Finite Group Databasebeta

← #358174

Subgroups — #358174

Order 512.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#433C211yesmaximal, characteristic, complemented
2C2×#2324C211yesmaximal, characteristic
3C2×#1762C211yesmaximal, characteristic, complemented
4C2×C4×#102C211yesmaximal, characteristic, complemented
5#13777C211yesmaximal, characteristic, complemented
6#11228C211yesmaximal, characteristic, complemented
7#11227C211yesmaximal, characteristic, complemented
8#11200C211yesmaximal, characteristic, complemented
9#11199C211yesmaximal, characteristic, complemented
10#11076C211yesmaximal, characteristic, complemented
11#11076C211yesmaximal, characteristic, complemented
12#10969C211yesmaximal, characteristic
13#10969C211yesmaximal, characteristic
14#10703C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C2×#433—24no—
20C2×#433—24no—
21C2×#433—24no—
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2324—24no—
33#2324C418yescomplemented
34C2×#390—21no—
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#388—21no—
38C2×#386—21no—
39C2×#385—21no—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46#1762—24no—
47C4×#102—24no—
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
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×D4C2×C414yes—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117C2×C414yes—
91C2×#117D414yes—
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
116#433—232no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—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×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97D414yescomplemented
144C2×C4×C8—22no—
145C2×C4×C8—22no—
146C2×C4×C8D414yescomplemented
147#390—28no—
148#390—22no—
149#390C2×C414yes—
150#389—22no—
151#389C2×C414yes—
152#388—28no—
153#386—28no—
154#385—28no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—22no—
159#380—22no—
160#380C2×C414yes—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4C2×C414yes—
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—
177C2×#95—21no—
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#340—22no—
187#340—22no—
188#340—22no—
189#340—22no—
190C25—21no—
191C25C2×D411yescharacteristic
192C22×D4—24no—
193C22×D4—24no—
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—81no—
207C22×D4—81no—
208C22×D4—81no—
209C22×D4—81no—
210C22×D4C22×C412yes—
211C22×D4#4112yes—
212C22×D4#4112yes—
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—21no—
232C23×C4—24no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4C22×C412yes—
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2411yescharacteristic
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×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C2×D412yes—
272C22×C8C2×D412yes—
273C22×C8C2×D412yes—
274C22×C8C2×D412yes—
275#121—28no—
276#121—28no—
277#121—28no—
278#121—28no—
279C4×D4—28no—
280C4×D4—28no—
281C4×D4—44no—
282C4×D4—44no—
283#117—28no—
284#117—28no—
285#117—28no—
286#117—28no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
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—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—21no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4C22⋊C414yes—
328C2×C4⋊C4C22⋊C414yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4#4112yes—
333C2×C4⋊C4#4112yes—
334C2×C4⋊C4#4112yes—
335C2×C4⋊C4#4112yes—
336C2×C4⋊C4#4112yes—
337C2×C4⋊C4#4112yes—
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—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—81no—
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⋊C4C22⋊C414yes—
364C2×C22⋊C4C22⋊C414yes—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—81no—
373C2×C42—81no—
374C2×C42—81no—
375C2×C42—81no—
376C2×C42—81no—
377C2×C42—81no—
378C2×C42C22×C412yes—
379C2×C42C22×C412yes—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C2×C42C2×D412yes—
383C2×C42C2×D412yes—
384C2×C42#4112yes—
385C2×C42#4112yes—
386C4⋊C8—28no—
387C4⋊C8—28no—
388#102—28no—
389#102—28no—
390#102—28no—
391#102—28no—
392C22⋊C8—28no—
393C22⋊C8—28no—
394#97—28no—
395C4×C8—28no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—42no—
402#95—42no—
403#95—81no—
404#95—81no—
405#95—81no—
406#95—81no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24C2×C22⋊C412yes—
437C24C22×D411yescharacteristic
438C2×D4—216no—
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—22no—
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—84no—
467C2×D4—84no—
468C2×D4—84no—
469C2×D4—84no—
470C2×D4—84no—
471C2×D4—84no—
472C2×D4#11714yes—
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—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
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—22no—
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—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—48no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4C2×C22⋊C412yes—
584C22×C4C2×C22⋊C412yes—
585C22×C4C2×C22⋊C412yes—
586C22×C4C2×C22⋊C412yes—
587C22×C4C2×C22⋊C412yes—
588C22×C4#12112yes—
589C22×C4#12112yes—
590C22×C4#12112yes—
591C22×C4#12112yes—
592C22×C4C23×C411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
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
605C22×C4C2×#4111yescharacteristic
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—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—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—28no—
