Finite Group Databasebeta

← C4×#19104764 #35223350

Subgroups — C4×#19104764 #35223350

Order 20864.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19104764C211yesmaximal, characteristic
2C4×#14579698C211yesmaximal, characteristic
3C4×Q8×D163C211yesmaximal, characteristic, complemented
4#23781771C211yesmaximal, characteristic, complemented
5#23781769C211yesmaximal, characteristic, complemented
6#23781766C211yesmaximal, characteristic, complemented
7#23781762C211yesmaximal, characteristic, complemented
8C4×Dic652C211yesmaximal, characteristic, complemented
9C4×#14579689C211yesmaximal, characteristic, complemented
10C4×#14579687C211yesmaximal, characteristic, complemented
11#23781704C211yesmaximal, characteristic, complemented
12#23781672C211yesmaximal, characteristic, complemented
13#23781663C211yesmaximal, characteristic
14C4×#14579682C211yesmaximal, characteristic, complemented
15C4×SD16×C163C211yesmaximal, characteristic, complemented
16C2×#14579698C2211yescharacteristic
17C2×Q8×D163C2211yescharacteristic
18#19104764C418yesdirect product factor
19C2×Dic652C2211yescharacteristic
20C2×#14579689C2211yescharacteristic
21C2×#14579687C2211yescharacteristic
22C2×#14579682C2211yescharacteristic
23C2×#14579682C2211yescharacteristic
24Q8×Dic163C2211yescharacteristic
25C4×Dic326—21no—
26C4×Dic326C2211yescharacteristic
27C4×Dic326C2211yescharacteristic
28#19104700—21no—
29#19104700C2211yescharacteristic
30#19104700C2211yescharacteristic
31D4×Dic163C2211yescharacteristic
32C4×C22⋊D163—21no—
33(C22⋊D163)⋊C4—21no—
34#19104693C2211yescharacteristic
35#19104691—21no—
36C4⋊C4×D163—21no—
37C4⋊C4×D163C2211yescharacteristic
38C2×C4×Dic163—21no—
39C42×D163—21no—
40C42×D163C2211yescharacteristic
41#19104669C2211yescharacteristic
42#19104668C2211yescharacteristic
43#19104666C2211yescharacteristic
44#19104660C2211yescharacteristic
45#19104660C2211yescharacteristic
46#19104659C2211yescharacteristic
47#19104658C2211yescharacteristic
48#19104658C2211yescharacteristic
49#19104656C2211yescharacteristic
50#19104645C2211yescharacteristic
51#19104645C2211yescharacteristic
52C4×C163⋊C8C2211yescharacteristic
53C2×SD16×C163C2211yescharacteristic
54C4×Q8×C163C2211yescharacteristic
55C4×D4×C163C2211yescharacteristic
56#106×C163C2211yescharacteristic
57#103×C163C2211yescharacteristic
58#102×C163C2211yescharacteristic
59C4×C8×C163C2211yescharacteristic
60#14579698—22no—
61#14579698C2×C414yes—
62C2×Dic326—21no—
63C2×Dic326C2311yescharacteristic
64C2×Dic326C2311yescharacteristic
65Q8×D163—22no—
66Q8×D163C2×C414yescomplemented
67C2×C22⋊D163—21no—
68C22×Dic163—21no—
69C22×Dic163—21no—
70C2×C4×D163—21no—
71C2×C4×D163—21no—
72C2×C4×D163D411yescharacteristic
73C2×C4×D163D411yescharacteristic
74C2×C4×D163C2311yescharacteristic
75Dic652C2×C414yescomplemented
76#14579689C2×C414yescomplemented
77#14579687C2×C414yescomplemented
78#14579682—22no—
79#14579682C2×C414yescomplemented
80C2×C163⋊C8C2311yescharacteristic
81C2×C163⋊C8C2311yescharacteristic
82C4⋊Dic163—21no—
83C4⋊Dic163C2311yescharacteristic
84C4⋊Dic163C2311yescharacteristic
85Dic163⋊C4—21no—
86Dic163⋊C4—21no—
87Dic163⋊C4—21no—
88Dic163⋊C4—21no—
89Dic163⋊C4—21no—
90C22⋊Dic163—21no—
91(C2×D163)⋊C4—21no—
92C4×Dic163—21no—
93C4×Dic163—21no—
94C4×Dic163—21no—
95C4×Dic163—21no—
