Finite Group Databasebeta

← #16818682

Subgroups — #16818682

Order 3712.

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

normal subgroups only

This group has 250 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#14271440C211yesmaximal, characteristic, complemented
3#14271370C211yesmaximal, characteristic, complemented
4#14270907C211yesmaximal, characteristic, complemented
5#14270895C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×#486C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×#127C2211yescharacteristic
11C2×#90785—21no—
12#11745302—21no—
13#11745301—22no—
14#11745300—21no—
15D4×Dic29—21no—
16C4×D116C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×#102—22no—
19C4×C8×C29C2211yescharacteristic
20#11745183—21no—
21#11745157—21no—
22#11745155—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29D412yes—
29C2×C22⋊D29—22no—
30C2×C22⋊D29—22no—
31C22×Dic29—22no—
32#90807—42no—
33#90807—42no—
34C2×D116D411yescharacteristic
35C2×C4×D29—21no—
36C2×Dic58D411yescharacteristic
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C42×C29C2311yescharacteristic
41C22⋊Dic29—22no—
42#90785—42no—
43#90781—21no—
44C4⋊Dic29D411yescharacteristic
45C4⋊Dic29D411yescharacteristic
46#90779—21no—
47C4×Dic29—21no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—22no—
51C22×D29—21no—
52Q8×C29—41no—
53Q8×C29—41no—
54D4×C29—42no—
55D4×C29—41no—
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C22⋊D29—44no—
64C22⋊D29—82no—
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—44no—
69D116—21no—
70D116—21no—
71C4×D29—41no—
72C4×D29—41no—
73Dic58—21no—
74Dic58D812yes—
75C8×C29—41no—
76#6597—41no—
77#6597—41no—
78#1641—291nomaximal, Sylow
79C22×C29—42no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29#12011yescharacteristic
83C2×D29—41no—
84C2×D29—41no—
85C2×D29—41no—
86C4×C29—21no—
87C4×C29—81no—
88C4×C29C2×D811yescharacteristic
89C4×C29#13511yescharacteristic
90C4×C29AGL(1,ℤ/8)11yescharacteristic
91C4×C29#13711yescharacteristic
92Dic29—22no—
93Dic29—41no—
94Dic29—41no—
95#550—291no—
96#486D2911yescharacteristic, complemented
97#474—291no—
98#462—291no—
99#331—291no—
100Q8⋊C8—291no—
101D4⋊C8—291no—
102C2×C29—82no—
103C2×C29#44711yescharacteristic
104C2×C29#45211yescharacteristic
105C2×C29#45511yescharacteristic
106D29—81no—
107C2×#41—581no—
108C2×Q16—581no—
109C4⋊Q8C2×D2911yescharacteristic
110#127—581no—
111#127C2×D2911yescharacteristic
112#121—581no—
113#121—582no—
114C4×Q8—291no—
115C4×D4—291no—
116C4×D4—581no—
117#107—581no—
118C4⋊C8—291no—
119C4⋊C8—291no—
120#103—581no—
121#102—22no—
122#102—581no—
123C4×C8C2×D2911yescharacteristic
124C29#164111yescharacteristic, complemented, Sylow
125#41—1162no—
126#41—1162no—
127C2×Q8—21no—
128C2×Q8—291no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—291no—
132C2×D4—582no—
133C2×D4—582no—
134C2×D4C22⋊D2912yes—
135C22×C4—582no—
136C22×C4—581no—
137Q16—1162no—
138C2×C8—21no—
139C2×C8—581no—
140C2×C8—581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—291no—
144C4⋊C4—291no—
145C4⋊C4—581no—
146C22⋊C4—582no—
147C22⋊C4—581no—
148C42—581no—
149C42C22×D2911yescharacteristic
150C23—22no—
151C23—581no—
152Q8—41no—
153Q8—41no—
154Q8—292no—
155Q8—581no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—581no—
162D4—581no—
163D4—1164no—
164D4—2322no—
165C2×C4—41no—
166C2×C4—581no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—1164no—
170C2×C4—1161no—
171C2×C4—1161no—
172C2×C4D4×D2911yescharacteristic
173C2×C4D4×D2911yescharacteristic
174C2×C4C2×C22⋊D2911yescharacteristic
175C8—41no—
176C8—1161no—
177C8—1161no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—1161no—
182C22—1161no—
183C22—1161no—
184C22#1174529911yescharacteristic
185C4—21no—
186C4—81no—
187C4—582no—
188C4—1161no—
189C4—1161no—
190C4D8×D2911yescharacteristic
191C4#1174527311yescharacteristic
192C4#1174527711yescharacteristic
193C4#1174527811yescharacteristic
194C2—82no—
195C2—2321no—
196C2#1427129511yescharacteristic
197C2#1427132211yescharacteristic
198C2#1427134011yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#486C2
socleC22×C29#120
prime radical#14271833C2
hypercenter#486D29
hypocenterC29#1641
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #14271440C2semidirect
3. #14271370C2semidirect
4. #14270907C2semidirect
5. #14270895C2semidirect
6. #14270892C2semidirect
7. C29×#486C2semidirect
96. #486D29semidirect
124. C29#1641semidirect

Maximal subgroups

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

subgroupindex
#142718332
#142714402
#142713702
#142709072
#142708952
#142708922
C29×#4862
#164129