Finite Group Databasebeta

← #35223277

Subgroups — #35223277

Order 20864.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19104743C211yesmaximal, characteristic, complemented
2C2×#19104741C211yesmaximal, characteristic, complemented
3#23782212C211yesmaximal, characteristic
4#23781741C211yesmaximal, characteristic, complemented
5#23781740C211yesmaximal, characteristic, complemented
6#23781738C211yesmaximal, characteristic, complemented
7#23781737C211yesmaximal, characteristic, complemented
8#23781735C211yesmaximal, characteristic, complemented
9C8×C22⋊D163C211yesmaximal, characteristic, complemented
10(C22⋊D163)⋊C8C211yesmaximal, characteristic, complemented
11C4⋊C8×D163C211yesmaximal, characteristic, complemented
12#23781630C211yesmaximal, characteristic, complemented
13#23781630C211yesmaximal, characteristic, complemented
14#23781617C211yesmaximal, characteristic, complemented
15#435×C163C211yesmaximal, characteristic, complemented
16C2×#14579699C2211yescharacteristic
17C2×#14579699C2211yescharacteristic
18#19104743—24no—
19#19104741—24no—
20C2×#14579683C2211yescharacteristic
21C2×#14579682C2211yescharacteristic
22C2×#14579682C2211yescharacteristic
23C2×#14579682C2211yescharacteristic
24C2×#14579682C2211yescharacteristic
25C22×C163⋊C8C2211yescharacteristic
26C2×C8×D163C2211yescharacteristic
27C2×C8×D163C2211yescharacteristic
28C2×C8×D163C2211yescharacteristic
29C2×C8×D163C2211yescharacteristic
30#19104734C411yescharacteristic
31#19104731C411yescharacteristic
32#19104721C411yescharacteristic
33#19104721C411yescharacteristic
34#19104710C411yescharacteristic
35#19104708C411yescharacteristic
36#19104708C411yescharacteristic
37#19104706C411yescharacteristic
38C4×D652C2211yescharacteristic
39C4×C22⋊D163C2211yescharacteristic
40C4×C22⋊D163C2211yescharacteristic
41C42×D163C2211yescharacteristic
42C4⋊(C163⋊C8)C2211yescharacteristic
43Dic163⋊C8C2211yescharacteristic
44Dic163⋊C8C2211yescharacteristic
45C22⋊(C163⋊C8)C2211yescharacteristic
46C22⋊(C163⋊C8)C2211yescharacteristic
47(C2×D163)⋊C8C2211yescharacteristic
48(C2×D163)⋊C8C2211yescharacteristic
49(C2×D163)⋊C8C2211yescharacteristic
50(C2×D163)⋊C8C2211yescharacteristic
51#19104646C2211yescharacteristic
52C8×Dic163C2211yescharacteristic
53C8×Dic163C2211yescharacteristic
54C2×M16×C163C2211yescharacteristic
55C22×C8×C163C2211yescharacteristic
56C4×D4×C163C2211yescharacteristic
57C4⋊C8×C163C2211yescharacteristic
58C22⋊C8×C163C2211yescharacteristic
59C22⋊C8×C163C2211yescharacteristic
60#97×C163C2211yescharacteristic
61#14579699—22no—
62#14579699—22no—
63#14579699—22no—
64#14579699—22no—
65C2×Dic326C2×C411yescharacteristic
66C2×Dic326C2×C411yescharacteristic
67C2×D652C2×C411yescharacteristic
68C2×D652C2×C411yescharacteristic
69C2×D652C2×C411yescharacteristic
