Finite Group Databasebeta

← #365403

Subgroups — #365403

Order 512.

2160 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1853C211yesmaximal, characteristic, complemented
4C2×#1853C211yesmaximal, characteristic, complemented
5C2×#1807C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7#13872C211yesmaximal, characteristic
8#11323C211yesmaximal, characteristic, complemented
9#11267C211yesmaximal, characteristic, complemented
10#11095C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29D4×C4⋊C4—24no—
30D4×C4⋊C4—24no—
31C2×#389—21no—
32C2×#386—21no—
33C2×#385—21no—
34C2×#385—21no—
35C2×#384C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42#1869C418yescomplemented
43#1853—24no—
44#1853—24no—
45#1807—24no—
46C2×#340—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1441—21no—
62#1439—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C22⋊#95—21no—
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8C2×C414yescomplemented
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—28no—
88C2×C4×D4—44no—
89C2×C4×D4—44no—
90C2×C4×D4C2×C414yes—
91C2×C4×D4Q814yes—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—22no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4—41no—
111C22×C4⋊C4—41no—
112C22×C4⋊C4—41no—
113C22×C4⋊C4—41no—
114C22×C4⋊C4D411yescharacteristic
115C22×C4⋊C4D414yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4D411yescharacteristic
130C22×C22⋊C4D411yescharacteristic
131C22×C42—21no—
132C22×C42C2311yescharacteristic
133C2×#106—22no—
134C2×#106—22no—
135C2×#106—22no—
136C2×#106—22no—
137C2×#106—22no—
138C2×#106—22no—
139C2×#106—22no—
140C2×#106—22no—
141C2×#106—41no—
142C2×#106—41no—
143C2×#106—41no—
144C2×#106—41no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—22no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—41no—
150C2×C22⋊C8—41no—
151C2×C22⋊C8C2×C414yescomplemented
152C2×C22⋊C8C2×C414yescomplemented
153C2×C22⋊C8C2×C414yescomplemented
154#389—28no—
155#386—44no—
156#385—28no—
157#385—28no—
158#384—22no—
159#384—22no—
160#380—22no—
161#380—22no—
162#380—22no—
163#380—22no—
164#380—22no—
165#380—22no—
166#380—22no—
167#380—41no—
168#380—41no—
169#380D414yes—
170C4×C4⋊C4—22no—
171C4×C4⋊C4—22no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—22no—
190#340—22no—
191#340—41no—
192#340—41no—
193#340D414yescomplemented
194#336C2×C414yescomplemented
195#336C2×C414yescomplemented
196C25C2×D411yescharacteristic
197C25C2×D411yescharacteristic
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4C4⋊C414yes—
203C22×D4SD1614yes—
204C22×D4SD1614yes—
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—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—24no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—81no—
249C23×C4—81no—
250C23×C4—81no—
251C23×C4—81no—
252C23×C4—81no—
253C23×C4—81no—
254C23×C4C22×C412yes—
255C23×C4C22×C412yes—
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×Q812yes—
263C23×C4C2×Q812yes—
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4C2411yescharacteristic
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—28no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—28no—
291C22×C8—44no—
292C22×C8—44no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8—44no—
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C412yes—
299C22×C8C22×C412yes—
300C22×C8C2×D412yes—
301C22×C8#4112yes—
302C4×D4—28no—
303C4×D4—28no—
304C4×D4—28no—
305C4×D4—28no—
306C4×D4—432no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—28no—
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—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—81no—
375C2×C4⋊C4—81no—
376C2×C4⋊C4C4⋊C414yes—
377C2×C4⋊C4C2×D412yes—
