Finite Group Databasebeta

← C29×#12299 #20307199

Subgroups — C29×#12299 #20307199

Order 7424.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3195C211yesmaximal, characteristic
2C29×#2239C212yesmaximal, complemented
3C29×#2091C211yesmaximal, characteristic
4C29×#1342C212yesmaximal, complemented
5C29×#1320C211yesmaximal, characteristic
6C2×C29×C22⋊Q8—21no—
7C29×#483—22no—
8C29×#470—21no—
9C29×#470C2212yes—
10C29×#451—22no—
11C29×#430—21no—
12C29×#430C2211yescharacteristic
13C29×#407—21no—
14C29×#407C2211yescharacteristic
15C29×#365—22no—
16C29×#362—22no—
17C29×#349C2212yes—
18C29×#338C2211yescharacteristic
19C22×Q8×C29—21no—
20C23×C4×C29D411yescharacteristic
21C2×Q16×C29—21no—
22C2×Q16×C29D412yes—
23C2×M16×C29—21no—
24C2×M16×C29—21no—
25C2×M16×C29D411yescharacteristic
26C2×M16×C29C2311yescharacteristic
27C29×C22⋊Q8—22no—
28C29×C22⋊Q8—22no—
29C29×C22⋊Q8—41no—
30C29×C22⋊Q8—41no—
31C2×C4⋊C4×C29—21no—
32C2×C4⋊C4×C29—41no—
33C2×C22⋊C4×C29—41no—
34C29×M32—22no—
35C29×#108—22no—
36C29×#108—42no—
37C29×#106—21no—
38C29×#106D412yes—
39C29×#103—22no—
40C29×#103—22no—
41C29×C22⋊C8—22no—
42C29×C22⋊C8—42no—
43C24×C29SD1611yescharacteristic
44C2×Q8×C29—22no—
45C2×Q8×C29—41no—
46C2×Q8×C29—81no—
47C2×Q8×C29—81no—
48C22×C4×C29—21no—
49C22×C4×C29—21no—
50C22×C4×C29—41no—
51C22×C4×C29—41no—
52C22×C4×C29—41no—
53C22×C4×C29—41no—
54C22×C4×C29SD1611yescharacteristic
55C22×C4×C29C2×D411yescharacteristic
56Q16×C29—42no—
57Q16×C29—81no—
58M16×C29—41no—
59M16×C29—41no—
60M16×C29—41no—
61M16×C29—41no—
62M16×C29—41no—
63M16×C29—41no—
64C2×C8×C29—22no—
65C2×C8×C29—21no—
66C2×C8×C29—41no—
67C2×C8×C29C2×D412yes—
68C4⋊C4×C29—22no—
69C4⋊C4×C29—41no—
70C4⋊C4×C29—42no—
71C4⋊C4×C29—42no—
72C22⋊C4×C29—42no—
73C22⋊C4×C29—42no—
74C16×C29—42no—
75#12299C2911yesmaximal, characteristic, direct product factor, Sylow
76C23×C29—21no—
77C23×C29—41no—
78C23×C29—42no—
79C23×C29C2×SD1611yescharacteristic
80Q8×C29—42no—
81Q8×C29—42no—
82Q8×C29—82no—
83C2×C4×C29—21no—
84C2×C4×C29—21no—
85C2×C4×C29—21no—
86C2×C4×C29—41no—
87C2×C4×C29—41no—
88C2×C4×C29—41no—
89C2×C4×C29—42no—
90C2×C4×C29—42no—
91C2×C4×C29—81no—
92C2×C4×C29—82no—
93C2×C4×C29—82no—
94C2×C4×C29#12011yescharacteristic
95C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
96C8×C29—22no—
97C8×C29—42no—
98C8×C29—41no—
99C8×C29—81no—
100#3195C2×C2911yescharacteristic
101#2239C2×C2912yescomplemented
102#2091C2×C2911yescharacteristic
103#1342C2×C2912yescomplemented
104#1320C2×C2911yescharacteristic
105C22×C29—22no—
106C22×C29—21no—
107C22×C29—41no—
108C22×C29—41no—
109C22×C29—42no—
110C22×C29—41no—
111C22×C29—81no—
112C22×C29#45011yescharacteristic
113C4×C29—21no—
114C4×C29—41no—
115C4×C29—82no—
116C4×C29—82no—
117C4×C29#45311yescharacteristic
118C4×C29#45811yescharacteristic
119C2×C22⋊Q8—21no—
120#483—22no—
121#470—21no—
122#470C22×C2912yes—
123#451—22no—
124#430—21no—
125#430C22×C2911yescharacteristic
126#407—21no—
127#407C22×C2911yescharacteristic
128#365—22no—
129#362—22no—
130#349C22×C2912yes—
131#338C22×C2911yescharacteristic
132C2×C29—21no—
133C2×C29—42no—
134C2×C29—41no—
135C2×C29#161311yescharacteristic
136C22×Q8—21no—
137C23×C4D4×C2911yescharacteristic
138C2×Q16—21no—
139C2×Q16D4×C2912yes—
140C2×M16—21no—
141C2×M16—21no—
142C2×M16D4×C2911yescharacteristic
143C2×M16C23×C2911yescharacteristic
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C22⋊Q8—41no—
147C22⋊Q8—41no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—41no—
150C2×C22⋊C4—41no—
151M32—22no—
152#108—22no—
153#108—42no—
154#106—21no—
155#106D4×C2912yes—
156#103—22no—
157#103—22no—
158C22⋊C8—22no—
159C22⋊C8—42no—
160C29#1229911yescharacteristic, direct product factor, Sylow
161C24SD16×C2911yescharacteristic
162C2×Q8—22no—
163C2×Q8—41no—
164C2×Q8—81no—
165C2×Q8—81no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4SD16×C2911yescharacteristic
173C22×C4C2×D4×C2911yescharacteristic
174Q16—42no—
175Q16—81no—
176M16—41no—
177M16—41no—
178M16—41no—
179M16—41no—
180M16—41no—
181M16—41no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8C2×D4×C2912yes—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C22⋊C4—42no—
191C22⋊C4—42no—
192C16—42no—
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×SD16×C2911yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—82no—
211C2×C4C29×#12011yescharacteristic
212C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
213C8—22no—
214C8—42no—
215C8—41no—
216C8—81no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22C29×#45011yescharacteristic
225C4—21no—
226C4—41no—
227C4—82no—
228C4—82no—
229C4C29×#45311yescharacteristic
230C4C29×#45811yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2C29×#161311yescharacteristic
subgroupG/H
center, socleC2×C29#1613
commutator, Frattini, cosocleC2×M16C23×C29
prime radicalC24×C29SD16
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2239C2semidirect
4. C29×#1342C2semidirect
75. #12299C29direct (N × H)
101. #2239C2×C29semidirect
103. #1342C2×C29semidirect
160. C29#12299direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31952
C29×#22392
C29×#20912
C29×#13422
C29×#13202
#1229929