Finite Group Databasebeta

← #16818620

Subgroups — #16818620

Order 3712.

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

normal subgroups only

This group has 256 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#14271833C211yesmaximal, characteristic
2#14271535C211yesmaximal, characteristic, complemented
3#14271459C211yesmaximal, characteristic, complemented
4#14271454C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#331C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C29×#127C2211yescharacteristic
10#11745302—21no—
11#11745301—22no—
12#11745300—21no—
13D4×Dic29—21no—
14C2×#90783—22no—
15C4×D116C2211yescharacteristic
16#11745231C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20#11745169—21no—
21#11745166—21no—
22#11745165—21no—
23#11745164—21no—
24C4×#6597C2211yescharacteristic
25C2×D4×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29D412yes—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—22no—
30C22×Dic29—22no—
31#90807—42no—
32#90807—42no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58—21no—
36C2×Dic58D411yescharacteristic
37C2×C8×C29—21no—
38C2×C8×C29—21no—
39C42×C29C2311yescharacteristic
40C22⋊Dic29—22no—
41#90783—44no—
42#90781—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29D411yescharacteristic
46C4⋊Dic29D411yescharacteristic
47#90779—21no—
48C4×Dic29—21no—
49C2×#6597—21no—
50C23×C29—22no—
51C22×D29—21no—
52D4×C29—42no—
53D4×C29—41no—
54D4×C29—41no—
55D4×C29—41no—
56D4×C29—41no—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C22⋊D29—44no—
61C22⋊D29—82no—
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29—44no—
66C2×Dic29—41no—
67D116—21no—
68D116—21no—
69C4×D29—41no—
70C4×D29—41no—
71Dic58—21no—
72Dic58—42no—
73Dic58SD1612yescomplemented
74C8×C29—41no—
75C8×C29—41no—
76#6597—22no—
77#1631—291nomaximal, Sylow
78C22×C29—42no—
79C22×C29—42no—
80C22×C29—42no—
81C22×C29#12011yescharacteristic
82C2×D29—41no—
83C2×D29—41no—
84C2×D29—41no—
85C4×C29—21no—
86C4×C29C2×SD1611yescharacteristic
87C4×C29#13511yescharacteristic
88C4×C29AGL(1,ℤ/8)11yescharacteristic
89C4×C29#13711yescharacteristic
90Dic29—22no—
91Dic29—41no—
92Dic29—41no—
93Dic29—81no—
94#550—291no—
95#492—291no—
96#477—291no—
97#476—291no—
98#331D2911yescharacteristic, complemented
99Q8⋊C8—291no—
100D4⋊C8—291no—
101C2×C29—82no—
102C2×C29#45011yescharacteristic
103C2×C29#45211yescharacteristic
104C2×C29#45311yescharacteristic
105D29—81no—
106C2×#41—581no—
107C2×SD16—582no—
108C4⋊Q8—291no—
109#127—581no—
110#127C2×D2911yescharacteristic
111#121—581no—
112#121—582no—
113C4×Q8—291no—
114C4×D4—291no—
115C4×D4—581no—
116#107—581no—
117#106—581no—
118C4⋊C8C2×D2911yescharacteristic
119C4⋊C8C2×D2911yescharacteristic
120#103—581no—
121#102—581no—
122C4×C8—291no—
123C29#163111yescharacteristic, complemented, Sylow
124#41—1162no—
125#41—1162no—
126C2×Q8—291no—
127C2×Q8—581no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—291no—
131C2×D4—582no—
132C2×D4—582no—
133C2×D4D11612yes—
134C22×C4—582no—
135C22×C4—581no—
136SD16—1164no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—581no—
140C4⋊C4—291no—
141C4⋊C4—291no—
142C4⋊C4—581no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C22⋊C4—582no—
146C22⋊C4—581no—
147C42—581no—
148C42C22×D2911yescharacteristic
149C23—22no—
150C23—581no—
151Q8—292no—
152Q8—581no—
153Q8—1162no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—581no—
160D4—581no—
161D4—1164no—
162D4—2322no—
163C2×C4—581no—
164C2×C4—581no—
165C2×C4—581no—
166C2×C4—1164no—
167C2×C4—1161no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4C2×D11611yescharacteristic
171C2×C4D4×D2911yescharacteristic
172C2×C4D4×D2911yescharacteristic
173C8—41no—
174C8—41no—
175C8—582no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1161no—
180C22—1161no—
181C22—1161no—
182C22#1174524411yescharacteristic
183C4—21no—
184C4—582no—
185C4—1161no—
186C4—1161no—
187C4—2321no—
188C4#1174527311yescharacteristic
189C4#1174527411yescharacteristic
190C4SD16×D2911yescharacteristic
191C4#1174527711yescharacteristic
192C2—82no—
193C2—2321no—
194C2#1427131511yescharacteristic
195C2#1427132611yescharacteristic
196C2#1427133311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#331C2
socleC22×C29#120
prime radical#14271833C2
hypercenter#331D29
hypocenterC29#1631
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14271535C2semidirect
3. #14271459C2semidirect
4. #14271454C2semidirect
5. #14270893C2semidirect
6. #14270890C2semidirect
7. C29×#331C2semidirect
73. Dic58SD16semidirect
98. #331D29semidirect
123. C29#1631semidirect

Maximal subgroups

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

subgroupindex
#142718332
#142715352
#142714592
#142714542
#142708932
#142708902
C29×#3312
#163129