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4#4112yes—
384C2×C4⋊C4#4112yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—81no—
403C2×C22⋊C4—81no—
404C2×C22⋊C4C4⋊C414yes—
405C2×C22⋊C4C4⋊C414yes—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—24no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42C22×C412yes—
414C2×C42C2×Q812yes—
415#106—44no—
416#106—44no—
417#106—44no—
418#106—44no—
419C22⋊C8—28no—
420C22⋊C8—28no—
421C22⋊C8—44no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—81no—
431#95—81no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24C2×C4⋊C412yes—
453C24C2×C4⋊C412yes—
454C24#12012yes—
455C24#12312yes—
456C24C2×SD1612yes—
457C24C2×SD1612yes—
458C24C2×SD1612yes—
459C24C2×SD1612yes—
460C24AGL(1,ℤ/8)12yes—
461C24#13712yes—
462C24C22×D411yescharacteristic
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4#106116yescomplemented
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—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
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—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—48no—
535C22×C4—48no—
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—48no—
557C22×C4—48no—
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×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—48no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4C2×C4⋊C412yes—
620C22×C4C2×C4⋊C412yes—
621C22×C4C2×C4⋊C412yes—
622C22×C4C2×C4⋊C412yes—
623C22×C4C4×D414yes—
624C22×C4C4×D414yes—
625C22×C4#12012yes—
626C22×C4C22⋊Q814yes—
627C22×C4C22⋊Q814yes—
628C22×C4#12312yes—
629C22×C4C2×SD1612yes—
630C22×C4C2×SD1612yes—
631C22×C4C23×C411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×Q811yescharacteristic
636C22×C4C2×#4111yescharacteristic
637C22×C4C2×#4111yescharacteristic
638C22×C4C2×#4111yescharacteristic
639C22×C4C2×#4111yescharacteristic
640C22×C4C2×#4111yescharacteristic
641C22×C4H(5,𝔽2)11yescharacteristic
642C22×C4H(5,𝔽2)11yescharacteristic
643C22×C4H(5,𝔽2)11yescharacteristic
644C22×C42−1+411yescharacteristic
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—416no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8C4×D414yescomplemented
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—28no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—41no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—41no—
701C4⋊C4—41no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—41no—
705C4⋊C4—41no—
706C4⋊C4—41no—
707C4⋊C4—41no—
708C4⋊C4—41no—
709C4⋊C4—41no—
710C4⋊C4—84no—
711C4⋊C4#12114yes—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—84no—
717C22⋊C4—84no—
718C22⋊C4—84no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—48no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23#38514yes—
787C23C2×#10614yes—
788C23C2×#10614yes—
789C23#42814yes—
790C23#44814yes—
791C23#45014yes—
792C23#48114yes—
793C23#48314yes—
794C23C22×C4⋊C411yescharacteristic
795C23C2×#12011yescharacteristic
796C23C2×#12311yescharacteristic
797C23D4211yescharacteristic
798C23#54611yescharacteristic
799C23#54611yescharacteristic
800C23#54711yescharacteristic
801C23C22×SD1611yescharacteristic
802C23C22×SD1611yescharacteristic
803C23C2×AGL(1,ℤ/8)11yescharacteristic
804C23C2×#13711yescharacteristic
805C23#57611yescharacteristic
806C23#57711yescharacteristic
807C23#57711yescharacteristic
808C23#57811yescharacteristic
809D4—232no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—816no—
875C2×C4—816no—
876C2×C4—816no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4#38514yes—
912C2×C4C2×#10614yes—
913C2×C4C2×C4×D411yescharacteristic
914C2×C4C2×C4×D411yescharacteristic
915C2×C4C2×C4×D411yescharacteristic
916C2×C4C4×#4111yescharacteristic
