Finite Group Databasebeta

← #16818656

Subgroups — #16818656

Order 3712.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic58C211yesmaximal, characteristic
2#14271513C211yesmaximal, characteristic, complemented
3#14271455C211yesmaximal, characteristic, complemented
4#14270908C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic
7C29×#476C211yesmaximal, characteristic
8C22×Dic58—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C4×D4×C29C2211yescharacteristic
11D4×Dic29—21no—
12#11745286—21no—
13#11745250—21no—
14#11745240—22no—
15#11745231C2211yescharacteristic
16C4×Dic58C2211yescharacteristic
17C29×#106—21no—
18C29×C4⋊C8C2211yescharacteristic
19C29×#102—21no—
20#11745183—22no—
21#11745158—21no—
22#11745155—21no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29D411yescharacteristic
27C22×C4×C29—21no—
28C22×Dic29—22no—
29C2×Dic58—22no—
30C2×Dic58—21no—
31C2×Dic58—42no—
32C2×Dic58—42no—
33C2×Dic58D411yescharacteristic
34C2×C8×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C22⋊C4×C29—21no—
39C42×C29C2311yescharacteristic
40C22⋊Dic29—22no—
41C4⋊Dic29—21no—
42C4⋊Dic29D411yescharacteristic
43C4⋊Dic29D412yes—
44#90779—22no—
45#90779—21no—
46C4×Dic29—21no—
47C2×#6597—21no—
48C2×#6597—21no—
49C23×C29—21no—
50Q8×C29—42no—
51D4×C29—21no—
52D4×C29Q1612yes—
53C2×C4×C29—21no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C2×Dic29—21no—
61C2×Dic29—21no—
62C2×Dic29—22no—
63C2×Dic29—44no—
64Dic58—21no—
65Dic58—44no—
66Dic58—41no—
67Dic58—41no—
68Dic58SD1612yes—
69C8×C29—41no—
70#6597—41no—
71#6597—41no—
72#1637—291nomaximal, Sylow
73C22×C29—22no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29#12011yescharacteristic
77C4×C29—21no—
78C4×C29—41no—
79C4×C29—81no—
80C4×C29C2×SD1611yescharacteristic
81C4×C29C2×Q1611yescharacteristic
82C4×C29AGL(1,ℤ/8)11yescharacteristic
83C4×C29#13711yescharacteristic
84Dic29—22no—
85Dic29—42no—
86Dic29—41no—
87D4×Q8—291no—
88#487—291no—
89#477—291no—
90#476D2911yescharacteristic
91#332—291no—
92Q8⋊C8—291no—
93D4⋊C8—291no—
94C2×C29—42no—
95C2×C29#45011yescharacteristic
96C2×C29#45111yescharacteristic
97C2×C29#45411yescharacteristic
98C22×Q8—581no—
99C4⋊Q8—291no—
100C4⋊Q8—581no—
101C4⋊Q8C2×D2911yescharacteristic
102C22⋊Q8—582no—
103C22⋊Q8—581no—
104C4×Q8—291no—
105C4×D4—581no—
106C4×D4C2×D2911yescharacteristic
107#107—581no—
108#106—21no—
109C4⋊C8—291no—
110C4⋊C8C2×D2911yescharacteristic
111#103—581no—
112#103—582no—
113#102—21no—
114C4×C8—291no—
115C29#163711yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—291no—
118C2×Q8—582no—
119C2×Q8—581no—
120C2×Q8—1162no—
121C2×Q8—1162no—
122C2×D4C22⋊D2911yescharacteristic
123C22×C4—21no—
124C22×C4—582no—
125C2×C8—21no—
126C2×C8—581no—
127C2×C8—581no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—292no—
131C4⋊C4—291no—
132C4⋊C4—582no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4C22⋊D2911yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—582no—
138C42—581no—
139C42C22×D2911yescharacteristic
140C23—21no—
141Q8—42no—
142Q8—292no—
143Q8—581no—
144Q8—1164no—
145Q8—1161no—
146Q8—1161no—
147D4—21no—
148D4#9078512yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—582no—
156C2×C4—1164no—
157C2×C4D4×D2911yescharacteristic
158C2×C4D4×D2911yescharacteristic
159C2×C4C2×C22⋊D2911yescharacteristic
160C8—41no—
161C8—1161no—
162C8—1161no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1174529911yescharacteristic
167C4—21no—
168C4—41no—
169C4—81no—
170C4—582no—
171C4—1162no—
172C4—1161no—
173C4SD16×D2911yescharacteristic
174C4#1174527611yescharacteristic
175C4C2×#9078511yescharacteristic
176C4#1174531311yescharacteristic
177C2—42no—
178C2#1427131211yescharacteristic
179C2#1427131811yescharacteristic
180C2#1427133411yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#476C2
socleC22×C29#120
prime radicalC2×D4×C29D4
hypercenter#476D29
hypocenterC29#1637
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14271513C2semidirect
3. #14271455C2semidirect
4. #14270908C2semidirect
5. #14270893C2semidirect
115. C29#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic582
#142715132
#142714552
#142709082
#142708932
D4⋊#65972
C29×#4762
#163729