Finite Group Databasebeta

← C29×#13140 #20308040

Subgroups — C29×#13140 #20308040

Order 7424.

314 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2155C211yesmaximal, characteristic, complemented
2C29×#2148C211yesmaximal, characteristic
3C29×#2145C211yesmaximal, characteristic
4C29×#1975C211yesmaximal, characteristic
5C29×#1773C211yesmaximal, characteristic, complemented
6C29×#1385C211yesmaximal, characteristic, complemented
7C29×#1377C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C2×C29×M32C2211yescharacteristic
10C2×C29×M32C2211yescharacteristic
11C2×C29×#108C2211yescharacteristic
12C2×C29×#108C2211yescharacteristic
13C29×#427C2211yescharacteristic
14C2×C29×#104—21no—
15C29×#408—21no—
16C29×#405—21no—
17C2×C29×#97C2211yescharacteristic
18C29×#365—22no—
19C29×#362C412yescomplemented
20C29×#361C412yescomplemented
21C29×#360—22no—
22C29×#339—21no—
23C2×#41×C29—21no—
24C29×#135—21no—
25C29×#135—21no—
26C29×#135—21no—
27C29×#135—21no—
28C2×Q16×C29C2×C411yescharacteristic
29C2×SD16×C29—21no—
30C2×D8×C29C2×C411yescharacteristic
31C2×M16×C29—21no—
32C2×M16×C29—21no—
33C22×C8×C29D411yescharacteristic
34C22×C8×C29C2311yescharacteristic
35C29×#117—21no—
36C2×C42×C29D411yescharacteristic
37C29×M32—21no—
38C29×M32—21no—
39C29×M32—21no—
40C29×M32C2×C412yes—
41C2×C16×C29—21no—
42C2×C16×C29—21no—
43C29×#108—21no—
44C29×#108—21no—
45C29×#108—21no—
46C29×#108C2×C412yes—
47C29×#107—21no—
48C29×#106D412yes—
49C29×#104—42no—
50C29×C22⋊C8—42no—
51C29×#97—21no—
52C29×#97—21no—
53C29×#97—41no—
54C4×C8×C29—41no—
55#41×C29—41no—
56#41×C29—41no—
57#41×C29—41no—
58#41×C29—41no—
59C2×Q8×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29—41no—
62C22×C4×C29—21no—
63C22×C4×C29—41no—
64C22×C4×C29C2×D411yescharacteristic
65Q16×C29—21no—
66Q16×C29—21no—
67SD16×C29—41no—
68SD16×C29—41no—
69D8×C29—21no—
70D8×C29—21no—
71M16×C29—22no—
72M16×C29—41no—
73M16×C29—41no—
74M16×C29—41no—
75C2×C8×C29—21no—
76C2×C8×C29—21no—
77C2×C8×C29—41no—
78C2×C8×C29—41no—
79C2×C8×C29SD1612yes—
80C2×C8×C29C22×C411yescharacteristic
81C2×C8×C29C2×D411yescharacteristic
82C2×C8×C29#4111yescharacteristic
83C2×C8×C29#4111yescharacteristic
84C2×C8×C29#4111yescharacteristic
85C2×C8×C29#4111yescharacteristic
86C4⋊C4×C29—22no—
87C22⋊C4×C29—41no—
88C42×C29—21no—
89C42×C29—21no—
90C42×C29—41no—
91C16×C29—22no—
92C16×C29—41no—
93#13140C2911yesmaximal, characteristic, direct product factor, Sylow
94C23×C29—41no—
95C23×C29#13511yescharacteristic
96Q8×C29—41no—
97Q8×C29—41no—
98D4×C29—41no—
99D4×C29—41no—
100D4×C29—81no—
101D4×C29—81no—
102C2×C4×C29—41no—
103C2×C4×C29—42no—
104C2×C4×C29—41no—
105C2×C4×C29—81no—
106C2×C4×C29—81no—
107C2×C4×C29—81no—
108C2×C4×C29C4×D411yescharacteristic
109C2×C4×C29#12111yescharacteristic
110C2×C4×C29#12311yescharacteristic
111C2×C4×C29C2×SD1611yescharacteristic
112C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
114C8×C29—22no—
115C8×C29—42no—
116C8×C29—81no—
117C8×C29#11711yescharacteristic
118C8×C29C4×D411yescharacteristic
119C8×C29#12411yescharacteristic
120C8×C29#12611yescharacteristic
121#2155C2×C2911yescharacteristic, complemented
122#2148C2×C2911yescharacteristic
123#2145C2×C2911yescharacteristic
124#1975C2×C2911yescharacteristic
125#1773C2×C2911yescharacteristic, complemented
126#1385C2×C2911yescharacteristic, complemented
127#1377C2×C2911yescharacteristic, complemented
128C22×C29—41no—
129C22×C29—82no—
130C22×C29—81no—
131C22×C29C4×SD1611yescharacteristic
132C22×C29#46311yescharacteristic
133C22×C29#48211yescharacteristic
134C4×C29—82no—
135C4×C29—81no—
136C4×C29—81no—
137C4×C29#38811yescharacteristic
138C4×C29#44211yescharacteristic
