Finite Group Databasebeta

← #395875

Subgroups — #395875

Order 512.

1386 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2351C211yesmaximal, characteristic
2C2×#2088C211yesmaximal, characteristic
3C2×#1865C211yesmaximal, characteristic
4C2×#1863C211yesmaximal, characteristic
5C2×#1805C211yesmaximal, characteristic
6#15221C211yesmaximal, characteristic
7#11328C211yesmaximal, characteristic
8#11325C211yesmaximal, characteristic
9#11293C211yesmaximal, characteristic
10#11268C211yesmaximal, characteristic
11#11208C211yesmaximal, characteristic
12#11202C211yesmaximal, characteristic
13#10789C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26#2351—24no—
27#2351—24no—
28C2×#389—21no—
29C2×#389—21no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#382—21no—
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×C4×C4⋊C4—21no—
38C2×C4×C4⋊C4C2211yescharacteristic
39#2088—24no—
40#1865—24no—
41#1863—24no—
42#1805—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1445—21no—
59#1444—21no—
60#1442—21no—
61#1442—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×Q8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—41no—
83C2×C4×Q8—41no—
84C2×C4×Q8—41no—
85C2×C4×Q8—41no—
86C2×C4×Q8D414yes—
87C2×C4×Q8Q814yes—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C42—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×#107—22no—
111C2×#107—41no—
112C2×#107—41no—
113C2×#106—22no—
114C2×#106—22no—
115C2×#106—41no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—41no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103D414yes—
130C2×#103Q814yes—
131#389—28no—
132#389—28no—
133#389—22no—
134#389—22no—
135#389—22no—
136#389—22no—
137#389—22no—
138#389—22no—
139#389—41no—
140#389D414yes—
141#382—28no—
142#382—22no—
143#382—22no—
144#382—22no—
145#382—41no—
146C4×C4⋊C4—28no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—22no—
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—21no—
163C2×#95D411yescharacteristic
164C2×#95D411yescharacteristic
165#340—22no—
166#340—22no—
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#336—22no—
176#336—22no—
177#336—22no—
178#336—22no—
179#336—41no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8C2×D412yes—
188C22×Q8C2×D412yes—
189C22×Q8C2×Q812yes—
190C22×Q8C2×Q812yes—
191C22×Q8#4112yes—
192C22×Q8#4112yes—
193C22×Q8#4112yes—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2411yescharacteristic
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
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×C8C2×D412yes—
236C22×C8C2×Q812yes—
237C4×Q8—28no—
238C4×Q8—28no—
239C4×Q8—28no—
240C4×Q8—28no—
241C4×Q8—28no—
242C4×Q8—44no—
243C4×Q8—44no—
244C4×Q8—44no—
245C4×Q8—44no—
246C4×Q8—44no—
247C4×Q8—44no—
248C4×Q8—44no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
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—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
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—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—81no—
309C2×C4⋊C4—81no—
310C2×C4⋊C4—81no—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C4⋊C4C2×D412yes—
314C2×C4⋊C4C2×D412yes—
315C2×C4⋊C4C2×Q812yes—
316C2×C4⋊C4C2×Q812yes—
317C2×C4⋊C4#4112yes—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C2×C42C2×Q812yes—
344C2×C42#4112yes—
345#107—44no—
346#106—44no—
347C4⋊C8—44no—
348#103—28no—
349#103—28no—
350#103—44no—
351#103—44no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—22no—
357#95—22no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—81no—
366#95—81no—
367#95—81no—
368C24C22×D411yescharacteristic
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8#12114yes—
391C2×Q8C22⋊Q814yes—
392C2×Q8C22⋊Q814yes—
393C2×Q8#12314yes—
394C2×Q8#12514yes—
395C2×Q8#12514yes—
396C2×Q8C4⋊Q814yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4#12012yes—
491C22×C4#12012yes—
492C22×C4C22⋊Q812yes—
493C22×C4C22⋊Q812yes—
494C22×C4#13512yes—
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×Q811yescharacteristic
499C22×C4C22×Q811yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C42−1+411yescharacteristic
