Finite Group Databasebeta

← #16818563

Subgroups — #16818563

Order 3712.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271873C211yesmaximal, characteristic, complemented
2#14271535C211yesmaximal, characteristic, complemented
3#14271355C211yesmaximal, characteristic
4#14270911C211yesmaximal, characteristic, complemented
5Q8⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#460C211yesmaximal, characteristic, complemented
8C2×SD16×C29—21no—
9C29×#127C2211yescharacteristic
10C4×Q8×C29C2211yescharacteristic
11#11745308—21no—
12C2×#90783—22no—
13C2×#90782—21no—
14#11745258—22no—
15C4⋊C4×D29—21no—
16C4×D116—21no—
17C4×D116C2211yescharacteristic
18#11745232—21no—
19#11745231C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C29×#102—21no—
22#11745180—21no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29—21no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×C4×D29—22no—
32C2×Dic58D412yes—
33SD16×C29—42no—
34C2×C8×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29D411yescharacteristic
37C42×C29—21no—
38C42×C29C2311yescharacteristic
39#90783—44no—
40#90782—42no—
41#90781—22no—
42#90781—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29D411yescharacteristic
46#90779—22no—
47#90779—22no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—41no—
51C22×D29—21no—
52Q8×C29—21no—
53Q8×C29—21no—
54D4×C29—42no—
55D4×C29—41no—
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×Dic29—21no—
65C2×Dic29—22no—
66D116—21no—
67D116SD1612yescomplemented
68C4×D29—41no—
69C4×D29—41no—
70C4×D29—82no—
71Dic58—42no—
72C8×C29—41no—
73#6597—22no—
74#6597—41no—
75#1622—291nomaximal, Sylow
76C22×C29—81no—
77C22×C29—81no—
78C22×C29—81no—
79C22×C29#12011yescharacteristic
80C2×D29—22no—
81C2×D29—41no—
82C2×D29—41no—
83C4×C29—21no—
84C4×C29—41no—
85C4×C29—41no—
86C4×C29C2×SD1611yescharacteristic
87C4×C29#13511yescharacteristic
88C4×C29AGL(1,ℤ/8)11yescharacteristic
89C4×C29#13711yescharacteristic
90Dic29—41no—
91Dic29—42no—
92#554—291no—
93#492—291no—
94#460D2911yescharacteristic, complemented
95#459—291no—
96#333—291no—
97Q8⋊C8—291no—
98D4⋊C8—291no—
99C2×C29—161no—
100C2×C29#44811yescharacteristic
101C2×C29#44911yescharacteristic
102C2×C29#45311yescharacteristic
103D29—42no—
104C2×SD16—21no—
105C2×SD16—582no—
106C2×D8—581no—
107C4⋊Q8—291no—
108#127C2×D2911yescharacteristic
109#125—581no—
110C22⋊Q8—582no—
111C22⋊Q8—581no—
112C4×Q8C2×D2911yescharacteristic
113C4×D4—291no—
114C4×D4—581no—
115C2×C4⋊C4—581no—
116C4⋊C8—291no—
117C4⋊C8C2×D2911yescharacteristic
118#102—21no—
119#102—581no—
120C4×C8—291no—
121C29#162211yescharacteristic, complemented, Sylow
122C2×Q8—292no—
123C2×Q8C22⋊D2911yescharacteristic
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—291no—
128C22×C4—582no—
129C22×C4—581no—
130SD16—42no—
131SD16—1164no—
132D8—1162no—
133C2×C8—21no—
134C2×C8—581no—
135C2×C8—581no—
136C4⋊C4—21no—
137C4⋊C4—291no—
138C4⋊C4—582no—
139C4⋊C4—582no—
140C4⋊C4—581no—
141C4⋊C4—581no—
142C4⋊C4C22⋊D2911yescharacteristic
143C22⋊C4—582no—
144C22⋊C4—581no—
145C42—21no—
146C42C22×D2911yescharacteristic
147C23—41no—
148C23—581no—
149Q8—21no—
150Q8—21no—
151Q8—1162no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—292no—
158D4—581no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—581no—
162C2×C4—582no—
163C2×C4—1161no—
164C2×C4—1161no—
165C2×C4—2322no—
166C2×C4D4×D2911yescharacteristic
167C2×C4D4×D2911yescharacteristic
168C2×C4C2×C22⋊D2911yescharacteristic
169C8—41no—
170C8—582no—
171C8—1161no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—582no—
176C22—1161no—
177C22—1161no—
178C22#1174529911yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—1161no—
183C4—1162no—
184C4SD16×D2911yescharacteristic
185C4#1174527711yescharacteristic
186C4#1174529411yescharacteristic
187C4#1174531211yescharacteristic
188C2—161no—
189C2—1162no—
190C2#1427130011yescharacteristic
191C2#1427130611yescharacteristic
192C2#1427132911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#460C2
socleC22×C29#120
prime radical#14271355C2
hypercenter#460D29
hypocenterC29#1622
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14271873C2semidirect
2. #14271535C2semidirect
4. #14270911C2semidirect
5. Q8⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×#460C2semidirect
67. D116SD16semidirect
94. #460D29semidirect
121. C29#1622semidirect

Maximal subgroups

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

subgroupindex
#142718732
#142715352
#142713552
#142709112
Q8⋊#65972
#142708902
C29×#4602
#162229