Finite Group Databasebeta

← #35228143

Subgroups — #35228143

Order 20864.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782398C211yesmaximal, characteristic, complemented
2#23782371C211yesmaximal, characteristic, complemented
3#23782370C211yesmaximal, characteristic, complemented
4#23782360C212yesmaximal, complemented
5#23782359C211yesmaximal, characteristic, complemented
6#23782344C212yesmaximal, complemented
7#23782340C212yesmaximal, complemented
8#23782312C211yesmaximal, characteristic, complemented
9#23782311C211yesmaximal, characteristic, complemented
10#23782304C212yesmaximal, complemented
11#23782299C211yesmaximal, characteristic, complemented
12#23782210C211yesmaximal, characteristic, complemented
13#23782200C211yesmaximal, characteristic, complemented
14#23782198C212yesmaximal, complemented
15#23782196C211yesmaximal, characteristic, complemented
16#23782175C212yesmaximal, complemented
17#23782173C212yesmaximal, complemented
18#23782133C211yesmaximal, characteristic, complemented
19C4×#14579698C211yesmaximal, characteristic, complemented
20C2×#19104697C211yesmaximal, characteristic, complemented
21C4×D4×D163C212yesmaximal, complemented
22C4×D4×D163C211yesmaximal, characteristic, complemented
23#553×C163C211yesmaximal, characteristic, complemented
24C2×#14579699C2211yescharacteristic
25C2×#14579698C2211yescharacteristic
26C2×#14579698C2212yescomplemented
27C22×D652C2211yescharacteristic
28C2×D4×D163C2212yes—
29C2×D4×D163C2211yescharacteristic
30C22×C4×D163C2212yescomplemented
31C22×C4×D163C2212yescomplemented
32#19104734C2211yescharacteristic, complemented
33#19104731C2211yescharacteristic
34#19104730C2212yescomplemented
35#19104729C2212yescomplemented
36#19104728C2212yescomplemented
37#19104726C2211yescharacteristic, complemented
38#19104725C2212yescomplemented
39#19104723C2211yescharacteristic, complemented
40#19104722C2211yescharacteristic, complemented
41#19104721C2212yescomplemented
42#19104721C2212yescomplemented
43#19104720C2212yescomplemented
44#19104720C2212yescomplemented
45#19104718C2212yescomplemented
46#19104717C2212yescomplemented
47#19104717C2212yescomplemented
48#19104717C2212yescomplemented
49#19104716C2212yescomplemented
50#19104715C2212yescomplemented
51#19104715C2211yescharacteristic, complemented
52#19104714C2212yescomplemented
53#19104714C2211yescharacteristic, complemented
54#19104713C2212yescomplemented
55#19104713C2212yescomplemented
56#19104713C2212yescomplemented
57#19104710C2211yescharacteristic
58#19104709C2211yescharacteristic, complemented
59#19104708C2212yes—
60#19104708C2212yescomplemented
61#19104708C2212yescomplemented
62#19104707C2212yescomplemented
63#19104706C2212yescomplemented
64#19104705C2212yes—
65#19104703C2212yes—
66#19104703C2212yescomplemented
67#19104703C2212yescomplemented
68C4×Dic326C2211yescharacteristic, complemented
69#19104700C2211yescharacteristic, complemented
70#19104700C2211yescharacteristic, complemented
