Finite Group Databasebeta

← D29×#354 #16821151

Subgroups — D29×#354 #16821151

Order 3712.

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

normal subgroups only

This group has 284 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#124×D29C211yesmaximal, characteristic
2#99×D29C212yesmaximal
3#14270958C211yesmaximal, characteristic, complemented
4#14270957C212yesmaximal, complemented
5C29×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D29C411yescharacteristic, complemented
7C2×D4×D29C2211yescharacteristic
8C29×#124C2211yescharacteristic
9#11745309C411yescharacteristic, complemented
10#11745298C2211yescharacteristic
11#11745247—22no—
12C22⋊C4×D29—22no—
13C22⋊C4×D29—22no—
14#11745237C411yescharacteristic, complemented
15C42×D29C411yescharacteristic, complemented
16C29×#99C2212yes—
17#11745182C2212yes—
18#11745154—22no—
19C23×D29D412yes—
20C2×Q8×C29C2×C411yescharacteristic, complemented
21C2×D4×C29C2311yescharacteristic
22C2×C22⋊D29D412yes—
23Q8×D29—41no—
24Q8×D29—41no—
25D4×D29—41no—
26D4×D29—41no—
27C2×D116C2×C411yescharacteristic
28C2×C4×D29—21no—
29C2×C4×D29—21no—
30C2×C4×D29—42no—
31C2×C4×D29C2×C411yescharacteristic
32C2×Dic58—21no—
33C2×Dic58C2×C411yescharacteristic, complemented
34C22⋊C4×C29—22no—
35C22⋊C4×C29—22no—
36C42×C29C2×C411yescharacteristic, complemented
37C22⋊Dic29—22no—
38C22⋊Dic29—22no—
39#90781—22no—
40#90781—22no—
41#90781—42no—
42C4×Dic29—21no—
43C4×Dic29C2×C411yescharacteristic, complemented
44C23×C29C2×D412yes—
45C22×D29—22no—
46C22×D29—22no—
47C22×D29—44no—
48C22×D29C22⋊C411yescharacteristic
49C22×D29C22⋊C412yes—
50Q8×C29—41no—
51D4×C29—41no—
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—42no—
55C2×C4×C29C22×C411yescharacteristic
56C22⋊D29—42no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—42no—
60C2×Dic29C22⋊C411yescharacteristic
61D116—41no—
62C4×D29—21no—
63C4×D29—21no—
64C4×D29—42no—
65C4×D29—41no—
66C4×D29—41no—
67C4×D29—84no—
68Dic58—42no—
69Dic58—41no—
70C2×#354—291nomaximal, Sylow
71C22×C29—22no—
72C22×C29—42no—
73C22×C29C2×C22⋊C411yescharacteristic
74C2×D29—22no—
75C2×D29—22no—
76C2×D29—44no—
77C2×D29—42no—
78C2×D29—82no—
79C2×D29#9911yescharacteristic
80C2×D29#9911yescharacteristic
81C4×C29—21no—
82C4×C29—41no—
83C4×C29—41no—
84C4×C29—82no—
85Dic29—21no—
86Dic29—41no—
87Dic29—41no—
88Dic29—82no—
89C2×#124—291no—
90C2×#99—292no—
91#354—291no—
92#354—292no—
93#354D2911yescharacteristic, direct product factor
94C2×C29—21no—
95C2×C29—42no—
96C2×C29C2×#9911yescharacteristic
97D29—21no—
98D29—42no—
99D29#35412yesdirect product factor
100C22×Q8—291no—
101C22×D4—291no—
102#124—291no—
103#124—291no—
104#124—291no—
105#124—582no—
106#124C2×D2911yescharacteristic
107C2×C22⋊C4—582no—
108C2×C22⋊C4—582no—
109C2×C42—291no—
110#99—292no—
111#99—582no—
112#99C2×D2912yes—
113C29C2×#35411yescharacteristic, complemented, Sylow
114C24—292no—
115C2×Q8—291no—
116C2×Q8—581no—
117C2×Q8—1161no—
118C2×Q8—1161no—
119C2×Q8C4×D2911yescharacteristic, complemented
120C2×D4—292no—
121C2×D4—291no—
122C2×D4—1161no—
123C2×D4—1161no—
124C2×D4C22×D2911yescharacteristic
125C22×C4—291no—
126C22×C4—581no—
127C22×C4—581no—
128C22×C4—1162no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—582no—
132C22⋊C4—582no—
133C22⋊C4—582no—
134C22⋊C4—582no—
135C22⋊C4—1162no—
136C42—291no—
137C42—581no—
138C42C4×D2911yescharacteristic, complemented
139C23—291no—
140C23—292no—
141C23—582no—
142C23—582no—
143C23—1164no—
144C23D4×D2912yes—
145Q8—41no—
146Q8—1161no—
147Q8—1162no—
148D4—41no—
149D4—1161no—
150D4—1162no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—291no—
155C2×C4—581no—
156C2×C4—581no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—1161no—
160C2×C4—1161no—
161C2×C4—1162no—
162C2×C4—1162no—
163C2×C4—2324no—
164C2×C4C2×C4×D2911yescharacteristic
165C22—22no—
166C22—42no—
167C22—291no—
168C22—291no—
169C22—582no—
170C22—582no—
171C22—1162no—
172C22—1164no—
173C22—2322no—
174C22C22⋊C4×D2911yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—581no—
180C4—1161no—
181C4—1161no—
182C4—2322no—
183C2—21no—
184C2—42no—
185C2—292no—
186C2—581no—
187C2—1162no—
188C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#354C2
socleC2×C29C2×#99
prime radicalC2×D4×D29C22
cosocleC2×D4×C29C23
hypercenter#354D29
hypocenterC29C2×#354
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #14270958C2semidirect
4. #14270957C2semidirect
5. C29×#354C2semidirect
6. C2×Q8×D29C4semidirect
9. #11745309C4semidirect
14. #11745237C4semidirect
15. C42×D29C4semidirect
20. C2×Q8×C29C2×C4semidirect
33. C2×Dic58C2×C4semidirect
36. C42×C29C2×C4semidirect
43. C4×Dic29C2×C4semidirect
93. #354D29direct (N × H)
99. D29#354direct (N × H)
113. C29C2×#354semidirect
119. C2×Q8C4×D29semidirect
138. C42C4×D29semidirect

Maximal subgroups

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

subgroupindex
#124×D292
#99×D292
#142709582
#142709572
C29×#3542
C2×#35429