Finite Group Databasebeta

← #359147

Subgroups — #359147

Order 512.

1784 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2324C211yesmaximal, characteristic
2C2×#2033C211yesmaximal, characteristic
3C2×C4×#107C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6C2×#1750C211yesmaximal, characteristic, complemented
7#13777C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11200C211yesmaximal, characteristic, complemented
11#11189C211yesmaximal, characteristic, complemented
12#11123C211yesmaximal, characteristic, complemented
13#11096C211yesmaximal, characteristic, complemented
14#10969C211yesmaximal, characteristic
15#10703C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2324—24no—
30#2324—24no—
31C2×#390—21no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#386—21no—
36C2×#385—21no—
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#2033C418yescomplemented
44C4×#107—24no—
45#1762—24no—
46C4×#102—24no—
47#1750—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1437—21no—
61#1437—21no—
62#1436—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#121—22no—
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121C2×C414yes—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4D414yes—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4D411yescharacteristic
94C22×C4⋊C4D411yescharacteristic
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×C42—21no—
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107C2×C414yescomplemented
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102C2×C414yes—
133C2×#102C2×C414yes—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8C2×C414yescomplemented
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145C2×C4×C8D414yescomplemented
146#390—28no—
147#390—22no—
148#390—22no—
149#389—22no—
150#389—22no—
151#388—28no—
152#386—28no—
153#385—28no—
154#380—22no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—22no—
159#380C2×C414yescomplemented
160C4×C4⋊C4—22no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4D414yes—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340C2×C414yescomplemented
187#336—22no—
188#336—22no—
189C25—21no—
190C25C2×D411yescharacteristic
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—21no—
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—81no—
206C22×D4—81no—
207C22×D4—81no—
208C22×D4—81no—
209C22×D4C22×C412yes—
210C22×D4C2×D412yes—
211C22×D4#4112yes—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
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—24no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4C22×C412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4#4112yes—
245C23×C4C2411yescharacteristic
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×C8C22×C412yes—
269C22×C8C22×C412yes—
270C22×C8C2×D412yes—
271C22×C8C2×D412yes—
272C22×C8#4112yes—
273C22×C8#4112yes—
274#121—28no—
275#121—28no—
276#121—28no—
277#121—28no—
278C4×D4—28no—
279C4×D4—28no—
280C4×D4—44no—
281C4×D4—44no—
282#117—44no—
283#117—44no—
284#117—44no—
285#117—44no—
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—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—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4C22×C412yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4C2×D412yes—
333C2×C4⋊C4C2×D412yes—
334C2×C4⋊C4#4112yes—
335C2×C4⋊C4#4112yes—
336C2×C4⋊C4#4112yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—81no—
355C2×C22⋊C4—81no—
356C2×C22⋊C4—81no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4—81no—
359C2×C22⋊C4—81no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4—81no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—24no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—81no—
374C2×C42—81no—
375C2×C42—81no—
376C2×C42—81no—
377C2×C42—81no—
378C2×C42—81no—
379C2×C42C2×D412yes—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C2×C42#4112yes—
383C2×C42#4112yes—
384C2×C42#4112yes—
385#107—28no—
386#107—28no—
387#102—28no—
388#102—28no—
389#102—28no—
390#102—28no—
391C22⋊C8—28no—
392C22⋊C8—28no—
393#97—44no—
394C4×C8—28no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—42no—
401#95—42no—
402#95—81no—
403#95—81no—
404#95—81no—
405#95—81no—
406C24—22no—
407C24—21no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24C4×D412yes—
436C24C22×D411yescharacteristic
437C2×D4—216no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
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—84no—
466C2×D4—84no—
467C2×D4—84no—
468C2×D4—84no—
469C2×D4—84no—
470C2×D4—84no—
471C2×D4C4×D414yes—
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—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
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—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
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—48no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4C4×D412yes—
585C22×C4#12012yes—
586C22×C4#12012yes—
587C22×C4#12112yes—
588C22×C4#12112yes—
589C22×C4#12312yes—
590C22×C4#12312yes—
591C22×C4C23×C411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
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—22no—
619C2×C8—22no—
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—41no—
632C2×C8C4×D414yes—
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—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
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—44no—