71#19104700C2211yescharacteristic, complemented
72C4×D652C2211yescharacteristic
73C4×D652C2212yescomplemented
74D4×Dic163C2211yescharacteristic, complemented
75D4×Dic163C2212yescomplemented
76D4×Dic163C2211yescharacteristic, complemented
77#19104697C2211yescharacteristic
78#19104697C2211yescharacteristic
79#19104697C2211yescharacteristic
80#19104697C2212yescomplemented
81#19104697C2212yescomplemented
82#19104697C2211yescharacteristic, complemented
83#19104697C2212yescomplemented
84#19104697C2211yescharacteristic, complemented
85C4×C22⋊D163C2211yescharacteristic
86C4×C22⋊D163C2212yes—
87C4×C22⋊D163C2211yescharacteristic, complemented
88C4×C22⋊D163C2212yescomplemented
89C4×C22⋊D163C2212yescomplemented
90(C22⋊D163)⋊C4C2211yescharacteristic
91(C22⋊D163)⋊C4C2211yescharacteristic, complemented
92(C22⋊D163)⋊C4C2212yescomplemented
93(C22⋊D163)⋊C4C2212yescomplemented
94(C22⋊D163)⋊C4C2212yescomplemented
95(C22⋊D163)⋊C4C2212yescomplemented
96#19104693C2212yescomplemented
97#19104693C2211yescharacteristic, complemented
98#19104692C2212yescomplemented
99#19104691C2212yescomplemented
100#19104691C2211yescharacteristic, complemented
101#19104691C2211yescharacteristic, complemented
102C4⋊C4×D163C2211yescharacteristic, complemented
103C4⋊C4×D163C2212yescomplemented
104C2×(C2×D163)⋊C4C2212yescomplemented
105C22⋊C4×D163C2212yescomplemented
106C22⋊C4×D163C2212yescomplemented
107C22⋊C4×D163C2212yescomplemented
108C2×C4×Dic163C2211yescharacteristic, complemented
109C2×C4×Dic163C2211yescharacteristic, complemented
110C42×D163C2212yescomplemented
111C42×D163C2211yescharacteristic, complemented
112#126×C163C2212yescomplemented
113#125×C163C2211yescharacteristic, complemented
114#123×C163C2212yescomplemented
115#121×C163C2211yescharacteristic
116#121×C163C2212yescomplemented
117#121×C163C2211yescharacteristic, complemented
118C4×D4×C163C2211yescharacteristic, complemented
119C4×D4×C163C2212yescomplemented
120C4×D4×C163C2211yescharacteristic, complemented
121#117×C163C2211yescharacteristic, complemented
122C2×C4⋊C4×C163C2211yescharacteristic, complemented
123C23×D163C2312yes—
124C23×D163C2312yes—
125#14579699—24no—
126#14579698—24no—
127#14579698—44no—
128C2×Dic326C2311yescharacteristic
129C2×Dic326C2311yescharacteristic
130C2×Dic326C2312yes—
131C2×D652—24no—
132C2×D652C2312yes—
133C2×D652C2312yes—
134C2×D652C2311yescharacteristic
135C2×D652C2311yescharacteristic
136C2×C22⋊D163C2312yes—
137C2×C22⋊D163C2312yes—
138C2×C22⋊D163C2311yescharacteristic
139C2×C22⋊D163C2312yes—
140C2×C22⋊D163C2312yes—
141C2×C22⋊D163C2312yes—
142C2×C22⋊D163C2311yescharacteristic
143D4×D163—24no—
144D4×D163—28no—
145C22×Dic163C2311yescharacteristic
146C22×Dic163C2312yes—
147C22×Dic163C2311yescharacteristic
148C22×Dic163C2311yescharacteristic
149C22×Dic163C2311yescharacteristic
150C2×C4×D163—44no—
151C2×C4×D163—44no—
152C2×C4×D163C2311yescharacteristic
153C2×C4×D163C2312yes—
154C2×C4×D163C2312yes—
155C2×C4×D163C2312yes—
156C2×C4×D163C2311yescharacteristic
