Finite Group Databasebeta

← #427581

Subgroups — #427581

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#484C211yesmaximal, characteristic
2C2×#2095C211yesmaximal, characteristic, complemented
3C2×#2036C211yesmaximal, characteristic
4C2×#2001C211yesmaximal, characteristic
5C2×#1969C211yesmaximal, characteristic, complemented
6C2×#1852C211yesmaximal, characteristic
7#15182C211yesmaximal, characteristic
8#14139C211yesmaximal, characteristic
9#11324C211yesmaximal, characteristic, complemented
10#11124C211yesmaximal, characteristic, complemented
11#11124C211yesmaximal, characteristic, complemented
12#11124C211yesmaximal, characteristic, complemented
13#11024C211yesmaximal, characteristic, complemented
14#10921C211yesmaximal, characteristic
15#10862C211yesmaximal, characteristic, complemented
16C23×Q16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C2×#484—24no—
21C2×#484—24no—
22C2×#484—24no—
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×#107C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#384C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44#2095—24no—
45#2036—24no—
46#2001—24no—
47#1969—24no—
48#1852—24no—
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1441—22no—
57#1441—22no—
58#1439—22no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—22no—
63C23×Q8C2311yescharacteristic
64C23×Q8C2311yescharacteristic
65C24×C4—21no—
66C24×C4C2311yescharacteristic
67C22×Q16—22no—
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—22no—
71C22×Q16—22no—
72C22×Q16—41no—
73C22×Q16—41no—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C22⋊Q8—22no—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8—22no—
85C2×C22⋊Q8—22no—
86C2×C22⋊Q8—41no—
87C2×C22⋊Q8—41no—
88C2×C22⋊Q8—41no—
89C2×C22⋊Q8—41no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4—41no—
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×C22⋊C4D412yes—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112#484—232no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—22no—
120C2×#107—22no—
121C2×#107—22no—
122C2×#107—22no—
123C2×#107—22no—
124C2×#107—41no—
125C2×#107—41no—
126C2×#107—41no—
127C2×#107D414yes—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—41no—
143C2×#103—41no—
144C2×#103—41no—
145C2×#103D414yes—
146C2×C22⋊C8—22no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8D414yes—
151C2×C22⋊C8D414yes—
152C2×C4×C8—22no—
153C2×C4×C8—22no—
154C2×C4×C8—41no—
155#391—22no—
156#391—22no—
157#391—22no—
158#391—41no—
159#391—41no—
160#391—41no—
161#391—41no—
162#391—41no—
163#384—22no—
164#384—41no—
165#380—22no—
166#380—22no—
167C4×C22⋊C4—41no—
168C4×C22⋊C4—41no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—21no—
174C2×#95—22no—
175C2×#95—22no—
176C2×#95—22no—
177C2×#95D412yes—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#336—22no—
183#336—22no—
184#336—41no—
185C25C2×D411yescharacteristic
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×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8C2×D412yes—
213C22×Q8#4112yes—
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—21no—
233C23×C4—21no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—44no—
238C23×C4—82no—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2411yescharacteristic
245C2×Q16—28no—
246C2×Q16—44no—
247C2×Q16—44no—
248C2×Q16—44no—
249C2×Q16—44no—
250C2×Q16—44no—
251C2×Q16—44no—
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×C8C2×D412yes—
273C22×C8C2×D412yes—
274C22×C8C2×D412yes—
275C22×C8C2×D412yes—
276C22×C8C2×D412yes—
277C22×C8C2×D412yes—
278C22×C8#4112yes—
279C22×C8#4112yes—
280C22⋊Q8—28no—
281C22⋊Q8—44no—
282C22⋊Q8—44no—
283C22⋊Q8—44no—
284C22⋊Q8—44no—
285C22⋊Q8—44no—
286C22⋊Q8—44no—
287C22⋊Q8—44no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
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—24no—
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—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—82no—
336C2×C4⋊C4C2×D412yes—
337C2×C4⋊C4C2×D412yes—
338C2×C4⋊C4C2×D412yes—
339C2×C4⋊C4#4112yes—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—82no—
350C2×C22⋊C4Q1618yescomplemented
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363#107—28no—
364#107—28no—
365#107—44no—
366#107—44no—
367#107—44no—
368#103—28no—
369#103—28no—
370#103—44no—
371#103—44no—
372#103—44no—
373#103—44no—
374C22⋊C8—28no—
375C22⋊C8—28no—
376C4×C8—44no—
377#95—42no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—42no—
383#95—82no—
384#95—82no—
385#95—82no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24#12712yes—
