Finite Group Databasebeta

← #384346

Subgroups — #384346

Order 512.

1344 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1968C211yesmaximal, characteristic
2C2×#1880C211yesmaximal, characteristic
3C2×#1834C211yesmaximal, characteristic, complemented
4#14001C211yesmaximal, characteristic
5#13976C211yesmaximal, characteristic, complemented
6#11220C211yesmaximal, characteristic, complemented
7#11189C211yesmaximal, characteristic
8#11066C211yesmaximal, characteristic
9#11050C211yesmaximal, characteristic, complemented
10#11049C211yesmaximal, characteristic
11#11023C211yesmaximal, characteristic
12#10932C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10797C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#388—21no—
33C2×#388—21no—
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#1968C418yescomplemented
38#1880—24no—
39#1834—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1444—21no—
54#1444—21no—
55#1439—21no—
56#1439—21no—
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4×#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C23×D4C2311yescharacteristic
64C22×SD16—22no—
65C22×SD16—22no—
66C22×SD16—22no—
67C22×SD16—22no—
68C22×SD16—41no—
69C22×SD16—41no—
70C22×SD16C2×C414yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—41no—
78C2×C4×Q8—41no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C42—21no—
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×#106—41no—
105C2×#106—41no—
106C2×#106C2×C414yes—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103C2×C414yes—
116C2×#102—22no—
117C2×#102—41no—
118C2×#102—41no—
119C2×#102—41no—
120C2×#102—41no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102C2×C414yes—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8C2×C414yes—
128#391—22no—
129#391—22no—
130#391—41no—
131#391C2×C414yes—
132#390—22no—
133#390—22no—
134#390—41no—
135#390—41no—
136#390—41no—
137#390C2×C414yes—
138#389—41no—
139#389—41no—
140#388—44no—
141#388—44no—
142#384—22no—
143#384—22no—
144#384—41no—
145#384—41no—
146C4×C4⋊C4—41no—
147C4×C4⋊C4—41no—
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×#95D411yescharacteristic
159C2×#95D411yescharacteristic
160C2×#95D411yescharacteristic
161C2×#95D411yescharacteristic
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340D414yes—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—41no—
174#336—41no—
175C25—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8C22×C412yes—
188C22×Q8#4112yes—
189C22×Q8#4112yes—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
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×D4C22×C412yes—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2411yescharacteristic
218C2×SD16—28no—
219C2×SD16—28no—
220C2×SD16—44no—
221C2×SD16—44no—
222C2×SD16—44no—
223C2×SD16—44no—
224C2×SD16—44no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8C22×C412yes—
250C22×C8C22×C412yes—
251C22×C8C2×D412yes—
252C22×C8#4112yes—
253C4×Q8—44no—
254C4×Q8—44no—
255C4×Q8—44no—
256C4×Q8—44no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—81no—
326C2×C22⋊C4—81no—
327C2×C22⋊C4—81no—
328C2×C22⋊C4—81no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42—42no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42C22×C412yes—
352C2×C42#4112yes—
353#106—44no—
354#103—44no—
355#103—44no—
356#103—44no—
357#102—44no—
358#102—44no—
359#102—44no—
360C4×C8—28no—
361#95—24no—
362#95—24no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—81no—
373#95—81no—
374#95SD1614yescomplemented
375C24—22no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24C22×D411yescharacteristic
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8#11714yes—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
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—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
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×C4C4×D412yes—
531C22×C4C4×D412yes—
532C22×C4C2×SD1612yes—
533C22×C4C2×SD1612yes—
534C22×C4C2×SD1612yes—
535C22×C4#13512yes—
536C22×C4AGL(1,ℤ/8)12yes—
537C22×C4#13712yes—
538C22×C4C23×C411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4H(5,𝔽2)11yescharacteristic
545C22×C4H(5,𝔽2)11yescharacteristic
546C22×C4H(5,𝔽2)11yescharacteristic
547C22×C4H(5,𝔽2)11yescharacteristic
548C22×C4H(5,𝔽2)11yescharacteristic
549C22×C4H(5,𝔽2)11yescharacteristic
550C22×C42−1+411yescharacteristic
551C22×C42−1+411yescharacteristic
552SD16—416no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8C4×D414yes—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—48no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—84no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C4⋊C4—84no—