638C4⋊C4—28no—
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—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
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—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—84no—
664C4⋊C4#11714yes—
665C22⋊C4—216no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—84no—
679C42—84no—
680C42—84no—
681C42C4×D414yes—
682C42C4×D414yes—
683C42#12014yes—
684C42#12314yes—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—42no—
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—
754C23—81no—
755C23C22×C22⋊C411yescharacteristic
756C23C2×#12111yescharacteristic
757C23C2×#12111yescharacteristic
758C23#52511yescharacteristic
759C23#52511yescharacteristic
760C23#52511yescharacteristic
761C23#52511yescharacteristic
762C23#57611yescharacteristic
763C23#57611yescharacteristic
764C23#57611yescharacteristic
765C23#57711yescharacteristic
766C23#57711yescharacteristic
767C23#57711yescharacteristic
768C23#57711yescharacteristic
769C23#57811yescharacteristic
770D4—24no—
771D4—24no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—816no—
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—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
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—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—816no—
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—81no—
870C2×C4#38614yes—
871C2×C4#38614yes—
872C2×C4C2×#11711yescharacteristic
873C2×C4C2×#11711yescharacteristic
874C2×C4C2×C4×D411yescharacteristic
875C2×C4C2×C4×D411yescharacteristic
876C2×C4C4×#4111yescharacteristic
877C2×C4C4×#4111yescharacteristic
878C2×C4C2×#12011yescharacteristic
879C2×C4C2×#12311yescharacteristic
880C2×C4#52511yescharacteristic
881C2×C4#52511yescharacteristic
882C2×C4#52511yescharacteristic
883C2×C4#52511yescharacteristic
884C2×C4#52511yescharacteristic
885C2×C4#52511yescharacteristic
886C2×C4#52911yescharacteristic
887C2×C4#52911yescharacteristic
888C2×C4#52911yescharacteristic
889C2×C4#52911yescharacteristic
890C2×C4#52911yescharacteristic
891C2×C4#52911yescharacteristic
892C2×C4#52911yescharacteristic
893C2×C4#52911yescharacteristic
894C2×C4#53211yescharacteristic
895C2×C4#53211yescharacteristic
896C2×C4#53211yescharacteristic
897C2×C4#53211yescharacteristic
898C2×C4#53211yescharacteristic
899C2×C4#53211yescharacteristic
900C8—42no—
901C8—42no—
902C8—42no—
903C8—42no—
904C22—42no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22—42no—
909C22—44no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—82no—
915C22—81no—
916C22—82no—
917C22—82no—
918C22—81no—
919C22—82no—
920C22—81no—
921C22—82no—
922C22—81no—
923C22—82no—
924C22—81no—
925C22—81no—
926C22—82no—
927C22—82no—
928C22—81no—
929C22—82no—
930C22—81no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22#228011yescharacteristic
935C22C2×#38611yescharacteristic
936C22#229711yescharacteristic
937C22#239211yescharacteristic
938C22#239211yescharacteristic
939C22#239211yescharacteristic
940C22#239211yescharacteristic
941C22#289711yescharacteristic
942C22#289711yescharacteristic
943C22#289711yescharacteristic
944C22#289811yescharacteristic
945C22#305711yescharacteristic
946C22#305811yescharacteristic
947C22#306011yescharacteristic
948C22#306111yescharacteristic
949C22#306211yescharacteristic
950C22#306211yescharacteristic
951C22#306211yescharacteristic
952C22#306311yescharacteristic
953C22#311811yescharacteristic
954C22#311811yescharacteristic
955C22#311811yescharacteristic
956C22#311911yescharacteristic
957C22#311911yescharacteristic
958C22#311911yescharacteristic
959C22#312011yescharacteristic
960C22#312111yescharacteristic
961C22#312211yescharacteristic
962C22#312211yescharacteristic
963C22#312311yescharacteristic
964C22#312411yescharacteristic
965C22#312411yescharacteristic
966C22#312511yescharacteristic
967C22#312511yescharacteristic
968C22#312611yescharacteristic
969C4—24no—
970C4—24no—
971C4—44no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—82no—
976C4—82no—
977C4—82no—
978C4—82no—
979C4—82no—
980C4—82no—
981C4#229011yescharacteristic
982C4#229011yescharacteristic
983C4#229311yescharacteristic
984C4#229311yescharacteristic
985C4#238811yescharacteristic
986C4#238811yescharacteristic
987C4#239511yescharacteristic
988C4#239511yescharacteristic
989C2—82no—
990C2—84no—
991C2#1383911yescharacteristic
992C2#2074411yescharacteristic
993C2#2074611yescharacteristic
994C2#2097511yescharacteristic
995C2#2097611yescharacteristic
996C2#2139711yescharacteristic
997C2#2139911yescharacteristic
998C2#2370211yescharacteristic
999C2#2370311yescharacteristic
1000C2#2370611yescharacteristic
1001C2#2370711yescharacteristic
1002C2#2371211yescharacteristic
1003C2#2371211yescharacteristic
1004C2#2371411yescharacteristic
1005C2#2371511yescharacteristic
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
1. C22×#433C2semidirect
3. C2×#1762C2semidirect
4. C2×C4×#102C2semidirect
5. #13777C2semidirect
6. #11228C2semidirect
7. #11227C2semidirect
8. #11200C2semidirect
9. #11199C2semidirect
10. #11076C2semidirect
11. #11076C2semidirect
14. #10703C2semidirect
15. C4×#340C2semidirect
33. #2324C4semidirect
143. C2×#97D4semidirect
146. C2×C4×C8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#4332
C2×#23242
C2×#17622
C2×C4×#1022
#137772
#112282
#112272
#112002
#111992
#110762
#109692
#107032
C4×#3402