Finite Group Databasebeta

← C29×#12307 #20307207

Subgroups — C29×#12307 #20307207

Order 7424.

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

normal subgroups only

This group has 318 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×#3253C211yesmaximal, characteristic
2C29×#2238C212yesmaximal, complemented
3C29×#2102C211yesmaximal, characteristic, complemented
4C29×#1339C212yesmaximal, complemented
5C29×#1327C211yesmaximal, characteristic, complemented
6C29×#532—21no—
7C29×#476—22no—
8C29×#469—21no—
9C29×#469C2212yes—
10C29×#459—22no—
11C29×#430C2211yescharacteristic
12C29×#423C2211yescharacteristic
13C29×#365—22no—
14C29×#361—22no—
15C29×#349C2212yes—
16C29×#344—21no—
17C29×#339—21no—
18C29×H(3,ℤ/4)C2211yescharacteristic
19C2×#41×C29—41no—
20C2×D8×C29—21no—
21C2×D8×C29D412yes—
22C2×M16×C29—21no—
23C2×M16×C29D411yescharacteristic
24C2×M16×C29C2311yescharacteristic
25C29×C4⋊Q8—21no—
26C29×#127—21no—
27C29×#124—41no—
28C29×#121—22no—
29C29×#121—41no—
30C4×D4×C29—22no—
31C4×D4×C29—41no—
32C29×#117—21no—
33C2×C42×C29D411yescharacteristic
34C29×M32—22no—
35C29×#108—22no—
36C29×#106—21no—
37C29×#106D412yes—
38C29×C4⋊C8—22no—
39C29×#102—22no—
40C29×#102—22no—
41#41×C29—84no—
42C2×Q8×C29—41no—
43C2×D4×C29—22no—
44C2×D4×C29—41no—
45C2×D4×C29—41no—
46C2×D4×C29—42no—
47C22×C4×C29—21no—
48C22×C4×C29—42no—
49C22×C4×C29C2×D411yescharacteristic
50D8×C29—42no—
51D8×C29—81no—
52M16×C29—41no—
53M16×C29—41no—
54M16×C29—41no—
55M16×C29—41no—
56C2×C8×C29—21no—
57C2×C8×C29—41no—
58C2×C8×C29C2×D412yes—
59C4⋊C4×C29—22no—
60C4⋊C4×C29—41no—
61C4⋊C4×C29—41no—
62C22⋊C4×C29—42no—
63C22⋊C4×C29—42no—
64C22⋊C4×C29—41no—
65C42×C29—21no—
66C42×C29—41no—
67C42×C29SD1611yescharacteristic
68C42×C29SD1611yescharacteristic
69C16×C29—42no—
70#12307C2911yesmaximal, characteristic, direct product factor, Sylow
71C23×C29—42no—
72C23×C29AGL(1,ℤ/8)11yescharacteristic
73Q8×C29—82no—
74D4×C29—42no—
75D4×C29—42no—
76D4×C29—82no—
77D4×C29—82no—
78D4×C29—84no—
79C2×C4×C29—21no—
80C2×C4×C29—21no—
81C2×C4×C29—21no—
82C2×C4×C29—21no—
83C2×C4×C29—42no—
84C2×C4×C29—42no—
85C2×C4×C29—84no—
86C2×C4×C29—81no—
87C2×C4×C29#12011yescharacteristic
88C2×C4×C29C2×SD1611yescharacteristic
89C8×C29—22no—
90C8×C29—41no—
91C8×C29—81no—
92#3253C2×C2911yescharacteristic
93#2238C2×C2912yescomplemented
94#2102C2×C2911yescharacteristic, complemented
95#1339C2×C2912yescomplemented
96#1327C2×C2911yescharacteristic, complemented
97C22×C29—21no—
98C22×C29—41no—
99C22×C29—82no—
100C22×C29—82no—
101C22×C29—82no—
102C22×C29#45011yescharacteristic
103C4×C29—22no—
104C4×C29—21no—
105C4×C29—41no—
106C4×C29—82no—
107C4×C29—161no—
108C4×C29#45411yescharacteristic
109C4×C29#45811yescharacteristic
110#532—21no—
111#476—22no—
112#469—21no—
113#469C22×C2912yes—
114#459—22no—
115#430C22×C2911yescharacteristic
116#423C22×C2911yescharacteristic
117#365—22no—
118#361—22no—
119#349C22×C2912yes—
120#344—21no—
121#339—21no—
122H(3,ℤ/4)C22×C2911yescharacteristic
123C2×C29—21no—
124C2×C29—41no—
125C2×C29—162no—
126C2×C29#161611yescharacteristic
127C2×#41—41no—
128C2×D8—21no—
129C2×D8D4×C2912yes—
130C2×M16—21no—
131C2×M16D4×C2911yescharacteristic
132C2×M16C23×C2911yescharacteristic
133C4⋊Q8—21no—
134#127—21no—
135#124—41no—
136#121—22no—
137#121—41no—
138C4×D4—22no—
139C4×D4—41no—
140#117—21no—
141C2×C42D4×C2911yescharacteristic
142M32—22no—
143#108—22no—
144#106—21no—
145#106D4×C2912yes—
146C4⋊C8—22no—
147#102—22no—
148#102—22no—
149C29#1230711yescharacteristic, direct product factor, Sylow
150#41—84no—
151C2×Q8—41no—
152C2×D4—22no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—21no—
157C22×C4—42no—
158C22×C4C2×D4×C2911yescharacteristic
159D8—42no—
160D8—81no—
161M16—41no—
162M16—41no—
163M16—41no—
164M16—41no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8C2×D4×C2912yes—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—41no—
174C42—21no—
175C42—41no—
176C42SD16×C2911yescharacteristic
177C42SD16×C2911yescharacteristic
178C16—42no—
179C23—42no—
180C23C29×AGL(1,ℤ/8)11yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—81no—
195C2×C4C29×#12011yescharacteristic
196C2×C4C2×SD16×C2911yescharacteristic
197C8—22no—
198C8—41no—
199C8—81no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22C29×#45011yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—161no—
211C4C29×#45411yescharacteristic
212C4C29×#45811yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2C29×#161611yescharacteristic
subgroupG/H
center, socleC2×C29#1616
commutator, Frattini, cosocleC2×M16C23×C29
prime radicalC29×#3253C2
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×#2238C2semidirect
3. C29×#2102C2semidirect
4. C29×#1339C2semidirect
5. C29×#1327C2semidirect
70. #12307C29direct (N × H)
93. #2238C2×C29semidirect
94. #2102C2×C29semidirect
95. #1339C2×C29semidirect
96. #1327C2×C29semidirect
149. C29#12307direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32532
C29×#22382
C29×#21022
C29×#13392
C29×#13272
#1230729