Finite Group Databasebeta

← #16818643

Subgroups — #16818643

Order 3712.

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

normal subgroups only

This group has 234 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#14271515C211yesmaximal, characteristic, complemented
2#14271453C211yesmaximal, characteristic, complemented
3#14271453C211yesmaximal, characteristic, complemented
4#14270909C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×#547C211yesmaximal, characteristic
8C2×#41×C29—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×#123—22no—
11C29×C22⋊Q8—21no—
12C29×#121—21no—
13C4×D4×C29C2211yescharacteristic
14C4×D4×C29C2211yescharacteristic
15C2×C4⋊C4×C29—21no—
16#11745231C2211yescharacteristic
17#11745180—21no—
18#11745180—21no—
19#11745158—22no—
20#11745156—21no—
21#11745156—21no—
22C4⋊#6597C2211yescharacteristic
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25#41×C29—42no—
26#41×C29—42no—
27C2×Q8×C29—21no—
28C2×D4×C29—22no—
29C2×D4×C29D411yescharacteristic
30C2×D4×C29D411yescharacteristic
31C22×C4×C29—22no—
32C22×C4×C29—21no—
33C22×C4×C29—21no—
34C2×Dic58—21no—
35C4⋊C4×C29—22no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C4⋊C4×C29D411yescharacteristic
39C4⋊C4×C29D412yes—
40C22⋊C4×C29—22no—
41C22⋊C4×C29—21no—
42C22⋊C4×C29—21no—
43C42×C29C2311yescharacteristic
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C2×#6597—21no—
47C2×#6597—21no—
48C2×#6597—21no—
49C23×C29—21no—
50C23×C29—21no—
51Q8×C29—41no—
52Q8×C29—41no—
53D4×C29—21no—
54D4×C29—21no—
55D4×C29—21no—
56D4×C29—44no—
57D4×C29SD1612yes—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—22no—
61C2×C4×C29—44no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C2×Dic29—41no—
70Dic58—42no—
71#6597—41no—
72#6597—41no—
73#6597—41no—
74#1635—291nomaximal, Sylow
75C22×C29—22no—
76C22×C29—41no—
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29#12011yescharacteristic
82C4×C29—21no—
83C4×C29—41no—
84C4×C29—42no—
85C4×C29—41no—
86C4×C29C2×SD1611yescharacteristic
87C4×C29#13511yescharacteristic
88C4×C29AGL(1,ℤ/8)11yescharacteristic
89C4×C29#13711yescharacteristic
90Dic29—81no—
91#547D2911yescharacteristic
92#487—291no—
93#476—291no—
94#476—291no—
95#332—291no—
96D4⋊C8—291no—
97D4⋊C8—291no—
98C2×C29—42no—
99C2×C29—81no—
100C2×C29#45011yescharacteristic
101C2×C29#45211yescharacteristic
102C2×C29#45411yescharacteristic
103C2×#41—21no—
104C4⋊Q8—291no—
105C4⋊Q8C2×D2911yescharacteristic
106#123—22no—
107C22⋊Q8—21no—
108#121—21no—
109C4×D4C2×D2911yescharacteristic
110C4×D4C2×D2911yescharacteristic
111C2×C4⋊C4—21no—
112#106—581no—
113#106—581no—
114C4⋊C8—291no—
115C4⋊C8—291no—
116#103—582no—
117#102—581no—
118#102—581no—
119C4×C8—291no—
120C29#163511yescharacteristic, complemented, Sylow
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—581no—
125C2×D4—22no—
126C2×D4C22⋊D2911yescharacteristic
127C2×D4C22⋊D2911yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—581no—
132C2×C8—581no—
133C2×C8—581no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—581no—
137C4⋊C4—581no—
138C4⋊C4C22⋊D2912yes—
139C4⋊C4C22⋊D2911yescharacteristic
140C4⋊C4C22⋊D2911yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D2911yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—1162no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#9078312yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1161no—
164C2×C4C2×C22⋊D2911yescharacteristic
165C2×C4C2×C22⋊D2911yescharacteristic
166C2×C4C2×C22⋊D2911yescharacteristic
167C8—1161no—
168C8—1161no—
169C8—1161no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1174531511yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—2321no—
182C4#1174529411yescharacteristic
183C4C2×#9078311yescharacteristic
184C4#1174531211yescharacteristic
185C4#1174531311yescharacteristic
186C2—42no—
187C2—81no—
188C2#1427131411yescharacteristic
189C2#1427132511yescharacteristic
190C2#1427133611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
Fitting, prime radicalC29×#547C2
socleC22×C29#120
hypercenter#547D29
hypocenterC29#1635
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14271515C2semidirect
2. #14271453C2semidirect
3. #14271453C2semidirect
4. #14270909C2semidirect
5. D4⋊#6597C2semidirect
6. D4⋊#6597C2semidirect
120. C29#1635semidirect

Maximal subgroups

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

subgroupindex
#142715152
#142714532
#142709092
D4⋊#65972
C29×#5472
#163529