Finite Group Databasebeta

← D29⋊#353 #16835758

Subgroups — D29⋊#353 #16835758

Order 3712.

368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D29⋊#99C212yesmaximal, complemented
2#14272068C212yesmaximal, complemented
3#14272067C212yesmaximal, complemented
4#127×D29C211yesmaximal, characteristic
5C2×D4×D29—22no—
6C2×D4×D29C411yescharacteristic, complemented
7C2×D4×D29C2211yescharacteristic
8C2×C22⋊#1181—22no—
9C29×#127C411yescharacteristic, complemented
10#11745302—22no—
11#11745302C411yescharacteristic, complemented
12#11745302C2211yescharacteristic
13#11745236C2211yescharacteristic
14C42×D29C411yescharacteristic, complemented
15#11745227—22no—
16#11745215C2214yescomplemented
17C23×D29—21no—
18C23×D29D412yes—
19C22×#1181—42no—
20C2×D4×C29—22no—
21C2×D4×C29C2×C411yescharacteristic
22C2×D4×C29C2×C411yescharacteristic, complemented
23C2×C22⋊D29—22no—
24C2×C22⋊D29—22no—
25C2×C22⋊D29—21no—
26C2×C22⋊D29D412yes—
27D4×D29—41no—
28D4×D29—41no—
29D4×D29—41no—
30D4×D29—41no—
31D4×D29—48no—
32C2×D116—22no—
33C2×D116C2×C411yescharacteristic, complemented
34C2×D116C2311yescharacteristic
35C2×C4×D29—21no—
36C2×C4×D29C2×C411yescharacteristic
37C22⋊#1181—24no—
38C22⋊#1181—42no—
39C42×C29C2×C411yescharacteristic, complemented
40C4×Dic29—21no—
41C4×Dic29C2×C411yescharacteristic, complemented
42C23×C29—21no—
43C23×C29C22⋊C412yes—
44C22×D29—22no—
45C22×D29—22no—
46C22×D29—21no—
47C22×D29—44no—
48C22×D29—44no—
49C22×D29—41no—
50C22×D29—41no—
51C22×D29C22⋊C411yescharacteristic
52C22×D29C2×D412yes—
53C2×#1181—44no—
54C2×#1181—84no—
55D4×C29—41no—
56D4×C29—41no—
57D4×C29—44no—
58C2×C4×C29—21no—
59C2×C4×C29C22×C411yescharacteristic
60C22⋊D29—42no—
61C22⋊D29—44no—
62C22⋊D29—44no—
63C22⋊D29—42no—
64C2×Dic29—21no—
65C2×Dic29C22⋊C411yescharacteristic
66D116—41no—
67D116—41no—
68D116—44no—
69C4×D29—24no—
70C4×D29—21no—
71C4×D29—21no—
72C2×#353—291nomaximal, Sylow
73C22×C29—22no—
74C22×C29—42no—
75C22×C29—42no—
76C22×C29—41no—
77C22×C29C2×C22⋊C411yescharacteristic
78C2×D29—22no—
79C2×D29—22no—
80C2×D29—44no—
81C2×D29—42no—
82C2×D29—42no—
83C2×D29—41no—
84C2×D29—82no—
85C2×D29—82no—
86C2×D29—82no—
87C2×D29#9911yescharacteristic
88C2×D29#9911yescharacteristic
89#1181—84no—
90C4×C29—22no—
91C4×C29—21no—
92Dic29—22no—
93Dic29—21no—
94C2×#127—291no—
95C2×#99—292no—
96#353—292no—
97#353—292no—
98C2×C29—21no—
99C2×C29—42no—
100C2×C29—81no—
101C2×C29C2×#9911yescharacteristic
102D29—21no—
103D29—42no—
104D29—81no—
105D29#35312yescomplemented
106C22×D4—291no—
107C22×D4—291no—
108C22×D4—582no—
109#127—291no—
110#127—291no—
111#127—291no—
112#127—582no—
113#127#118111yescharacteristic, complemented
114C2×C22⋊C4—582no—
115C2×C42—291no—
116#99—294no—
117#99—582no—
118C29C2×#35311yescharacteristic, complemented, Sylow
119C24—292no—
120C24—581no—
121C2×D4—22no—
122C2×D4—292no—
123C2×D4—291no—
124C2×D4—291no—
125C2×D4—582no—
126C2×D4—581no—
127C2×D4—582no—
128C2×D4—582no—
129C2×D4—1161no—
130C2×D4—1161no—
131C2×D4—1161no—
132C2×D4—1161no—
133C2×D4—1168no—
134C2×D4C2×#118111yescharacteristic
135C2×D4C2×#118111yescharacteristic, complemented
136C22×C4—291no—
137C22×C4—581no—
138C22×C4—1162no—
139C22⋊C4—584no—
140C22⋊C4—1162no—
141C42—291no—
142C42—581no—
143C42C2×#118111yescharacteristic, complemented
144C23—21no—
145C23—291no—
146C23—292no—
147C23—582no—
148C23—582no—
149C23—581no—
150C23—1161no—
151C23—1161no—
152C23—1164no—
153C23—1164no—
154C23C22⋊#118112yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—1161no—
159D4—1161no—
160D4—1164no—
161D4—1162no—
162D4—1164no—
163D4—1164no—
164D4—1162no—
165C2×C4—21no—
166C2×C4—291no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—584no—
170C2×C4—581no—
171C2×C4—1164no—
172C2×C4—2324no—
173C2×C4C22×#118111yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—291no—
179C22—291no—
180C22—582no—
181C22—582no—
182C22—1162no—
183C22—1162no—
184C22—1164no—
185C22—1161no—
186C22—2322no—
187C22—2322no—
188C22—2322no—
189C22C2×C22⋊#118111yescharacteristic
190C4—22no—
191C4—21no—
192C4—582no—
193C4—581no—
194C4—2324no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—292no—
199C2—581no—
200C2—1162no—
201C2—2321no—
202C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC2×C29C2×#99
prime radical#127×D29C2
cosocleC2×D116C23
hypercenter#127#1181
hypocenterC29C2×#353
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D29⋊#99C2semidirect
2. #14272068C2semidirect
3. #14272067C2semidirect
6. C2×D4×D29C4semidirect
9. C29×#127C4semidirect
11. #11745302C4semidirect
14. C42×D29C4semidirect
16. #11745215C22semidirect
22. C2×D4×C29C2×C4semidirect
33. C2×D116C2×C4semidirect
39. C42×C29C2×C4semidirect
41. C4×Dic29C2×C4semidirect
105. D29#353semidirect
113. #127#1181semidirect
118. C29C2×#353semidirect
135. C2×D4C2×#1181semidirect
143. C42C2×#1181semidirect

Maximal subgroups

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

subgroupindex
D29⋊#992
#142720682
#142720672
#127×D292
C2×#35329