139C4×C29#46011yescharacteristic
140C4×C29#48111yescharacteristic
141C2×#135C22×C2911yescharacteristic
142C2×M32C22×C2911yescharacteristic
143C2×M32C22×C2911yescharacteristic
144C2×#108C22×C2911yescharacteristic
145C2×#108C22×C2911yescharacteristic
146#427C22×C2911yescharacteristic
147C2×#104—21no—
148#408—21no—
149#405—21no—
150C2×#97C22×C2911yescharacteristic
151#365—22no—
152#362C4×C2912yescomplemented
153#361C4×C2912yescomplemented
154#360—22no—
155#339—21no—
156C2×C29—21no—
157C2×C29—21no—
158C2×C29—21no—
159C2×C29—161no—
160C2×C29#192611yescharacteristic
161C2×#41—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165#135—21no—
166C2×Q16C2×C4×C2911yescharacteristic
167C2×SD16—21no—
168C2×D8C2×C4×C2911yescharacteristic
169C2×M16—21no—
170C2×M16—21no—
171C22×C8D4×C2911yescharacteristic
172C22×C8C23×C2911yescharacteristic
173#117—21no—
174C2×C42D4×C2911yescharacteristic
175M32—21no—
176M32—21no—
177M32—21no—
178M32C2×C4×C2912yes—
179C2×C16—21no—
180C2×C16—21no—
181#108—21no—
182#108—21no—
183#108—21no—
184#108C2×C4×C2912yes—
185#107—21no—
186#106D4×C2912yes—
187#104—42no—
188C22⋊C8—42no—
189#97—21no—
190#97—21no—
191#97—41no—
192C4×C8—41no—
193C29#1314011yescharacteristic, direct product factor, Sylow
194#41—41no—
195#41—41no—
196#41—41no—
197#41—41no—
198C2×Q8—21no—
199C2×D4—21no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C2911yescharacteristic
204Q16—21no—
205Q16—21no—
206SD16—41no—
207SD16—41no—
208D8—21no—
209D8—21no—
210M16—22no—
211M16—41no—
212M16—41no—
213M16—41no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8SD16×C2912yes—
219C2×C8C22×C4×C2911yescharacteristic
220C2×C8C2×D4×C2911yescharacteristic
221C2×C8#41×C2911yescharacteristic
222C2×C8#41×C2911yescharacteristic
223C2×C8#41×C2911yescharacteristic
224C2×C8#41×C2911yescharacteristic
225C4⋊C4—22no—
226C22⋊C4—41no—
227C42—21no—
228C42—21no—
229C42—41no—
230C16—22no—
231C16—41no—
232C23—41no—
233C23C29×#13511yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—81no—
239D4—81no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C4×D4×C2911yescharacteristic
247C2×C4C29×#12111yescharacteristic
248C2×C4C29×#12311yescharacteristic
249C2×C4C2×SD16×C2911yescharacteristic
250C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
251C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
252C8—22no—
253C8—42no—
254C8—81no—
255C8C29×#11711yescharacteristic
256C8C4×D4×C2911yescharacteristic
257C8C29×#12411yescharacteristic
258C8C29×#12611yescharacteristic
259C22—41no—
260C22—82no—
261C22—81no—
262C22C4×SD16×C2911yescharacteristic
263C22C29×#46311yescharacteristic
264C22C29×#48211yescharacteristic
265C4—81no—
266C4—82no—
267C4—81no—
268C4C29×#38811yescharacteristic
269C4C29×#44211yescharacteristic
270C4C29×#46011yescharacteristic
271C4C29×#48111yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—161no—
276C2C29×#192611yescharacteristic
subgroupG/H
centerC4×C29#481
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
socleC2×C29#1926
prime radicalC2×C29×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C2×C29×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2155C2semidirect
5. C29×#1773C2semidirect
6. C29×#1385C2semidirect
7. C29×#1377C2semidirect
19. C29×#362C4semidirect
20. C29×#361C4semidirect
93. #13140C29direct (N × H)
121. #2155C2×C29semidirect
125. #1773C2×C29semidirect
126. #1385C2×C29semidirect
127. #1377C2×C29semidirect
152. #362C4×C29semidirect
153. #361C4×C29semidirect
193. C29#13140direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#21552
C29×#21482
C29×#21452
C29×#19752
C29×#17732
C29×#13852
C29×#13772
#1314029