96C4×Dic163—21no—
97C4×Dic163—21no—
98C4×Dic163D411yescharacteristic
99C4×Dic163D411yescharacteristic
100C4×Dic163C2311yescharacteristic
101C2×Q8×C163C2311yescharacteristic
102C2×D4×C163C2311yescharacteristic
103C22×C4×C163—21no—
104SD16×C163C2×C414yescomplemented
105C2×C8×C163C2311yescharacteristic
106C2×C8×C163C2311yescharacteristic
107C4⋊C4×C163—21no—
108C4⋊C4×C163C2311yescharacteristic
109C4⋊C4×C163C2311yescharacteristic
110C22⋊C4×C163—21no—
111C42×C163—21no—
112C42×C163C2311yescharacteristic
113C22×D163C2×D411yescharacteristic
114Dic326—21no—
115Dic326—21no—
116Dic326—24no—
117Dic326C22×C412yes—
118Dic326C22×C412yes—
119C22⋊D163—24no—
120C2×Dic163—21no—
121C2×Dic163—21no—
122C2×Dic163—24no—
123C2×Dic163—21no—
124C2×Dic163—21no—
125C2×Dic163—42no—
126C2×Dic163C2×D411yescharacteristic
127C2×Dic163C2×D411yescharacteristic
128C2×Dic163C2×D411yescharacteristic
129C4×D163—24no—
130C4×D163—22no—
131C4×D163—41no—
132C4×D163—42no—
133C4×D163C22×C412yes—
134C4×D163#4112yes—
135C163⋊C8—21no—
136C163⋊C8C22×C412yes—
137C23×C163—21no—
138Q8×C163—21no—
139Q8×C163C22×C412yes—
140D4×C163—21no—
141D4×C163C22×C412yes—
142C2×C4×C163—21no—
143C2×C4×C163—21no—
144C2×C4×C163—21no—
145C2×C4×C163—42no—
146C2×C4×C163C2×D411yescharacteristic
147C2×C4×C163C2×D411yescharacteristic
148C2×C4×C163C2411yescharacteristic
149C8×C163—21no—
150C8×C163C22×C412yes—
151C22×C163—22no—
152C22×C163—41no—
153C22×C163—41no—
154C22×C163C22×D411yescharacteristic
155C2×D163—21no—
156C2×D163—21no—
157C2×D163C4×D412yes—
158C4×C163—22no—
159C4×C163—21no—
160C4×C163—41no—
161C4×C163—41no—
162C4×C163#13712yescomplemented
163C4×C163C23×C411yescharacteristic
164C4×C163C2×#4111yescharacteristic
165Dic163—22no—
166Dic163—22no—
167Dic163—21no—
168Dic163—21no—
169Dic163—41no—
170Dic163—41no—
171Dic163C4×D412yes—
172C2×C163—42no—
173C2×C163C2×C4×D411yescharacteristic
174C2×C163C2×#13711yescharacteristic
175C2×C163#57511yescharacteristic
176D163—22no—
177C163C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—1631nomaximal, Sylow
179C2×#137—1631no—
180C4×#41—1631no—
181C2×C4×Q8—1631no—
182#441—1631no—
183#441—1631no—
184#440—1631no—
185#440—1631no—
186C4×Q16—1631no—
187C4×Q16—1631no—
188C4×SD16—1631no—
189C4×SD16D16311yescharacteristic, complemented
190#428—1631no—
191#419—1631no—
192#417—1631no—
193C4×M16—1631no—
194C2×#41—1631no—
195C22×Q8—1631no—
196#137—1638no—
197C2×Q16—1631no—
198C2×Q16—1631no—
199C2×SD16—1631no—
200C2×SD16C2×D16311yescharacteristic
201C2×M16—1631no—
202C2×M16—1631no—
203C4×Q8—3261no—
204C4×Q8—3261no—
205C4×Q8—1631no—
206C4×Q8—1631no—
207C4×Q8—1631no—
208C4×Q8—1631no—
209C4×Q8—1631no—
210C4×Q8C2×D16311yescharacteristic
211C4×D4—3261no—
212C4×D4—3261no—
213C4×D4—1631no—
214C4×D4C2×D16311yescharacteristic
215#117—3261no—
216#117—1631no—
217C2×C4⋊C4—3261no—
218C2×C4⋊C4—1631no—
219C2×C42—3261no—
220C2×C42—3261no—
221C2×C42—1631no—
222#107—1631no—
223#107—1631no—
224#106—1631no—
225#106C2×D16311yescharacteristic
226#103—1631no—
227#103—1631no—
228#103—1631no—
229#103—1631no—
230#103—1631no—
231#103C2×D16311yescharacteristic
232#102—1631no—
233#102C2×D16311yescharacteristic
234#97—1631no—
235#97—1631no—
236C4×C8—1631no—
237C4×C8C2×D16311yescharacteristic
238#41—3262no—
239#41—1634no—
240C2×Q8—3261no—
241C2×Q8—3262no—
242C2×Q8—1634no—
