Finite Group Databasebeta

← C2×C29×#1325 #20306346

Subgroups — C2×C29×#1325 #20306346

Order 7424.

598 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C2×C29×#384C211yesmaximal, characteristic
2C2×C29×#324C212yesmaximal
3C29×#1325C214yesmaximal, direct product factor
4C22×C4⋊C4×C29—22no—
5C22×C4⋊C4×C29C411yescharacteristic
6C22×C4⋊C4×C29C2211yescharacteristic
7C22×C42×C29C411yescharacteristic
8C2×C29×C22⋊C8—22no—
9C29×#384—22no—
10C29×#384C412yes—
11C29×#384C2212yes—
12C29×#324—22no—
13C29×#324C2214yes—
14C23×C4×C29—21no—
15C23×C4×C29—21no—
16C23×C4×C29C2×C411yescharacteristic
17C23×C4×C29D412yes—
18C22×C8×C29—42no—
19C2×C4⋊C4×C29—24no—
20C2×C4⋊C4×C29—21no—
21C2×C4⋊C4×C29—24no—
22C2×C4⋊C4×C29—41no—
23C2×C4⋊C4×C29—41no—
24C2×C4⋊C4×C29—41no—
25C2×C4⋊C4×C29—41no—
26C2×C4⋊C4×C29—48no—
27C2×C4⋊C4×C29C2×C412yes—
28C2×C4⋊C4×C29C2×C411yescharacteristic
29C2×C4⋊C4×C29D412yes—
30C2×C4⋊C4×C29C2311yescharacteristic
31C2×C42×C29—21no—
32C2×C42×C29—22no—
33C2×C42×C29C814yescomplemented
34C2×C42×C29C2×C412yes—
35C29×C22⋊C8—24no—
36C29×C22⋊C8—42no—
37C24×C29C22⋊C411yescharacteristic
38C22×C4×C29—24no—
39C22×C4×C29—24no—
40C22×C4×C29—24no—
41C22×C4×C29—21no—
42C22×C4×C29—21no—
43C22×C4×C29—22no—
44C22×C4×C29—22no—
45C22×C4×C29—22no—
46C22×C4×C29—22no—
47C22×C4×C29—22no—
48C22×C4×C29—44no—
49C22×C4×C29—44no—
50C22×C4×C29—41no—
51C22×C4×C29—41no—
52C22×C4×C29C22⋊C411yescharacteristic
53C22×C4×C29C22⋊C412yes—
54C22×C4×C29C2×C812yes—
55C22×C4×C29M1612yes—
56C22×C4×C29C22×C411yescharacteristic
57C22×C4×C29C2×D412yes—
58C2×C8×C29—44no—
59C2×C8×C29—84no—
60C4⋊C4×C29—41no—
61C4⋊C4×C29—42no—
62C4⋊C4×C29—41no—
63C4⋊C4×C29—42no—
64C4⋊C4×C29—48no—
65C4⋊C4×C29—48no—
66C4⋊C4×C29—42no—
67C42×C29—24no—
68C42×C29—22no—
69C42×C29C2×C814yescomplemented
70C2×#1325C2911yesmaximal, characteristic, direct product factor, Sylow
71C23×C29—22no—
72C23×C29—22no—
73C23×C29C22⋊C812yes—
74C23×C29#9911yescharacteristic
75C23×C29#9911yescharacteristic
76C23×C29#10112yes—
77C23×C29C2×C22⋊C411yescharacteristic
78C2×C4×C29—24no—
79C2×C4×C29—216no—
80C2×C4×C29—24no—
81C2×C4×C29—22no—
82C2×C4×C29—22no—
83C2×C4×C29—22no—
84C2×C4×C29—22no—
85C2×C4×C29—24no—
86C2×C4×C29—21no—
87C2×C4×C29—21no—
88C2×C4×C29—21no—
89C2×C4×C29—21no—
90C2×C4×C29—22no—
91C2×C4×C29—22no—
92C2×C4×C29—44no—
93C2×C4×C29—42no—
94C2×C4×C29—42no—
95C2×C4×C29—44no—
96C2×C4×C29—42no—
97C2×C4×C29—82no—
98C2×C4×C29—82no—
99C2×C4×C29—82no—
100C2×C4×C29C22⋊C812yes—
101C2×C4×C29C22×C811yescharacteristic
102C2×C4×C29C2×M1611yescharacteristic
103C8×C29—84no—
104C2×#384C2×C2911yescharacteristic
105C2×#324C2×C2912yes—
106#1325C2×C2914yesdirect product factor
107C22×C29—24no—
108C22×C29—24no—
109C22×C29—21no—
110C22×C29—21no—
111C22×C29—21no—
112C22×C29—21no—
113C22×C29#32412yes—
114C22×C29#32412yes—
115C22×C29#35312yes—
116C22×C29#35612yes—
117C22×C29C2×C22⋊C811yescharacteristic
118C22×C29C2×#9911yescharacteristic
119C22×C29C2×#10111yescharacteristic
120C4×C29—28no—
121C4×C29—22no—
122C4×C29—21no—
123C4×C29—21no—
124C4×C29—42no—
