Finite Group Databasebeta

← #160654

Subgroups — #160654

Order 512.

1028 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34320C211yesmaximal, characteristic
2#22835C211yesmaximal, characteristic, complemented
3#21996C211yesmaximal, characteristic, complemented
4#7601C211yesmaximal, characteristic, complemented
5#7600C211yesmaximal, characteristic, complemented
6#7594C211yesmaximal, characteristic, complemented
7#7592C211yesmaximal, characteristic, complemented
8#7584C211yesmaximal, characteristic, complemented
9#7583C211yesmaximal, characteristic, complemented
10#7582C211yesmaximal, characteristic, complemented
11#7578C211yesmaximal, characteristic, complemented
12#7574C211yesmaximal, characteristic, complemented
13#7572C211yesmaximal, characteristic, complemented
14#7565C211yesmaximal, characteristic, complemented
15#7563C211yesmaximal, characteristic, complemented
16C2×#546C411yescharacteristic
17#2374—21no—
18#2367C411yescharacteristic
19#2363—21no—
20#2363C411yescharacteristic
21#2360C411yescharacteristic
22#2358—21no—
23#2357C411yescharacteristic
24#2352C411yescharacteristic
25#2342—21no—
26#2341C411yescharacteristic
27D4×C22⋊C4C411yescharacteristic
28#2335—21no—
29#2333—21no—
30#2321—21no—
31C4×#124C2211yescharacteristic
32C4×C22⋊Q8C2211yescharacteristic
33C4×#121C2211yescharacteristic
34#2297C2211yescharacteristic
35#2293C2211yescharacteristic
36C2×#390C2211yescharacteristic
37#2273—21no—
38C42×D4C2211yescharacteristic
39#1954—21no—
40#1923—21no—
41#1923—21no—
42#1923—21no—
43#1916—21no—
44#1869—21no—
45#1850—21no—
46#1839C2211yescharacteristic, complemented
47#1831C2211yescharacteristic, complemented
48#1831C2211yescharacteristic, complemented
49#1817C2211yescharacteristic
50#1817C2211yescharacteristic
51#1817C2211yescharacteristic, complemented
52#1797C2211yescharacteristic
53C8×C4⋊C4—21no—
54C4×C4⋊C8C2211yescharacteristic, complemented
55C4×C22⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic, complemented
57C4×C22⋊C8C2211yescharacteristic, complemented
58C2×#336C2211yescharacteristic, complemented
59#1272C2211yescharacteristic, complemented
60#1272C2211yescharacteristic, complemented
61#1272C2211yescharacteristic, complemented
62#1272C2211yescharacteristic, complemented
63#1271C2211yescharacteristic, complemented
64#1271C2211yescharacteristic, complemented
65#1271C2211yescharacteristic, complemented
66#1271C2211yescharacteristic, complemented
67#1270C2211yescharacteristic
68#1270C2211yescharacteristic
69#1270C2211yescharacteristic
70#1270C2211yescharacteristic
71#1270C2211yescharacteristic
72#1270C2211yescharacteristic
73#1270C2211yescharacteristic
74#1270C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C23×D4C2×C411yescharacteristic
77C23×C8—21no—
78#546—24no—
79#546C818yescomplemented
80C2×#124C2×C411yescharacteristic
81C2×#123—21no—
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×#121—21no—
84C2×#121C2×C411yescharacteristic
85C2×#120—21no—
86C2×C4×Q8C2×C411yescharacteristic
87C2×C4×Q8C2×C411yescharacteristic
88C2×C4×D4—21no—
89C2×C4×D4C2×C411yescharacteristic
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4C2×C411yescharacteristic
92C2×C4×D4C2×C411yescharacteristic
93C2×C4×D4D411yescharacteristic
94C2×C4×D4D411yescharacteristic
95C2×#117—21no—
96C2×#117C2×C411yescharacteristic
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C22⋊C8—21no—
111C2×C22⋊C8—21no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C4×C8—21no—
116C2×C4×C8—21no—
117C2×C4×C8—21no—
118C2×C4×C8—21no—
119#391C2×C411yescharacteristic
120#391C2311yescharacteristic
121#390—21no—
122#390—21no—
123#390—21no—
124#390—21no—
125#390—21no—
126#390C2×C411yescharacteristic
127#390C2×C411yescharacteristic
128#390C2×C411yescharacteristic
129#390C2×C411yescharacteristic
130#390C2311yescharacteristic
131#390C2311yescharacteristic
132#389—21no—
133#389C2×C411yescharacteristic
134#389C2311yescharacteristic
