Finite Group Databasebeta

← #35212780

Subgroups — #35212780

Order 20864.

780 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic163⋊C4C211yesmaximal, characteristic, complemented
2C22×(C2×D163)⋊C4C211yesmaximal, characteristic
3C22×(C2×D163)⋊C4C211yesmaximal, characteristic
4C22×(C2×D163)⋊C4C211yesmaximal, characteristic
5C2×C163⋊#95C211yesmaximal, characteristic, complemented
6C2×C163⋊#95C211yesmaximal, characteristic, complemented
7C2×#95×C163C211yesmaximal, characteristic, complemented
8C24×D163C2211yescharacteristic
9C23×Dic163C2211yescharacteristic
10C23×Dic163C2211yescharacteristic
11C23×Dic163C2211yescharacteristic
12C2×Dic163⋊C4—22no—
13C2×Dic163⋊C4—22no—
14C2×Dic163⋊C4—22no—
15C2×(C2×D163)⋊C4—22no—
16C2×(C2×D163)⋊C4—22no—
17C2×(C2×D163)⋊C4—22no—
18C2×(C2×D163)⋊C4—22no—
19C2×(C2×D163)⋊C4—22no—
20C2×(C2×D163)⋊C4—22no—
21C2×(C2×D163)⋊C4—22no—
22C2×(C2×D163)⋊C4—22no—
23C2×(C2×D163)⋊C4C414yescomplemented
24C163⋊#95—22no—
25C163⋊#95—22no—
26C23×C4×C163C2211yescharacteristic
27C23×C4×C163C2211yescharacteristic
28C23×C4×C163C2211yescharacteristic
29#95×C163—22no—
30C23×D163—21no—
31C23×D163—21no—
32C23×D163—21no—
33C23×D163—21no—
34C23×D163—21no—
35C23×D163—21no—
36C23×D163—21no—
37C23×D163—21no—
38C23×D163—21no—
39C23×D163—21no—
40C23×D163—21no—
41C23×D163—21no—
42C23×D163C2×C412yes—
43C23×D163D412yes—
44C23×D163Q812yes—
45C22×Dic163—21no—
46C22×Dic163—21no—
47C22×Dic163—21no—
48C22×Dic163—21no—
49C22×Dic163—21no—
50C22×Dic163—21no—
51C22×Dic163—21no—
52C22×Dic163—21no—
53C22×Dic163—21no—
54C22×Dic163—21no—
55C22×Dic163—21no—
56C22×Dic163—21no—
57C22×Dic163—21no—
58C22×Dic163—21no—
59C22×Dic163—21no—
60C22×Dic163—21no—
61C22×Dic163C2×C412yes—
62C22×Dic163D412yes—
63C22×Dic163D412yes—
64C22×Dic163D412yes—
65C22×Dic163D412yes—
66Dic163⋊C4—28no—
67(C2×D163)⋊C4—28no—
68(C2×D163)⋊C4—28no—
69(C2×D163)⋊C4—28no—
70C24×C163C2311yescharacteristic
71C22×C4×C163—21no—
72C22×C4×C163—21no—
73C22×C4×C163—21no—
74C22×C4×C163—21no—
75C22×C4×C163—21no—
76C22×C4×C163—21no—
77C22×C4×C163—21no—
78C22×C4×C163—21no—
79C22×C4×C163—21no—
80C22×C4×C163—21no—
81C22×C4×C163—21no—
82C22×C4×C163—21no—
83C22×C4×C163—21no—
84C22×C4×C163—21no—
85C22×C4×C163—21no—
86C22×C4×C163—21no—
87C22×C4×C163—21no—
88C22×C4×C163—21no—
89C22×C4×C163C2×C412yes—
90C22×C4×C163D412yes—
91C22×C4×C163D412yes—
92C22×D163—22no—
93C22×D163—22no—
94C22×D163—22no—
95C22×D163—22no—
96C22×D163—22no—
97C22×D163—22no—
98C22×D163—22no—
99C22×D163—22no—
100C22×D163—22no—
101C22×D163—22no—
102C22×D163—22no—
103C22×D163—22no—
104C22×D163—22no—
105C22×D163—22no—
106C22×D163—22no—
107C22×D163—22no—
108C22×D163—22no—
109C22×D163—22no—
110C22×D163—41no—
111C22×D163—41no—
112C22×D163—41no—
113C22×D163—41no—
114C22×D163—41no—
115C22×D163—41no—
116C22×D163—41no—
117C22×D163—41no—
118C22×D163—41no—
119C22×D163—41no—
120C22×D163—41no—
121C22×D163—41no—
122C22×D163—41no—
123C22×D163—41no—
124C22×D163—41no—
125C22×D163—41no—
126C22×D163C4⋊C414yescomplemented
127C2×Dic163—22no—
128C2×Dic163—22no—
129C2×Dic163—22no—
130C2×Dic163—22no—
