Finite Group Databasebeta

← C29×#3480 #16817194

Subgroups — C29×#3480 #16817194

Order 3712.

1112 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#559C213yesmaximal, complemented
2C29×#557C211yesmaximal, characteristic, complemented
3C29×#556C213yesmaximal, complemented
4C29×#553C216yesmaximal, complemented
5C29×#550C211yesmaximal, characteristic, complemented
6C29×#548C212yesmaximal, complemented
7C29×#532C213yesmaximal, complemented
8C29×#529C216yesmaximal, complemented
9C4×#41×C29C213yesmaximal, complemented
10C4×#41×C29C212yesmaximal, complemented
11C2×C4×Q8×C29C211yesmaximal, characteristic, complemented
12C2×#41×C29C2213yes—
13C2×#41×C29C2212yes—
14C22×Q8×C29C2211yescharacteristic
15C29×C4⋊Q8C2213yes—
16C29×#127C2213yes—
17C29×#126C22112yes—
18C29×#125C2216yes—
19C29×#124C2216yes—
20C29×#124C2216yes—
21C29×#123C22112yes—
22C29×C22⋊Q8C2216yes—
23C29×#121C2216yes—
24C29×#121C2216yes—
25C29×#121C2216yes—
26C4×Q8×C29C2211yescharacteristic
27C4×Q8×C29C2213yes—
28C4×Q8×C29C2211yescharacteristic
29C4×Q8×C29C2213yes—
30C4×Q8×C29C2212yes—
31C4×Q8×C29C2213yes—
32C4×Q8×C29C2213yes—
33C4×D4×C29C2216yes—
34C4×D4×C29C2216yes—
35C4×D4×C29C2213yes—
36C4×D4×C29C2216yes—
37C4×D4×C29C2216yes—
38C4×D4×C29C2213yes—
39C4×D4×C29C2216yes—
40C29×#117C2211yescharacteristic
41C29×#117C2216yes—
42C29×#117C2216yes—
43C2×C4⋊C4×C29C2213yes—
44C2×C42×C29C2213yes—
45C2×C42×C29C2216yes—
46#41×C29—28no—
47#41×C29—212no—
48C2×Q8×C29—24no—
49C2×Q8×C29C2313yes—
50C2×Q8×C29C2313yes—
51C2×Q8×C29C2311yescharacteristic
52C2×D4×C29C2316yes—
53C2×D4×C29C2316yes—
54C2×D4×C29C2313yes—
55C2×D4×C29C2316yes—
56C22×C4×C29C2313yes—
57C22×C4×C29C2316yes—
58C22×C4×C29C2316yes—
59C22×C4×C29C2313yes—
60C22×C4×C29C2316yes—
61C22×C4×C29C2311yescharacteristic
62C4⋊C4×C29C2313yes—
63C4⋊C4×C29C2313yes—
64C4⋊C4×C29C2316yes—
65C4⋊C4×C29C2311yescharacteristic
66C4⋊C4×C29C2311yescharacteristic
67C4⋊C4×C29C2316yes—
68C4⋊C4×C29C2316yes—
69C4⋊C4×C29C2316yes—
70C4⋊C4×C29C2316yes—
71C22⋊C4×C29C2312yes—
72C22⋊C4×C29C2316yes—
73C22⋊C4×C29C23112yes—
74C22⋊C4×C29C2316yes—
75C22⋊C4×C29C23112yes—
76C42×C29C2316yes—
77C42×C29C2316yes—
78C42×C29C2313yes—
79C42×C29C2313yes—
80C42×C29C2312yes—
81C42×C29C2313yes—
82C42×C29C2313yes—
83C23×C29C2416yes—
84C23×C29C2411yescharacteristic
85Q8×C29—26no—
86Q8×C29—26no—
87Q8×C29#4114yescomplemented
88D4×C29—212no—
89D4×C29—212no—
90D4×C29—26no—
91D4×C29—46no—
92C2×C4×C29—26no—
93C2×C4×C29—212no—
94C2×C4×C29—212no—
95C2×C4×C29—46no—
96C2×C4×C29—43no—
97C2×C4×C29#4114yescomplemented
98C2×C4×C29C2412yes—
99C2×C4×C29C2413yes—
100C2×C4×C29C2412yes—
101C2×C4×C29C2413yes—
102C2×C4×C29C2416yes—
103C2×C4×C29C2413yes—
104C2×C4×C29C2411yescharacteristic
105C2×C4×C29C2413yes—
106C2×C4×C29C2411yescharacteristic
107#3480C2911yesmaximal, characteristic, direct product factor, Sylow
108C22×C29—21no—
109C22×C29—21no—
110C22×C29—26no—
111C22×C29—26no—
112C22×C29—26no—
113C22×C29C2×#4112yes—
114C22×C29C2511yescharacteristic
115C4×C29—22no—
116C4×C29—26no—
117C4×C29—23no—
118C4×C29—22no—
119C4×C29—23no—
120C4×C29—23no—
121C4×C29C2×#4112yes—
122C4×C29C2×#4116yes—
123C4×C29C2×#4112yes—
124#559C2×C2913yescomplemented
125#557C2×C2911yescharacteristic, complemented
126#556C2×C2913yescomplemented
127#553C2×C2916yescomplemented
128#550C2×C2911yescharacteristic, complemented
129#548C2×C2912yescomplemented
130#532C2×C2913yescomplemented
131#529C2×C2916yescomplemented
132C4×#41C2×C2913yescomplemented
133C4×#41C2×C2912yescomplemented
134C2×C4×Q8C2×C2911yescharacteristic, complemented
135C2×C29—22no—
136C2×C29—46no—
137C2×C29C22×#4111yescharacteristic
138C2×C29C22×#4111yescharacteristic
