Finite Group Databasebeta

← #16818564

Subgroups — #16818564

Order 3712.

236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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#14271537C211yesmaximal, characteristic, complemented
2#14271363C211yesmaximal, characteristic, complemented
3#14271358C211yesmaximal, characteristic
4#14270912C211yesmaximal, characteristic, complemented
5Q8⋊#6597C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×#554C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C29×#125—21no—
10C29×C22⋊Q8—21no—
11C29×C22⋊Q8—22no—
12C4×Q8×C29C2211yescharacteristic
13C4×D4×C29—21no—
14C4×D4×C29C2211yescharacteristic
15C2×C4⋊C4×C29—21no—
16C2×#90784—22no—
17C2×#90784—21no—
18C2×#90782—21no—
19#11745236C2211yescharacteristic
20#11745157—21no—
21#11745157—21no—
22C4⋊#6597C2211yescharacteristic
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×Q8×C29D412yes—
27C2×D4×C29D411yescharacteristic
28C22×C4×C29—22no—
29C22×C4×C29—21no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116—21no—
33C4⋊C4×C29—22no—
34C4⋊C4×C29—22no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29D411yescharacteristic
39C4⋊C4×C29D411yescharacteristic
40C22⋊C4×C29—22no—
41C22⋊C4×C29—21no—
42C42×C29—21no—
43C42×C29C2311yescharacteristic
44#90784—44no—
45#90784—42no—
46#90782—42no—
47C2×#6597—21no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—21no—
51C22×D29—41no—
52Q8×C29—21no—
53Q8×C29—21no—
54Q8×C29—42no—
55D4×C29—21no—
56D4×C29SD1612yescomplemented
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—22no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29—82no—
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67D116—42no—
68D116—41no—
69D116—41no—
70D116—41no—
71D116—41no—
72#6597—22no—
73#6597—41no—
74#6597—41no—
75#1622—291nomaximal, Sylow
76C22×C29—22no—
77C22×C29—41no—
78C22×C29—41no—
79C22×C29#12011yescharacteristic
80C2×D29—81no—
81C2×D29—81no—
82C2×D29—81no—
83C4×C29—21no—
84C4×C29—41no—
85C4×C29—41no—
86C4×C29—41no—
87C4×C29—42no—
88C4×C29C2×SD1611yescharacteristic
89C4×C29#13511yescharacteristic
90C4×C29AGL(1,ℤ/8)11yescharacteristic
91C4×C29#13711yescharacteristic
92#554D2911yescharacteristic, complemented
93#492—291no—
94#460—291no—
95#459—291no—
96#333—291no—
97Q8⋊C8—291no—
98D4⋊C8—291no—
99C2×C29—42no—
100C2×C29#44811yescharacteristic
101C2×C29#44911yescharacteristic
102C2×C29#45311yescharacteristic
103D29—161no—
104C2×SD16—581no—
105C2×SD16—582no—
106C2×D8—581no—
107C4⋊Q8C2×D2911yescharacteristic
108#127—291no—
109#125—21no—
110C22⋊Q8—21no—
111C22⋊Q8—22no—
112C4×Q8C2×D2911yescharacteristic
113C4×D4—21no—
114C4×D4C2×D2911yescharacteristic
115C2×C4⋊C4—21no—
116C4⋊C8—291no—
117C4⋊C8—291no—
118#102—581no—
119#102—581no—
120C4×C8—291no—
121C29#162211yescharacteristic, complemented, Sylow
122C2×Q8C22⋊D2911yescharacteristic
123C2×Q8C22⋊D2912yes—
124C2×D4—581no—
125C2×D4—581no—
126C2×D4—581no—
127C2×D4C22⋊D2911yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130SD16—1164no—
131SD16—1162no—
132D8—1162no—
133C2×C8—581no—
134C2×C8—581no—
135C2×C8—581no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4C22⋊D2911yescharacteristic
142C4⋊C4C22⋊D2911yescharacteristic
143C22⋊C4—22no—
144C22⋊C4—21no—
145C42—21no—
146C42C22×D2911yescharacteristic
147C23—21no—
148C23—1161no—
149Q8—21no—
150Q8—21no—
151Q8—42no—
152D4—21no—
153D4—1162no—
154D4—1161no—
155D4—1161no—
156D4—1161no—
157D4—1161no—
158D4#9078412yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—82no—
166C2×C4C2×C22⋊D2911yescharacteristic
167C2×C4C2×C22⋊D2911yescharacteristic
168C2×C4C2×C22⋊D2911yescharacteristic
169C8—582no—
170C8—1161no—
171C8—1161no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—2321no—
176C22—2321no—
177C22—2321no—
178C22#1174531511yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—41no—
183C4—42no—
184C4C2×#9078411yescharacteristic
185C4#1174530411yescharacteristic
186C4#1174531111yescharacteristic
187C4#1174531211yescharacteristic
188C2—42no—
189C2—4641no—
190C2#1427130211yescharacteristic
191C2#1427130811yescharacteristic
192C2#1427133111yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#554C2
socleC22×C29#120
prime radical#14271358C2
hypercenter#554D29
hypocenterC29#1622
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #14271537C2semidirect
2. #14271363C2semidirect
4. #14270912C2semidirect
5. Q8⋊#6597C2semidirect
6. D4⋊#6597C2semidirect
7. C29×#554C2semidirect
56. D4×C29SD16semidirect
92. #554D29semidirect
121. C29#1622semidirect
158. D4#90784semidirect

Maximal subgroups

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

subgroupindex
#142715372
#142713632
#142713582
#142709122
Q8⋊#65972
D4⋊#65972
C29×#5542
#162229