Finite Group Databasebeta

← C29×#3093 #16816807

Subgroups — C29×#3093 #16816807

Order 3712.

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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×#525C211yesmaximal, characteristic
2C2×C29×#117C211yesmaximal, characteristic, complemented
3C29×#485C214yesmaximal, complemented
4C29×#482C214yesmaximal, complemented
5C29×#428C212yesmaximal, complemented
6C29×#417C212yesmaximal, complemented
7C29×#407C211yesmaximal, characteristic, complemented
8C2×#41×C29C2211yescharacteristic
9C23×C4×C29C2211yescharacteristic
10C2×M16×C29C2212yes—
11C29×#123—21no—
12C29×C22⋊Q8C2212yes—
13C29×#121C2212yes—
14C29×#120—21no—
15C4×D4×C29—22no—
16C29×#117—22no—
17C29×#117C2211yescharacteristic
18C29×#117C2214yes—
19C2×C4⋊C4×C29C2212yes—
20C2×C22⋊C4×C29—21no—
21C2×C42×C29—21no—
22C29×#107C2214yescomplemented
23C29×#106C2214yescomplemented
24C29×#103C2214yescomplemented
25C29×#102C2214yescomplemented
26C29×C22⋊C8C2214yes—
27C24×C29D411yescharacteristic
28#41×C29—24no—
29C2×Q8×C29C2311yescharacteristic
30C2×D4×C29—22no—
31C2×D4×C29—21no—
32C2×D4×C29C2311yescharacteristic
33C22×C4×C29—24no—
34C22×C4×C29—22no—
35C22×C4×C29—21no—
36C22×C4×C29D411yescharacteristic
37C22×C4×C29D412yes—
38C22×C4×C29C2312yes—
39C22×C4×C29C2311yescharacteristic
40M16×C29—24no—
41C2×C8×C29C2314yes—
42C4⋊C4×C29—22no—
43C4⋊C4×C29—22no—
44C4⋊C4×C29C2314yes—
45C4⋊C4×C29C2312yes—
46C22⋊C4×C29—24no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—22no—
49C22⋊C4×C29—22no—
50C42×C29—24no—
51C42×C29—21no—
52C23×C29—22no—
53C23×C29—21no—
54C23×C29—42no—
55C23×C29C2×D412yes—
56C23×C29C2×D411yescharacteristic
57Q8×C29—22no—
58D4×C29—22no—
59D4×C29—44no—
60D4×C29—42no—
61C2×C4×C29—22no—
62C2×C4×C29—24no—
63C2×C4×C29—24no—
64C2×C4×C29—24no—
65C2×C4×C29—22no—
66C2×C4×C29—21no—
67C2×C4×C29—44no—
68C2×C4×C29—42no—
69C2×C4×C29C2×D412yes—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29#4114yes—
72C2×C4×C29C2411yescharacteristic
73C8×C29—24no—
74#3093C2911yesmaximal, characteristic, direct product factor, Sylow
75C22×C29—22no—
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—22no—
79C22×C29—44no—
80C22×C29—41no—
81C22×C29—42no—
82C22×C29#12312yes—
83C22×C29C22×D411yescharacteristic
84C4×C29—22no—
85C4×C29—41no—
86C4×C29—44no—
87C4×C29—42no—
88C4×C29#12312yes—
89C4×C29C2×#4112yes—
90#525C2×C2911yescharacteristic
91C2×#117C2×C2911yescharacteristic, complemented
92#485C2×C2914yescomplemented
93#482C2×C2914yescomplemented
94#428C2×C2912yescomplemented
95#417C2×C2912yescomplemented
96#407C2×C2911yescharacteristic, complemented
97C2×C29—22no—
98C2×C29—42no—
99C2×C29—81no—
100C2×C29C2×#12311yescharacteristic
101C2×C29#57512yes—
102C2×#41C22×C2911yescharacteristic
103C23×C4C22×C2911yescharacteristic
104C2×M16C22×C2912yes—
105#123—21no—
106C22⋊Q8C22×C2912yes—
107#121C22×C2912yes—
108#120—21no—
109C4×D4—22no—
110#117—22no—
111#117C22×C2914yes—
112#117C22×C2911yescharacteristic
113C2×C4⋊C4C22×C2912yes—
114C2×C22⋊C4—21no—
115C2×C42—21no—
116#107C22×C2914yescomplemented
117#106C22×C2914yescomplemented
118#103C22×C2914yescomplemented
119#102C22×C2914yescomplemented
120C22⋊C8C22×C2914yes—
121C29#309311yescharacteristic, direct product factor, Sylow
122C24D4×C2911yescharacteristic
123#41—24no—
124C2×Q8C23×C2911yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C23×C2911yescharacteristic
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4D4×C2911yescharacteristic
132C22×C4D4×C2912yes—
133C22×C4C23×C2912yes—
134C22×C4C23×C2911yescharacteristic
135M16—24no—
136C2×C8C23×C2914yes—
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4C23×C2914yes—
140C4⋊C4C23×C2912yes—
141C22⋊C4—24no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C42—24no—
146C42—21no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×D4×C2912yes—
151C23C2×D4×C2911yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4C2×D4×C2912yes—
165C2×C4C2×D4×C2911yescharacteristic
166C2×C4#41×C2914yes—
167C2×C4C24×C2911yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22C29×#12312yes—
177C22C22×D4×C2911yescharacteristic
178C4—22no—
179C4—41no—
180C4—44no—
181C4—42no—
182C4C29×#12312yes—
183C4C2×#41×C2912yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×C29×#12311yescharacteristic
188C2C29×#57512yes—
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#117C2semidirect
3. C29×#485C2semidirect
4. C29×#482C2semidirect
5. C29×#428C2semidirect
6. C29×#417C2semidirect
7. C29×#407C2semidirect
22. C29×#107C22semidirect
23. C29×#106C22semidirect
24. C29×#103C22semidirect
25. C29×#102C22semidirect
74. #3093C29direct (N × H)
91. C2×#117C2×C29semidirect
92. #485C2×C29semidirect
93. #482C2×C29semidirect
94. #428C2×C29semidirect
95. #417C2×C29semidirect
96. #407C2×C29semidirect
116. #107C22×C29semidirect
117. #106C22×C29semidirect
118. #103C22×C29semidirect
119. #102C22×C29semidirect
121. C29#3093direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5252
C2×C29×#1172
C29×#4852
C29×#4822
C29×#4282
C29×#4172
C29×#4072
#309329