Finite Group Databasebeta

← #16820632

Subgroups — #16820632

Order 3712.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11745250C211yesmaximal, characteristic
2C2×#11745164C211yesmaximal, characteristic
3C2×#11745158C211yesmaximal, characteristic
4#14271068C211yesmaximal, characteristic
5#14270925C211yesmaximal, characteristic
6#14270917C211yesmaximal, characteristic
7C29×#340C211yesmaximal, characteristic
8C22×Dic58—21no—
9C22×Dic58C2211yescharacteristic
10C22×C8×C29C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×C4⋊Dic29C2211yescharacteristic
14C2×#90779—21no—
15C2×C4×Dic29C2211yescharacteristic
16C22×#6597C2211yescharacteristic
17#11745250—22no—
18#11745250—22no—
19#11745179—21no—
20#11745179—21no—
21#11745164—22no—
22#11745158—22no—
23C22×C4×C29—21no—
24C22×C4×C29—21no—
25C22×C4×C29C2311yescharacteristic
26C22×Dic29—21no—
27C22×Dic29—21no—
28C22×Dic29D411yescharacteristic
29C22×Dic29D411yescharacteristic
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58—24no—
35C2×Dic58—21no—
36C2×Dic58—42no—
37C2×Dic58—42no—
38C2×Dic58Q812yescomplemented
39C2×C8×C29—21no—
40C2×C8×C29—21no—
41C2×C8×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29D412yes—
46C4⋊Dic29—21no—
47C4⋊Dic29D412yes—
48#90779—24no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C2×#6597—21no—
52C2×#6597—21no—
53C2×#6597—21no—
54C23×C29C2×D411yescharacteristic
55C2×C4×C29—22no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×Q811yescharacteristic
64C2×C4×C29#4111yescharacteristic
65C2×C4×C29#4111yescharacteristic
66C2×C4×C29#4111yescharacteristic
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29SD1612yes—
78C2×Dic29Q1612yes—
79Dic58—22no—
80Dic58—22no—
81Dic58—48no—
82Dic58—41no—
83Dic58—41no—
84C8×C29—41no—
85#6597—41no—
86#2024—291nomaximal, Sylow
87C22×C29#12011yescharacteristic
88C22×C29C22⋊Q811yescharacteristic
89C22×C29#12411yescharacteristic
90C22×C29C2×SD1611yescharacteristic
91C22×C29C2×Q1611yescharacteristic
92C22×C29AGL(1,ℤ/8)11yescharacteristic
93C22×C29#13711yescharacteristic
94C4×C29—42no—
95C4×C29—81no—
96C4×C29C22⋊Q811yescharacteristic
97C4×C29C22⋊Q811yescharacteristic
98C4×C29#12411yescharacteristic
99C4×C29#12411yescharacteristic
100Dic29—22no—
101Dic29—22no—
102Dic29—42no—
103Dic29—42no—
104C2×C4⋊Q8—291no—
105C2×#103—291no—
106C2×#103—291no—
107#391—291no—
108#340—291no—
109#340D2911yescharacteristic
110#336—291no—
111C2×C29#39311yescharacteristic
112C2×C29#45011yescharacteristic
113C2×C29#45111yescharacteristic
114C2×C29#47511yescharacteristic
115C2×C29#47711yescharacteristic
116C2×C29#48711yescharacteristic
117C2×C29#48911yescharacteristic
118C22×Q8—291no—
119C22×Q8—581no—
120C22×C8—291no—
121C22×C8C2×D2911yescharacteristic
122C4⋊Q8—582no—
123C4⋊Q8—582no—
124C2×C4⋊C4—291no—
125C2×C4⋊C4—581no—
126C2×C4⋊C4C2×D2911yescharacteristic
127C2×C4⋊C4C2×D2911yescharacteristic
128C2×C42—291no—
129#103—582no—
130#103—582no—
131#95—581no—
132#95—581no—
133C29#202411yescharacteristic, complemented, Sylow
134C2×Q8—292no—
135C2×Q8—584no—
136C2×Q8—581no—
137C2×Q8—581no—
138C2×Q8—581no—
139C2×Q8—581no—
140C2×Q8—581no—
141C2×Q8—1162no—
142C2×Q8—1162no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—291no—
146C22×C4—291no—
147C22×C4—581no—
148C22×C4—581no—
149C22×C4C22×D2911yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—581no—
154C2×C8—581no—
155C2×C8—581no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—292no—
160C4⋊C4—584no—
161C4⋊C4—581no—
162C4⋊C4D11612yes—
163C42—581no—
164C42—581no—
165C23D4×D2911yescharacteristic
166Q8—582no—
167Q8—582no—
168Q8—1168no—
169Q8—1161no—
170Q8—1161no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—292no—
178C2×C4—292no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—582no—
184C2×C4—582no—
185C2×C4—1161no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4—1161no—
189C2×C4C2×D11611yescharacteristic
190C2×C4#9080511yescharacteristic
191C2×C4#9080511yescharacteristic
192C2×C4D4×D2911yescharacteristic
193C2×C4#9080711yescharacteristic
194C2×C4Q8×D2911yescharacteristic
195C8—41no—
196C8—1161no—
197C22#1174524411yescharacteristic
198C22#1174524711yescharacteristic
199C22#1174525811yescharacteristic
200C22#1174527311yescharacteristic
201C22SD16×D2911yescharacteristic
202C22#1174527711yescharacteristic
203C22Q16×D2911yescharacteristic
204C4—42no—
205C4—81no—
206C4—582no—
207C4—582no—
208C4—1162no—
209C4—1162no—
210C4#1174523711yescharacteristic
211C4#1174524711yescharacteristic
212C4#1174525811yescharacteristic
213C4#1174525911yescharacteristic
214C2#1427107611yescharacteristic
215C2#1427131511yescharacteristic
216C2#1427132011yescharacteristic
217C2#1427144711yescharacteristic
218C2#1427145711yescharacteristic
219C2#1427151211yescharacteristic
220C2#1427152111yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#340C2
socle, prime radicalC23×C29C2×D4
hypercenter#340D29
hypocenterC29#2024
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic58Q8semidirect
133. C29#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#117452502
C2×#117451642
C2×#117451582
#142710682
#142709252
#142709172
C29×#3402
#202429