Finite Group Databasebeta

← #367196

Subgroups — #367196

Order 512.

1696 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1877C211yesmaximal, characteristic
2C2×#1877C211yesmaximal, characteristic
3C2×#1877C211yesmaximal, characteristic
4C2×#1802C211yesmaximal, characteristic
5C2×C4×#102C211yesmaximal, characteristic
6#14000C211yesmaximal, characteristic, complemented
7D4×#95C211yesmaximal, characteristic
8#11315C211yesmaximal, characteristic, complemented
9#11267C211yesmaximal, characteristic, complemented
10#11190C211yesmaximal, characteristic, complemented
11#11077C211yesmaximal, characteristic, complemented
12#10926C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10807C211yesmaximal, characteristic, complemented
15#10788C211yesmaximal, characteristic
16C23×SD16C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C22×#95—21no—
34#1877—24no—
35#1877—24no—
36#1877C418yescomplemented
37#1802—24no—
38C4×#102—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1442—21no—
53#1442—21no—
54#1436—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C22⋊#95—21no—
63C4×#95C2211yescharacteristic
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C24×C4—21no—
68C24×C4—21no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16—22no—
72C22×SD16—22no—
73C22×SD16—22no—
74C22×SD16—22no—
75C22×SD16C2×C414yes—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—41no—
91C2×C4×D4—41no—
92C2×C4×D4—41no—
93C2×C4×D4—41no—
94C2×C4×D4—41no—
95C2×C4×D4—41no—
96C2×C4×D4C2×C414yes—
97C2×C4×D4D414yes—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—41no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103C2×C414yescomplemented
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×#102D414yes—
134C2×C4×C8—22no—
135C2×C4×C8—41no—
136C2×C4×C8—41no—
137#391—22no—
138#391—22no—
139#391—22no—
140#391—22no—
141#391—41no—
142#391C2×C414yescomplemented
143#384—22no—
144#384—41no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—44no—
163C2×#95D411yescharacteristic
164C2×#95D411yescharacteristic
165C2×#95D411yescharacteristic
166C2×#95D411yescharacteristic
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—41no—
175#340C2×C414yescomplemented
176#336—22no—
177#336—22no—
178#336—41no—
179#336C2×C414yescomplemented
180C25—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8C22×C412yes—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4C22×C412yes—
203C22×D4C2×D412yes—
204C22×D4C2×D412yes—
205C22×D4#4112yes—
206C22×D4#4112yes—
207C22×D4#4112yes—
208C22×D4#4112yes—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—21no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4—81no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2411yescharacteristic
244C2×SD16—28no—
245C2×SD16—28no—
246C2×SD16—28no—
247C2×SD16—44no—
248C2×SD16—44no—
249C2×SD16—44no—
250C2×SD16—44no—
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×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C2×D412yes—
279C4×D4—28no—
280C4×D4—28no—
281C4×D4—44no—
282C4×D4—44no—
283C4×D4—44no—
284C4×D4—44no—
285C4×D4—44no—
286C4×D4—44no—
287C4×D4—44no—
288C4×D4—44no—
289C4×D4—44no—
290C4×D4—44no—
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—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4C22×C412yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C2×D412yes—
331C2×C4⋊C4C2×D412yes—
332C2×C4⋊C4#4112yes—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—42no—
357C2×C42—81no—
358C2×C42—81no—
359C2×C42C22×C412yes—
360C2×C42C2×D412yes—
361C2×C42#4112yes—
362C2×C42#4112yes—
363C4⋊C8—44no—
364#103—44no—
365#103—44no—
366#103—44no—
367#102—28no—
368#102—28no—
369#102—44no—
370C4×C8—44no—
371#95—24no—
372#95—24no—
373#95—22no—
374#95—22no—
375#95—41no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—81no—
385#95—81no—
386#95—81no—
387#95—81no—
388#95—81no—
389#95SD1614yescomplemented
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24C22×D411yescharacteristic
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
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—22no—
454C2×D4—22no—
455C2×D4#11714yes—
456C2×D4C4×D414yes—
457C2×D4C4×D414yes—
458C2×D4#12114yes—
459C2×D4#12314yes—
460C2×D4#12414yes—
461C2×D4#12614yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
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—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—41no—
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—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—48no—
542C22×C4—48no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4—84no—
558C22×C4—84no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4C4×D412yes—
566C22×C4C4×D412yes—
567C22×C4#12112yes—
568C22×C4#12112yes—
569C22×C4C2×SD1612yes—
570C22×C4C2×SD1612yes—
571C22×C4C2×SD1612yes—
572C22×C4#13512yes—
573C22×C4#13712yes—
