Finite Group Databasebeta

← #16830880

Subgroups — #16830880

Order 3712.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#14271720C211yesmaximal, characteristic, complemented
2#14271713C211yesmaximal, characteristic
3#14271459C212yesmaximal, complemented
4#14271444C212yesmaximal, complemented
5#14271409C214yesmaximal, complemented
6#14271369C212yesmaximal, complemented
7#14271364C212yesmaximal, complemented
8C29×#423C211yesmaximal, characteristic, complemented
9C2×#90805—21no—
10C2×M16×C29C2212yes—
11C2×C42×C29C2211yescharacteristic
12#11745292—21no—
13#11745292C2212yes—
14#11745288—21no—
15#11745286—21no—
16#11745286C2212yes—
17C2×#90773C2214yes—
18#11745237—21no—
19#11745236C2211yescharacteristic
20C4×D116—21no—
21C4×D116C2212yes—
22#11745232—21no—
23#11745231C2211yescharacteristic
24#11745231C2211yescharacteristic
25#11745231C2211yescharacteristic
26C4×Dic58—21no—
27C4×Dic58C2212yes—
28C29×C4⋊C8C2212yes—
29C29×C4⋊C8C2212yes—
30#11745169C2214yes—
31#11745166C2214yes—
32#11745164C2214yes—
33C22×C4×C29D411yescharacteristic
34C22×C4×C29D411yescharacteristic
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37#90805—44no—
38C2×D116—21no—
39C2×D116—21no—
40C2×D116C2312yes—
41C2×C4×D29—22no—
42C2×Dic58—21no—
43C2×Dic58—21no—
44C2×Dic58C2312yes—
45M16×C29—42no—
46C2×C8×C29C2314yes—
47C42×C29D411yescharacteristic
48C42×C29D411yescharacteristic
49C42×C29C2311yescharacteristic
50C42×C29C2311yescharacteristic
51C22⋊Dic29—22no—
52#90781—22no—
53#90781—22no—
54C4⋊Dic29—21no—
55C4⋊Dic29—21no—
56C4⋊Dic29—21no—
57C4⋊Dic29—21no—
58C4⋊Dic29C2312yes—
59C4⋊Dic29C2312yes—
60#90779—22no—
61#90779—22no—
62C4×Dic29—22no—
63#90773—44no—
64C23×C29C2×D411yescharacteristic
65C22×D29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2411yescharacteristic
76C22⋊D29—44no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—22no—
80D116—22no—
81D116—22no—
82D116—42no—
83D116—42no—
84C4×D29—44no—
85Dic58—22no—
86Dic58—22no—
87Dic58—42no—
88Dic58—42no—
89C8×C29—24no—
90#3254—291nomaximal, Sylow
91C22×C29—21no—
92C22×C29—21no—
93C22×C29—21no—
94C22×C29C22×D411yescharacteristic
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—42no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29AGL(1,ℤ/8)12yes—
102C4×C29#13712yes—
103C4×C29H(5,𝔽2)11yescharacteristic
104C4×C292−1+411yescharacteristic
105Dic29—42no—
106Dic29—42no—
107Dic29—42no—
108#533—291no—
109#532—291no—
110#477—292no—
111#474—292no—
112#468—294no—
113#461—292no—
114#460—292no—
115#423D2911yescharacteristic, complemented
116C2×C29—41no—
117C2×C29#53711yescharacteristic
118C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C29C2×#13711yescharacteristic
120D29—82no—
121C2×#41—581no—
122C2×SD16—294no—
123C2×M16C2×D2912yes—
124C4⋊Q8—291no—
125C4⋊Q8—291no—
126C4⋊Q8—291no—
127#127—291no—
128#125—581no—
129#124—581no—
130C22⋊Q8—292no—
131C22⋊Q8—581no—
132#121—292no—
133#121—581no—
134C4×Q8—292no—
135C4×Q8—581no—
136C4×D4—292no—
137C4×D4—581no—
138#117—581no—
139C2×C42C2×D2911yescharacteristic
140#107—294no—
141C4⋊C8C2×D2912yes—
142C4⋊C8C2×D2912yes—
143#103—294no—
144#102—294no—
145C29#325411yescharacteristic, complemented, Sylow
146#41—1164no—
147C2×Q8—292no—
148C2×Q8—581no—
149C2×Q8—581no—
150C2×D4—292no—
151C2×D4—582no—
152C2×D4—581no—
153C2×D4—581no—
154C22×C4—582no—
155C22×C4D11611yescharacteristic
156C22×C4D11611yescharacteristic
157C22×C4C22×D2911yescharacteristic
158SD16—1164no—
159M16—42no—
160C2×C8C22×D2914yes—
161C4⋊C4—292no—
162C4⋊C4—292no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—582no—
167C4⋊C4—582no—
168C4⋊C4—581no—
169C22⋊C4—582no—
170C22⋊C4—582no—
171C22⋊C4—582no—
172C42—582no—
173C42D11611yescharacteristic
174C42D11611yescharacteristic
175C42C22×D2911yescharacteristic
176C42C22×D2911yescharacteristic
177C23—582no—
178C23C2×D11611yescharacteristic
179Q8—582no—
180Q8—582no—
181Q8—1162no—
182Q8—1162no—
183D4—582no—
184D4—582no—
185D4—1162no—
186D4—1164no—
187D4—1162no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—582no—
195C2×C4—1164no—
196C2×C4C2×D11611yescharacteristic
197C2×C4C2×D11611yescharacteristic
198C2×C4C2×D11611yescharacteristic
199C2×C4C2×D11611yescharacteristic
200C2×C4C2×D11611yescharacteristic
201C2×C4C23×D2911yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—1162no—
207C22—1162no—
208C22—1162no—
209C22C22×D11611yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1162no—
214C4—1162no—
215C4—1162no—
216C4#1174527012yes—
217C4#1174527112yes—
218C4#1174535911yescharacteristic
219C4#1174536211yescharacteristic
220C2—41no—
221C2—2322no—
222C2#1427174411yescharacteristic
223C2C2×#1174527011yescharacteristic
224C2C2×#1174527111yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#423C2
socleC22×C29C22×D4
prime radical#14271713C2
hypercenter#423D29
hypocenterC29#3254
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #14271720C2semidirect
3. #14271459C2semidirect
4. #14271444C2semidirect
5. #14271409C2semidirect
6. #14271369C2semidirect
7. #14271364C2semidirect
8. C29×#423C2semidirect
115. #423D29semidirect
145. C29#3254semidirect

Maximal subgroups

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

subgroupindex
#142717202
#142717132
#142714592
#142714442
#142714092
#142713692
#142713642
C29×#4232
#325429