610C4⋊C4—84no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—84no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—48no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—84no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—81no—
653C23—81no—
654C23—81no—
655C23—81no—
656C23—81no—
657C23—81no—
658C23—81no—
659C23—81no—
660C23—81no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23—81no—
666C23C2×C4×D411yescharacteristic
667C23#53511yescharacteristic
668C23#53511yescharacteristic
669C23D4211yescharacteristic
670C23#54611yescharacteristic
671C23#54711yescharacteristic
672C23#54811yescharacteristic
673C23C22×SD1611yescharacteristic
674C23C2×#13511yescharacteristic
675C23C2×AGL(1,ℤ/8)11yescharacteristic
676C23C2×#13711yescharacteristic
677C23#57611yescharacteristic
678C23#57711yescharacteristic
679C23#57711yescharacteristic
680C23#57811yescharacteristic
681Q8—24no—
682Q8—24no—
683Q8—42no—
684Q8—42no—
685Q8—42no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4C4×SD1614yes—
787C2×C4#44014yes—
788C2×C4C2×#11711yescharacteristic
789C2×C4C2×C4×D411yescharacteristic
790C2×C4#51811yescharacteristic
791C2×C4#51811yescharacteristic
792C2×C4#52011yescharacteristic
793C2×C4#52011yescharacteristic
794C2×C4#53511yescharacteristic
795C2×C4#53711yescharacteristic
796C2×C4#53811yescharacteristic
797C2×C4#53811yescharacteristic
798C2×C4#53911yescharacteristic
799C2×C4#53911yescharacteristic
800C2×C4#54011yescharacteristic
801C2×C4#54011yescharacteristic
802C2×C4#54011yescharacteristic
803C2×C4#54211yescharacteristic
804C2×C4#54611yescharacteristic
805C2×C4#54611yescharacteristic
806C2×C4#54811yescharacteristic
807C2×C4#55111yescharacteristic
808C2×C4#55111yescharacteristic
809C2×C4#55211yescharacteristic
810C2×C4#55311yescharacteristic
811C2×C4#55311yescharacteristic
812C2×C4H(3,𝔽4)11yescharacteristic
813C2×C4#56211yescharacteristic
814C2×C4#56211yescharacteristic
815C2×C4#56311yescharacteristic
816C8—24no—
817C8—42no—
818C8—81no—
819C8—81no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—161no—
828C22—161no—
829C22—161no—
830C22—161no—
831C22—161no—
832C22—161no—
833C22—161no—
834C22—161no—
835C22#232811yescharacteristic
836C22#235211yescharacteristic
837C22#236111yescharacteristic
838C22#267011yescharacteristic
839C22#267611yescharacteristic
840C22#270611yescharacteristic
841C22#272311yescharacteristic
842C22C2×C4×SD1611yescharacteristic
843C22C2×#44011yescharacteristic
844C22#295111yescharacteristic
845C22#295211yescharacteristic
846C22#320611yescharacteristic
847C22#320711yescharacteristic
848C22#320811yescharacteristic
849C22#321011yescharacteristic
850C22#322411yescharacteristic
851C22#322411yescharacteristic
852C22#322511yescharacteristic
853C22#322511yescharacteristic
854C22#326411yescharacteristic
855C22#327011yescharacteristic
856C22D4×SD1611yescharacteristic
857C22#328211yescharacteristic
858C22#329811yescharacteristic
859C22#330511yescharacteristic
860C22#332911yescharacteristic
861C22#333211yescharacteristic
862C22#333511yescharacteristic
863C22#333711yescharacteristic
864C22#334311yescharacteristic
865C22#334611yescharacteristic
866C22#336211yescharacteristic
867C22#336411yescharacteristic
868C22#336811yescharacteristic
869C22#336911yescharacteristic
870C4—24no—
871C4—24no—
872C4—44no—
873C4—42no—
874C4—42no—
875C4—82no—
876C4—81no—
877C4—82no—
878C4—82no—
879C4—81no—
880C4—82no—
881C4—161no—
882C4—161no—
883C4#231811yescharacteristic
884C4#232411yescharacteristic
885C4#234211yescharacteristic
886C4#237911yescharacteristic
887C4#270711yescharacteristic
888C4#271111yescharacteristic
889C4#275311yescharacteristic
890C4#276111yescharacteristic
891C2—162no—
892C2#1437711yescharacteristic
893C2#2226811yescharacteristic
894C2#2227411yescharacteristic
895C2#2275911yescharacteristic
896C2#2276711yescharacteristic
897C2#2302211yescharacteristic
898C2#2303211yescharacteristic
899C2#3052211yescharacteristic
900C2#3052911yescharacteristic
901C2#3087611yescharacteristic
902C2#3088111yescharacteristic
903C2#3193111yescharacteristic
904C2#3193211yescharacteristic
905C2#3242711yescharacteristic
906C2#3243011yescharacteristic
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
3. C2×#1834C2semidirect
5. #13976C2semidirect
6. #11220C2semidirect
9. #11050C2semidirect
12. #10932C2semidirect
13. #10908C2semidirect
14. #10797C2semidirect
15. #10789C2semidirect
37. #1968C4semidirect
374. #95SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#19682
C2×#18802
C2×#18342
#140012
#139762
#112202
#111892
#110662
#110502
#110492
#110232
#109322
#109082
#107972
#107892