157C2×C4×D163C2311yescharacteristic
158C2×C4×D163C2312yes—
159C2×C4×D163C2312yes—
160C2×C4×D163C2312yes—
161C2×C4×D163C2312yes—
162C2×C4×D163C2312yes—
163C4⋊Dic163C2311yescharacteristic
164C4⋊Dic163C2312yes—
165C4⋊Dic163C2311yescharacteristic
166C4⋊Dic163C2312yes—
167Dic163⋊C4C2311yescharacteristic
168Dic163⋊C4C2312yes—
169Dic163⋊C4C2312yes—
170Dic163⋊C4C2311yescharacteristic
171Dic163⋊C4C2311yescharacteristic
172Dic163⋊C4C2311yescharacteristic
173Dic163⋊C4C2312yes—
174Dic163⋊C4C2312yes—
175Dic163⋊C4C2312yes—
176Dic163⋊C4C2312yes—
177C22⋊Dic163C2312yes—
178C22⋊Dic163C2312yes—
179C22⋊Dic163C2312yes—
180C22⋊Dic163C2311yescharacteristic
181C22⋊Dic163C2311yescharacteristic
182C22⋊Dic163C2312yes—
183(C2×D163)⋊C4C2311yescharacteristic
184(C2×D163)⋊C4C2312yes—
185(C2×D163)⋊C4C2312yes—
186(C2×D163)⋊C4C2312yes—
187(C2×D163)⋊C4C2312yes—
188(C2×D163)⋊C4C2312yes—
189(C2×D163)⋊C4C2312yes—
190(C2×D163)⋊C4C2312yes—
191(C2×D163)⋊C4C2312yes—
192(C2×D163)⋊C4C2312yes—
193(C2×D163)⋊C4C2311yescharacteristic
194(C2×D163)⋊C4C2312yes—
195(C2×D163)⋊C4C2312yes—
196C4×Dic163C2311yescharacteristic
197C4×Dic163C2311yescharacteristic
198C4×Dic163C2311yescharacteristic
199C4×Dic163C2312yes—
200C4×Dic163C2311yescharacteristic
201C4×Dic163C2312yes—
202C4×Dic163C2311yescharacteristic
203C4×Dic163C2311yescharacteristic
204C4×Dic163C2311yescharacteristic
205C4×Dic163C2311yescharacteristic
206C4×Dic163C2311yescharacteristic
207C2×D4×C163C2312yes—
208C2×D4×C163C2311yescharacteristic
209C2×D4×C163C2311yescharacteristic
210C2×D4×C163C2312yes—
211C22×C4×C163C2311yescharacteristic
212C22×C4×C163C2311yescharacteristic
213C22×C4×C163C2312yes—
214C22×C4×C163C2312yes—
215C4⋊C4×C163C2311yescharacteristic
216C4⋊C4×C163C2311yescharacteristic
217C4⋊C4×C163C2312yes—
218C4⋊C4×C163C2311yescharacteristic
219C4⋊C4×C163C2312yes—
220C4⋊C4×C163C2311yescharacteristic
221C4⋊C4×C163C2312yes—
222C22⋊C4×C163C2312yes—
223C22⋊C4×C163C2311yescharacteristic
224C22⋊C4×C163C2312yes—
225C22⋊C4×C163C2312yes—
226C22⋊C4×C163C2311yescharacteristic
227C22⋊C4×C163C2312yes—
228C42×C163C2312yes—
229C42×C163C2311yescharacteristic
230C22×D163—24no—
231C22×D163—24no—
232C22×D163—24no—
233C22×D163—24no—
234C22×D163—42no—
235C22×D163—42no—
236C22×D163C2412yes—
237C22×D163C2412yes—
238C22×D163C2411yescharacteristic
239Dic326—22no—
240Dic326—22no—
241Dic326—42no—
242D652—24no—
243D652—24no—
244D652—22no—
245D652#4114yescomplemented
246C22⋊D163—24no—
247C22⋊D163—22no—
248C22⋊D163—24no—
249C22⋊D163—24no—
250C22⋊D163—42no—
251C22⋊D163—42no—
252C22⋊D163#4114yescomplemented
253C2×Dic163—22no—
254C2×Dic163—22no—
255C2×Dic163—22no—
256C2×Dic163—24no—
257C2×Dic163—22no—
258C2×Dic163C2411yescharacteristic
259C2×Dic163C2411yescharacteristic
260C2×Dic163C2412yes—
261C2×Dic163C2411yescharacteristic
262C2×Dic163C2411yescharacteristic
263C2×Dic163C2411yescharacteristic
264C2×Dic163C2412yes—
265C2×Dic163C2411yescharacteristic
266C2×Dic163C2411yescharacteristic
267C4×D163—22no—
268C4×D163—24no—