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#386—21no—
150#386—21no—
151#386—21no—
152#386—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#382C2×C411yescharacteristic
160#381—21no—
161#380—21no—
162#380C2×C411yescharacteristic
163#380C2×C411yescharacteristic
164#379—21no—
165C4×C4⋊C4—21no—
166C4×C4⋊C4C2×C411yescharacteristic
167C4×C4⋊C4C2×C411yescharacteristic
168C4×C4⋊C4C2×C411yescharacteristic
169C4×C4⋊C4C2×C411yescharacteristic
170C4×C4⋊C4D411yescharacteristic
171C4×C4⋊C4D411yescharacteristic
172C4×C22⋊C4—21no—
173C4×C22⋊C4—21no—
174C4×C22⋊C4—21no—
175C4×C22⋊C4—21no—
176C4×C22⋊C4—21no—
177C4×C22⋊C4—21no—
178C4×C22⋊C4—21no—
179C4×C22⋊C4—21no—
180C4×C22⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C43C2311yescharacteristic
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336C2311yescharacteristic
201#336C2311yescharacteristic
202#336C2311yescharacteristic
203#336C2311yescharacteristic
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208C25—21no—
209C2×#41—22no—
210C2×#41—81no—
211C2×#41—81no—
212C2×#41C2×C814yes—
213C22×Q8C22×C411yescharacteristic
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—22no—
218C22×D4—81no—
219C22×D4—81no—
220C22×D4C22⋊C411yescharacteristic
221C22×D4C2×C814yescomplemented
222C22×D4C22×C411yescharacteristic
223C22×D4C22×C411yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
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—42no—
244C22×C8—81no—
245C22×C8—81no—
246#124—22no—
247#124C2×C814yescomplemented
248#123—28no—
249C22⋊Q8—22no—
250C22⋊Q8C2×C814yescomplemented
251#121—22no—
252#121—28no—
253#121C2×C814yes—
254#120—28no—
255C4×Q8—81no—
256C4×Q8—81no—
257C4×D4—22no—
258C4×D4—41no—
259C4×D4—41no—
260C4×D4—42no—
261C4×D4—81no—
262C4×D4—81no—
263C4×D4—81no—
264C4×D4—81no—
265C4×D4C2×C814yes—
266C4×D4C2×C814yescomplemented
267C4×D4M1614yes—
268#117—81no—
269#117—81no—
270#117—81no—
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—81no—
278C2×C4⋊C4C22⋊C411yescharacteristic
279C2×C4⋊C4C22⋊C411yescharacteristic
280C2×C4⋊C4C22⋊C411yescharacteristic
281C2×C4⋊C4C22×C411yescharacteristic
282C2×C4⋊C4C22×C411yescharacteristic
283C2×C4⋊C4C22×C411yescharacteristic
284C2×C4⋊C4C22×C411yescharacteristic
285C2×C4⋊C4C22×C411yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—81no—
313C2×C22⋊C4—81no—
314C2×C22⋊C4C22⋊C411yescharacteristic
315C2×C22⋊C4C22⋊C411yescharacteristic
316C2×C22⋊C4C22⋊C411yescharacteristic
317C2×C22⋊C4C22⋊C411yescharacteristic
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—81no—
327C2×C42—81no—
328C2×C42C22×C411yescharacteristic
329C2×C42C22×C411yescharacteristic
330C2×C42C22×C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C2×D411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2411yescharacteristic
341C4⋊C8—42no—
342C4⋊C8—42no—
343C4⋊C8—81no—
344C4⋊C8—81no—
345C22⋊C8—42no—
346C22⋊C8—42no—
347C22⋊C8—42no—
348C22⋊C8—81no—
349C22⋊C8—81no—
350C22⋊C8—81no—
351C22⋊C8—81no—
352C4×C8—42no—
353C4×C8—81no—
354C4×C8—81no—
355C4×C8—81no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95C22⋊C411yescharacteristic
370#95C22⋊C411yescharacteristic
371#95C22⋊C411yescharacteristic
372#95C22⋊C411yescharacteristic
373#95C22⋊C411yescharacteristic
374#95C22⋊C411yescharacteristic
375C24—21no—
376C24—21no—
377C24—24no—
378C24—42no—
379C24—42no—
380C24—81no—
381C24—81no—
382C24—81no—
383C24—81no—
384C24C2×C22⋊C411yescharacteristic
385C24C2×C22⋊C411yescharacteristic
386#41—84no—
387#41—84no—
388C2×Q8—21no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8C22×C812yes—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—24no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—81no—
404C2×D4—81no—
405C2×D4—84no—
406C2×D4—84no—
407C2×D4—81no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4C22⋊C814yes—
412C2×D4C22×C812yes—
413C2×D4C22×C812yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—81no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×C22⋊C411yescharacteristic