396C24C2×Q1614yes—
397C24C22×D411yescharacteristic
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—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
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—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×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
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—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—48no—
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—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—88no—
546C22×C4—88no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4#12712yes—
550C22×C4C2×Q1614yes—
551C22×C4C2×Q1614yes—
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C4H(5,𝔽2)11yescharacteristic
562C22×C4H(5,𝔽2)11yescharacteristic
563C22×C4H(5,𝔽2)11yescharacteristic
564C22×C42−1+411yescharacteristic
565C22×C42−1+411yescharacteristic
566Q16—416no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8#12014yes—
594C2×C8#12314yes—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—88no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—84no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23#49414yes—
658C23#52511yescharacteristic
659C23C2×#12711yescharacteristic
660C23#53411yescharacteristic
661C23D4211yescharacteristic
662C23D4211yescharacteristic
663C23#54711yescharacteristic
664C23#54711yescharacteristic
665C23C22×Q1612yes—
666C23#57512yes—
667C23#57612yes—
668C23#57812yes—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—81no—
678Q8—81no—
679Q8—81no—
680Q8—81no—
681Q8—81no—
682Q8—81no—
683Q8—81no—
684Q8—81no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—82no—
742C2×C4—81no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—82no—
748C2×C4—81no—
749C2×C4—82no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—81no—
759C2×C4C2×#12011yescharacteristic
760C2×C4C2×#12311yescharacteristic
761C2×C4#52511yescharacteristic
762C2×C4#53211yescharacteristic
763C2×C4#53511yescharacteristic
764C2×C4#53611yescharacteristic
765C2×C4#53711yescharacteristic
766C2×C4#53711yescharacteristic
767C2×C4#53811yescharacteristic
768C2×C4#53911yescharacteristic
769C2×C4#54011yescharacteristic
770C2×C4#54211yescharacteristic
771C2×C4D4211yescharacteristic
772C2×C4D4211yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4#54611yescharacteristic
775C2×C4#54611yescharacteristic
776C2×C4#54611yescharacteristic
777C2×C4#54611yescharacteristic
778C2×C4#54711yescharacteristic
779C2×C4#54711yescharacteristic
780C2×C4#54711yescharacteristic
781C2×C4#54811yescharacteristic
782C2×C4#55011yescharacteristic
783C2×C4#55111yescharacteristic
784C2×C4#55911yescharacteristic
785C2×C4#56211yescharacteristic
786C2×C4#56211yescharacteristic
787C8—24no—
788C8—24no—
789C8—42no—
790C8—42no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—44no—
800C22—42no—
801C22—44no—
802C22#243311yescharacteristic
803C22#245511yescharacteristic
804C22#246111yescharacteristic
805C22#250111yescharacteristic
806C22#253911yescharacteristic
807C22#267111yescharacteristic
808C22#268211yescharacteristic
809C22#310412yes—
810C22#312412yes—
811C22C2×#49411yescharacteristic
812C22#315311yescharacteristic
813C22#315511yescharacteristic
814C22#315611yescharacteristic
815C22#318912yes—
816C22#320312yes—
817C22#326812yes—
818C22#327312yes—
819C22D4×Q1612yes—
820C22D4×Q1612yes—
821C22#333812yes—
822C22#333812yes—
823C22#334912yes—
824C22#335212yes—
825C4—42no—
826C4—44no—
827C4—44no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—161no—
835C4—161no—
836C4#240711yescharacteristic
837C4#241811yescharacteristic
838C4#243011yescharacteristic
839C4#244511yescharacteristic
840C4#267211yescharacteristic
841C4#268111yescharacteristic
842C4#270611yescharacteristic
843C4#271011yescharacteristic
844C2—44no—
845C2#1537011yescharacteristic
846C2#2578011yescharacteristic
847C2#2579311yescharacteristic
848C2#2655912yes—
849C2#2679012yes—
850C2#2793011yescharacteristic
851C2#2794311yescharacteristic
852C2#2830411yescharacteristic
853C2#2832711yescharacteristic
854C2#3056312yes—
855C2#3119012yes—
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2095C2semidirect
5. C2×#1969C2semidirect
9. #11324C2semidirect
10. #11124C2semidirect
11. #11124C2semidirect
12. #11124C2semidirect
13. #11024C2semidirect
15. #10862C2semidirect
350. C2×C22⋊C4Q16semidirect

Maximal subgroups

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

subgroupindex
C22×#4842
C2×#20952
C2×#20362
C2×#20012
C2×#19692
C2×#18522
#151822
#141392
#113242
#111242
#110242
#109212
#108622