917C2×C4#51811yescharacteristic
918C2×C4#52011yescharacteristic
919C2×C4C2×#12111yescharacteristic
920C2×C4C2×C22⋊Q811yescharacteristic
921C2×C4C2×C22⋊Q811yescharacteristic
922C2×C4#52511yescharacteristic
923C2×C4#52911yescharacteristic
924C2×C4#53211yescharacteristic
925C2×C4#53411yescharacteristic
926C2×C4#53711yescharacteristic
927C2×C4#53811yescharacteristic
928C2×C4#53911yescharacteristic
929C2×C4D4211yescharacteristic
930C2×C4#54611yescharacteristic
931C2×C4#54611yescharacteristic
932C2×C4#54611yescharacteristic
933C2×C4#54711yescharacteristic
934C2×C4D4×Q811yescharacteristic
935C2×C4#55111yescharacteristic
936C2×C4#55111yescharacteristic
937C2×C4#55211yescharacteristic
938C2×C4#55411yescharacteristic
939C2×C4#55411yescharacteristic
940C2×C4#55411yescharacteristic
941C8—24no—
942C8—42no—
943C8—42no—
944C8—42no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22#185318yescomplemented
975C22C2×#38511yescharacteristic
976C22D4×C4⋊C411yescharacteristic
977C22#234911yescharacteristic
978C22#241011yescharacteristic
979C22#241811yescharacteristic
980C22#241911yescharacteristic
981C22#243011yescharacteristic
982C22C22×#10611yescharacteristic
983C22C2×#42811yescharacteristic
984C22#291211yescharacteristic
985C22#291311yescharacteristic
986C22C2×#45011yescharacteristic
987C22C2×#44811yescharacteristic
988C22#301211yescharacteristic
989C22#301311yescharacteristic
990C22C2×#48311yescharacteristic
991C22C2×#48111yescharacteristic
992C22#309611yescharacteristic
993C22#309711yescharacteristic
994C22#326411yescharacteristic
995C22#327011yescharacteristic
996C22D4×SD1611yescharacteristic
997C22D4×SD1611yescharacteristic
998C22#329511yescharacteristic
999C22#329511yescharacteristic
1000C22#329811yescharacteristic
1001C22#329811yescharacteristic
1002C22#330611yescharacteristic
1003C22#331011yescharacteristic
1004C22#331611yescharacteristic
1005C22#332011yescharacteristic
1006C22#333511yescharacteristic
1007C22#333511yescharacteristic
1008C22#334311yescharacteristic
1009C22#334611yescharacteristic
1010C4—24no—
1011C4—24no—
1012C4—44no—
1013C4—42no—
1014C4—42no—
1015C4—82no—
1016C4—82no—
1017C4—82no—
1018C4—82no—
1019C4—82no—
1020C4—161no—
1021C4—161no—
1022C4C4×#12111yescharacteristic
1023C4#232511yescharacteristic
1024C4#235811yescharacteristic
1025C4#235911yescharacteristic
1026C4#241711yescharacteristic
1027C4#244911yescharacteristic
1028C4#245011yescharacteristic
1029C4#256411yescharacteristic
1030C2—28no—
1031C2—44no—
1032C2#1397511yescharacteristic
1033C2C2×#185311yescharacteristic
1034C2#2084911yescharacteristic
1035C2D4×#10611yescharacteristic
1036C2#2266111yescharacteristic
1037C2#2270311yescharacteristic
1038C2#2271111yescharacteristic
1039C2#2442911yescharacteristic
1040C2#2443211yescharacteristic
1041C2#2486311yescharacteristic
1042C2#2486511yescharacteristic
1043C2#2493511yescharacteristic
1044C2#2493711yescharacteristic
1045C2#2553111yescharacteristic
1046C2#2554311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1853C2semidirect
4. C2×#1853C2semidirect
5. C2×#1807C2semidirect
6. C22×#340C2semidirect
8. #11323C2semidirect
9. #11267C2semidirect
10. #11095C2semidirect
11. #11095C2semidirect
12. #10908C2semidirect
13. #10908C2semidirect
14. #10730C2semidirect
15. #10730C2semidirect
42. #1869C4semidirect
78. C23×C8C2×C4semidirect
151. C2×C22⋊C8C2×C4semidirect
152. C2×C22⋊C8C2×C4semidirect
153. C2×C22⋊C8C2×C4semidirect
193. #340D4semidirect
194. #336C2×C4semidirect
195. #336C2×C4semidirect
469. C2×D4#106semidirect
673. C2×C8C4×D4semidirect
974. C22#1853semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×#18692
C2×#18532
C2×#18072
C22×#3402
#138722
#113232
#112672
#110952
#109082
#107302