125C4×C29—42no—
126C4×C29—82no—
127C22×C4⋊C4—22no—
128C22×C4⋊C4C4×C2911yescharacteristic
129C22×C4⋊C4C22×C2911yescharacteristic
130C22×C42C4×C2911yescharacteristic
131C2×C22⋊C8—22no—
132#384—22no—
133#384C4×C2912yes—
134#384C22×C2912yes—
135#324—22no—
136#324C22×C2914yes—
137C2×C29—21no—
138C2×C29—22no—
139C2×C29—21no—
140C2×C29#132514yesdirect product factor
141C2×C29C2×#32411yescharacteristic
142C2×C29C2×#35311yescharacteristic
143C2×C29C2×#35611yescharacteristic
144C23×C4—21no—
145C23×C4—21no—
146C23×C4C2×C4×C2911yescharacteristic
147C23×C4D4×C2912yes—
148C22×C8—42no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—48no—
157C2×C4⋊C4C2×C4×C2912yes—
158C2×C4⋊C4C2×C4×C2911yescharacteristic
159C2×C4⋊C4D4×C2912yes—
160C2×C4⋊C4C23×C2911yescharacteristic
161C2×C42—21no—
162C2×C42—22no—
163C2×C42C8×C2914yescomplemented
164C2×C42C2×C4×C2912yes—
165C22⋊C8—24no—
166C22⋊C8—42no—
167C29C2×#132511yescharacteristic, direct product factor, Sylow
168C24C22⋊C4×C2911yescharacteristic
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—22no—
172C22×C4—24no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—44no—
180C22×C4—44no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4C22⋊C4×C2911yescharacteristic
184C22×C4C22⋊C4×C2912yes—
185C22×C4C2×C8×C2912yes—
186C22×C4M16×C2912yes—
187C22×C4C22×C4×C2911yescharacteristic
188C22×C4C2×D4×C2912yes—
189C2×C8—44no—
190C2×C8—84no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—48no—
196C4⋊C4—48no—
197C4⋊C4—42no—
198C42—22no—
199C42—24no—
200C42C2×C8×C2914yescomplemented
201C23—22no—
202C23—22no—
203C23C29×C22⋊C812yes—
204C23C29×#9911yescharacteristic
205C23C29×#9911yescharacteristic
206C23C29×#10112yes—
207C23C2×C22⋊C4×C2911yescharacteristic
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4—82no—
230C2×C4C29×C22⋊C812yes—
231C2×C4C22×C8×C2911yescharacteristic
232C2×C4C2×M16×C2911yescharacteristic
233C8—84no—
234C22—24no—
235C22—24no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—21no—
240C22C29×#32412yes—
241C22C29×#32412yes—
242C22C29×#35312yes—
243C22C29×#35612yes—
244C22C2×C29×C22⋊C811yescharacteristic
245C22C2×C29×#9911yescharacteristic
246C22C2×C29×#10111yescharacteristic
247C4—28no—
248C4—21no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—42no—
253C4—82no—
254C2—21no—
255C2—22no—
256C2—21no—
257C2C29×#132514yesdirect product factor
258C2C2×C29×#32411yescharacteristic
259C2C2×C29×#35311yescharacteristic
260C2C2×C29×#35611yescharacteristic
subgroupG/H
center, socleC23×C29#99
commutatorC2×C4C22×C8×C29
Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C24×C29 ◁ C22×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1325C2direct (N × H)
33. C2×C42×C29C8semidirect
69. C42×C29C2×C8semidirect
70. C2×#1325C29direct (N × H)
106. #1325C2×C29direct (N × H)
140. C2×C29#1325direct (N × H)
163. C2×C42C8×C29semidirect
167. C29C2×#1325direct (N × H)
200. C42C2×C8×C29semidirect
257. C2C29×#1325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3842
C2×C29×#3242
C29×#13252
C2×#132529