131C2×Dic163—22no—
132C2×Dic163—22no—
133C2×Dic163—22no—
134C2×Dic163—22no—
135C2×Dic163—22no—
136C2×Dic163—22no—
137C2×Dic163—22no—
138C2×Dic163—22no—
139C2×Dic163—41no—
140C2×Dic163—41no—
141C2×Dic163—41no—
142C2×Dic163—41no—
143C2×Dic163—41no—
144C2×Dic163—41no—
145C2×Dic163—41no—
146C2×Dic163—41no—
147C2×Dic163C22⋊C414yescomplemented
148C23×C163C22×C411yescharacteristic
149C23×C163C2×D411yescharacteristic
150C23×C163C2×D411yescharacteristic
151C23×C163C2×D411yescharacteristic
152C23×C163C2×D411yescharacteristic
153C23×C163C2×D411yescharacteristic
154C23×C163C2×D411yescharacteristic
155C23×C163C2×D411yescharacteristic
156C23×C163C2×Q811yescharacteristic
157C23×C163#4111yescharacteristic
158C23×C163#4111yescharacteristic
159C23×C163#4111yescharacteristic
160C23×C163#4111yescharacteristic
161C23×C163#4111yescharacteristic
162C23×C163#4111yescharacteristic
163C2×C4×C163—22no—
164C2×C4×C163—22no—
165C2×C4×C163—22no—
166C2×C4×C163—22no—
167C2×C4×C163—22no—
168C2×C4×C163—22no—
169C2×C4×C163—22no—
170C2×C4×C163—22no—
171C2×C4×C163—22no—
172C2×C4×C163—41no—
173C2×C4×C163—41no—
174C2×C4×C163—41no—
175C2×C4×C163—41no—
176C2×C4×C163—41no—
177C2×C4×C163—41no—
178C2×C4×C163—41no—
179C2×C4×C163—41no—
180C2×C4×C163—41no—
181C2×C4×C163—41no—
182C2×C4×C163—41no—
183C2×C4×C163—41no—
184C22×C163C2×C22⋊C411yescharacteristic
185C22×C163C2×C4⋊C411yescharacteristic
186C22×C163#11711yescharacteristic
187C22×C163C4×D411yescharacteristic
188C22×C163C4×D411yescharacteristic
189C22×C163C4×D411yescharacteristic
190C22×C163C4×D411yescharacteristic
191C22×C163#12011yescharacteristic
192C22×C163#12011yescharacteristic
193C22×C163#12011yescharacteristic
194C22×C163#12111yescharacteristic
195C22×C163#12111yescharacteristic
196C22×C163#12111yescharacteristic
197C22×C163#12111yescharacteristic
198C22×C163#12111yescharacteristic
199C22×C163#12111yescharacteristic
200C22×C163#12111yescharacteristic
201C22×C163#12111yescharacteristic
202C22×C163C22⋊Q811yescharacteristic
203C22×C163C22⋊Q811yescharacteristic
204C22×C163C22⋊Q811yescharacteristic
205C22×C163C22⋊Q811yescharacteristic
206C22×C163C22⋊Q811yescharacteristic
207C22×C163C22⋊Q811yescharacteristic
208C22×C163#12311yescharacteristic
209C22×C163#12311yescharacteristic
210C22×C163#12311yescharacteristic
211C22×C163#12311yescharacteristic
212C22×C163#12311yescharacteristic
213C22×C163#12411yescharacteristic
214C22×C163#12411yescharacteristic
215C22×C163#12411yescharacteristic
216C22×C163#12611yescharacteristic
217C22×C163#12611yescharacteristic
218C22×C163#12711yescharacteristic
219C2×D163—24no—
220C2×D163—24no—
221C2×D163—24no—
222C2×D163—42no—
223C2×D163—42no—
224C2×D163—42no—
225C2×D163—42no—
226C2×D163—42no—
227C2×D163—42no—
228C2×D163—42no—
229C2×D163—42no—
230C2×D163—42no—
231C2×D163—42no—
232C2×D163—42no—
233C2×D163—42no—
234C4×C163—42no—
235C4×C163—42no—
236C4×C163—42no—
237Dic163—24no—
238Dic163—42no—
239Dic163—42no—
240C2×C163#38011yescharacteristic
241C2×C163#38511yescharacteristic
242C2×C163#38511yescharacteristic
243C2×C163#38611yescharacteristic