456C22×C4C2×C22⋊C411yescharacteristic
457C22×C4C2×C22⋊C411yescharacteristic
458C22×C4C2×C22⋊C411yescharacteristic
459C22×C4C2×C22⋊C411yescharacteristic
460C22×C4C2×C22⋊C411yescharacteristic
461C22×C4C2×C22⋊C411yescharacteristic
462C22×C4C2×C22⋊C411yescharacteristic
463C22×C4C2×C22⋊C411yescharacteristic
464C22×C4C2×C22⋊C411yescharacteristic
465C22×C4C22×C812yes—
466C22×C4C22×C812yes—
467C22×C4C2×M1612yes—
468C22×C4C2×M1612yes—
469C22×C4C23×C411yescharacteristic
470C22×C4C22×D411yescharacteristic
471C22×C4C22×D411yescharacteristic
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—84no—
497C4⋊C4—21no—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4C22⋊C814yes—
512C4⋊C4C22×C812yes—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
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—42no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C22⋊C4C22⋊C814yes—
544C22⋊C4C22⋊C814yes—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—81no—
560C42—81no—
561C42—81no—
562C42—81no—
563C42—81no—
564C42—81no—
565C42C22×C812yes—
566C42C2×M1612yes—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—22no—
580C23—22no—
581C23—48no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—84no—
595C23—84no—
596C23—162no—
597C23—162no—
598C23—162no—
599C23—162no—
600C23C2×C22⋊C812yes—
601C23C2×C22⋊C812yes—
602C23C22×C22⋊C411yescharacteristic
603Q8—42no—
604Q8—42no—
605D4—44no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—42no—
610D4—84no—
611D4—84no—
612D4—84no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
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—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—162no—
677C2×C4—162no—
678C2×C4—162no—
679C2×C4C2×C22⋊C812yes—
680C2×C4C2×C22⋊C812yes—
681C2×C4C2×C22⋊C812yes—
682C2×C4C2×C22⋊C812yes—
683C2×C4#42112yes—
684C2×C4C23×C811yescharacteristic
685C2×C4C22×M1611yescharacteristic
686C2×C4#57511yescharacteristic
687C2×C4#57511yescharacteristic
688C2×C4#57611yescharacteristic
689C2×C4#57711yescharacteristic
690C8—42no—
691C8—81no—
692C8—81no—
693C8—81no—
694C8—81no—
695C8—81no—
696C8—81no—
697C8—81no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—168no—
727C22C22×C22⋊C811yescharacteristic
728C22#288311yescharacteristic
729C22#288811yescharacteristic
730C22#289611yescharacteristic
731C22#289711yescharacteristic
732C22C2×#42111yescharacteristic
733C22#290111yescharacteristic
734C4—22no—
735C4—22no—
736C4—21no—
737C4—21no—
738C4—22no—
739C4—21no—
740C4—21no—
741C4—22no—
742C4—22no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C2—42no—
757C2—42no—
758C2—82no—
759C2—82no—
760C2#1735011yescharacteristic
761C2#1743711yescharacteristic
762C2#1743811yescharacteristic
763C2#1759711yescharacteristic
764C2#1762511yescharacteristic
765C2#1768111yescharacteristic
766C2#1776611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
prime radicalC2×#546C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22835C2semidirect
3. #21996C2semidirect
4. #7601C2semidirect
5. #7600C2semidirect
6. #7594C2semidirect
7. #7592C2semidirect
8. #7584C2semidirect
9. #7583C2semidirect
10. #7582C2semidirect
11. #7578C2semidirect
12. #7574C2semidirect
13. #7572C2semidirect
14. #7565C2semidirect
15. #7563C2semidirect
46. #1839C22semidirect
47. #1831C22semidirect
48. #1831C22semidirect
51. #1817C22semidirect
54. C4×C4⋊C8C22semidirect
56. C4×C22⋊C8C22semidirect
57. C4×C22⋊C8C22semidirect
58. C2×#336C22semidirect
59. #1272C22semidirect
60. #1272C22semidirect
61. #1272C22semidirect
62. #1272C22semidirect
63. #1271C22semidirect
64. #1271C22semidirect
65. #1271C22semidirect
66. #1271C22semidirect
79. #546C8semidirect
221. C22×D4C2×C8semidirect
247. #124C2×C8semidirect
250. C22⋊Q8C2×C8semidirect
266. C4×D4C2×C8semidirect

Maximal subgroups

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

subgroupindex
#343202
#228352
#219962
#76012
#76002
#75942
#75922
#75842
#75832
#75822
#75782
#75742
#75722
#75652
#75632