Finite Group Databasebeta

← D29×#353 #16821148

Subgroups — D29×#353 #16821148

Order 3712.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#127×D29C211yesmaximal, characteristic
2#99×D29C212yesmaximal, complemented
3#14270956C211yesmaximal, characteristic, complemented
4#14270955C212yesmaximal, complemented
5C29×#353C211yesmaximal, characteristic, complemented
6C2×D4×D29—22no—
7C2×D4×D29C411yescharacteristic, complemented
8C2×D4×D29C2211yescharacteristic
9C29×#127C2211yescharacteristic
10#11745302—22no—
11#11745302C411yescharacteristic, complemented
12#11745302C2211yescharacteristic
13C22⋊C4×D29—22no—
14#11745236C411yescharacteristic, complemented
15C42×D29C411yescharacteristic, complemented
16C29×#99C2212yescomplemented
17#11745182C2212yescomplemented
18#11745154—22no—
19C23×D29—21no—
20C23×D29D412yes—
21C2×D4×C29—22no—
22C2×D4×C29C2×C411yescharacteristic, complemented
23C2×D4×C29C2311yescharacteristic
24C2×C22⋊D29—22no—
25C2×C22⋊D29—22no—
26C2×C22⋊D29—21no—
27C2×C22⋊D29D412yes—
28D4×D29—41no—
29D4×D29—41no—
30D4×D29—41no—
31D4×D29—41no—
32D4×D29—48no—
33C2×D116—22no—
34C2×D116C2×C411yescharacteristic
35C2×D116C2×C411yescharacteristic, complemented
36C2×C4×D29—21no—
37C2×C4×D29—42no—
38C2×C4×D29C2×C411yescharacteristic
39C22⋊C4×C29—22no—
40C42×C29C2×C411yescharacteristic, complemented
41C22⋊Dic29—22no—
42#90781—42no—
43C4×Dic29—21no—
44C4×Dic29C2×C411yescharacteristic, complemented
45C23×C29—21no—
46C23×C29C2×D412yes—
47C22×D29—22no—
48C22×D29—22no—
49C22×D29—21no—
50C22×D29—44no—
51C22×D29—44no—
52C22×D29—41no—
53C22×D29—41no—
54C22×D29C22⋊C411yescharacteristic
55C22×D29C22⋊C412yes—
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—44no—
59C2×C4×C29—21no—
60C2×C4×C29—42no—
61C2×C4×C29C22×C411yescharacteristic
62C22⋊D29—42no—
63C22⋊D29—44no—
64C22⋊D29—44no—
65C22⋊D29—42no—
66C2×Dic29—21no—
67C2×Dic29—42no—
68C2×Dic29C22⋊C411yescharacteristic
69D116—41no—
70D116—41no—
71D116—44no—
72C4×D29—24no—
73C4×D29—21no—
74C4×D29—21no—
75C4×D29—84no—
76C2×#353—291nomaximal, Sylow
77C22×C29—22no—
78C22×C29—42no—
79C22×C29—42no—
80C22×C29—41no—
81C22×C29C2×C22⋊C411yescharacteristic
82C2×D29—22no—
83C2×D29—22no—
84C2×D29—44no—
85C2×D29—42no—
86C2×D29—42no—
87C2×D29—41no—
88C2×D29—82no—
89C2×D29—82no—
90C2×D29—82no—
91C2×D29#9911yescharacteristic
92C2×D29#9911yescharacteristic
93C4×C29—22no—
94C4×C29—21no—
95C4×C29—82no—
96Dic29—22no—
97Dic29—21no—
98Dic29—82no—
99C2×#127—291no—
100C2×#99—292no—
101#353—291no—
102#353—292no—
103#353D2911yescharacteristic, direct product factor
104C2×C29—21no—
105C2×C29—42no—
106C2×C29—81no—
107C2×C29C2×#9911yescharacteristic
108D29—21no—
109D29—42no—
110D29—81no—
111D29#35312yesdirect product factor
112C22×D4—291no—
113C22×D4—291no—
114C22×D4—582no—
115#127—291no—
116#127—291no—
117#127—291no—
118#127—582no—
119#127C2×D2911yescharacteristic
120C2×C22⋊C4—582no—
121C2×C42—291no—
122#99—292no—
123#99—582no—
124#99C2×D2912yescomplemented
125C29C2×#35311yescharacteristic, complemented, Sylow
126C24—292no—
127C24—581no—
128C2×D4—22no—
129C2×D4—292no—
130C2×D4—291no—
131C2×D4—291no—
132C2×D4—582no—
133C2×D4—581no—
134C2×D4—582no—
135C2×D4—582no—
136C2×D4—1161no—
137C2×D4—1161no—
138C2×D4—1161no—
139C2×D4—1161no—
140C2×D4—1168no—
141C2×D4C4×D2911yescharacteristic, complemented
142C2×D4C22×D2911yescharacteristic
143C22×C4—291no—
144C22×C4—581no—
145C22×C4—1162no—
146C22⋊C4—22no—
147C22⋊C4—582no—
148C22⋊C4—1162no—
149C42—291no—
150C42—581no—
151C42C4×D2911yescharacteristic, complemented
152C23—21no—
153C23—291no—
154C23—292no—
155C23—582no—
156C23—582no—
157C23—581no—
158C23—1161no—
159C23—1161no—
160C23—1164no—
161C23—1164no—
162C23D4×D2912yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—1161no—
167D4—1161no—
168D4—1164no—
169D4—1162no—
170D4—1164no—
171D4—1164no—
172D4—1162no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—291no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—584no—
179C2×C4—581no—
180C2×C4—1162no—
181C2×C4—2324no—
182C2×C4C2×C4×D2911yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—291no—
188C22—291no—
189C22—582no—
190C22—582no—
191C22—1162no—
192C22—1162no—
193C22—1164no—
194C22—1161no—
195C22—2322no—
196C22—2322no—
197C22—2322no—
198C22C22⋊C4×D2911yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—582no—
203C4—581no—
204C4—2322no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—292no—
209C2—581no—
210C2—1162no—
211C2—2321no—
212C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#353C2
socleC2×C29C2×#99
prime radical#127×D29C2
cosocleC2×D4×C29C23
hypercenter#353D29
hypocenterC29C2×#353
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D29C2semidirect
3. #14270956C2semidirect
4. #14270955C2semidirect
5. C29×#353C2semidirect
7. C2×D4×D29C4semidirect
11. #11745302C4semidirect
14. #11745236C4semidirect
15. C42×D29C4semidirect
16. C29×#99C22semidirect
17. #11745182C22semidirect
22. C2×D4×C29C2×C4semidirect
35. C2×D116C2×C4semidirect
40. C42×C29C2×C4semidirect
44. C4×Dic29C2×C4semidirect
103. #353D29direct (N × H)
111. D29#353direct (N × H)
124. #99C2×D29semidirect
125. C29C2×#353semidirect
141. C2×D4C4×D29semidirect
151. C42C4×D29semidirect

Maximal subgroups

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

subgroupindex
#127×D292
#99×D292
#142709562
#142709552
C29×#3532
C2×#35329