661C4⋊C4—44no—
662C4⋊C4—84no—
663C4⋊C4C4×D414yes—
664C22⋊C4—216no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—48no—
668C22⋊C4—84no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C42—41no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—84no—
678C42—84no—
679C42—84no—
680C42#12114yes—
681C42#12114yes—
682C42#12314yes—
683C42#12414yes—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—42no—
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—
752C23—81no—
753C23—81no—
754C23C2×C4×D411yescharacteristic
755C23C2×#12011yescharacteristic
756C23C2×#12111yescharacteristic
757C23C2×#12311yescharacteristic
758C23#52511yescharacteristic
759C23#52511yescharacteristic
760C23#53211yescharacteristic
761C23#57611yescharacteristic
762C23#57611yescharacteristic
763C23#57611yescharacteristic
764C23#57611yescharacteristic
765C23#57711yescharacteristic
766C23#57711yescharacteristic
767C23#57811yescharacteristic
768C23#57811yescharacteristic
769D4—24no—
770D4—24no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777D4—816no—
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—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
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—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—816no—
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×C4—81no—
868C2×C4—81no—
869C2×C4#39414yes—
870C2×C4#39414yes—
871C2×C4C2×C4×D411yescharacteristic
872C2×C4C2×C4×D411yescharacteristic
873C2×C4C2×C4×D411yescharacteristic
874C2×C4C4×#4111yescharacteristic
875C2×C4C4×#4111yescharacteristic
876C2×C4C4×#4111yescharacteristic
877C2×C4C2×#12111yescharacteristic
878C2×C4C2×#12111yescharacteristic
879C2×C4C2×#12311yescharacteristic
880C2×C4#52511yescharacteristic
881C2×C4#52511yescharacteristic
882C2×C4#52511yescharacteristic
883C2×C4#52511yescharacteristic
884C2×C4#52511yescharacteristic
885C2×C4#52511yescharacteristic
886C2×C4C2×#12411yescharacteristic
887C2×C4#52911yescharacteristic
888C2×C4#52911yescharacteristic
889C2×C4#52911yescharacteristic
890C2×C4#52911yescharacteristic
891C2×C4#52911yescharacteristic
892C2×C4#52911yescharacteristic
893C2×C4#52911yescharacteristic
894C2×C4#52911yescharacteristic
895C2×C4#52911yescharacteristic
896C2×C4#53211yescharacteristic
897C2×C4#53211yescharacteristic
898C2×C4#53211yescharacteristic
899C8—24no—
900C8—42no—
901C8—42no—
902C8—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—44no—
911C22—42no—
912C22—44no—
913C22—82no—
914C22—81no—
915C22—82no—
916C22—82no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—81no—
922C22—82no—
923C22—81no—
924C22—82no—
925C22—82no—
926C22—81no—
927C22—81no—
928C22—82no—
929C22—81no—
930C22—82no—
931C22—81no—
932C22—82no—
933C22C4×#12011yescharacteristic
934C22C4×#12111yescharacteristic
935C22C4×#12311yescharacteristic
936C22C2×#39411yescharacteristic
937C22#238811yescharacteristic
938C22#239211yescharacteristic
939C22#239511yescharacteristic
940C22#294611yescharacteristic
941C22#294711yescharacteristic
942C22#294811yescharacteristic
943C22#295111yescharacteristic
944C22#300811yescharacteristic
945C22#301111yescharacteristic
946C22#301211yescharacteristic
947C22#301211yescharacteristic
948C22#305711yescharacteristic
949C22#305811yescharacteristic
950C22#306111yescharacteristic
951C22#306111yescharacteristic
952C22#309611yescharacteristic
953C22#309611yescharacteristic
954C22#309811yescharacteristic
955C22#309811yescharacteristic
956C22#311811yescharacteristic
957C22#311911yescharacteristic
958C22#312011yescharacteristic
959C22#312111yescharacteristic
960C22#312211yescharacteristic
961C22#312211yescharacteristic
962C22#312411yescharacteristic
963C22#312411yescharacteristic
964C22#317511yescharacteristic
965C22#317611yescharacteristic
966C22#317811yescharacteristic
967C22#317911yescharacteristic
968C4—24no—
969C4—24no—
970C4—42no—
971C4—44no—
972C4—82no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—81no—
977C4—82no—
978C4—81no—
979C4—82no—
980C4C4×#12111yescharacteristic
981C4C4×#12111yescharacteristic
982C4C4×#12311yescharacteristic
983C4C4×#12411yescharacteristic
984C4#239211yescharacteristic
985C4#239211yescharacteristic
986C4#239511yescharacteristic
987C4#239811yescharacteristic
988C2—82no—
989C2—84no—
990C2C4×#39411yescharacteristic
991C2#2145811yescharacteristic
992C2#2146511yescharacteristic
993C2#2152411yescharacteristic
994C2#2153511yescharacteristic
995C2#2158611yescharacteristic
996C2#2159011yescharacteristic
997C2#2348611yescharacteristic
998C2#2348811yescharacteristic
999C2#2358011yescharacteristic
1000C2#2358511yescharacteristic
1001C2#2370311yescharacteristic
1002C2#2370611yescharacteristic
1003C2#2376711yescharacteristic
1004C2#2377011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×C4×#107C2semidirect
4. C2×#1762C2semidirect
5. C2×C4×#102C2semidirect
6. C2×#1750C2semidirect
7. #13777C2semidirect
8. #11293C2semidirect
9. #11219C2semidirect
10. #11200C2semidirect
11. #11189C2semidirect
12. #11123C2semidirect
13. #11096C2semidirect
15. #10703C2semidirect
43. #2033C4semidirect
121. C2×#107C2×C4semidirect
139. C2×C22⋊C8C2×C4semidirect
145. C2×C4×C8D4semidirect
159. #380C2×C4semidirect
186. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23242
C2×#20332
C2×C4×#1072
C2×#17622
C2×C4×#1022
C2×#17502
#137772
#112932
#112192
#112002
#111892
#111232
#110962
#109692
#107032