70C2×C22⋊D163C2×C411yescharacteristic
71C2×C22⋊D163C2×C411yescharacteristic
72C2×C22⋊D163C2×C411yescharacteristic
73C2×C22⋊D163C2×C411yescharacteristic
74C2×C22⋊D163C2×C411yescharacteristic
75C2×C22⋊D163C2×C411yescharacteristic
76C2×C4×D163C2×C411yescharacteristic
77C2×C4×D163C2×C411yescharacteristic
78C2×C4×D163C2311yescharacteristic
79C2×C4×D163C2311yescharacteristic
80C2×C4×D163C2311yescharacteristic
81#14579683—22no—
82#14579682—22no—
83#14579682—22no—
84#14579682—22no—
85#14579682D414yescomplemented
86C2×C163⋊C8—22no—
87C2×C163⋊C8C2311yescharacteristic
88C2×C163⋊C8C2311yescharacteristic
89C2×C163⋊C8C2311yescharacteristic
90C2×C163⋊C8C2311yescharacteristic
91C8×D163—22no—
92C8×D163—22no—
93C8×D163—22no—
94C8×D163—22no—
95C4⋊Dic163C2×C411yescharacteristic
96Dic163⋊C4C2×C411yescharacteristic
97Dic163⋊C4C2×C411yescharacteristic
98C22⋊Dic163C2×C411yescharacteristic
99C22⋊Dic163C2×C411yescharacteristic
100(C2×D163)⋊C4C2×C411yescharacteristic
101(C2×D163)⋊C4C2×C411yescharacteristic
102(C2×D163)⋊C4C2×C411yescharacteristic
103(C2×D163)⋊C4C2×C411yescharacteristic
104C4×Dic163C2×C411yescharacteristic
105C4×Dic163C2×C411yescharacteristic
106C4×Dic163C2311yescharacteristic
107C2×D4×C163C2×C411yescharacteristic
108C22×C4×C163C2311yescharacteristic
109C22×C4×C163C2311yescharacteristic
110M16×C163—22no—
111C2×C8×C163—22no—
112C2×C8×C163C2311yescharacteristic
113C2×C8×C163C2311yescharacteristic
114C2×C8×C163C2311yescharacteristic
115C2×C8×C163C2311yescharacteristic
116C4⋊C4×C163C2×C411yescharacteristic
117C22⋊C4×C163C2×C411yescharacteristic
118C22⋊C4×C163C2×C411yescharacteristic
119C42×C163C2311yescharacteristic
120C22×D163C22×C411yescharacteristic
121C22×D163C22×C411yescharacteristic
122C22×D163C22×C411yescharacteristic
123Dic326—22no—
124Dic326—22no—
125D652—22no—
126D652—22no—
127D652—41no—
128C22⋊D163—22no—
129C22⋊D163—22no—
130C22⋊D163—22no—
131C22⋊D163—22no—
132C22⋊D163—22no—
133C22⋊D163—22no—
134C2×Dic163C22×C411yescharacteristic
135C2×Dic163C22×C411yescharacteristic
136C2×Dic163C22×C411yescharacteristic
137C2×Dic163C22×C411yescharacteristic
138C2×Dic163C22×C411yescharacteristic
139C4×D163—21no—
140C4×D163—21no—
141C4×D163—21no—
142C4×D163—21no—
143C4×D163—22no—
144C4×D163—41no—
145C4×D163C2×D412yes—
146C4×D163#4112yes—
147C163⋊C8—21no—
148C163⋊C8—21no—
149C163⋊C8—21no—
150C163⋊C8C2×D412yes—
151C23×C163C22×C411yescharacteristic
152C23×C163C22×C411yescharacteristic
153D4×C163—41no—
154C2×C4×C163—21no—
155C2×C4×C163—21no—
156C2×C4×C163—21no—
157C2×C4×C163—21no—
158C2×C4×C163C22×C411yescharacteristic
159C2×C4×C163C22×C411yescharacteristic
160C2×C4×C163C22×C411yescharacteristic
161C2×C4×C163C22×C411yescharacteristic
162C2×C4×C163C2411yescharacteristic
163C8×C163—21no—
164C8×C163—21no—
165C8×C163—21no—
166C8×C163C2×D412yes—
167C22×C163—21no—
