Finite Group Databasebeta

← #16818726

Subgroups — #16818726

Order 3712.

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

normal subgroups only

This group has 240 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#14271818C211yesmaximal, characteristic
2#14271566C211yesmaximal, characteristic, complemented
3#14271365C211yesmaximal, characteristic, complemented
4#14270908C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#474C211yesmaximal, characteristic, complemented
8C2×#90805—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C4×D4×C29C2211yescharacteristic
11C2×#90784—21no—
12#11745300—21no—
13#11745286—21no—
14C4⋊C4×D29—21no—
15#11745245—22no—
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×#107—21no—
19C29×C4⋊C8C2211yescharacteristic
20C29×#102—21no—
21#11745183—21no—
22#11745155—22no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29D411yescharacteristic
27C22×C4×C29—21no—
28C2×C22⋊D29—22no—
29#90805—42no—
30#90805—42no—
31C2×D116D411yescharacteristic
32C2×C4×D29—22no—
33C2×C4×D29—21no—
34C2×Dic58—21no—
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29D411yescharacteristic
39C22⋊C4×C29—21no—
40C42×C29C2311yescharacteristic
41C22⋊Dic29—22no—
42#90784—42no—
43#90781—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29D411yescharacteristic
46C4⋊Dic29D412yes—
47#90779—22no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—21no—
51C22×D29—21no—
52Q8×C29—41no—
53Q8×C29—41no—
54D4×C29—21no—
55D4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C22⋊D29—44no—
64C2×Dic29—21no—
65C2×Dic29—22no—
66D116—21no—
67D116D812yes—
68C4×D29—44no—
69C4×D29—41no—
70C4×D29—41no—
71Dic58—41no—
72Dic58—41no—
73C8×C29—41no—
74#6597—22no—
75#6597—41no—
76#1647—291nomaximal, Sylow
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29#12011yescharacteristic
81C2×D29—22no—
82C2×D29—41no—
83C2×D29—41no—
84C4×C29—21no—
85C4×C29—41no—
86C4×C29—81no—
87C4×C29C2×D811yescharacteristic
88C4×C29#13511yescharacteristic
89C4×C29AGL(1,ℤ/8)11yescharacteristic
90C4×C29#13711yescharacteristic
91Dic29—42no—
92Dic29—41no—
93#547—291no—
94#500—291no—
95#474D2911yescharacteristic, complemented
96#461—291no—
97#332—291no—
98D4⋊C8—291no—
99D4⋊C8—291no—
100C2×C29—81no—
101C2×C29#44711yescharacteristic
102C2×C29#45211yescharacteristic
103C2×C29#45611yescharacteristic
104D29—42no—
105C2×#41—581no—
106C2×SD16—581no—
107C4⋊Q8—291no—
108C4⋊Q8C2×D2911yescharacteristic
109#123—582no—
110C22⋊Q8—581no—
111#121—581no—
112C4×D4—291no—
113C4×D4C2×D2911yescharacteristic
114C2×C4⋊C4—581no—
115#107—21no—
116#107—582no—
117C4⋊C8—291no—
118C4⋊C8C2×D2911yescharacteristic
119#103—581no—
120#102—21no—
121C4×C8—291no—
122C29#164711yescharacteristic, complemented, Sylow
123#41—1162no—
124#41—1162no—
125C2×Q8—21no—
126C2×Q8—581no—
127C2×D4—291no—
128C2×D4—582no—
129C2×D4C22⋊D2911yescharacteristic
130C22×C4—21no—
131C22×C4—582no—
132C22×C4—581no—
133SD16—1162no—
134C2×C8—21no—
135C2×C8—581no—
136C2×C8—581no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—291no—
140C4⋊C4—292no—
141C4⋊C4—582no—
142C4⋊C4—581no—
143C4⋊C4C22⋊D2911yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—582no—
146C22⋊C4—581no—
147C42C22×D2911yescharacteristic
148C23—21no—
149C23—581no—
150Q8—41no—
151Q8—41no—
152Q8—1161no—
153Q8—1161no—
154D4—21no—
155D4—21no—
156D4—292no—
157D4—581no—
158D4—1164no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—581no—
164C2×C4—582no—
165C2×C4—1164no—
166C2×C4—1161no—
167C2×C4—1161no—
168C2×C4D4×D2911yescharacteristic
169C2×C4D4×D2911yescharacteristic
170C2×C4C2×C22⋊D2911yescharacteristic
171C8—41no—
172C8—582no—
173C8—1161no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—582no—
178C22—1161no—
179C22—1161no—
180C22#1174529911yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—1162no—
185C4—1161no—
186C4D8×D2911yescharacteristic
187C4#1174527311yescharacteristic
188C4#1174530411yescharacteristic
189C4#1174531211yescharacteristic
190C2—81no—
191C2—1162no—
192C2#1427129511yescharacteristic
193C2#1427132311yescharacteristic
194C2#1427134411yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#474C2
socleC22×C29#120
prime radical#14271818C2
hypercenter#474D29
hypocenterC29#1647
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. #14271566C2semidirect
3. #14271365C2semidirect
4. #14270908C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×#474C2semidirect
95. #474D29semidirect
122. C29#1647semidirect

Maximal subgroups

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

subgroupindex
#142718182
#142715662
#142713652
#142709082
D4⋊#65972
#142708902
C29×#4742
#164729