Finite Group Databasebeta

← C29×#7104 #20302004

Subgroups — C29×#7104 #20302004

Order 7424.

368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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×#1445C211yesmaximal, characteristic
2C29×#1280C212yesmaximal
3C22×C4⋊C4×C29C411yescharacteristic
4C2×C29×C22⋊C8—22no—
5C2×C29×#95—22no—
6C2×C29×#95C411yescharacteristic
7C2×C29×#95C2211yescharacteristic
8C23×C4×C29—21no—
9C23×C4×C29—21no—
10C23×C4×C29C2×C411yescharacteristic
11C23×C4×C29D412yes—
12C22×C8×C29—42no—
13C2×C4⋊C4×C29—21no—
14C2×C4⋊C4×C29—41no—
15C2×C4⋊C4×C29—41no—
16C2×C4⋊C4×C29C812yescomplemented
17C29×C22⋊C8—24no—
18C29×C22⋊C8—42no—
19C29×#95—41no—
20C29×#95—41no—
21C29×#95—42no—
22C29×#95—42no—
23C24×C29C22⋊C411yescharacteristic
24C22×C4×C29—21no—
25C22×C4×C29—22no—
26C22×C4×C29—21no—
27C22×C4×C29—22no—
28C22×C4×C29—22no—
29C22×C4×C29—22no—
30C22×C4×C29—42no—
31C22×C4×C29—42no—
32C22×C4×C29—42no—
33C22×C4×C29—42no—
34C22×C4×C29—41no—
35C22×C4×C29—41no—
36C22×C4×C29—41no—
37C22×C4×C29—41no—
38C22×C4×C29—42no—
39C22×C4×C29—42no—
40C22×C4×C29—42no—
41C22×C4×C29C2×C811yescharacteristic
42C22×C4×C29M1611yescharacteristic
43C22×C4×C29D812yes—
44C22×C4×C29SD1612yes—
45C2×C8×C29—44no—
46C2×C8×C29—82no—
47C2×C8×C29—82no—
48C4⋊C4×C29—42no—
49C4⋊C4×C29—42no—
50#7104C2911yesmaximal, characteristic, direct product factor, Sylow
51C23×C29—22no—
52C23×C29—21no—
53C23×C29—21no—
54C23×C29C22⋊C811yescharacteristic
55C23×C29#9911yescharacteristic
56C23×C29#10011yescharacteristic
57C23×C29#10212yes—
58C23×C29#10412yes—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—22no—
62C2×C4×C29—22no—
63C2×C4×C29—42no—
64C2×C4×C29—42no—
65C2×C4×C29—42no—
66C2×C4×C29—42no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—42no—
70C2×C4×C29—42no—
71C2×C4×C29—42no—
72C2×C4×C29—44no—
73C2×C4×C29—42no—
74C2×C4×C29—44no—
75C2×C4×C29—82no—
76C2×C4×C29—81no—
77C2×C4×C29—82no—
78C2×C4×C29—82no—
79C2×C4×C29—81no—
80C2×C4×C29—81no—
81C2×C4×C29—81no—
82C8×C29—84no—
83#1445C2×C2911yescharacteristic
84#1280C2×C2912yes—
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—22no—
90C22×C29—22no—
91C22×C29—22no—
92C22×C29—22no—
93C22×C29#32311yescharacteristic
94C22×C29D4⋊C812yes—
95C22×C29#32712yes—
96C22×C29#32911yescharacteristic
97C22×C29#33111yescharacteristic
98C22×C29#35212yes—
99C22×C29#35411yescharacteristic
100C22×C29#35611yescharacteristic
101C4×C29—41no—
102C4×C29—41no—
103C4×C29—42no—
104C4×C29—42no—
105C4×C29—82no—
106C4×C29—82no—
107C22×C4⋊C4C4×C2911yescharacteristic
108C2×C22⋊C8—22no—
109C2×#95—22no—
110C2×#95C4×C2911yescharacteristic
111C2×#95C22×C2911yescharacteristic
112C2×C29—21no—
113C2×C29—22no—
114C2×C29—21no—
115C2×C29#127011yescharacteristic
116C2×C29#131711yescharacteristic
117C2×C29#131911yescharacteristic
118C2×C29#134412yes—
119C2×C29#134612yes—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4C2×C4×C2911yescharacteristic
123C23×C4D4×C2912yes—
124C22×C8—42no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4C8×C2912yescomplemented
129C22⋊C8—24no—
130C22⋊C8—42no—
131#95—41no—
132#95—41no—
133#95—42no—
134#95—42no—
135C29#710411yescharacteristic, direct product factor, Sylow
136C24C22⋊C4×C2911yescharacteristic
137C22×C4—21no—
138C22×C4—22no—
139C22×C4—21no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4C2×C8×C2911yescharacteristic
155C22×C4M16×C2911yescharacteristic
156C22×C4D8×C2912yes—
157C22×C4SD16×C2912yes—
158C2×C8—44no—
159C2×C8—82no—
160C2×C8—82no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23C29×C22⋊C811yescharacteristic
167C23C29×#9911yescharacteristic
168C23C29×#10011yescharacteristic
169C23C29×#10212yes—
170C23C29×#10412yes—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—44no—
187C2×C4—82no—
188C2×C4—81no—
189C2×C4—82no—
190C2×C4—82no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—81no—
194C8—84no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22C29×#32311yescharacteristic
204C22C29×D4⋊C812yes—
205C22C29×#32712yes—
206C22C29×#32911yescharacteristic
207C22C29×#33111yescharacteristic
208C22C29×#35212yes—
209C22C29×#35411yescharacteristic
210C22C29×#35611yescharacteristic
211C4—41no—
212C4—41no—
213C4—42no—
214C4—42no—
215C4—82no—
216C4—82no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2C29×#127011yescharacteristic
221C2C29×#131711yescharacteristic
222C2C29×#131911yescharacteristic
223C2C29×#134412yes—
224C2C29×#134612yes—
subgroupG/H
center, socleC23×C29#99
commutatorC22×C4C2×C8×C29
Frattini, cosocleC2×#95C22×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C24×C29 ◁ C2×C29×#95 ◁ G

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊C4×C29C8semidirect
50. #7104C29direct (N × H)
128. C2×C4⋊C4C8×C29semidirect
135. C29#7104direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#14452
C29×#12802
#710429