Finite Group Databasebeta

← #16818721

Subgroups — #16818721

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#14271879C211yesmaximal, characteristic
2#14271513C211yesmaximal, characteristic, complemented
3#14271444C211yesmaximal, characteristic, complemented
4#14271369C211yesmaximal, characteristic, complemented
5#14270890C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#333C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9#11745309—22no—
10C2×#90773—21no—
11#11745257—21no—
12#11745257—21no—
13#11745254—21no—
14#11745254—21no—
15C4×D116C2211yescharacteristic
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20#11745183—22no—
21#11745169—21no—
22#11745166—21no—
23#11745164—21no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29D412yes—
26C2×D116—22no—
27C2×D116D411yescharacteristic
28C2×D116D411yescharacteristic
29C2×C4×D29—21no—
30C2×C4×D29—21no—
31C2×Dic58—21no—
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C42×C29C2311yescharacteristic
37#90781—22no—
38#90781—22no—
39#90781—21no—
40#90781—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44C4⋊Dic29D411yescharacteristic
45C4×Dic29—22no—
46C2×#6597—21no—
47#90773—42no—
48C22×D29—21no—
49C22×D29—21no—
50Q8×C29—42no—
51C2×C4×C29—22no—
52C2×C4×C29C2×D411yescharacteristic
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×Dic29—21no—
56C2×Dic29—21no—
57C2×Dic29—41no—
58D116—21no—
59D116—21no—
60D116—21no—
61D116—21no—
62D116—82no—
63C4×D29—41no—
64C4×D29—41no—
65C4×D29—41no—
66C4×D29—41no—
67Dic58—41no—
68Dic58—41no—
69C8×C29—41no—
70C8×C29—41no—
71#6597—41no—
72#1646—291nomaximal, Sylow
73C22×C29#12011yescharacteristic
74C2×D29—41no—
75C2×D29—41no—
76C2×D29—41no—
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—41no—
80C4×C29—21no—
81C4×C29—42no—
82C4×C29#13511yescharacteristic
83C4×C29#13511yescharacteristic
84C4×C29AGL(1,ℤ/8)11yescharacteristic
85C4×C29#13711yescharacteristic
86Dic29—41no—
87Dic29—41no—
88Dic29—81no—
89#555—291no—
90#487—291no—
91#474—291no—
92#461—291no—
93#333D2911yescharacteristic, complemented
94D4⋊C8—291no—
95D4⋊C8—291no—
96C2×C29#44911yescharacteristic
97C2×C29#45211yescharacteristic
98C2×C29#45511yescharacteristic
99D29—81no—
100D29—81no—
101C2×SD16—581no—
102C4⋊Q8—291no—
103C4⋊Q8C2×D2911yescharacteristic
104#124—582no—
105#121—581no—
106#121—581no—
107C4×D4—291no—
108C4×D4—291no—
109#117—581no—
110#117—581no—
111#107—581no—
112C4⋊C8C2×D2911yescharacteristic
113C4⋊C8C2×D2911yescharacteristic
114#103—581no—
115#103—582no—
116#102—581no—
117C4×C8—291no—
118C29#164611yescharacteristic, complemented, Sylow
119C2×Q8—581no—
120C2×Q8D11612yes—
121C2×D4—291no—
122C2×D4—291no—
123C2×D4—582no—
124C22×C4—581no—
125C22×C4—581no—
126SD16—1162no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—581no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—291no—
133C4⋊C4—291no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C22⋊C4—582no—
137C22⋊C4—582no—
138C22⋊C4—581no—
139C22⋊C4—581no—
140C42—582no—
141C42C22×D2911yescharacteristic
142C23—581no—
143C23—581no—
144Q8—42no—
145Q8—1161no—
146Q8—1161no—
147D4—581no—
148D4—581no—
149D4—581no—
150D4—581no—
151D4—2322no—
152C2×C4—22no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—1161no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4—1161no—
159C2×C4—1161no—
160C2×C4C2×D11611yescharacteristic
161C2×C4D4×D2911yescharacteristic
162C2×C4D4×D2911yescharacteristic
163C8—41no—
164C8—41no—
165C8—1161no—
166C22—1161no—
167C22—1161no—
168C22—1161no—
169C22—1161no—
170C22—1161no—
171C22—1161no—
172C22#1174524411yescharacteristic
173C4—21no—
174C4—42no—
175C4—1161no—
176C4—1161no—
177C4—2321no—
178C4#1174527611yescharacteristic
179C4#1174527811yescharacteristic
180C4#1174528011yescharacteristic
181C4#1174528111yescharacteristic
182C2—2321no—
183C2—2321no—
184C2#1427131111yescharacteristic
185C2#1427132811yescharacteristic
186C2#1427134311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#333C2
socleC22×C29#120
prime radical#14271879C2
hypercenter#333D29
hypocenterC29#1646
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14271513C2semidirect
3. #14271444C2semidirect
4. #14271369C2semidirect
5. #14270890C2semidirect
6. #14270890C2semidirect
7. C29×#333C2semidirect
93. #333D29semidirect
118. C29#1646semidirect

Maximal subgroups

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

subgroupindex
#142718792
#142715132
#142714442
#142713692
#142708902
C29×#3332
#164629