Finite Group Databasebeta

← #387×D163 #35216956

Subgroups — #387×D163 #35216956

Order 20864.

712 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D163C211yesmaximal, characteristic
2C2×C4⋊C4×D163C211yesmaximal, characteristic
3C2×C42×D163C211yesmaximal, characteristic
4#23781552C211yesmaximal, characteristic, complemented
5#23781551C211yesmaximal, characteristic, complemented
6#23781550C211yesmaximal, characteristic, complemented
7#23781549C211yesmaximal, characteristic, complemented
8#23781548C211yesmaximal, characteristic, complemented
9#23781547C211yesmaximal, characteristic, complemented
10#23781546C211yesmaximal, characteristic, complemented
11#95×D163C211yesmaximal, characteristic
12#95×D163C211yesmaximal, characteristic
13#95×D163C211yesmaximal, characteristic
14#95×D163C211yesmaximal, characteristic
15#387×C163C211yesmaximal, characteristic, complemented
16C22×C4×D163C2211yescharacteristic
17C22×C4×D163C2211yescharacteristic
18C22×C4×D163C2211yescharacteristic
19C22×C4×D163C2211yescharacteristic
20C22×C4×D163C2211yescharacteristic
21C22×C4×D163C2211yescharacteristic
22C22×C4×D163C2211yescharacteristic
23C2×C4⋊Dic163C2211yescharacteristic
24C2×C4⋊Dic163C2211yescharacteristic
25C2×Dic163⋊C4C2211yescharacteristic
26C2×Dic163⋊C4C2211yescharacteristic
27C2×Dic163⋊C4C2211yescharacteristic
28C2×Dic163⋊C4C2211yescharacteristic
29C4⋊C4×D163—24no—
30C4⋊C4×D163C418yescomplemented
31C2×C4×Dic163C2211yescharacteristic
32C2×C4×Dic163C2211yescharacteristic
33C2×C4×Dic163C2211yescharacteristic
34C42×D163—24no—
35C163⋊#95C2211yescharacteristic
36C163⋊#95C2211yescharacteristic
37C163⋊#95C2211yescharacteristic
38C163⋊#95C2211yescharacteristic
39C163⋊#95C2211yescharacteristic
40C163⋊#95C2211yescharacteristic
41C163⋊#95C2211yescharacteristic
42C163⋊#95C2211yescharacteristic
43C163⋊#95C2211yescharacteristic
44C163⋊#95C2211yescharacteristic
45C163⋊#95C2211yescharacteristic
46C163⋊#95C2211yescharacteristic
47C2×C4⋊C4×C163C2211yescharacteristic
48C2×C4⋊C4×C163C2211yescharacteristic
49C2×C42×C163C2211yescharacteristic
50#95×C163C2211yescharacteristic
51#95×C163C2211yescharacteristic
52#95×C163C2211yescharacteristic
53#95×C163C2211yescharacteristic
54C23×D163C2311yescharacteristic
55C22×Dic163C2311yescharacteristic
56C22×Dic163C2311yescharacteristic
57C22×Dic163C2311yescharacteristic
58C22×Dic163C2311yescharacteristic
59C22×Dic163C2311yescharacteristic
60C22×Dic163C2311yescharacteristic
61C22×Dic163C2311yescharacteristic
62C2×C4×D163—22no—
63C2×C4×D163—22no—
64C2×C4×D163—22no—
65C2×C4×D163—22no—
66C2×C4×D163—22no—
67C2×C4×D163—22no—
68C2×C4×D163—22no—
69C2×C4×D163—22no—
70C2×C4×D163—22no—
71C2×C4×D163—22no—
72C2×C4×D163—22no—
73C2×C4×D163—22no—
74C2×C4×D163—22no—
75C2×C4×D163—22no—
76C2×C4×D163—22no—
77C2×C4×D163—22no—
78C2×C4×D163C2×C414yes—
79C2×C4×D163C2×C414yes—
80C2×C4×D163C2×C414yes—
81C2×C4×D163D414yes—
82C2×C4×D163Q814yes—
83C4⋊Dic163—22no—
84C4⋊Dic163C2×C414yescomplemented
85Dic163⋊C4—22no—
86Dic163⋊C4—22no—
87Dic163⋊C4C2×C414yescomplemented
88Dic163⋊C4C2×C414yescomplemented
89C4×Dic163—22no—
90C4×Dic163—22no—
91C4×Dic163—22no—
92C22×C4×C163C2311yescharacteristic
93C22×C4×C163C2311yescharacteristic
94C22×C4×C163C2311yescharacteristic
95C22×C4×C163C2311yescharacteristic
96C22×C4×C163C2311yescharacteristic
97C22×C4×C163C2311yescharacteristic
98C22×C4×C163C2311yescharacteristic
99C4⋊C4×C163—22no—