269C4×D163—22no—
270C4×D163—24no—
271C4×D163—22no—
272C4×D163—24no—
273C4×D163—24no—
274C4×D163—42no—
275C4×D163—42no—
276C4×D163—42no—
277C4×D163—42no—
278C23×C163C2412yes—
279C23×C163C2411yescharacteristic
280C23×C163C2411yescharacteristic
281D4×C163—24no—
282D4×C163—22no—
283D4×C163—22no—
284D4×C163—42no—
285C2×C4×C163—22no—
286C2×C4×C163—22no—
287C2×C4×C163—42no—
288C2×C4×C163—42no—
289C2×C4×C163C2411yescharacteristic
290C2×C4×C163C2411yescharacteristic
291C2×C4×C163C2412yes—
292C2×C4×C163C2412yes—
293C2×C4×C163C2411yescharacteristic
294C2×C4×C163C2411yescharacteristic
295C2×C4×C163C2412yes—
296C2×C4×C163C2411yescharacteristic
297C22×C163—21no—
298C22×C163—21no—
299C22×C163—21no—
300C22×C163—21no—
301C22×C163—22no—
302C22×C163—22no—
303C22×C163—22no—
304C22×C163—21no—
305C22×C163C2×#4112yes—
306C22×C163C2511yescharacteristic
307C2×D163—21no—
308C2×D163—22no—
309C2×D163—21no—
310C2×D163—22no—
311C2×D163—22no—
312C2×D163—22no—
313C2×D163—22no—
314C2×D163—48no—
315C2×D163—48no—
316C2×D163C2×#4114yes—
317C2×D163C2×#4112yes—
318C4×C163—21no—
319C4×C163—21no—
320C4×C163—22no—
321C4×C163—21no—
322C4×C163—21no—
323C4×C163—22no—
324C4×C163—22no—
325C4×C163C2×#4112yes—
326Dic163—21no—
327Dic163—21no—
328Dic163—22no—
329Dic163—21no—
330Dic163—21no—
331Dic163—22no—
332Dic163—21no—
333Dic163C2×#4112yes—
334Dic163H(5,𝔽2)12yes—
335C2×C163—22no—
336C2×C163—42no—
337C2×C163—41no—
338C2×C163C22×#4111yescharacteristic
339C2×C163C22×#4111yescharacteristic
340C2×C163C2×H(5,𝔽2)11yescharacteristic
341D163—22no—
342D163—24no—
343D163—42no—
344C163#348111yescharacteristic, complemented, Sylow
345#3481—1631nomaximal, Sylow
346#559—1631no—
347#554—1631no—
348#554—1631no—
349#553—1632no—
350#553—1631no—
351#553D16311yescharacteristic, complemented
352#551—1632no—
353#551—1632no—
354#546—1632no—
355#546—1631no—
356#546—1631no—
357D42—1631no—
358#532—1631no—
359#529—1632no—
360#529—1631no—
361#529—1631no—
362#525—1632no—
363#525—1632no—
364C4×#41—1631no—
365C4×#41—1631no—
366C2×C4×D4—1632no—
367C2×C4×D4—1631no—
368C2×C4×D4—1631no—
369C2×#41—1631no—
370C2×#41—1632no—
371C2×#41—1631no—
372C22×D4—1631no—
373C22×D4—1632no—
374C22×D4—1631no—
375C23×C4—1632no—
376C23×C4—1632no—
377C4⋊Q8—1631no—
378#127—1631no—
379#126—1632no—
380#126—1632no—
381#126—1632no—
382#126C2×D16312yescomplemented
383#125—1632no—
384#125—1631no—
385#125C2×D16311yescharacteristic, complemented
386#124—1631no—
387#124—1632no—
388#124—1632no—
389#124—1631no—
390#123—1632no—
391#123—1632no—
392#123—1632no—
393#123—1632no—
394#123—1632no—
395#123—1632no—
396#123—1632no—
397#123C2×D16312yescomplemented
398C22⋊Q8—1632no—
399C22⋊Q8—1631no—
400C22⋊Q8—1632no—
401C22⋊Q8—1632no—
402C22⋊Q8—1632no—
403C22⋊Q8—1632no—
404C22⋊Q8—1631no—
405#121—1632no—
406#121—1632no—
407#121—1631no—
408#121—1631no—
409#121—1632no—
410#121—1632no—
411#121—1632no—
412#121C2×D16311yescharacteristic
413#121C2×D16312yescomplemented
414#121C2×D16311yescharacteristic, complemented
