C22#330511yescharacteristic
963C22#333411yescharacteristic
964C22#333511yescharacteristic
965C22#334011yescharacteristic
966C22#334111yescharacteristic
967C4—24no—
968C4—24no—
969C4—24no—
970C4—42no—
971C4—44no—
972C4—42no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4—161no—
978C4—161no—
979C4C4×#12411yescharacteristic
980C4#233711yescharacteristic
981C4#236711yescharacteristic
982C4#237211yescharacteristic
983C4#245911yescharacteristic
984C4#246111yescharacteristic
985C4#247211yescharacteristic
986C4#247411yescharacteristic
987C2—44no—
988C2—162no—
989C2#1409811yescharacteristic
990C2#2140111yescharacteristic
991C2#2141211yescharacteristic
992C2D4×#10211yescharacteristic
993C2#2241611yescharacteristic
994C2#2248511yescharacteristic
995C2#2248911yescharacteristic
996C2#2778711yescharacteristic
997C2#2779111yescharacteristic
998C2#2806211yescharacteristic
999C2#2806511yescharacteristic
1000C2#2890711yescharacteristic
1001C2#2890911yescharacteristic
1002C2#2897511yescharacteristic
1003C2#2898111yescharacteristic
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
4. C2×C8×C22⋊C4C2semidirect
5. #13876C2semidirect
6. #11384C2semidirect
7. #11199C2semidirect
8. #11049C2semidirect
10. #10931C2semidirect
11. #10925C2semidirect
12. #10925C2semidirect
13. #10806C2semidirect
14. #10721C2semidirect
15. C4×#340C2semidirect
28. #2491C4semidirect
631. C2×C8#124semidirect
672. C22⋊C4#102semidirect

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×#18932
C2×C8×C22⋊C42
#138762
#113842
#111992
#110492
#109692
#109312
#109252
#108062
#107212
C4×#3402