100C4⋊C4×C163C2×C414yescomplemented
101C42×C163—22no—
102C22×D163C22×C412yes—
103C22×D163C2×D412yes—
104C22×D163C2×Q812yes—
105C22×D163#4112yes—
106C22×D163#4112yes—
107C22×D163#4112yes—
108C22×D163#4112yes—
109C2×Dic163—21no—
110C2×Dic163—21no—
111C2×Dic163—21no—
112C2×Dic163—21no—
113C2×Dic163—21no—
114C2×Dic163—21no—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163—21no—
118C2×Dic163—21no—
119C2×Dic163—21no—
120C2×Dic163—21no—
121C2×Dic163—21no—
122C2×Dic163—21no—
123C2×Dic163—21no—
124C2×Dic163—21no—
125C2×Dic163C22×C412yes—
126C2×Dic163C22×C412yes—
127C2×Dic163C22×C412yes—
128C2×Dic163C2×D412yes—
129C2×Dic163C2×Q812yes—
130C4×D163—28no—
131C4×D163—28no—
132C4×D163—28no—
133C4×D163—28no—
134C4×D163—28no—
135C4×D163—44no—
136C4×D163—44no—
137C23×C163C2411yescharacteristic
138C2×C4×C163—21no—
139C2×C4×C163—21no—
140C2×C4×C163—21no—
141C2×C4×C163—21no—
142C2×C4×C163—21no—
143C2×C4×C163—21no—
144C2×C4×C163—21no—
145C2×C4×C163—21no—
146C2×C4×C163—21no—
147C2×C4×C163—21no—
148C2×C4×C163—21no—
149C2×C4×C163—21no—
150C2×C4×C163—21no—
151C2×C4×C163—21no—
152C2×C4×C163—21no—
153C2×C4×C163—21no—
154C2×C4×C163C22×C412yes—
155C2×C4×C163C22×C412yes—
156C2×C4×C163C22×C412yes—
157C2×C4×C163C2×D412yes—
158C2×C4×C163C2×Q812yes—
159C22×C163C23×C411yescharacteristic
160C22×C163C22×D411yescharacteristic
161C22×C163C22×Q811yescharacteristic
162C22×C163C2×#4111yescharacteristic
163C22×C163C2×#4111yescharacteristic
164C22×C163C2×#4111yescharacteristic
165C22×C163C2×#4111yescharacteristic
166C2×D163#11714yes—
167C2×D163C4×D414yes—
168C2×D163C4×Q814yes—
169C2×D163C22⋊Q814yes—
170C2×D163#12314yes—
171C2×D163#12514yes—
172C2×D163#12614yes—
173C4×C163—22no—
174C4×C163—22no—
175C4×C163—22no—
176C4×C163—22no—
177C4×C163—22no—
178C4×C163—41no—
179C4×C163—41no—
180Dic163—22no—
181Dic163—22no—
182Dic163—22no—
183Dic163—22no—
184Dic163—22no—
185Dic163—41no—
186Dic163—41no—
187C2×C163C2×#11711yescharacteristic
188C2×C163C2×C4×D411yescharacteristic
189C2×C163C2×C4×Q811yescharacteristic
190C2×C163C2×C22⋊Q811yescharacteristic
191C2×C163C2×#12311yescharacteristic
192C2×C163C2×#12511yescharacteristic
193C2×C163C2×#12611yescharacteristic
194D163#38718yesdirect product factor
195C163C2×#38711yescharacteristic, complemented, Sylow
196C2×#387—1631nomaximal, Sylow
197C22×C4⋊C4—1631no—
198C22×C4⋊C4—1631no—
199C22×C42—1631no—
200#387—1631no—
201#387—1631no—
202#387—1631no—
203#387—1631no—
204#387—1631no—
205#387—1631no—
206#387—1631no—
207#387D16311yescharacteristic, direct product factor
208C2×#95—1631no—
209C2×#95—1631no—
210C2×#95—1631no—
211C2×#95—1631no—
212C23×C4—1631no—
213C23×C4—1631no—
214C23×C4—1631no—
215C23×C4—1631no—
216C23×C4—1631no—
217C23×C4—1631no—
218C23×C4—1631no—
219C2×C4⋊C4—3264no—
220C2×C4⋊C4—1631no—
221C2×C4⋊C4—1631no—
222C2×C4⋊C4—1631no—
223C2×C4⋊C4—1631no—
224C2×C4⋊C4—1631no—
225C2×C4⋊C4—1631no—
226C2×C4⋊C4—1638no—
227C2×C4⋊C4C2×D16311yescharacteristic
228C2×C4⋊C4C2×D16311yescharacteristic
229C2×C42—3264no—
230C2×C42—1631no—
231C2×C42—1631no—
232C2×C42—1631no—
233C2×C42C2×D16311yescharacteristic
234#95—1631no—
235#95—1631no—
236#95—1631no—
237#95—1631no—
238#95—1631no—
239#95—1631no—
240#95—1631no—
241#95—1631no—
242#95—1631no—
243#95—1631no—
244#95—1631no—
245#95—1631no—
246#95C2×D16311yescharacteristic
247#95C2×D16311yescharacteristic
248#95C2×D16311yescharacteristic
249#95C2×D16311yescharacteristic
250C24—1631no—
251C22×C4—3262no—
