Finite Group Databasebeta

← C29×#10584 #20305484

Subgroups — C29×#10584 #20305484

Order 7424.

374 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2844C211yesmaximal, characteristic
2C29×#1847C211yesmaximal, characteristic
3C29×#1836C212yesmaximal
4C29×#1295C212yesmaximal
5C29×#1295C211yesmaximal, characteristic
6C2×C29×#107—21no—
7C2×C29×#106—21no—
8C2×C29×#97C2212yes—
9C2×C29×#97C2211yescharacteristic
10C29×#400—21no—
11C29×#400—22no—
12C29×#395—21no—
13C29×#395—22no—
14C29×#384C2211yescharacteristic
15C29×#382C2212yes—
16C29×#382C2211yescharacteristic
17C29×#340—22no—
18C29×#340—22no—
19C22×Q8×C29—21no—
20C22×C8×C29—21no—
21C22×C8×C29—22no—
22C2×C4⋊C4×C29—21no—
23C2×C4⋊C4×C29—22no—
24C2×C4⋊C4×C29—21no—
25C2×C4⋊C4×C29—22no—
26C2×C4⋊C4×C29D411yescharacteristic
27C2×C4⋊C4×C29D411yescharacteristic
28C2×C4⋊C4×C29D412yes—
29C2×C4⋊C4×C29D412yes—
30C2×C42×C29C2311yescharacteristic
31C29×#107—42no—
32C29×#106—42no—
33C29×#97—21no—
34C29×#97—22no—
35C29×#97Q812yescomplemented
36C29×#97Q814yescomplemented
37C29×#95—21no—
38C29×#95—22no—
39C29×#95—21no—
40C29×#95—22no—
41C29×#95—22no—
42C29×#95—22no—
43C2×Q8×C29—81no—
44C2×Q8×C29—82no—
45C22×C4×C29—21no—
46C22×C4×C29—22no—
47C22×C4×C29—21no—
48C22×C4×C29—22no—
49C22×C4×C29—41no—
50C22×C4×C29C2×D411yescharacteristic
51C22×C4×C29C2×D412yes—
52C2×C8×C29—22no—
53C2×C8×C29—22no—
54C2×C8×C29—22no—
55C2×C8×C29—24no—
56C2×C8×C29—42no—
57C2×C8×C29—42no—
58C4⋊C4×C29—42no—
59C4⋊C4×C29—42no—
60C4⋊C4×C29—41no—
61C4⋊C4×C29—41no—
62C4⋊C4×C29—44no—
63C4⋊C4×C29—41no—
64C4⋊C4×C29—41no—
65C4⋊C4×C29—81no—
66C4⋊C4×C29—82no—
67C42×C29C2×Q811yescharacteristic
68C42×C29C2×Q812yes—
69C42×C29#4111yescharacteristic
70#10584C2911yesmaximal, characteristic, direct product factor, Sylow
71C23×C29#12011yescharacteristic
72Q8×C29—84no—
73C2×C4×C29—21no—
74C2×C4×C29—22no—
75C2×C4×C29—22no—
76C2×C4×C29—21no—
77C2×C4×C29—41no—
78C2×C4×C29—41no—
79C2×C4×C29—42no—
80C2×C4×C29—42no—
81C2×C4×C29—42no—
82C2×C4×C29—42no—
83C2×C4×C29—42no—
84C2×C4×C29—42no—
85C2×C4×C29—42no—
86C2×C4×C29—42no—
87C2×C4×C29—81no—
88C2×C4×C29—82no—
89C2×C4×C29C22⋊Q811yescharacteristic
90C2×C4×C29C22⋊Q812yes—
91C2×C4×C29C4⋊Q811yescharacteristic
92C2×C4×C29C4⋊Q812yes—
93C8×C29—24no—
94C8×C29—44no—
95#2844C2×C2911yescharacteristic
96#1847C2×C2911yescharacteristic
97#1836C2×C2912yes—
98#1295C2×C2912yes—
99#1295C2×C2911yescharacteristic
100C22×C29#39511yescharacteristic
101C22×C29#45311yescharacteristic
102C22×C29#45412yes—
103C22×C29#45512yes—
104C22×C29#45611yescharacteristic
105C4×C29—21no—
106C4×C29—21no—
107C4×C29—22no—
108C4×C29—22no—
109C4×C29—81no—
110C4×C29—81no—
111C4×C29—82no—
112C4×C29—82no—
113C4×C29—161no—
114C2×#107—21no—
115C2×#106—21no—
116C2×#97C22×C2912yes—
117C2×#97C22×C2911yescharacteristic
118#400—22no—
119#400—21no—
120#395—22no—
121#395—21no—
122#384C22×C2911yescharacteristic
123#382C22×C2912yes—
124#382C22×C2911yescharacteristic
125#340—22no—
126#340—22no—
127C2×C29#165711yescharacteristic
128C2×C29#165911yescharacteristic
129C2×C29#166412yes—
130C2×C29#206011yescharacteristic
131C2×C29#206112yes—
132C22×Q8—21no—
133C22×C8—21no—
134C22×C8—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4D4×C2912yes—
140C2×C4⋊C4D4×C2912yes—
141C2×C4⋊C4D4×C2911yescharacteristic
142C2×C4⋊C4D4×C2911yescharacteristic
143C2×C42C23×C2911yescharacteristic
144#107—42no—
145#106—42no—
146#97—21no—
147#97—22no—
148#97Q8×C2912yescomplemented
149#97Q8×C2914yescomplemented
150#95—22no—
151#95—21no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156C29#1058411yescharacteristic, direct product factor, Sylow
157C2×Q8—81no—
158C2×Q8—82no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4C2×D4×C2911yescharacteristic
165C22×C4C2×D4×C2912yes—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—24no—
170C2×C8—42no—
171C2×C8—42no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—44no—
179C4⋊C4—81no—
180C4⋊C4—82no—
181C42C2×Q8×C2911yescharacteristic
182C42C2×Q8×C2912yes—
183C42#41×C2911yescharacteristic
184C23C29×#12011yescharacteristic
185Q8—84no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—82no—
202C2×C4C29×C22⋊Q811yescharacteristic
203C2×C4C29×C22⋊Q812yes—
204C2×C4C29×C4⋊Q811yescharacteristic
205C2×C4C29×C4⋊Q812yes—
206C8—24no—
207C8—44no—
208C22C29×#39511yescharacteristic
209C22C29×#45311yescharacteristic
210C22C29×#45412yes—
211C22C29×#45512yes—
212C22C29×#45611yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—82no—
220C4—82no—
221C4—161no—
222C2C29×#165711yescharacteristic
223C2C29×#165911yescharacteristic
224C2C29×#166412yes—
225C2C29×#206011yescharacteristic
226C2C29×#206112yes—
subgroupG/H
center, socle, prime radicalC23×C29#120
commutator, Frattini, cosocleC2×C42C23×C29
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
35. C29×#97Q8semidirect
36. C29×#97Q8semidirect
70. #10584C29direct (N × H)
148. #97Q8×C29semidirect
149. #97Q8×C29semidirect
156. C29#10584direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#28442
C29×#18472
C29×#18362
C29×#12952
#1058429