Finite Group Databasebeta

← #19147394

Subgroups — #19147394

Order 5504.

326 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 123 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#14583627C211yesmaximal, characteristic
2#14583267C212yesmaximal
3#14583249C211yesmaximal, characteristic
4#14583206C212yesmaximal
5#14583184C211yesmaximal, characteristic
6#14583106C211yesmaximal, characteristic
7#14583106C212yesmaximal
8#14583030C211yesmaximal, characteristic
9#14583004C212yesmaximal
10C4×#10621885C211yesmaximal, characteristic
11C43×#557C211yesmaximal, characteristic
12C2×#10621885C2211yescharacteristic
13C2×#10621885C2212yes—
14#13063325C2211yescharacteristic
15#13063323—21no—
16#13063317C2212yes—
17#13063315—22no—
18C4×Dic86C2211yescharacteristic
19C4×Dic86C2212yes—
20#13063290—21no—
21#13063258C2211yescharacteristic
22#13063256C2212yes—
23C4⋊(C43⋊C8)C2211yescharacteristic
24C4⋊(C43⋊C8)C2212yes—
25#13063249C2212yes—
26#13063249C2212yes—
27#13063249C2212yes—
28#13063249C2211yescharacteristic
29#13063249C2212yes—
30#13063248C2211yescharacteristic
31#13063236C2212yes—
32C4×C43⋊C8C2211yescharacteristic
33C4⋊Q8×C43C2211yescharacteristic
34C4⋊Q8×C43C2212yes—
35#125×C43—21no—
36#125×C43—22no—
37C4×Q8×C43—21no—
38C4×Q8×C43C2211yescharacteristic
39C4×Q8×C43C2212yes—
40C4×Q8×C43C2211yescharacteristic
41C2×Q8×C43D411yescharacteristic
42C2×Q8×C43C2311yescharacteristic
43C2×Q8×C43C2312yes—
44C2×Dic86—21no—
45C2×Dic86C2311yescharacteristic
46C4⋊C4×C43—22no—
47C4⋊C4×C43—21no—
48C4⋊C4×C43—22no—
49C4⋊C4×C43—21no—
50C4⋊C4×C43—22no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43D411yescharacteristic
53C4⋊C4×C43D412yes—
54C4⋊C4×C43C2311yescharacteristic
55C42×C43—22no—
56C42×C43—21no—
57C42×C43C2311yescharacteristic
58C42×C43C2312yes—
59#10621885—22no—
60#10621885—24no—
61C4⋊Dic43—21no—
62C4⋊Dic43C2312yes—
63C4⋊Dic43C2311yescharacteristic
64Dic43⋊C4—22no—
65Dic43⋊C4—21no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68C4×Dic43—22no—
69C4×Dic43—21no—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72C2×C43⋊C8C2312yes—
73Q8×C43—22no—
74Q8×C43—21no—
75Q8×C43—22no—
76Q8×C43—21no—
77Q8×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2411yescharacteristic
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89Dic86—21no—
90Dic86—42no—
91Dic86#4112yes—
92C43⋊C8—21no—
93C43⋊C8—22no—
94C43⋊C8—21no—
95C22×C43C22×D411yescharacteristic
96C4×C43—22no—
97C4×C43—22no—
98C4×C43—21no—
99C4×C43—42no—
100C4×C43—41no—
101C4×C43—41no—
102C4×C43#13712yes—
103C4×C43C2×#4111yescharacteristic
104C4×C432−1+411yescharacteristic
105Dic43—22no—
106Dic43—42no—
107Dic43—41no—
108#3374—431nomaximal, Sylow
109C2×C43#54811yescharacteristic
110C2×C43C2×#13711yescharacteristic
111C2×C43#57811yescharacteristic
112#557—431no—
113#557D4311yescharacteristic
114#491—432no—
115#487—431no—
116#479—432no—
117#475—431no—
118#462—432no—
119#462—431no—
120#446—431no—
121#441—432no—
122C4×Q16—431no—
123C43#337411yescharacteristic, complemented, Sylow
124C2×Q16—431no—
125C2×Q16—432no—
126C4⋊Q8—431no—
127C4⋊Q8—861no—
128C4⋊Q8C2×D4311yescharacteristic
129C4⋊Q8C2×D4312yes—
130#125—21no—
131#125—22no—
132#125—432no—
133#125—862no—
134C4×Q8—21no—
135C4×Q8—431no—
136C4×Q8—432no—
137C4×Q8—861no—
138C4×Q8C2×D4311yescharacteristic
139C4×Q8C2×D4312yes—
140C4×Q8C2×D4311yescharacteristic
141#107—431no—
142#106—432no—
143C4⋊C8—431no—
144C4⋊C8—432no—
145#103—431no—
146#103—432no—
147#103—432no—
148#103—432no—
149#103—432no—
150#103—431no—
151#97—432no—
152C4×C8—431no—
153C2×Q8—431no—
154C2×Q8—861no—
155C2×Q8C22⋊D4311yescharacteristic
156C2×Q8C22×D4311yescharacteristic
157C2×Q8C22×D4312yes—
158Q16—862no—
159Q16—864no—
160C2×C8—431no—
161C2×C8—431no—
162C2×C8—432no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—432no—
170C4⋊C4—431no—
171C4⋊C4—861no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—861no—
176C4⋊C4C22⋊D4311yescharacteristic
177C4⋊C4C22⋊D4312yes—
178C4⋊C4C22×D4311yescharacteristic
179C42—22no—
180C42—21no—
181C42—862no—
182C42—861no—
183C42C22×D4311yescharacteristic
184C42C22×D4312yes—
185Q8—22no—
186Q8—21no—
187Q8—22no—
188Q8—21no—
189Q8—22no—
190Q8—432no—
191Q8—861no—
192Q8—1722no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—862no—
199C2×C4C2×C22⋊D4312yes—
200C2×C4C2×C22⋊D4312yes—
201C2×C4C2×C22⋊D4311yescharacteristic
202C2×C4C2×C22⋊D4311yescharacteristic
203C2×C4C23×D4311yescharacteristic
204C8—861no—
205C8—862no—
206C8—861no—
207C22C22×C22⋊D4311yescharacteristic
208C4—22no—
209C4—22no—
210C4—21no—
211C4—42no—
212C4—41no—
213C4—41no—
214C4—862no—
215C4—1722no—
216C4—1721no—
217C4#1306335612yes—
218C4#41×D4311yescharacteristic
219C4#1306337211yescharacteristic
220C2#1458355611yescharacteristic
221C2C2×#1306335611yescharacteristic
222C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#557C2
socleC22×C43C22×D4
hypercenter#557D43
hypocenterC43#3374
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
123. C43#3374semidirect