Finite Group Databasebeta

← #16818639

Subgroups — #16818639

Order 3712.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271878C211yesmaximal, characteristic
2#14271543C211yesmaximal, characteristic, complemented
3#14271454C211yesmaximal, characteristic, complemented
4#14271453C211yesmaximal, characteristic, complemented
5#14270911C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C29C2211yescharacteristic
9#11745300—21no—
10#11745292—21no—
11#11745288—21no—
12C2×Dic116—22no—
13#11745254—21no—
14#11745247—22no—
15C4×D116C2211yescharacteristic
16#11745231C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C4×C8×C29C2211yescharacteristic
20#11745180—21no—
21#11745169—21no—
22#11745165—21no—
23#11745156—21no—
24C4⋊#6597C2211yescharacteristic
25C2×D4×C29D411yescharacteristic
26C22×C4×C29—21no—
27C2×C22⋊D29—22no—
28C2×D116D411yescharacteristic
29C2×C4×D29—21no—
30C2×Dic58—21no—
31C2×Dic58D412yes—
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29D411yescharacteristic
35C22⋊C4×C29—21no—
36C42×C29C2311yescharacteristic
37C22⋊Dic29—22no—
38#90781—22no—
39#90781—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29D411yescharacteristic
45C4×Dic29—22no—
46C2×#6597—21no—
47Dic116—44no—
48C23×C29—21no—
49C22×D29—21no—
50D4×C29—21no—
51D4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C22⋊D29—82no—
59C2×Dic29—21no—
60C2×Dic29—22no—
61C2×Dic29—41no—
62D116—21no—
63D116—21no—
64C4×D29—41no—
65C4×D29—41no—
66Dic58—42no—
67Dic58—42no—
68C8×C29—22no—
69C8×C29—41no—
70#6597—41no—
71#1634—291nomaximal, Sylow
72C22×C29—41no—
73C22×C29—41no—
74C22×C29—41no—
75C22×C29#12011yescharacteristic
76C2×D29—41no—
77C2×D29—41no—
78C2×D29—41no—
79C4×C29—21no—
80C4×C29—41no—
81C4×C29#13511yescharacteristic
82C4×C29#13511yescharacteristic
83C4×C29#13711yescharacteristic
84C4×C29#13711yescharacteristic
85Dic29—41no—
86Dic29—42no—
87Dic29—81no—
88#555—291no—
89#494—291no—
90#476—291no—
91#476—291no—
92#333—291no—
93D4⋊C8—291no—
94D4⋊C8D2911yescharacteristic, complemented
95C2×C29—81no—
96C2×C29#45211yescharacteristic
97C2×C29#45211yescharacteristic
98C2×C29#45311yescharacteristic
99D29—81no—
100C2×Q16—582no—
101C4⋊Q8—291no—
102C4⋊Q8—291no—
103#124—582no—
104#121—581no—
105#121—581no—
106C4×D4—291no—
107C4×D4C2×D2911yescharacteristic
108#117—581no—
109#117—581no—
110#106—581no—
111#106—581no—
112C4⋊C8—291no—
113C4⋊C8C2×D2911yescharacteristic
114#102—581no—
115#102—581no—
116C4×C8C2×D2911yescharacteristic
117C29#163411yescharacteristic, complemented, Sylow
118C2×Q8—292no—
119C2×Q8—581no—
120C2×D4—291no—
121C2×D4—582no—
122C2×D4D11611yescharacteristic
123C22×C4—21no—
124C22×C4—581no—
125Q16—1164no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—581no—
129C4⋊C4—291no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4D11611yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—582no—
137C22⋊C4—582no—
138C22⋊C4—581no—
139C42—582no—
140C42C22×D2911yescharacteristic
141C23—21no—
142C23—581no—
143Q8—1162no—
144Q8—1162no—
145D4—21no—
146D4—21no—
147D4—581no—
148D4—581no—
149D4—2322no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—581no—
154C2×C4—582no—
155C2×C4—1161no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4C2×D11611yescharacteristic
159C2×C4D4×D2911yescharacteristic
160C2×C4D4×D2911yescharacteristic
161C8—22no—
162C8—41no—
163C8—1161no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—1161no—
168C22—1161no—
169C22—1161no—
170C22#1174524411yescharacteristic
171C4—21no—
172C4—41no—
173C4—1161no—
174C4—1162no—
175C4—2321no—
176C4#1174526611yescharacteristic
177C4#1174527111yescharacteristic
178C4#1174527411yescharacteristic
179C4#1174527711yescharacteristic
180C2—81no—
181C2—2321no—
182C2#1427132611yescharacteristic
183C2#1427132711yescharacteristic
184C2#1427133211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29#120
prime radical#14271878C2
hypercenterD4⋊C8D29
hypocenterC29#1634
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271543C2semidirect
3. #14271454C2semidirect
4. #14271453C2semidirect
5. #14270911C2semidirect
6. #14270892C2semidirect
7. C29×D4⋊C8C2semidirect
94. D4⋊C8D29semidirect
117. C29#1634semidirect

Maximal subgroups

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

subgroupindex
#142718782
#142715432
#142714542
#142714532
#142709112
#142708922
C29×D4⋊C82
#163429