Finite Group Databasebeta

← #16819894

Subgroups — #16819894

Order 3712.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11745237C211yesmaximal, characteristic
2#14271640C211yesmaximal, characteristic, complemented
3#14271169C211yesmaximal, characteristic
4#14271167C211yesmaximal, characteristic
5C2×#11745172C211yesmaximal, characteristic, complemented
6#14270923C211yesmaximal, characteristic, complemented
7C29×#339C211yesmaximal, characteristic, complemented
8C22×D116C2211yescharacteristic
9C22×Dic58C2211yescharacteristic
10C2×M16×C29C2211yescharacteristic
11C29×#117C2211yescharacteristic
12C2×C42×C29C2211yescharacteristic
13C2×#90781—22no—
14#11745288C2211yescharacteristic
15C2×#90777C2211yescharacteristic
16#11745249—22no—
17#11745239—22no—
18#11745237—22no—
19#11745237C414yescomplemented
20C4×Dic58—22no—
21#11745172—22no—
22#11745169—22no—
23#11745157—22no—
24C23×D29—21no—
25C22×C4×C29—21no—
26C22×C4×C29C2311yescharacteristic
27C22×Dic29D412yes—
28C2×D116—21no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116—21no—
33C2×D116C2×C412yes—
34C2×Dic58—21no—
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58—21no—
38C2×Dic58C2×C412yes—
39C2×Dic58D412yes—
40M16×C29—21no—
41M16×C29—21no—
42C2×C8×C29—21no—
43C4⋊C4×C29D412yes—
44C22⋊C4×C29—21no—
45C42×C29—21no—
46C42×C29—21no—
47C42×C29C2×C412yes—
48C22⋊Dic29—21no—
49#90781—28no—
50C4⋊Dic29D412yes—
51#90779—24no—
52C4×Dic29—24no—
53C4×Dic29—21no—
54#90777—21no—
55#90777—21no—
56C2×#6597—21no—
57C23×C29C2×D411yescharacteristic
58C22×D29—22no—
59C22×D29—44no—
60C22×D29—41no—
61C22×D29—41no—
62C2×C4×C29—22no—
63C2×C4×C29—22no—
64C2×C4×C29—42no—
65C2×C4×C29C22×C411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29#4111yescharacteristic
70C2×C4×C29#4111yescharacteristic
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—22no—
74C2×Dic29C22⋊C414yes—
75D116—22no—
76D116—22no—
77D116—41no—
78D116—41no—
79Dic58—22no—
80Dic58—22no—
81Dic58—22no—
82Dic58—22no—
83C8×C29—41no—
84#6597—41no—
85#1888—291nomaximal, Sylow
86C22×C29—22no—
87C22×C29C2×C22⋊C411yescharacteristic
88C22×C29#12011yescharacteristic
89C22×C29#12311yescharacteristic
90C2×D29—44no—
91C2×D29—42no—
92C2×D29—82no—
93C2×D29—82no—
94C4×C29—42no—
95C4×C29—42no—
96C4×C29C4×D411yescharacteristic
97C4×C29C4×D411yescharacteristic
98C4×C29#12111yescharacteristic
99C4×C29#12111yescharacteristic
100Dic29—24no—
101Dic29—42no—
102C2×#124—291no—
103#519—291no—
104#418—291no—
105#418—291no—
106C2×#101—291no—
107#339—291no—
108#339D2911yescharacteristic, complemented
109C2×C29—21no—
110C2×C29—21no—
111C2×C29#38611yescharacteristic
112C2×C29#45412yes—
113D29—82no—
114C22×Q8—291no—
115C22×D4—291no—
116C2×M16—291no—
117C2×M16C2×D2911yescharacteristic
118#124—294no—
119#124—582no—
120C4×Q8—582no—
121C4×Q8—582no—
122#117—291no—
123#117—582no—
124#117C2×D2911yescharacteristic
125C2×C22⋊C4—582no—
126C2×C42C2×D2911yescharacteristic
127#102—582no—
128#102—582no—
129#101—582no—
130C29#188811yescharacteristic, complemented, Sylow
131C24—581no—
132C2×Q8—292no—
133C2×Q8—292no—
134C2×Q8—581no—
135C2×Q8—581no—
136C2×Q8—581no—
137C2×Q8—581no—
138C2×D4—292no—
139C2×D4—581no—
140C2×D4—581no—
141C2×D4—581no—
142C2×D4—581no—
143C2×D4—581no—
144C22×C4—21no—
145C22×C4—292no—
146C22×C4C22×D2911yescharacteristic
147M16—21no—
148M16—21no—
149M16—581no—
150M16—581no—
151C2×C8—21no—
152C2×C8—581no—
153C4⋊C4—292no—
154C4⋊C4—584no—
155C4⋊C4D11612yes—
156C22⋊C4—21no—
157C22⋊C4—588no—
158C22⋊C4—581no—
159C42—21no—
160C42—21no—
161C42—584no—
162C42—581no—
163C42C4×D2912yes—
164C23—582no—
165C23—1164no—
166C23—1161no—
167C23—1161no—
168C23D4×D2911yescharacteristic
169Q8—582no—
170Q8—582no—
171Q8—582no—
172Q8—582no—
173D4—582no—
174D4—582no—
175D4—1161no—
176D4—1161no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—294no—
181C2×C4—582no—
182C2×C4—582no—
183C2×C4—582no—
184C2×C4C2×C4×D2911yescharacteristic
185C2×C4C2×D11611yescharacteristic
186C2×C4#9080511yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C2×C4D4×D2911yescharacteristic
189C2×C4#9080911yescharacteristic
190C8—41no—
191C8—1161no—
192C22—22no—
193C22—1164no—
194C22—1162no—
195C22—2322no—
196C22—2322no—
197C22C22⋊C4×D2911yescharacteristic
198C22#1174524411yescharacteristic
199C22#1174525611yescharacteristic
200C4—42no—
201C4—42no—
202C4—584no—
203C4—1162no—
204C4C4×D11611yescharacteristic
205C4#1174524611yescharacteristic
206C4#1174525511yescharacteristic
207C4#1174525711yescharacteristic
208C2—21no—
209C2—21no—
210C2—2322no—
211C2#1427104111yescharacteristic
212C2#1427133712yes—
subgroupG/H
centerC22#11745244
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#339C2
socleC22×C29#120
prime radicalC22×D116C22
cosocleC22×C4×C29C23
hypercenter#339D29
hypocenterC29#1888
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14271640C2semidirect
5. C2×#11745172C2semidirect
6. #14270923C2semidirect
7. C29×#339C2semidirect
19. #11745237C4semidirect
108. #339D29semidirect
130. C29#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#117452372
#142716402
#142711692
#142711672
C2×#117451722
#142709232
C29×#3392
#188829