Finite Group Databasebeta

← C29×#12302 #20307202

Subgroups — C29×#12302 #20307202

Order 7424.

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

normal subgroups only

This group has 310 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×#3202C211yesmaximal, characteristic
2C29×#2239C212yesmaximal, complemented
3C29×#2098C211yesmaximal, characteristic
4C29×#1340C212yesmaximal, complemented
5C29×#1321C211yesmaximal, characteristic
6C29×#536—21no—
7C29×#485—22no—
8C29×#470C2212yes—
9C29×#467—21no—
10C29×#451—22no—
11C29×#430C2211yescharacteristic
12C29×#424—21no—
13C29×#421—21no—
14C29×#408C2211yescharacteristic
15C29×#365—22no—
16C29×#362—22no—
17C29×#349C2212yes—
18C29×H(3,ℤ/4)C2211yescharacteristic
19C2×#41×C29D411yescharacteristic
20C22×Q8×C29—21no—
21C2×Q16×C29—21no—
22C2×Q16×C29D412yes—
23C2×M16×C29—21no—
24C2×M16×C29C2311yescharacteristic
25C22×C8×C29D411yescharacteristic
26C29×C4⋊Q8—41no—
27C29×#124—41no—
28C29×#123—41no—
29C29×#123—41no—
30C29×C22⋊Q8—22no—
31C29×C22⋊Q8—22no—
32C29×#117—21no—
33C29×#117—21no—
34C29×M32—22no—
35C29×#108—22no—
36C29×#107—21no—
37C29×#106D412yes—
38C29×C4⋊C8—42no—
39C29×#104—42no—
40C29×#103—22no—
41C29×#103—22no—
42C29×C22⋊C8—22no—
43#41×C29—41no—
44#41×C29—41no—
45C2×Q8×C29—22no—
46C2×Q8×C29—41no—
47C2×Q8×C29—81no—
48C2×Q8×C29—81no—
49C2×Q8×C29SD1611yescharacteristic
50C2×D4×C29—21no—
51C2×D4×C29SD1611yescharacteristic
52C22×C4×C29—21no—
53C22×C4×C29—41no—
54C22×C4×C29C2×D411yescharacteristic
55Q16×C29—42no—
56Q16×C29—81no—
57M16×C29—41no—
58M16×C29—41no—
59M16×C29—41no—
60C2×C8×C29—21no—
61C2×C8×C29—41no—
62C2×C8×C29—41no—
63C2×C8×C29C2×D412yes—
64C4⋊C4×C29—22no—
65C4⋊C4×C29—41no—
66C4⋊C4×C29—42no—
67C4⋊C4×C29—42no—
68C22⋊C4×C29—41no—
69C22⋊C4×C29—42no—
70C22⋊C4×C29—41no—
71C22⋊C4×C29—42no—
72C42×C29—22no—
73C42×C29—41no—
74C16×C29—42no—
75#12302C2911yesmaximal, characteristic, direct product factor, Sylow
76C23×C29—21no—
77C23×C29AGL(1,ℤ/8)11yescharacteristic
78Q8×C29—41no—
79Q8×C29—42no—
80Q8×C29—42no—
81Q8×C29—82no—
82D4×C29—41no—
83D4×C29—81no—
84C2×C4×C29—21no—
85C2×C4×C29—21no—
86C2×C4×C29—21no—
87C2×C4×C29—41no—
88C2×C4×C29—41no—
89C2×C4×C29—42no—
90C2×C4×C29—42no—
91C2×C4×C29—42no—
92C2×C4×C29—82no—
93C2×C4×C29#12011yescharacteristic
94C2×C4×C29C2×SD1611yescharacteristic
95C8×C29—22no—
96C8×C29—41no—
97C8×C29—81no—
98#3202C2×C2911yescharacteristic
99#2239C2×C2912yescomplemented
100#2098C2×C2911yescharacteristic
101#1340C2×C2912yescomplemented
102#1321C2×C2911yescharacteristic
103C22×C29—21no—
104C22×C29—41no—
105C22×C29—42no—
106C22×C29—41no—
107C22×C29#45011yescharacteristic
108C4×C29—21no—
109C4×C29—41no—
110C4×C29—82no—
111C4×C29—82no—
112C4×C29—82no—
113C4×C29#45311yescharacteristic
114C4×C29#45811yescharacteristic
115#536—21no—
116#485—22no—
117#470C22×C2912yes—
118#467—21no—
119#451—22no—
120#430C22×C2911yescharacteristic
121#424—21no—
122#421—21no—
123#408C22×C2911yescharacteristic
124#365—22no—
125#362—22no—
126#349C22×C2912yes—
127H(3,ℤ/4)C22×C2911yescharacteristic
128C2×C29—21no—
129C2×C29—41no—
130C2×C29—81no—
131C2×C29#161311yescharacteristic
132C2×#41D4×C2911yescharacteristic
133C22×Q8—21no—
134C2×Q16—21no—
135C2×Q16D4×C2912yes—
136C2×M16—21no—
137C2×M16C23×C2911yescharacteristic
138C22×C8D4×C2911yescharacteristic
139C4⋊Q8—41no—
140#124—41no—
141#123—41no—
142#123—41no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145#117—21no—
146#117—21no—
147M32—22no—
148#108—22no—
149#107—21no—
150#106D4×C2912yes—
151C4⋊C8—42no—
152#104—42no—
153#103—22no—
154#103—22no—
155C22⋊C8—22no—
156C29#1230211yescharacteristic, direct product factor, Sylow
157#41—41no—
158#41—41no—
159C2×Q8—22no—
160C2×Q8—41no—
161C2×Q8—81no—
162C2×Q8—81no—
163C2×Q8SD16×C2911yescharacteristic
164C2×D4—21no—
165C2×D4SD16×C2911yescharacteristic
166C22×C4—21no—
167C22×C4—41no—
168C22×C4C2×D4×C2911yescharacteristic
169Q16—42no—
170Q16—81no—
171M16—41no—
172M16—41no—
173M16—41no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C2×D4×C2912yes—
178C4⋊C4—22no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—41no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—22no—
187C42—41no—
188C16—42no—
189C23—21no—
190C23C29×AGL(1,ℤ/8)11yescharacteristic
191Q8—41no—
192Q8—42no—
193Q8—42no—
194Q8—82no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—82no—
206C2×C4C29×#12011yescharacteristic
207C2×C4C2×SD16×C2911yescharacteristic
208C8—22no—
209C8—41no—
210C8—81no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22C29×#45011yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4C29×#45311yescharacteristic
222C4C29×#45811yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2C29×#161311yescharacteristic
subgroupG/H
center, socleC2×C29#1613
commutator, Frattini, cosocleC2×M16C23×C29
prime radicalC2×#41×C29D4
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×#1340C2semidirect
75. #12302C29direct (N × H)
99. #2239C2×C29semidirect
101. #1340C2×C29semidirect
156. C29#12302direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32022
C29×#22392
C29×#20982
C29×#13402
C29×#13212
#1230229