508C22×C42−1+411yescharacteristic
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C4⋊C4—216no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—44no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—84no—
572C4⋊C4—84no—
573C4⋊C4C22⋊Q814yes—
574C42—216no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—48no—
584C42—48no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C23C2×#12011yescharacteristic
590C23C2×C22⋊Q811yescharacteristic
591C23#52511yescharacteristic
592C23D4211yescharacteristic
593C23#54611yescharacteristic
594C23#54811yescharacteristic
595C23D4×Q811yescharacteristic
596C23C2×#13511yescharacteristic
597C23#57511yescharacteristic
598C23#57511yescharacteristic
599C23#57511yescharacteristic
600C23#57711yescharacteristic
601C23#57711yescharacteristic
602C23#57811yescharacteristic
603C23#57811yescharacteristic
604Q8—24no—
605Q8—24no—
606Q8—24no—
607Q8—24no—
608Q8—24no—
609Q8—24no—
610Q8—24no—
611Q8#39818yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4C2×#12111yescharacteristic
711C2×C4C2×C22⋊Q811yescharacteristic
712C2×C4C2×C22⋊Q811yescharacteristic
713C2×C4C2×C22⋊Q811yescharacteristic
714C2×C4C2×#12311yescharacteristic
715C2×C4#52511yescharacteristic
716C2×C4#52511yescharacteristic
717C2×C4C2×#12511yescharacteristic
718C2×C4C2×#12511yescharacteristic
719C2×C4C2×C4⋊Q811yescharacteristic
720C2×C4#53411yescharacteristic
721C2×C4#53611yescharacteristic
722C2×C4#53911yescharacteristic
723C2×C4#53911yescharacteristic
724C2×C4#54411yescharacteristic
725C2×C4#54411yescharacteristic
726C2×C4D4211yescharacteristic
727C2×C4#54611yescharacteristic
728C2×C4#54711yescharacteristic
729C2×C4#54711yescharacteristic
730C2×C4#54811yescharacteristic
731C2×C4D4×Q811yescharacteristic
732C2×C4#55211yescharacteristic
733C2×C4#55211yescharacteristic
734C2×C4#55311yescharacteristic
735C2×C4#55311yescharacteristic
736C2×C4#55411yescharacteristic
737C2×C4#55411yescharacteristic
738C8—42no—
739C8—42no—
740C8—81no—
741C8—81no—
742C22#240911yescharacteristic
743C22#241011yescharacteristic
744C22#244011yescharacteristic
745C22#244211yescharacteristic
746C22#244311yescharacteristic
747C22#247311yescharacteristic
748C22#284811yescharacteristic
749C22#300211yescharacteristic
750C22#300511yescharacteristic
751C22#301011yescharacteristic
752C22#301111yescharacteristic
753C22#307611yescharacteristic
754C22#308011yescharacteristic
755C22#308211yescharacteristic
756C22#308211yescharacteristic
757C22#310211yescharacteristic
758C22#311111yescharacteristic
759C22#312111yescharacteristic
760C22#312111yescharacteristic
761C22#326911yescharacteristic
762C22#327111yescharacteristic
763C22#327711yescharacteristic
764C22#328211yescharacteristic
765C22#330111yescharacteristic
766C22#331311yescharacteristic
767C22#332111yescharacteristic
768C22#332711yescharacteristic
769C22#336411yescharacteristic
770C22#337111yescharacteristic
771C22#337111yescharacteristic
772C22#337711yescharacteristic
773C22#338311yescharacteristic
774C22#338811yescharacteristic
775C22#338811yescharacteristic
776C22#339011yescharacteristic
777C4—28no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—81no—
788C4—82no—
789C4—161no—
790C4—161no—
791C4C2×#39811yescharacteristic
792C4#241311yescharacteristic
793C4#244011yescharacteristic
794C4#244211yescharacteristic
795C4#244311yescharacteristic
796C4#247311yescharacteristic
797C4#257911yescharacteristic
798C4#262711yescharacteristic
799C2#1472811yescharacteristic
800C2#2433611yescharacteristic
801C2#2434011yescharacteristic
802C2#2442511yescharacteristic
803C2#2444711yescharacteristic
804C2#2604811yescharacteristic
805C2#2605711yescharacteristic
806C2#2611611yescharacteristic
807C2#2612311yescharacteristic
808C2#2616511yescharacteristic
809C2#2618911yescharacteristic
810C2#2730811yescharacteristic
811C2#2731911yescharacteristic
812C2#3296111yescharacteristic
813C2#3296411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#23512
C2×#20882
C2×#18652
C2×#18632
C2×#18052
#152212
#113282
#113252
#112932
#112682
#112082
#112022
#107892