243C2×Q8—1631no—
244C2×Q8—1631no—
245C2×Q8C22×D16311yescharacteristic
246C2×D4—3261no—
247C2×D4C22×D16311yescharacteristic
248C22×C4—21no—
249C22×C4—3261no—
250C22×C4—3261no—
251C22×C4—3261no—
252C22×C4—3261no—
253C22×C4—1631no—
254C22×C4—1631no—
255C22×C4—1631no—
256Q16—1634no—
257Q16—1634no—
258SD16—1634no—
259SD16C4×D16314yescomplemented
260M16—3262no—
261M16—1634no—
262C2×C8—1631no—
263C2×C8—1631no—
264C2×C8C22×D16311yescharacteristic
265C2×C8C22×D16311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3261no—
268C4⋊C4—3261no—
269C4⋊C4—3261no—
270C4⋊C4—3261no—
271C4⋊C4—3261no—
272C4⋊C4—3261no—
273C4⋊C4—1631no—
274C4⋊C4—1631no—
275C4⋊C4C22×D16311yescharacteristic
276C4⋊C4C22×D16311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3261no—
279C22⋊C4—3261no—
280C42—21no—
281C42—3261no—
282C42—3261no—
283C42—3261no—
284C42—3261no—
285C42—3261no—
286C42—3261no—
287C42—1631no—
288C42—1631no—
289C42—1631no—
290C42C22×D16311yescharacteristic
291C23—21no—
292C23—1631no—
293Q8—21no—
294Q8—3264no—
295Q8—3261no—
296Q8—3261no—
297Q8—1632no—
298Q8—1632no—
299Q8C2×C4×D16312yes—
300D4—21no—
301D4—3264no—
302D4C2×C4×D16312yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—3264no—
308C2×C4—3261no—
309C2×C4—3261no—
310C2×C4—3264no—
311C2×C4—3262no—
312C2×C4—3261no—
313C2×C4—3261no—
314C2×C4—6521no—
315C2×C4—6522no—
316C2×C4—6522no—
317C2×C4—1631no—
318C2×C4—1631no—
319C2×C4—1631no—
320C2×C4—1632no—
321C2×C4—1632no—
322C2×C4D4×D16311yescharacteristic
323C2×C4D4×D16311yescharacteristic
324C2×C4C23×D16311yescharacteristic
325C8—21no—
326C8—3261no—
327C8—1632no—
328C8C2×C4×D16312yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—3261no—
333C22—3261no—
334C22—1632no—
335C22C2×D4×D16311yescharacteristic
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—3261no—
341C4—3261no—
342C4—3262no—
343C4—3262no—
344C4—6521no—
345C4—6521no—
346C4—1632no—
347C4#1910476412yesdirect product factor
348C4C22×C4×D16311yescharacteristic
349C4#41×D16311yescharacteristic
350C2—42no—
351C2—3262no—
352C2C4×D4×D16311yescharacteristic
353C2C2×#1910476411yescharacteristic
354C2#2378246211yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutatorC4×C163C23×C4
FrattiniC2×C4C23×D163
FittingC4×SD16×C163C2
socleC22×C163C22×D4
prime radicalC2×#14579698C22
cosocleC2×C4×C163C24
hypercenterC4×SD16D163
hypocenterC163C4×#137
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D163C2semidirect
4. #23781771C2semidirect
5. #23781769C2semidirect
6. #23781766C2semidirect
7. #23781762C2semidirect
8. C4×Dic652C2semidirect
9. C4×#14579689C2semidirect
10. C4×#14579687C2semidirect
11. #23781704C2semidirect
12. #23781672C2semidirect
14. C4×#14579682C2semidirect
15. C4×SD16×C163C2semidirect
18. #19104764C4direct (N × H)
66. Q8×D163C2×C4semidirect
75. Dic652C2×C4semidirect
76. #14579689C2×C4semidirect
77. #14579687C2×C4semidirect
79. #14579682C2×C4semidirect
104. SD16×C163C2×C4semidirect
162. C4×C163#137semidirect
177. C163C4×#137semidirect
189. C4×SD16D163semidirect
259. SD16C4×D163semidirect
347. C4#19104764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191047642
C4×#145796982
C4×Q8×D1632
#237817712
#237817692
#237817662
#237817622
C4×Dic6522
C4×#145796892
C4×#145796872
#237817042
#237816722
#237816632
C4×#145796822
C4×SD16×C1632
C4×#137163