244C2×C163#38811yescharacteristic
245C2×C163#38811yescharacteristic
246C2×C163#39011yescharacteristic
247C2×C163#39211yescharacteristic
248C2×C163#39311yescharacteristic
249C2×C163#39411yescharacteristic
250C2×C163#39411yescharacteristic
251C2×C163#39611yescharacteristic
252C2×C163#39611yescharacteristic
253C2×C163#39711yescharacteristic
254C2×C163#39911yescharacteristic
255D163—44no—
256C163#143911yescharacteristic, complemented, Sylow
257#1439—1631nomaximal, Sylow
258C22×C4⋊C4—1631no—
259C22×C22⋊C4—1631no—
260C22×C22⋊C4—1631no—
261C22×C22⋊C4—1631no—
262C2×#95—1631no—
263C2×#95—1631no—
264C2×#95D16311yescharacteristic, complemented
265C25—1631no—
266C23×C4—1631no—
267C23×C4—1631no—
268C23×C4—1631no—
269C23×C4C2×D16311yescharacteristic
270C23×C4C2×D16311yescharacteristic
271C23×C4C2×D16311yescharacteristic
272C2×C4⋊C4—3262no—
273C2×C4⋊C4—3262no—
274C2×C4⋊C4—3262no—
275C2×C22⋊C4—3262no—
276C2×C22⋊C4—3262no—
277C2×C22⋊C4—3262no—
278C2×C22⋊C4—3262no—
279C2×C22⋊C4—3262no—
280C2×C22⋊C4—3262no—
281C2×C22⋊C4—3262no—
282C2×C22⋊C4—3262no—
283C2×C22⋊C4—1634no—
284#95—22no—
285#95—3262no—
286#95—3262no—
287C24—3261no—
288C24—3261no—
289C24—3261no—
290C24—3261no—
291C24—3261no—
292C24—3261no—
293C24—3261no—
294C24—3261no—
295C24—3261no—
296C24—3261no—
297C24—3261no—
298C24—3261no—
299C24—1632no—
300C24—1632no—
301C24—1632no—
302C24C22×D16311yescharacteristic
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—3261no—
322C22×C4—3261no—
323C22×C4—3261no—
324C22×C4—3261no—
325C22×C4—3261no—
326C22×C4—3261no—
327C22×C4—3261no—
328C22×C4—3261no—
329C22×C4—3261no—
330C22×C4—3261no—
331C22×C4—3261no—
332C22×C4—3261no—
333C22×C4—3261no—
334C22×C4—3261no—
335C22×C4—3261no—
336C22×C4—3261no—
337C22×C4—1632no—
338C22×C4—1632no—
339C22×C4—1632no—
340C22×C4—1632no—
341C22×C4—1632no—
342C22×C4C4×D16312yes—
343C22×C4C22⋊D16312yes—
344C22×C4D65212yes—
345C4⋊C4—3268no—
346C22⋊C4—3268no—
347C22⋊C4—3268no—
348C22⋊C4—3268no—
349C23—3262no—
350C23—3262no—
351C23—3262no—
352C23—3262no—
353C23—3262no—
354C23—3262no—
355C23—3262no—
356C23—3262no—
357C23—3262no—
358C23—3262no—
359C23—3262no—
360C23—3262no—
361C23—3262no—
362C23—3262no—
363C23—3262no—
364C23—3262no—
365C23—3262no—
366C23—3262no—
367C23—6521no—
368C23—6521no—
369C23—6521no—
370C23—6521no—
371C23—6521no—
372C23—6521no—
373C23—6521no—
374C23—6521no—
375C23—6521no—
376C23—6521no—
377C23—6521no—
378C23—6521no—
379C23—6521no—
380C23—6521no—
381C23—6521no—
382C23—6521no—
383C23—1634no—
384C23C2×C4×D16311yescharacteristic
385C23D4×D16311yescharacteristic
386C23D4×D16311yescharacteristic
387C23D4×D16311yescharacteristic
388C23D4×D16311yescharacteristic
389C23D4×D16311yescharacteristic
390C23C2×C22⋊D16311yescharacteristic
391C23C2×D65211yescharacteristic
392C23Q8×D16311yescharacteristic
393C23#1457969811yescharacteristic
394C23#1457969911yescharacteristic
395C23#1457969911yescharacteristic
396C23#1457969911yescharacteristic
397C23#1457969911yescharacteristic
398C23#1457970011yescharacteristic
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—3262no—
