Finite Group Databasebeta

← #16818636

Subgroups — #16818636

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#14271542C211yesmaximal, characteristic, complemented
3#14271450C211yesmaximal, characteristic, complemented
4#14270911C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#476C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C4×D4×C29C2211yescharacteristic
10C2×#90785—22no—
11#11745300—21no—
12#11745292—21no—
13#11745288—21no—
14#11745254—21no—
15#11745247—22no—
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic
18C29×#106—21no—
19C29×C4⋊C8C2211yescharacteristic
20C29×#102—21no—
21#11745157—21no—
22#11745156—21no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D4×C29D411yescharacteristic
27C22×C4×C29—21no—
28C2×C22⋊D29—22no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×Dic58D412yes—
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C22⋊C4×C29—21no—
37C42×C29C2311yescharacteristic
38C22⋊Dic29—22no—
39#90785—44no—
40#90781—22no—
41#90781—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29D411yescharacteristic
45C4×Dic29—22no—
46C2×#6597—21no—
47C2×#6597—21no—
48C23×C29—21no—
49C22×D29—21no—
50Q8×C29—42no—
51D4×C29—21no—
52D4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D411yescharacteristic
60C22⋊D29—82no—
61C2×Dic29—21no—
62C2×Dic29—22no—
63D116—21no—
64D116—21no—
65C4×D29—41no—
66C4×D29—41no—
67Dic58—42no—
68C8×C29—41no—
69#6597—22no—
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—81no—
82C4×C29#13511yescharacteristic
83C4×C29#13511yescharacteristic
84C4×C29#13711yescharacteristic
85C4×C29#13711yescharacteristic
86Dic29—41no—
87Dic29—42no—
88#555—291no—
89#494—291no—
90#476—291no—
91#476D2911yescharacteristic, complemented
92#333—291no—
93D4⋊C8—291no—
94D4⋊C8—291no—
95C2×C29—81no—
96C2×C29#45211yescharacteristic
97C2×C29#45211yescharacteristic
98C2×C29#45311yescharacteristic
99D29—81no—
100C2×Q16—582no—
101C4⋊Q8—291no—
102C4⋊Q8C2×D2911yescharacteristic
103#124—582no—
104#121—581no—
105#121—581no—
106C4×D4—291no—
107C4×D4C2×D2911yescharacteristic
108#117—581no—
109#117—581no—
110#106—21no—
111#106—581no—
112C4⋊C8—291no—
113C4⋊C8C2×D2911yescharacteristic
114#102—21no—
115#102—581no—
116C4×C8—291no—
117C29#163411yescharacteristic, complemented, Sylow
118C2×Q8—21no—
119C2×Q8—292no—
120C2×D4—291no—
121C2×D4—582no—
122C2×D4C22⋊D2911yescharacteristic
123C22×C4—21no—
124C22×C4—581no—
125Q16—1164no—
126C2×C8—21no—
127C2×C8—581no—
128C2×C8—581no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—291no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4C22⋊D2911yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—582no—
137C22⋊C4—582no—
138C22⋊C4—581no—
139C42—582no—
140C42C22×D2911yescharacteristic
141C23—21no—
142C23—581no—
143Q8—42no—
144Q8—1162no—
145D4—21no—
146D4—21no—
147D4—581no—
148D4—581no—
149D4—2322no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—581no—
155C2×C4—582no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4D4×D2911yescharacteristic
159C2×C4D4×D2911yescharacteristic
160C2×C4C2×C22⋊D2911yescharacteristic
161C8—41no—
162C8—582no—
163C8—1161no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—1161no—
168C22—1161no—
169C22—1161no—
170C22#1174529911yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—1161no—
175C4—1162no—
176C4#1174527711yescharacteristic
177C4#1174527811yescharacteristic
178C4#1174530411yescharacteristic
179C4#1174531211yescharacteristic
180C2—81no—
181C2—2321no—
182C2#1427132211yescharacteristic
183C2#1427132311yescharacteristic
184C2#1427132911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#476C2
socleC22×C29#120
prime radical#14271878C2
hypercenter#476D29
hypocenterC29#1634
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14271542C2semidirect
3. #14271450C2semidirect
4. #14270911C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×#476C2semidirect
91. #476D29semidirect
117. C29#1634semidirect

Maximal subgroups

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

subgroupindex
#142718782
#142715422
#142714502
#142709112
D4⋊#65972
#142708902
C29×#4762
#163429