415#120—1632no—
416#120—1632no—
417#120—1632no—
418#120—1632no—
419C4×Q8—1631no—
420C4×Q8—1631no—
421C4×Q8—1631no—
422C4×Q8—1631no—
423C4×D4—1632no—
424C4×D4—1631no—
425C4×D4—1631no—
426C4×D4—1632no—
427C4×D4—1632no—
428C4×D4—1632no—
429C4×D4—1631no—
430C4×D4—1631no—
431C4×D4—1631no—
432C4×D4—1632no—
433C4×D4—1632no—
434C4×D4—1631no—
435C4×D4—1631no—
436C4×D4—1632no—
437C4×D4—1631no—
438C4×D4—1631no—
439C4×D4—1631no—
440C4×D4—1632no—
441C4×D4—1632no—
442C4×D4—1631no—
443C4×D4—1632no—
444C4×D4—1632no—
445C4×D4—1631no—
446C4×D4—1632no—
447C4×D4C2×D16312yescomplemented
448C4×D4C2×D16311yescharacteristic, complemented
449C4×D4C2×D16311yescharacteristic, complemented
450#117—1631no—
451#117—1632no—
452#117—1631no—
453#117—1631no—
454#117—1632no—
455#117—1632no—
456#117C2×D16311yescharacteristic, complemented
457C2×C4⋊C4—1632no—
458C2×C4⋊C4—1631no—
459C2×C4⋊C4C2×D16311yescharacteristic, complemented
460C2×C22⋊C4—1632no—
461C2×C22⋊C4—1632no—
462C2×C22⋊C4—1632no—
463C2×C22⋊C4—1632no—
464C2×C42—1631no—
465C2×C42—1631no—
466C2×C42—1631no—
467C2×C42—1632no—
468C24—1632no—
469C24—1632no—
470#41—3264no—
471#41—3264no—
472#41—6524no—
473C2×Q8—1631no—
474C2×Q8—1631no—
475C2×Q8—1632no—
476C2×D4—3264no—
477C2×D4—3268no—
478C2×D4—3264no—
479C2×D4—1631no—
480C2×D4—1632no—
481C2×D4—1632no—
482C2×D4—1632no—
483C2×D4—1632no—
484C2×D4—1632no—
485C2×D4—1631no—
486C2×D4—1632no—
487C2×D4—1632no—
488C2×D4—1631no—
489C2×D4—1631no—
490C2×D4C22×D16311yescharacteristic
491C2×D4C22×D16312yes—
492C2×D4C22×D16311yescharacteristic
493C2×D4C22×D16312yes—
494C22×C4—6524no—
495C22×C4—6524no—
496C22×C4—1631no—
497C22×C4—1631no—
498C22×C4—1631no—
499C22×C4—1631no—
500C22×C4—1632no—
501C22×C4—1631no—
502C22×C4—1632no—
503C22×C4—1632no—
504C22×C4—1631no—
505C22×C4—1632no—
506C22×C4—1631no—
507C22×C4—1632no—
508C22×C4—1632no—
509C22×C4—1632no—
510C22×C4—1632no—
511C22×C4—1632no—
512C22×C4C22×D16311yescharacteristic
513C22×C4C22×D16311yescharacteristic
514C22×C4C22×D16312yes—
515C22×C4C22×D16312yes—
516C4⋊C4—1631no—
517C4⋊C4—1632no—
518C4⋊C4—1631no—
519C4⋊C4—1632no—
520C4⋊C4—1632no—
521C4⋊C4—1631no—
522C4⋊C4—1631no—
523C4⋊C4—1632no—
524C4⋊C4—1631no—
525C4⋊C4—1632no—
526C4⋊C4—1631no—
527C4⋊C4—1632no—
528C4⋊C4—1632no—
529C4⋊C4—1632no—
530C4⋊C4C22×D16311yescharacteristic
531C4⋊C4C22×D16312yes—
532C4⋊C4C22×D16311yescharacteristic
533C4⋊C4C22×D16312yes—
534C4⋊C4C22×D16311yescharacteristic
535C4⋊C4C22×D16312yes—
536C4⋊C4C22×D16311yescharacteristic
537C22⋊C4—1632no—
538C22⋊C4—1632no—
539C22⋊C4—1632no—
540C22⋊C4—1631no—
541C22⋊C4—1631no—
542C22⋊C4—1632no—
543C22⋊C4—1632no—
544C22⋊C4—1631no—
545C22⋊C4—1632no—
546C22⋊C4—1632no—
547C22⋊C4—1632no—
548C22⋊C4—1632no—
549C22⋊C4—1632no—
550C22⋊C4—1632no—
551C22⋊C4—1632no—
552C22⋊C4—1631no—
553C22⋊C4—1632no—
554C22⋊C4—1632no—
555C22⋊C4—1632no—
556C22⋊C4C22×D16311yescharacteristic
557C22⋊C4C22×D16312yes—
558C22⋊C4C22×D16312yes—
559C22⋊C4C22×D16311yescharacteristic
560C22⋊C4C22×D16312yes—