168C22×C163—21no—
169C22×C163—21no—
170C22×C163—21no—
171C22×C163—21no—
172C22×C163—21no—
173C22×C163C23×C411yescharacteristic
174C2×D163—21no—
175C2×D163—21no—
176C2×D163—21no—
177C2×D163—21no—
178C2×D163—21no—
179C2×D163—21no—
180C2×D163—21no—
181C2×D163—21no—
182C2×D163C4×D412yes—
183C4×C163—21no—
184C4×C163—21no—
185C4×C163—21no—
186C4×C163—21no—
187C4×C163C22×D411yescharacteristic
188C4×C163C2×#4111yescharacteristic
189Dic163—21no—
190Dic163—21no—
191Dic163—21no—
192Dic163C4×D412yes—
193Dic163#13112yescomplemented
194C2×C163—41no—
195C2×C163—41no—
196C2×C163C2×C4×D411yescharacteristic
197C2×C163C2×#13111yescharacteristic
198C2×C163#56811yescharacteristic
199D163—22no—
200D163—41no—
201D163—41no—
202C163#293511yescharacteristic, complemented, Sylow
203#2935—1631nomaximal, Sylow
204C2×#131—1631no—
205C2×#131—1631no—
206#532—1631no—
207#436—1631no—
208#436—1631no—
209#435—1631no—
210#435—1631no—
211#435—1631no—
212#435D16311yescharacteristic, complemented
213C8×D4—1631no—
214C8×D4—1631no—
215C2×C4⋊C8—1631no—
216#408—1631no—
217#408—1631no—
218C4×M16—1631no—
219C2×#41—1631no—
220C2×#41—1631no—
221#131—3264no—
222#131—3264no—
223C2×M16—1631no—
224C2×M16—1631no—
225C2×M16—1631no—
226C2×M16—1631no—
227C2×M16—1631no—
228C2×M16C2×D16311yescharacteristic
229C22×C8—1631no—
230C22×C8—1631no—
231C22×C8—1631no—
232C22×C8—1631no—
233C22×C8—1631no—
234C22×C8C2×D16311yescharacteristic
235C4⋊Q8—1631no—
236#127—1631no—
237#124—1631no—
238#124—1631no—
239#121—1631no—
240#121—1631no—
241#121—1631no—
242#121—1631no—
243C4×D4—1631no—
244C4×D4—1631no—
245C4×D4—1631no—
246C4×D4C2×D16311yescharacteristic
247C2×C42—1631no—
248C4⋊C8—1631no—
249C4⋊C8—1631no—
250C4⋊C8—1631no—
251C4⋊C8C2×D16311yescharacteristic
252C22⋊C8—1631no—
253C22⋊C8—1631no—
254C22⋊C8—1631no—
255C22⋊C8—1631no—
256C22⋊C8—1631no—
257C22⋊C8—1631no—
258C22⋊C8C2×D16311yescharacteristic
259C22⋊C8C2×D16311yescharacteristic
260#97—1631no—
261#97C2×D16311yescharacteristic
262C4×C8—1631no—
263C4×C8—1631no—
264#41—3262no—
265#41—3262no—
266#41—3262no—
267#41—3262no—
268C2×Q8—1631no—
269C2×Q8—1631no—
270C2×D4—1631no—
271C2×D4—1631no—
272C2×D4—1631no—
273C2×D4—1631no—
274C2×D4—1631no—
275C2×D4—1631no—
276C2×D4—1631no—
277C2×D4—1631no—
278C2×D4—1631no—
279C2×D4C4×D16311yescharacteristic
280C22×C4—1631no—
281C22×C4—1631no—
282C22×C4—1631no—
283C22×C4—1631no—
284C22×C4—1631no—
285C22×C4C22×D16311yescharacteristic
286C22×C4C22×D16311yescharacteristic
287M16—22no—
288M16—3262no—
289M16—3262no—
290M16—3262no—
291M16—3262no—
292M16—1634no—
293C2×C8—22no—
294C2×C8—3262no—
295C2×C8—3262no—
296C2×C8—3262no—
297C2×C8—3262no—
298C2×C8—3262no—
299C2×C8—1631no—
300C2×C8—1631no—
301C2×C8—1631no—
302C2×C8—1631no—
303C2×C8C22×D16311yescharacteristic
304C2×C8C22×D16311yescharacteristic