139C2×C29#58511yescharacteristic
140C2×#41C22×C2913yes—
141C2×#41C22×C2912yes—
142C22×Q8C22×C2911yescharacteristic
143C4⋊Q8C22×C2913yes—
144#127C22×C2913yes—
145#126C22×C29112yes—
146#125C22×C2916yes—
147#124C22×C2916yes—
148#124C22×C2916yes—
149#123C22×C29112yes—
150C22⋊Q8C22×C2916yes—
151#121C22×C2916yes—
152#121C22×C2916yes—
153#121C22×C2916yes—
154C4×Q8C22×C2911yescharacteristic
155C4×Q8C22×C2913yes—
156C4×Q8C22×C2911yescharacteristic
157C4×Q8C22×C2913yes—
158C4×Q8C22×C2912yes—
159C4×Q8C22×C2913yes—
160C4×Q8C22×C2913yes—
161C4×D4C22×C2916yes—
162C4×D4C22×C2916yes—
163C4×D4C22×C2913yes—
164C4×D4C22×C2916yes—
165C4×D4C22×C2916yes—
166C4×D4C22×C2913yes—
167C4×D4C22×C2916yes—
168#117C22×C2911yescharacteristic
169#117C22×C2916yes—
170#117C22×C2916yes—
171C2×C4⋊C4C22×C2913yes—
172C2×C42C22×C2913yes—
173C2×C42C22×C2916yes—
174C29#348011yescharacteristic, direct product factor, Sylow
175#41—28no—
176#41—212no—
177C2×Q8—24no—
178C2×Q8C23×C2913yes—
179C2×Q8C23×C2913yes—
180C2×Q8C23×C2911yescharacteristic
181C2×D4C23×C2916yes—
182C2×D4C23×C2916yes—
183C2×D4C23×C2913yes—
184C2×D4C23×C2916yes—
185C22×C4C23×C2913yes—
186C22×C4C23×C2916yes—
187C22×C4C23×C2916yes—
188C22×C4C23×C2913yes—
189C22×C4C23×C2916yes—
190C22×C4C23×C2911yescharacteristic
191C4⋊C4C23×C2913yes—
192C4⋊C4C23×C2913yes—
193C4⋊C4C23×C2916yes—
194C4⋊C4C23×C2911yescharacteristic
195C4⋊C4C23×C2911yescharacteristic
196C4⋊C4C23×C2916yes—
197C4⋊C4C23×C2916yes—
198C4⋊C4C23×C2916yes—
199C4⋊C4C23×C2916yes—
200C22⋊C4C23×C2912yes—
201C22⋊C4C23×C2916yes—
202C22⋊C4C23×C29112yes—
203C22⋊C4C23×C2916yes—
204C22⋊C4C23×C29112yes—
205C42C23×C2912yes—
206C42C23×C2913yes—
207C42C23×C2913yes—
208C42C23×C2916yes—
209C42C23×C2916yes—
210C42C23×C2913yes—
211C42C23×C2913yes—
212C23C24×C2916yes—
213C23C24×C2911yescharacteristic
214Q8—26no—
215Q8—26no—
216Q8#41×C2914yescomplemented
217D4—212no—
218D4—212no—
219D4—26no—
220D4—46no—
221C2×C4—26no—
222C2×C4—212no—
223C2×C4—212no—
224C2×C4—46no—
225C2×C4—43no—
226C2×C4#41×C2914yescomplemented
227C2×C4C24×C2912yes—
228C2×C4C24×C2912yes—
229C2×C4C24×C2913yes—
230C2×C4C24×C2913yes—
231C2×C4C24×C2916yes—
232C2×C4C24×C2913yes—
233C2×C4C24×C2911yescharacteristic
234C2×C4C24×C2911yescharacteristic
235C2×C4C24×C2913yes—
236C22—21no—
237C22—21no—
238C22—26no—
239C22—26no—
240C22—26no—
241C22C2×#41×C2912yes—
242C22C25×C2911yescharacteristic
243C4—22no—
244C4—26no—
245C4—23no—
246C4—22no—
247C4—23no—
248C4—23no—
249C4C2×#41×C2912yes—
250C4C2×#41×C2916yes—
251C4C2×#41×C2912yes—
252C2—22no—
253C2—46no—
254C2C22×#41×C2911yescharacteristic
255C2C22×#41×C2911yescharacteristic
256C2C29×#58511yescharacteristic
subgroupG/H
centerC2×C4×C29C24
commutator, Frattini, cosocleC22C25×C29
socleC22×C29C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#559C2semidirect
2. C29×#557C2semidirect
3. C29×#556C2semidirect
4. C29×#553C2semidirect
5. C29×#550C2semidirect
6. C29×#548C2semidirect
7. C29×#532C2semidirect
8. C29×#529C2semidirect
9. C4×#41×C29C2semidirect
10. C4×#41×C29C2semidirect
11. C2×C4×Q8×C29C2semidirect
87. Q8×C29#41semidirect
97. C2×C4×C29#41semidirect
107. #3480C29direct (N × H)
124. #559C2×C29semidirect
125. #557C2×C29semidirect
126. #556C2×C29semidirect
127. #553C2×C29semidirect
128. #550C2×C29semidirect
129. #548C2×C29semidirect
130. #532C2×C29semidirect
131. #529C2×C29semidirect
132. C4×#41C2×C29semidirect
133. C4×#41C2×C29semidirect
134. C2×C4×Q8C2×C29semidirect
174. C29#3480direct (N × H)
216. Q8#41×C29semidirect
226. C2×C4#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#5592
C29×#5572
C29×#5562
C29×#5532
C29×#5502
C29×#5482
C29×#5322
C29×#5292
C4×#41×C292
C2×C4×Q8×C292
#348029