252C22×C4—3262no—
253C22×C4—3262no—
254C22×C4—3262no—
255C22×C4—3262no—
256C22×C4—3262no—
257C22×C4—3262no—
258C22×C4—3262no—
259C22×C4—3262no—
260C22×C4—3262no—
261C22×C4—3262no—
262C22×C4—3262no—
263C22×C4—3262no—
264C22×C4—3262no—
265C22×C4—3262no—
266C22×C4—3262no—
267C22×C4—1631no—
268C22×C4—1631no—
269C22×C4—1631no—
270C22×C4—1631no—
271C22×C4—1631no—
272C22×C4—1631no—
273C22×C4—1631no—
274C22×C4—1634no—
275C22×C4—1634no—
276C22×C4—1634no—
277C22×C4—1634no—
278C22×C4—1634no—
279C22×C4C22×D16311yescharacteristic
280C22×C4C22×D16311yescharacteristic
281C22×C4C22×D16311yescharacteristic
282C22×C4C22×D16311yescharacteristic
283C22×C4C22×D16311yescharacteristic
284C22×C4C22×D16311yescharacteristic
285C22×C4C22×D16311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—3262no—
288C4⋊C4—3262no—
289C4⋊C4—3262no—
290C4⋊C4—1634no—
291C4⋊C4—1634no—
292C4⋊C4—1634no—
293C4⋊C4C4×D16314yescomplemented
294C42—22no—
295C42—3262no—
296C42—3262no—
297C42—3262no—
298C23—1632no—
299C23—1632no—
300C23—1632no—
301C23—1632no—
302C23—1632no—
303C23—1632no—
304C23—1632no—
305C23C23×D16311yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3268no—
323C2×C4—3268no—
324C2×C4—3268no—
325C2×C4—3268no—
326C2×C4—3268no—
327C2×C4—3261no—
328C2×C4—3261no—
329C2×C4—3261no—
330C2×C4—3261no—
331C2×C4—3261no—
332C2×C4—3261no—
333C2×C4—3261no—
334C2×C4—3261no—
335C2×C4—3261no—
336C2×C4—3261no—
337C2×C4—3261no—
338C2×C4—3261no—
339C2×C4—3261no—
340C2×C4—3261no—
341C2×C4—3261no—
342C2×C4—3261no—
343C2×C4—6524no—
344C2×C4—6524no—
345C2×C4—1632no—
346C2×C4—1632no—
347C2×C4—1632no—
348C2×C4—1632no—
349C2×C4—1632no—
350C2×C4C2×C4×D16312yes—
351C2×C4C2×C4×D16312yes—
352C2×C4C2×C4×D16312yes—
353C2×C4D4×D16312yes—
354C2×C4Q8×D16312yes—
355C22—1634no—
356C22—1634no—
357C22—1634no—
358C22—1634no—
359C22—1634no—
360C22—1634no—
361C22—1634no—
362C22C22×C4×D16311yescharacteristic
363C22C2×D4×D16311yescharacteristic
364C22C2×Q8×D16311yescharacteristic
365C22#41×D16311yescharacteristic
366C22#41×D16311yescharacteristic
367C22#41×D16311yescharacteristic
368C22#41×D16311yescharacteristic
369C4—22no—
370C4—22no—
371C4—22no—
372C4—22no—
373C4—22no—
374C4—41no—
375C4—41no—
376C4—3262no—
377C4—3262no—
378C4—3262no—
379C4—3262no—
380C4—3262no—
381C4—6521no—
382C4—6521no—
383C2—1638no—
384C2#117×D16311yescharacteristic
385C2C4×D4×D16311yescharacteristic
386C2C4×Q8×D16311yescharacteristic
387C2C22⋊Q8×D16311yescharacteristic
388C2#123×D16311yescharacteristic
389C2#125×D16311yescharacteristic
390C2#126×D16311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D163
commutatorC22×C163C23×C4
Fitting#387×C163C2
socle, cosocleC23×C163C24
prime radicalC23×D163C23
hypercenter#387D163
hypocenterC163C2×#387
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #23781552C2semidirect
5. #23781551C2semidirect
6. #23781550C2semidirect
7. #23781549C2semidirect
8. #23781548C2semidirect
9. #23781547C2semidirect
10. #23781546C2semidirect
15. #387×C163C2semidirect
30. C4⋊C4×D163C4semidirect
84. C4⋊Dic163C2×C4semidirect
87. Dic163⋊C4C2×C4semidirect
88. Dic163⋊C4C2×C4semidirect
100. C4⋊C4×C163C2×C4semidirect
194. D163#387direct (N × H)
195. C163C2×#387semidirect
207. #387D163direct (N × H)
293. C4⋊C4C4×D163semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1632
C2×C42×D1632
#237815522
#237815512
#237815502
#237815492
#237815482
#237815472
#237815462
#95×D1632
#387×C1632
C2×#387163