305C2×C8C22×D16311yescharacteristic
306C2×C8C22×D16311yescharacteristic
307C4⋊C4—1631no—
308C4⋊C4—1631no—
309C4⋊C4—1631no—
310C4⋊C4C4×D16311yescharacteristic
311C22⋊C4—1631no—
312C22⋊C4—1631no—
313C22⋊C4—1631no—
314C22⋊C4—1631no—
315C22⋊C4—1631no—
316C22⋊C4—1631no—
317C22⋊C4C4×D16311yescharacteristic
318C22⋊C4C4×D16311yescharacteristic
319C42—1631no—
320C42—1631no—
321C42—1631no—
322C42C22×D16311yescharacteristic
323C23—1631no—
324C23—1631no—
325C23—1631no—
326C23C2×C4×D16311yescharacteristic
327C23C2×C4×D16311yescharacteristic
328Q8—3262no—
329Q8—3262no—
330D4—41no—
331D4—3262no—
332D4—3262no—
333D4—3262no—
334D4—3262no—
335D4—3262no—
336D4—3262no—
337D4—3262no—
338D4—3262no—
339D4—6521no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—3262no—
345C2×C4—3261no—
346C2×C4—3261no—
347C2×C4—3261no—
348C2×C4—3261no—
349C2×C4—6521no—
350C2×C4—1631no—
351C2×C4—1631no—
352C2×C4—1631no—
353C2×C4—1631no—
354C2×C4—1631no—
355C2×C4—1632no—
356C2×C4—1632no—
357C2×C4C2×C4×D16311yescharacteristic
358C2×C4C2×C4×D16311yescharacteristic
359C2×C4C2×C4×D16311yescharacteristic
360C2×C4C2×C4×D16311yescharacteristic
361C2×C4C23×D16311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—3261no—
366C8—3261no—
367C8—3261no—
368C8—1632no—
369C8D4×D16312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—3261no—
377C22—3261no—
378C22—3261no—
379C22—3261no—
380C22—3261no—
381C22—3261no—
382C22—3261no—
383C22—3261no—
384C22—1632no—
385C22C22×C4×D16311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—3261no—
391C4—3261no—
392C4—3261no—
393C4—1632no—
394C4—1632no—
395C4C2×D4×D16311yescharacteristic
396C4#41×D16311yescharacteristic
397C2—41no—
398C2—41no—
399C2—3262no—
400C2—6521no—
401C2—6521no—
402C2C4×D4×D16311yescharacteristic
403C2#131×D16311yescharacteristic
404C2#2378243111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D163
commutator, socleC22×C163C23×C4
Fitting#435×C163C2
prime radical#23782212C2
cosocleC2×C4×C163C24
hypercenter#435D163
hypocenterC163#2935
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#19104743C2semidirect
2. C2×#19104741C2semidirect
4. #23781741C2semidirect
5. #23781740C2semidirect
6. #23781738C2semidirect
7. #23781737C2semidirect
8. #23781735C2semidirect
9. C8×C22⋊D163C2semidirect
10. (C22⋊D163)⋊C8C2semidirect
11. C4⋊C8×D163C2semidirect
12. #23781630C2semidirect
13. #23781630C2semidirect
14. #23781617C2semidirect
15. #435×C163C2semidirect
85. #14579682D4semidirect
193. Dic163#131semidirect
202. C163#2935semidirect
212. #435D163semidirect

Maximal subgroups

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

subgroupindex
C2×#191047432
C2×#191047412
#237822122
#237817412
#237817402
#237817382
#237817372
#237817352
C8×C22⋊D1632
(C22⋊D163)⋊C82
C4⋊C8×D1632
#237816302
#237816172
#435×C1632
#2935163