561C22⋊C4C22×D16312yes—
562C42—1631no—
563C42—1631no—
564C42—1631no—
565C42—1631no—
566C42—1632no—
567C42—1631no—
568C42—1631no—
569C42—1631no—
570C42—1631no—
571C42—1632no—
572C42—1631no—
573C42C22×D16312yes—
574C42C22×D16311yescharacteristic
575C23—3264no—
576C23—3264no—
577C23—3264no—
578C23—3264no—
579C23—6522no—
580C23—6522no—
581C23—1632no—
582C23—1632no—
583C23—1631no—
584C23C23×D16312yes—
585C23C23×D16311yescharacteristic
586C23C23×D16311yescharacteristic
587Q8—3262no—
588Q8—3262no—
589Q8—6522no—
590D4—24no—
591D4—22no—
592D4—22no—
593D4—42no—
594D4—3264no—
595D4—3264no—
596D4—3264no—
597D4—3264no—
598D4—3262no—
599D4—3264no—
600D4—3262no—
601D4—6522no—
602D4—6522no—
603D4—1634no—
604D4—1634no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—3264no—
610C2×C4—3262no—
611C2×C4—3262no—
612C2×C4—3264no—
613C2×C4—3264no—
614C2×C4—3264no—
615C2×C4—3262no—
616C2×C4—3262no—
617C2×C4—3264no—
618C2×C4—3262no—
619C2×C4—3262no—
620C2×C4—3262no—
621C2×C4—6522no—
622C2×C4—6522no—
623C2×C4—6522no—
624C2×C4—6522no—
625C2×C4—1631no—
626C2×C4—1632no—
627C2×C4—1631no—
628C2×C4—1631no—
629C2×C4—1631no—
630C2×C4—1631no—
631C2×C4—1632no—
632C2×C4—1631no—
633C2×C4—1631no—
634C2×C4C23×D16311yescharacteristic
635C2×C4C23×D16311yescharacteristic
636C2×C4C23×D16311yescharacteristic
637C2×C4C23×D16312yes—
638C2×C4C23×D16311yescharacteristic
639C2×C4C23×D16312yes—
640C2×C4C23×D16312yes—
641C2×C4C23×D16311yescharacteristic
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—21no—
650C22—3262no—
651C22—3261no—
652C22—3262no—
653C22—3261no—
654C22—3262no—
655C22—3262no—
656C22—3262no—
657C22—6528no—
658C22—6528no—
659C22—1632no—
660C22—1634no—
661C22#41×D16312yes—
662C22C24×D16311yescharacteristic
663C4—21no—
664C4—21no—
665C4—22no—
666C4—21no—
667C4—21no—
668C4—22no—
669C4—22no—
670C4—3261no—
671C4—3261no—
672C4—3261no—
673C4—3262no—
674C4—3261no—
675C4—3262no—
676C4—3261no—
677C4—1632no—
678C4—1632no—
679C4#41×D16312yes—
680C2—22no—
681C2—42no—
682C2—41no—
683C2—3264no—
684C2—3262no—
685C2—6522no—
686C2C2×#41×D16311yescharacteristic
687C2C2×#41×D16311yescharacteristic
688C2H(5,𝔽2)×D16311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D163
commutator, socle, cosocleC22×C163C25
Fitting#553×C163C2
hypercenter#553D163
hypocenterC163#3481
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23782398C2semidirect
2. #23782371C2semidirect
3. #23782370C2semidirect
4. #23782360C2semidirect
5. #23782359C2semidirect
6. #23782344C2semidirect
7. #23782340C2semidirect
8. #23782312C2semidirect
9. #23782311C2semidirect
10. #23782304C2semidirect
11. #23782299C2semidirect
12. #23782210C2semidirect
13. #23782200C2semidirect
14. #23782198C2semidirect
15. #23782196C2semidirect
16. #23782175C2semidirect
17. #23782173C2semidirect
18. #23782133C2semidirect
19. C4×#14579698C2semidirect
20. C2×#19104697C2semidirect
21. C4×D4×D163C2semidirect
22. C4×D4×D163C2semidirect
23. #553×C163C2semidirect
26. C2×#14579698C22semidirect
30. C22×C4×D163C22semidirect
