Finite Group Databasebeta

← #16818610

Subgroups — #16818610

Order 3712.

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

normal subgroups only

This group has 314 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
1D4×D116C211yesmaximal, characteristic
2#14271536C211yesmaximal, characteristic, complemented
3#14271454C211yesmaximal, characteristic, complemented
4#14271453C211yesmaximal, characteristic, complemented
5#14270906C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D29—21no—
9C22×D116—21no—
10C4×D4×C29C2211yescharacteristic
11#11745292—21no—
12C2×#90773—22no—
13#11745257—21no—
14#11745244—22no—
15#11745236C2211yescharacteristic
16C4×D116C2211yescharacteristic
17#11745231C2211yescharacteristic, complemented
18C29×C4⋊C8C2211yescharacteristic, complemented
19C4×C8×C29C2211yescharacteristic, complemented
20#11745180—21no—
21#11745169—21no—
22#11745165—21no—
23#11745156—21no—
24C4⋊#6597C2211yescharacteristic, complemented
25C23×D29—22no—
26C2×D4×C29D411yescharacteristic
27C22×C4×C29—21no—
28C2×C22⋊D29—22no—
29D4×D29—42no—
30D4×D29—42no—
31C2×D116—22no—
32C2×D116—21no—
33C2×D116—21no—
34C2×D116—42no—
35C2×D116—42no—
36C2×D116D411yescharacteristic
37C2×D116D412yes—
38C2×C4×D29—21no—
39C2×Dic58—21no—
40C2×C8×C29—21no—
41C2×C8×C29—21no—
42C4⋊C4×C29D411yescharacteristic
43C22⋊C4×C29—21no—
44C42×C29C2311yescharacteristic
45#90781—22no—
46#90781—21no—
47C4⋊Dic29—21no—
48C4⋊Dic29—21no—
49C4⋊Dic29D411yescharacteristic
50C2×#6597—21no—
51#90773—44no—
52C23×C29—21no—
53C22×D29—21no—
54C22×D29—22no—
55C22×D29—44no—
56C22×D29—44no—
57C22×D29—82no—
58D4×C29—21no—
59D4×C29SD1612yescomplemented
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—44no—
67C2×Dic29—21no—
68C2×Dic29—41no—
69D116—21no—
70D116—42no—
71D116—44no—
72D116—41no—
73D116—41no—
74D116—41no—
75D116—41no—
76D116SD1612yescomplemented
77C4×D29—41no—
78C4×D29—41no—
79Dic58—42no—
80C8×C29—22no—
81C8×C29—41no—
82#6597—41no—
83#1629—291nomaximal, Sylow
84C22×C29—22no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29#12011yescharacteristic
88C2×D29—22no—
89C2×D29—41no—
90C2×D29—41no—
91C2×D29—42no—
92C2×D29—42no—
93C2×D29—42no—
94C2×D29—88no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29C2×SD1611yescharacteristic
98C4×C29C2×SD1611yescharacteristic
99C4×C29AGL(1,ℤ/8)11yescharacteristic
100C4×C29AGL(1,ℤ/8)11yescharacteristic
101Dic29—41no—
102Dic29—81no—
103D42—291no—
104#492—291no—
105#476—291no—
106#476—291no—
107#331—291no—
108D4⋊C8—291no—
109D4⋊C8D2911yescharacteristic, complemented
110C2×C29—42no—
111C2×C29#45011yescharacteristic
112C2×C29#45011yescharacteristic
113C2×C29#45311yescharacteristic
114D29—42no—
115D29—82no—
116C22×D4—581no—
117C22×D4—581no—
118C2×SD16—582no—
119C4⋊Q8—291no—
120#127—291no—
121#121—581no—
122#121—581no—
123#120—582no—
124C4×D4—291no—
125C4×D4C2×D2911yescharacteristic
126#106—581no—
127#106—581no—
128C4⋊C8—291no—
129C4⋊C8C2×D2911yescharacteristic, complemented
130#102—581no—
131#102—581no—
132C4×C8C2×D2911yescharacteristic, complemented
133C29#162911yescharacteristic, complemented, Sylow
134C24—582no—
135C2×Q8—581no—
136C2×D4—291no—
137C2×D4—292no—
138C2×D4—582no—
139C2×D4—582no—
140C2×D4—581no—
141C2×D4—581no—
142C2×D4—1162no—
143C2×D4—1162no—
144C2×D4—1162no—
145C2×D4—1162no—
146C2×D4D11611yescharacteristic
147C22×C4—21no—
148C22×C4—581no—
149SD16—1164no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—581no—
153C4⋊C4—291no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4D11611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—582no—
159C22⋊C4—581no—
160C42C22×D2911yescharacteristic
161C23—21no—
162C23—581no—
163C23—582no—
164C23—1164no—
165C23—1164no—
166C23—2322no—
167Q8—1162no—
168D4—21no—
169D4—292no—
170D4—581no—
171D4—1162no—
172D4—1164no—
173D4—1164no—
174D4—1161no—
175D4—1161no—
176D4—1161no—
177D4—1161no—
178D4#9077312yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—581no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4—1161no—
186C2×C4C2×D11611yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C2×C4D4×D2911yescharacteristic
189C8—22no—
190C8—41no—
191C8—1161no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—582no—
196C22—1161no—
197C22—1161no—
198C22—1162no—
199C22—1162no—
200C22—1162no—
201C22—2328no—
202C22#1174524411yescharacteristic
203C4—21no—
204C4—41no—
205C4—1161no—
206C4—2321no—
207C4C2×#9077311yescharacteristic
208C4#1174527011yescharacteristic
209C4#1174527311yescharacteristic
210C4SD16×D2911yescharacteristic
211C2—42no—
212C2—1162no—
213C2—2322no—
214C2#1427131511yescharacteristic
215C2#1427131611yescharacteristic
216C2#1427133211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29#120
prime radicalD4×D116C2
hypercenterD4⋊C8D29
hypocenterC29#1629
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. #14271536C2semidirect
3. #14271454C2semidirect
4. #14271453C2semidirect
5. #14270906C2semidirect
6. #14270892C2semidirect
7. C29×D4⋊C8C2semidirect
17. #11745231C22semidirect
18. C29×C4⋊C8C22semidirect
19. C4×C8×C29C22semidirect
24. C4⋊#6597C22semidirect
59. D4×C29SD16semidirect
76. D116SD16semidirect
109. D4⋊C8D29semidirect
129. C4⋊C8C2×D29semidirect
132. C4×C8C2×D29semidirect
133. C29#1629semidirect
178. D4#90773semidirect

Maximal subgroups

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

subgroupindex
D4×D1162
#142715362
#142714542
#142714532
#142709062
#142708922
C29×D4⋊C82
#162929