Finite Group Databasebeta

← #16818719

Subgroups — #16818719

Order 3712.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271878C211yesmaximal, characteristic
2#14271515C211yesmaximal, characteristic, complemented
3#14271365C211yesmaximal, characteristic, complemented
4#14270911C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#474C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C4×D4×C29C2211yescharacteristic
10C2×#90784—21no—
11#11745300—21no—
12#11745292—21no—
13#11745288—21no—
14#11745254—21no—
15#11745247—22no—
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×#107—21no—
19C29×C4⋊C8C2211yescharacteristic
20C29×#102—21no—
21#11745183—21no—
22#11745158—22no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29D411yescharacteristic
27C22×C4×C29—21no—
28C2×C22⋊D29—22no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×Dic58D412yes—
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C22⋊C4×C29—21no—
37C42×C29C2311yescharacteristic
38C22⋊Dic29—22no—
39#90784—42no—
40#90781—22no—
41#90781—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29D411yescharacteristic
45C4×Dic29—22no—
46C2×#6597—21no—
47C2×#6597—21no—
48C23×C29—21no—
49C22×D29—21no—
50Q8×C29—41no—
51Q8×C29—41no—
52D4×C29—21no—
53D4×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C22⋊D29—82no—
62C2×Dic29—21no—
63C2×Dic29—22no—
64D116—21no—
65D116—21no—
66C4×D29—41no—
67C4×D29—41no—
68Dic58—42no—
69C8×C29—41no—
70#6597—41no—
71#6597—41no—
72#1646—291nomaximal, Sylow
73C22×C29—41no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29#12011yescharacteristic
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—41no—
80C4×C29—21no—
81C4×C29—41no—
82C4×C29—81no—
83C4×C29#13511yescharacteristic
84C4×C29#13511yescharacteristic
85C4×C29AGL(1,ℤ/8)11yescharacteristic
86C4×C29#13711yescharacteristic
87Dic29—41no—
88Dic29—42no—
89#555—291no—
90#487—291no—
91#474D2911yescharacteristic, complemented
92#461—291no—
93#333—291no—
94D4⋊C8—291no—
95D4⋊C8—291no—
96C2×C29—81no—
97C2×C29#44911yescharacteristic
98C2×C29#45211yescharacteristic
99C2×C29#45511yescharacteristic
100D29—81no—
101C2×SD16—581no—
102C4⋊Q8—291no—
103C4⋊Q8C2×D2911yescharacteristic
104#124—582no—
105#121—581no—
106#121—581no—
107C4×D4—291no—
108C4×D4C2×D2911yescharacteristic
109#117—581no—
110#117—581no—
111#107—21no—
112C4⋊C8—291no—
113C4⋊C8C2×D2911yescharacteristic
114#103—582no—
115#103—581no—
116#102—21no—
117C4×C8—291no—
118C29#164611yescharacteristic, complemented, Sylow
119C2×Q8—21no—
120C2×Q8—292no—
121C2×D4—291no—
122C2×D4—582no—
123C2×D4C22⋊D2911yescharacteristic
124C22×C4—21no—
125C22×C4—581no—
126SD16—1162no—
127C2×C8—21no—
128C2×C8—581no—
129C2×C8—581no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—291no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4C22⋊D2911yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—582no—
138C22⋊C4—582no—
139C22⋊C4—581no—
140C42—582no—
141C42C22×D2911yescharacteristic
142C23—21no—
143C23—581no—
144Q8—41no—
145Q8—41no—
146Q8—1162no—
147D4—21no—
148D4—21no—
149D4—581no—
150D4—581no—
151D4—2322no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—581no—
157C2×C4—582no—
158C2×C4—1161no—
159C2×C4—1161no—
160C2×C4D4×D2911yescharacteristic
161C2×C4D4×D2911yescharacteristic
162C2×C4C2×C22⋊D2911yescharacteristic
163C8—41no—
164C8—1161no—
165C8—1161no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—1161no—
170C22—1161no—
171C22—1161no—
172C22#1174529911yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—1161no—
177C4—1162no—
178C4#1174527311yescharacteristic
179C4#1174527411yescharacteristic
180C4#1174530411yescharacteristic
181C4#1174531211yescharacteristic
182C2—81no—
183C2—2321no—
184C2#1427130511yescharacteristic
185C2#1427132311yescharacteristic
186C2#1427133911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#474C2
socleC22×C29#120
prime radical#14271878C2
hypercenter#474D29
hypocenterC29#1646
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #14271515C2semidirect
3. #14271365C2semidirect
4. #14270911C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×#474C2semidirect
91. #474D29semidirect
118. C29#1646semidirect

Maximal subgroups

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

subgroupindex
#142718782
#142715152
#142713652
#142709112
D4⋊#65972
#142708902
C29×#4742
#164629