Finite Group Databasebeta

← #19135735

Subgroups — #19135735

Order 5504.

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×#13063324C211yesmaximal, characteristic
2C2×#13063250C211yesmaximal, characteristic
3C2×#13063248C211yesmaximal, characteristic
4#14582804C211yesmaximal, characteristic
5#14582661C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C43×#340C211yesmaximal, characteristic
8C22×Dic86—21no—
9C22×Dic86C2211yescharacteristic
10C22×C43⋊C8C2211yescharacteristic
11#13063324—22no—
12#13063324—22no—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4—21no—
15C2×C4×Dic43C2211yescharacteristic
16#13063250—22no—
17#13063248—22no—
18C43⋊#95—21no—
19C43⋊#95—21no—
20C22×C8×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22C2×C4⋊C4×C43C2211yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43C2311yescharacteristic
26C22×Dic43—21no—
27C22×Dic43—21no—
28C22×Dic43D411yescharacteristic
29C22×Dic43D411yescharacteristic
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×Dic86—21no—
33C2×Dic86—21no—
34C2×Dic86—24no—
35C2×Dic86—21no—
36C2×Dic86—42no—
37C2×Dic86—42no—
38C2×Dic86Q812yescomplemented
39C2×C8×C43—21no—
40C2×C8×C43—21no—
41C2×C8×C43—21no—
42C4⋊C4×C43—21no—
43C4⋊C4×C43—21no—
44C4⋊C4×C43—21no—
45C4⋊C4×C43D412yes—
46C4⋊Dic43—21no—
47C4⋊Dic43D412yes—
48Dic43⋊C4—24no—
49C4×Dic43—21no—
50C4×Dic43—21no—
51C2×C43⋊C8—21no—
52C2×C43⋊C8—21no—
53C2×C43⋊C8—21no—
54C23×C43C2×D411yescharacteristic
55C2×C4×C43—22no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×Q811yescharacteristic
64C2×C4×C43#4111yescharacteristic
65C2×C4×C43#4111yescharacteristic
66C2×C4×C43#4111yescharacteristic
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—21no—
71C2×Dic43—22no—
72C2×Dic43—22no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43SD1612yes—
78C2×Dic43Q1612yes—
79Dic86—22no—
80Dic86—22no—
81Dic86—48no—
82Dic86—41no—
83Dic86—41no—
84C8×C43—41no—
85C43⋊C8—41no—
86C22×C43#12011yescharacteristic
87C22×C43C22⋊Q811yescharacteristic
88C22×C43#12411yescharacteristic
89C22×C43C2×SD1611yescharacteristic
90C22×C43C2×Q1611yescharacteristic
91C22×C43AGL(1,ℤ/8)11yescharacteristic
92C22×C43#13711yescharacteristic
93C4×C43—42no—
94C4×C43—81no—
95C4×C43C22⋊Q811yescharacteristic
96C4×C43C22⋊Q811yescharacteristic
97C4×C43#12411yescharacteristic
98C4×C43#12411yescharacteristic
99Dic43—22no—
100Dic43—22no—
101Dic43—42no—
102Dic43—42no—
103#2024—431nomaximal, Sylow
104C2×C43#39311yescharacteristic
105C2×C43#45011yescharacteristic
106C2×C43#45111yescharacteristic
107C2×C43#47511yescharacteristic
108C2×C43#47711yescharacteristic
109C2×C43#48711yescharacteristic
110C2×C43#48911yescharacteristic
111C2×C4⋊Q8—431no—
112C2×#103—431no—
113C2×#103—431no—
114#391—431no—
115#340—431no—
116#340D4311yescharacteristic
117#336—431no—
118C43#202411yescharacteristic, complemented, Sylow
119C22×Q8—431no—
120C22×Q8—861no—
121C22×C8—431no—
122C22×C8C2×D4311yescharacteristic
123C4⋊Q8—862no—
124C4⋊Q8—862no—
125C2×C4⋊C4—431no—
126C2×C4⋊C4—861no—
127C2×C4⋊C4C2×D4311yescharacteristic
128C2×C4⋊C4C2×D4311yescharacteristic
129C2×C42—431no—
130#103—862no—
131#103—862no—
132#95—861no—
133#95—861no—
134C2×Q8—432no—
135C2×Q8—864no—
136C2×Q8—861no—
137C2×Q8—861no—
138C2×Q8—861no—
139C2×Q8—861no—
140C2×Q8—861no—
141C2×Q8—1722no—
142C2×Q8—1722no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—431no—
146C22×C4—431no—
147C22×C4—861no—
148C22×C4—861no—
149C22×C4C22×D4311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—861no—
154C2×C8—861no—
155C2×C8—861no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—432no—
160C4⋊C4—864no—
161C4⋊C4—861no—
162C4⋊C4D17212yes—
163C42—861no—
164C42—861no—
165C23D4×D4311yescharacteristic
166Q8—862no—
167Q8—862no—
168Q8—1728no—
169Q8—1721no—
170Q8—1721no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—432no—
178C2×C4—432no—
179C2×C4—861no—
180C2×C4—861no—
181C2×C4—861no—
182C2×C4—861no—
183C2×C4—862no—
184C2×C4—862no—
185C2×C4—1721no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—1721no—
189C2×C4C2×D17211yescharacteristic
190C2×C4#1062189811yescharacteristic
191C2×C4#1062189811yescharacteristic
192C2×C4D4×D4311yescharacteristic
193C2×C4#1062190011yescharacteristic
194C2×C4Q8×D4311yescharacteristic
195C8—41no—
196C8—1721no—
197C22#1306329511yescharacteristic
198C22#1306330311yescharacteristic
199C22#1306331111yescharacteristic
200C22SD16×D4311yescharacteristic
201C22Q16×D4311yescharacteristic
202C22#1306334911yescharacteristic
203C22#1306335411yescharacteristic
204C4—42no—
205C4—81no—
206C4—862no—
207C4—862no—
208C4—1722no—
209C4—1722no—
210C4#1306330311yescharacteristic
211C4#1306330511yescharacteristic
212C4#1306331111yescharacteristic
213C4#1306331311yescharacteristic
214C2#1458281211yescharacteristic
215C2#1458305111yescharacteristic
216C2#1458305611yescharacteristic
217C2#1458318311yescharacteristic
218C2#1458319311yescharacteristic
219C2#1458324811yescharacteristic
220C2#1458325711yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#340C2
socleC23×C43C2×D4
hypercenter#340D43
hypocenterC43#2024
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic86Q8semidirect
118. C43#2024semidirect