574C22×C4C23×C411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4C2×#4111yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583C22×C4C2×#4111yescharacteristic
584C22×C4H(5,𝔽2)11yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C22×C42−1+411yescharacteristic
588SD16—416no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
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—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—84no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23C2×C4×D411yescharacteristic
695C23C2×#12111yescharacteristic
696C23#52511yescharacteristic
697C23D4211yescharacteristic
698C23#54611yescharacteristic
699C23#54611yescharacteristic
700C23#54811yescharacteristic
701C23C22×SD1611yescharacteristic
702C23C2×#13511yescharacteristic
703C23C2×#13711yescharacteristic
704C23#57511yescharacteristic
705C23#57611yescharacteristic
706C23#57611yescharacteristic
707C23#57711yescharacteristic
708C23#57811yescharacteristic
709Q8—42no—
710Q8—42no—
711Q8—42no—
712Q8—42no—
713Q8—81no—
714Q8—81no—
715Q8—81no—
716Q8—81no—
717D4—24no—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—24no—
722D4—24no—
723D4—24no—
724D4#38818yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—816no—
784C2×C4—816no—
785C2×C4—816no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4C4×SD1614yes—
818C2×C4#46114yes—
819C2×C4C2×#11711yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4C2×C4×D411yescharacteristic
822C2×C4C4×#4111yescharacteristic
823C2×C4#51811yescharacteristic
824C2×C4#52011yescharacteristic
825C2×C4C2×#12111yescharacteristic
826C2×C4C2×#12311yescharacteristic
827C2×C4C2×#12411yescharacteristic
828C2×C4C2×#12611yescharacteristic
829C2×C4#52911yescharacteristic
830C2×C4#53211yescharacteristic
831C2×C4#53411yescharacteristic
832C2×C4#53711yescharacteristic
833C2×C4#53811yescharacteristic
834C2×C4#53911yescharacteristic
835C2×C4#54611yescharacteristic
836C2×C4#54611yescharacteristic
837C2×C4#54711yescharacteristic
838C2×C4#55111yescharacteristic
839C2×C4#55111yescharacteristic
840C2×C4#55111yescharacteristic
841C2×C4#55111yescharacteristic
842C2×C4#55211yescharacteristic
843C2×C4#55211yescharacteristic
844C2×C4#55311yescharacteristic
845C2×C4#55311yescharacteristic
846C2×C4#55311yescharacteristic
847C8—42no—
848C8—42no—
849C8—42no—
850C8—81no—
851C22—28no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22C4×#12111yescharacteristic
867C22#235211yescharacteristic
868C22#235811yescharacteristic
869C22#241211yescharacteristic
870C22#241611yescharacteristic
871C22#247211yescharacteristic
872C22#248111yescharacteristic
873C22C2×C4×SD1611yescharacteristic
874C22C4×#13711yescharacteristic
875C22#294611yescharacteristic
876C22#295111yescharacteristic
877C22C2×#46111yescharacteristic
878C22#303511yescharacteristic
879C22#304111yescharacteristic
880C22#304611yescharacteristic
881C22#310111yescharacteristic
882C22#310711yescharacteristic
883C22#311811yescharacteristic
884C22#312411yescharacteristic
885C22#327311yescharacteristic
886C22#327611yescharacteristic
887C22#328011yescharacteristic
888C22D4×SD1611yescharacteristic
889C22#329511yescharacteristic
890C22#329511yescharacteristic
891C22#329611yescharacteristic
892C22#330211yescharacteristic
893C22#331111yescharacteristic
894C22#331411yescharacteristic
895C22#331411yescharacteristic
896C22#331511yescharacteristic
897C22#335911yescharacteristic
898C22#336111yescharacteristic
899C22#337011yescharacteristic
900C22#337211yescharacteristic
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—81no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—161no—
914C4C2×#38811yescharacteristic
915C4#232511yescharacteristic
916C4#235311yescharacteristic
917C4#235911yescharacteristic
918C4#248811yescharacteristic
919C4#249811yescharacteristic
920C4#251011yescharacteristic
921C4#254311yescharacteristic
922C2—48no—
923C2#1399911yescharacteristic
924C2C4×#46111yescharacteristic
925C2#2150911yescharacteristic
926C2#2277011yescharacteristic
927C2#2277611yescharacteristic
928C2#2286211yescharacteristic
929C2#2287411yescharacteristic
930C2#2453011yescharacteristic
931C2#2453611yescharacteristic
932C2#2473011yescharacteristic
933C2#2473511yescharacteristic
934C2#2722411yescharacteristic
935C2#2723711yescharacteristic
936C2#2755211yescharacteristic
937C2#2756511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #14000C2semidirect
8. #11315C2semidirect
9. #11267C2semidirect
10. #11190C2semidirect
11. #11077C2semidirect
12. #10926C2semidirect
13. #10876C2semidirect
14. #10807C2semidirect
36. #1877C4semidirect
124. C2×#103C2×C4semidirect
142. #391C2×C4semidirect
175. #340C2×C4semidirect
179. #336C2×C4semidirect
389. #95SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#18772
C2×#18022
C2×C4×#1022
#140002
D4×#952
#113152
#112672
#111902
#110772
#109262
#108762
#108072
#107882