31. C22×C4×D163C22semidirect
32. #19104734C22semidirect
34. #19104730C22semidirect
35. #19104729C22semidirect
36. #19104728C22semidirect
37. #19104726C22semidirect
38. #19104725C22semidirect
39. #19104723C22semidirect
40. #19104722C22semidirect
41. #19104721C22semidirect
42. #19104721C22semidirect
43. #19104720C22semidirect
44. #19104720C22semidirect
45. #19104718C22semidirect
46. #19104717C22semidirect
47. #19104717C22semidirect
48. #19104717C22semidirect
49. #19104716C22semidirect
50. #19104715C22semidirect
51. #19104715C22semidirect
52. #19104714C22semidirect
53. #19104714C22semidirect
54. #19104713C22semidirect
55. #19104713C22semidirect
56. #19104713C22semidirect
58. #19104709C22semidirect
60. #19104708C22semidirect
61. #19104708C22semidirect
62. #19104707C22semidirect
63. #19104706C22semidirect
66. #19104703C22semidirect
67. #19104703C22semidirect
68. C4×Dic326C22semidirect
69. #19104700C22semidirect
70. #19104700C22semidirect
71. #19104700C22semidirect
73. C4×D652C22semidirect
74. D4×Dic163C22semidirect
75. D4×Dic163C22semidirect
76. D4×Dic163C22semidirect
80. #19104697C22semidirect
81. #19104697C22semidirect
82. #19104697C22semidirect
83. #19104697C22semidirect
84. #19104697C22semidirect
87. C4×C22⋊D163C22semidirect
88. C4×C22⋊D163C22semidirect
89. C4×C22⋊D163C22semidirect
91. (C22⋊D163)⋊C4C22semidirect
92. (C22⋊D163)⋊C4C22semidirect
93. (C22⋊D163)⋊C4C22semidirect
94. (C22⋊D163)⋊C4C22semidirect
95. (C22⋊D163)⋊C4C22semidirect
96. #19104693C22semidirect
97. #19104693C22semidirect
98. #19104692C22semidirect
99. #19104691C22semidirect
100. #19104691C22semidirect
101. #19104691C22semidirect
102. C4⋊C4×D163C22semidirect
103. C4⋊C4×D163C22semidirect
104. C2×(C2×D163)⋊C4C22semidirect
105. C22⋊C4×D163C22semidirect
106. C22⋊C4×D163C22semidirect
107. C22⋊C4×D163C22semidirect
108. C2×C4×Dic163C22semidirect
109. C2×C4×Dic163C22semidirect
110. C42×D163C22semidirect
111. C42×D163C22semidirect
112. #126×C163C22semidirect
113. #125×C163C22semidirect
114. #123×C163C22semidirect
116. #121×C163C22semidirect
117. #121×C163C22semidirect
118. C4×D4×C163C22semidirect
119. C4×D4×C163C22semidirect
120. C4×D4×C163C22semidirect
121. #117×C163C22semidirect
122. C2×C4⋊C4×C163C22semidirect
245. D652#41semidirect
252. C22⋊D163#41semidirect
344. C163#3481semidirect
351. #553D163semidirect
382. #126C2×D163semidirect
385. #125C2×D163semidirect
397. #123C2×D163semidirect
413. #121C2×D163semidirect
414. #121C2×D163semidirect
447. C4×D4C2×D163semidirect
448. C4×D4C2×D163semidirect
449. C4×D4C2×D163semidirect
456. #117C2×D163semidirect
459. C2×C4⋊C4C2×D163semidirect

Maximal subgroups

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

subgroupindex
#237823982
#237823712
#237823702
#237823602
#237823592
#237823442
#237823402
#237823122
#237823112
#237823042
#237822992
#237822102
#237822002
#237821982
#237821962
#237821752
#237821732
#237821332
C4×#145796982
C2×#191046972
C4×D4×D1632
#553×C1632
#3481163