Finite Group Databasebeta

← C29×#9985 #20304885

Subgroups — C29×#9985 #20304885

Order 7424.

502 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3095C212yesmaximal
2C29×#2817C211yesmaximal, characteristic
3C29×#1820C211yesmaximal, characteristic
4C29×#1511C212yesmaximal
5C29×#1306C211yesmaximal, characteristic
6C2×C29×C22⋊Q8C2212yes—
7C2×C29×#117C2211yescharacteristic
8C29×#485—24no—
9C29×#484—22no—
10C29×#483—22no—
11C29×#428—22no—
12C29×#419—22no—
13C29×#407C2212yes—
14C29×#400—22no—
15C29×#397—22no—
16C29×#395—22no—
17C29×#381C2211yescharacteristic
18C29×#381C2211yescharacteristic
19C29×#342—22no—
20C29×#328—24no—
21C22×Q8×C29D412yes—
22C23×C4×C29C2311yescharacteristic
23C2×M16×C29—22no—
24C29×C22⋊Q8—22no—
25C29×C22⋊Q8—22no—
26C29×C22⋊Q8—22no—
27C29×C22⋊Q8—22no—
28C29×#117—22no—
29C29×#117—22no—
30C2×C4⋊C4×C29—22no—
31C2×C4⋊C4×C29—22no—
32C2×C4⋊C4×C29D412yes—
33C2×C4⋊C4×C29D412yes—
34C2×C22⋊C4×C29—21no—
35C2×C22⋊C4×C29—22no—
36C2×C22⋊C4×C29—21no—
37C2×C22⋊C4×C29D412yes—
38C2×C42×C29—21no—
39C29×#107—24no—
40C29×#106—24no—
41C29×#103—24no—
42C29×#103—24no—
43C29×C22⋊C8—22no—
44C29×C22⋊C8D414yes—
45C29×#95—24no—
46C29×#95—22no—
47C29×#95—22no—
48C29×#95—22no—
49C24×C29C2×D411yescharacteristic
50C2×Q8×C29—22no—
51C2×Q8×C29—22no—
52C2×Q8×C29—44no—
53C22×C4×C29—22no—
54C22×C4×C29—22no—
55C22×C4×C29—22no—
56C22×C4×C29—22no—
57C22×C4×C29—42no—
58C22×C4×C29—41no—
59C22×C4×C29C2×D412yes—
60C22×C4×C29C2×D411yescharacteristic
61C22×C4×C29C2×D412yes—
62C22×C4×C29#4111yescharacteristic
63M16×C29—44no—
64C2×C8×C29—24no—
65C4⋊C4×C29—22no—
66C4⋊C4×C29—22no—
67C4⋊C4×C29—22no—
68C4⋊C4×C29—22no—
69C4⋊C4×C29—42no—
70C4⋊C4×C29—42no—
71C4⋊C4×C29—82no—
72C22⋊C4×C29—41no—
73C22⋊C4×C29—42no—
74C22⋊C4×C29—41no—
75C22⋊C4×C29—42no—
76C22⋊C4×C29—42no—
77C22⋊C4×C29—42no—
78C42×C29—42no—
79#9985C2911yesmaximal, characteristic, direct product factor, Sylow
80C23×C29—22no—
81C23×C29—42no—
82C23×C29#12011yescharacteristic
83C23×C29#12111yescharacteristic
84C23×C29#12711yescharacteristic
85Q8×C29—44no—
86Q8×C29—82no—
87C2×C4×C29—24no—
88C2×C4×C29—41no—
89C2×C4×C29—42no—
90C2×C4×C29—41no—
91C2×C4×C29—44no—
92C2×C4×C29—44no—
93C2×C4×C29—42no—
94C2×C4×C29—42no—
95C2×C4×C29—42no—
96C2×C4×C29—42no—
97C2×C4×C29—44no—
98C2×C4×C29—82no—
99C2×C4×C29—81no—
100C2×C4×C29—82no—
101C2×C4×C29#12012yes—
102C2×C4×C29#12112yes—
103C8×C29—44no—
104#3095C2×C2912yes—
105#2817C2×C2911yescharacteristic
106#1820C2×C2911yescharacteristic
107#1511C2×C2912yes—
108#1306C2×C2911yescharacteristic
109C22×C29—22no—
110C22×C29—22no—
111C22×C29—22no—
112C22×C29—21no—
113C22×C29—21no—
114C22×C29—82no—
115C22×C29#39211yescharacteristic
116C22×C29#45812yes—
117C4×C29—22no—
118C4×C29—22no—
119C4×C29—82no—
120C4×C29—82no—
121C4×C29—82no—
122C4×C29—82no—
123C4×C29—161no—
124C2×C22⋊Q8C22×C2912yes—
125C2×#117C22×C2911yescharacteristic
126#485—24no—
127#484—22no—
128#483—22no—
129#428—22no—
130#419—22no—
131#407C22×C2912yes—
132#400—22no—
133#397—22no—
134#395—22no—
135#381C22×C2911yescharacteristic
136#381C22×C2911yescharacteristic
137#342—22no—
138#328—24no—
139C2×C29—22no—
140C2×C29—41no—
141C2×C29—41no—
142C2×C29#200912yes—
143C2×C29#202211yescharacteristic
144C22×Q8D4×C2912yes—
145C23×C4C23×C2911yescharacteristic
146C2×M16—22no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151#117—22no—
152#117—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4D4×C2912yes—
156C2×C4⋊C4D4×C2912yes—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4D4×C2912yes—
161C2×C42—21no—
162#107—24no—
163#106—24no—
164#103—24no—
165#103—24no—
166C22⋊C8—22no—
167C22⋊C8D4×C2914yes—
168#95—24no—
169#95—22no—
170#95—22no—
171#95—22no—
172C29#998511yescharacteristic, direct product factor, Sylow
173C24C2×D4×C2911yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—41no—
183C22×C4C2×D4×C2912yes—
184C22×C4C2×D4×C2911yescharacteristic
185C22×C4C2×D4×C2912yes—
186C22×C4#41×C2911yescharacteristic
187M16—44no—
188C2×C8—24no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—82no—
196C22⋊C4—41no—
197C22⋊C4—42no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C42—42no—
203C23—22no—
204C23—42no—
205C23C29×#12011yescharacteristic
206C23C29×#12111yescharacteristic
207C23C29×#12711yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4C29×#12012yes—
225C2×C4C29×#12112yes—
226C8—44no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22C29×#39211yescharacteristic
234C22C29×#45812yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—82no—
241C4—161no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2C29×#200912yes—
246C2C29×#202211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
79. #9985C29direct (N × H)
172. C29#9985direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30952
C29×#28172
C29×#18202
C29×#15112
C29×#13062
#998529