Finite Group Databasebeta

← #16818597

Subgroups — #16818597

Order 3712.

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

normal subgroups only

This group has 250 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
1Q8×D116C211yesmaximal, characteristic, complemented
2#14271510C211yesmaximal, characteristic, complemented
3#14271363C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic
5#14270908C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D29—21no—
9C4×Q8×C29C2211yescharacteristic
10C2×#90784—21no—
11C2×D232—21no—
12#11745259—21no—
13#11745259—22no—
14#11745236C2211yescharacteristic
15C4×D116—21no—
16C4×D116C2211yescharacteristic
17#11745231—21no—
18#11745231C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20C4×C8×C29C2211yescharacteristic
21#11745169—22no—
22#11745169—21no—
23#11745157—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26Q8×D29—42no—
27Q8×D29—42no—
28C2×D116—21no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116D411yescharacteristic
32C2×C4×D29—22no—
33C2×C4×D29—21no—
34C2×Dic58—22no—
35C2×Dic58—21no—
36C2×C8×C29—21no—
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C42×C29—21no—
41C42×C29C2311yescharacteristic
42#90784—42no—
43#90781—22no—
44#90781—21no—
45C4⋊Dic29—22no—
46C4⋊Dic29—21no—
47C4⋊Dic29D411yescharacteristic
48C4⋊Dic29D412yes—
49C2×#6597—21no—
50D232—42no—
51C22×D29—21no—
52C22×D29—41no—
53Q8×C29—21no—
54Q8×C29D812yescomplemented
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C2×Dic29—21no—
61C2×Dic29—22no—
62D116—21no—
63D116—42no—
64D116—41no—
65D116—41no—
66D116—41no—
67D116—41no—
68D116SD1612yescomplemented
69C4×D29—44no—
70C4×D29—41no—
71C4×D29—41no—
72Dic58—44no—
73Dic58—41no—
74Dic58—41no—
75C8×C29—41no—
76C8×C29—41no—
77#6597—41no—
78#1627—291nomaximal, Sylow
79C22×C29#12011yescharacteristic
80C2×D29—22no—
81C2×D29—41no—
82C2×D29—41no—
83C2×D29—81no—
84C2×D29—81no—
85C2×D29—81no—
86C4×C29—22no—
87C4×C29—21no—
88C4×C29—41no—
89C4×C29C2×D811yescharacteristic
90C4×C29C2×SD1611yescharacteristic
91C4×C29AGL(1,ℤ/8)11yescharacteristic
92C4×C29#13711yescharacteristic
93Dic29—41no—
94Dic29—42no—
95D4×Q8—291no—
96#486—291no—
97#460—291no—
98#459—291no—
99#332—291no—
100Q8⋊C8D2911yescharacteristic, complemented
101D4⋊C8—291no—
102C2×C29#44711yescharacteristic
103C2×C29#44811yescharacteristic
104C2×C29#45411yescharacteristic
105D29—42no—
106D29—161no—
107C22×Q8—581no—
108C2×SD16—581no—
109C2×D8—581no—
110C4⋊Q8—291no—
111C4⋊Q8—581no—
112#127—291no—
113C22⋊Q8—582no—
114C22⋊Q8—581no—
115C4×Q8C2×D2911yescharacteristic
116C4×D4—291no—
117C4×D4—581no—
118C4⋊C8—291no—
119C4⋊C8C2×D2911yescharacteristic
120#102—581no—
121#102—582no—
122#102—581no—
123C4×C8C2×D2911yescharacteristic
124C29#162711yescharacteristic, complemented, Sylow
125C2×Q8—582no—
126C2×Q8—581no—
127C2×Q8—1162no—
128C2×Q8—1162no—
129C2×Q8D11611yescharacteristic
130C2×D4—291no—
131C2×D4—581no—
132C2×D4—581no—
133C2×D4—581no—
134C22×C4—582no—
135C22×C4—581no—
136SD16—1162no—
137D8—1162no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—581no—
141C4⋊C4—21no—
142C4⋊C4—291no—
143C4⋊C4—292no—
144C4⋊C4—582no—
145C4⋊C4—581no—
146C4⋊C4D11611yescharacteristic
147C22⋊C4—582no—
148C22⋊C4—581no—
149C42—21no—
150C42C22×D2911yescharacteristic
151C23—581no—
152C23—1161no—
153Q8—21no—
154Q8—1164no—
155Q8—1161no—
156Q8—1161no—
157Q8D23212yescomplemented
158D4—292no—
159D4—581no—
160D4—1162no—
161D4—1161no—
162D4—1161no—
163D4—1161no—
164D4—1161no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—582no—
168C2×C4—581no—
169C2×C4—1164no—
170C2×C4—1161no—
171C2×C4—1161no—
172C2×C4C2×D11611yescharacteristic
173C2×C4D4×D2911yescharacteristic
174C2×C4D4×D2911yescharacteristic
175C8—41no—
176C8—41no—
177C8—1161no—
178C22—582no—
179C22—1161no—
180C22—1161no—
181C22—2321no—
182C22—2321no—
183C22—2321no—
184C22#1174524411yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—1162no—
189C4—1161no—
190C4C2×D23211yescharacteristic
191C4#1174527011yescharacteristic
192C4SD16×D2911yescharacteristic
193C4#1174528011yescharacteristic
194C2—1162no—
195C2—4641no—
196C2#1427129911yescharacteristic
197C2#1427130311yescharacteristic
198C2#1427133711yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#14271359C2
hypercenterQ8⋊C8D29
hypocenterC29#1627
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. Q8×D116C2semidirect
2. #14271510C2semidirect
3. #14271363C2semidirect
5. #14270908C2semidirect
6. #14270892C2semidirect
7. C29×Q8⋊C8C2semidirect
54. Q8×C29D8semidirect
68. D116SD16semidirect
100. Q8⋊C8D29semidirect
124. C29#1627semidirect
157. Q8D232semidirect

Maximal subgroups

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

subgroupindex
Q8×D1162
#142715102
#142713632
#142713592
#142709082
#142708922
C29×Q8⋊C82
#162729