421C2×C4—3262no—
422C2×C4—3262no—
423C2×C4—3262no—
424C2×C4—3262no—
425C2×C4—3262no—
426C2×C4—3262no—
427C2×C4—3262no—
428C2×C4—3262no—
429C2×C4—3262no—
430C2×C4—3262no—
431C2×C4—3262no—
432C2×C4—6521no—
433C2×C4—6521no—
434C2×C4—6521no—
435C2×C4—6521no—
436C2×C4—6521no—
437C2×C4—6521no—
438C2×C4—6521no—
439C2×C4—6521no—
440C2×C4—1634no—
441C22—3264no—
442C22—3264no—
443C22—3264no—
444C22—6522no—
445C22—6522no—
446C22—6522no—
447C22—6522no—
448C22—6522no—
449C22—6522no—
450C22—6522no—
451C22—6522no—
452C22—6522no—
453C22—6522no—
454C22—6522no—
455C22—6522no—
456C22C22⋊C4×D16311yescharacteristic
457C22C4⋊C4×D16311yescharacteristic
458C22#1910469211yescharacteristic
459C22(C22⋊D163)⋊C411yescharacteristic
460C22C4×C22⋊D16311yescharacteristic
461C22#1910469711yescharacteristic
462C22C4×D65211yescharacteristic
463C22#1910470311yescharacteristic
464C22#1910470511yescharacteristic
465C22#1910470511yescharacteristic
466C22#1910470711yescharacteristic
467C22#1910470811yescharacteristic
468C22#1910470811yescharacteristic
469C22#1910470811yescharacteristic
470C22#1910470811yescharacteristic
471C22#1910470811yescharacteristic
472C22#1910470911yescharacteristic
473C22#1910471011yescharacteristic
474C22#1910471111yescharacteristic
475C22#1910471311yescharacteristic
476C22#1910471311yescharacteristic
477C22#1910471311yescharacteristic
478C22#1910471311yescharacteristic
479C22#1910471511yescharacteristic
480C22#1910471711yescharacteristic
481C22#1910471811yescharacteristic
482C22#1910472011yescharacteristic
483C22#1910472011yescharacteristic
484C22#1910472011yescharacteristic
485C22#1910472111yescharacteristic
486C22#1910472111yescharacteristic
487C22#1910472311yescharacteristic
488C22#1910472911yescharacteristic
489C22#1910473011yescharacteristic
490C22#1910473111yescharacteristic
491C4—42no—
492C4—42no—
493C4—42no—
494C4—3264no—
495C4—6522no—
496C4—6522no—
497C2—6524no—
498C2#2378152411yescharacteristic
499C2#2378153611yescharacteristic
500C2#2378153911yescharacteristic
501C2#2378154311yescharacteristic
502C2#2378155411yescharacteristic
503C2#2378155611yescharacteristic
504C2#2378156511yescharacteristic
505C2#2378157411yescharacteristic
506C2#2378157811yescharacteristic
507C2#2378158011yescharacteristic
508C2#2378158311yescharacteristic
509C2#2378158711yescharacteristic
510C2#2378158911yescharacteristic
511C2#2378159411yescharacteristic
512C2#2378160011yescharacteristic
subgroupG/H
center, FrattiniC24C22×D163
commutatorC23×C163C22×C4
FittingC2×#95×C163C2
socle, cosocleC24×C163C23
prime radicalC24×D163C22
hypercenterC2×#95D163
hypocenterC163#1439
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C22×Dic163⋊C4C2semidirect
5. C2×C163⋊#95C2semidirect
6. C2×C163⋊#95C2semidirect
7. C2×#95×C163C2semidirect
23. C2×(C2×D163)⋊C4C4semidirect
126. C22×D163C4⋊C4semidirect
147. C2×Dic163C22⋊C4semidirect
256. C163#1439semidirect
264. C2×#95D163semidirect

Maximal subgroups

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

subgroupindex
C22×Dic163⋊C42
C22×(C2×D163)⋊C42
C2×C163⋊#952
C2×#95×C1632
#1439163