Finite Group Databasebeta

← #19147271

Subgroups — #19147271

Order 5504.

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

normal subgroups only

This group has 336 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
1Q8×Dic86C211yesmaximal, characteristic
2#14583627C211yesmaximal, characteristic
3#14583250C211yesmaximal, characteristic
4#14583248C212yesmaximal
5#14583194C211yesmaximal, characteristic
6#14583193C212yesmaximal
7#14583109C211yesmaximal, characteristic
8#14583107C212yesmaximal
9C8×Dic86C211yesmaximal, characteristic
10#14582991C212yesmaximal
11C4×Q16×C43C211yesmaximal, characteristic
12C2×#10621885C2212yes—
13#13063325—21no—
14#13063325C2211yescharacteristic
15#13063325C2211yescharacteristic
16#13063324—22no—
17#13063324C2212yes—
18#13063323C2212yes—
19#13063317—21no—
20#13063315—22no—
21Q8×Dic43C2212yes—
22C4×Dic86—21no—
23C4×Dic86—21no—
24C4×Dic86C2211yescharacteristic
25#13063290C2212yes—
26#13063258C2212yes—
27C4⋊(C43⋊C8)C2211yescharacteristic
28Dic43⋊C8C2212yes—
29#13063250C2212yes—
30#13063250C2212yes—
31#13063249C2212yes—
32#13063248C2212yes—
33C8×Dic43C2212yes—
34C2×Q16×C43C2211yescharacteristic
35C4×Q8×C43C2211yescharacteristic
36C4×Q8×C43C2211yescharacteristic
37#107×C43C2211yescharacteristic
38#103×C43C2211yescharacteristic
39#103×C43C2211yescharacteristic
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43C2311yescharacteristic
42C2×Q8×C43C2311yescharacteristic
43C2×Dic86—21no—
44C2×Dic86—22no—
45C2×Dic86D411yescharacteristic
46C2×Dic86C2312yes—
47Q16×C43—22no—
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2311yescharacteristic
53C4⋊C4×C43C2311yescharacteristic
54C42×C43—21no—
55C42×C43—21no—
56C42×C43C2311yescharacteristic
57#10621885—24no—
58C4⋊Dic43—21no—
59C4⋊Dic43—21no—
60C4⋊Dic43—21no—
61C4⋊Dic43—22no—
62C4⋊Dic43D411yescharacteristic
63C4⋊Dic43C2312yes—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4D412yes—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43C2312yes—
72C2×C43⋊C8C2312yes—
73Q8×C43—21no—
74Q8×C43—21no—
75Q8×C43—21no—
76Q8×C43#4112yes—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2411yescharacteristic
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88Dic86—22no—
89Dic86—22no—
90Dic86—82no—
91Dic86—81no—
92Dic86Q1614yescomplemented
93C8×C43—21no—
94C8×C43—21no—
95C43⋊C8—22no—
96C22×C43C22×D411yescharacteristic
97C4×C43—22no—
98C4×C43—21no—
99C4×C43—41no—
100C4×C43—41no—
101C4×C43—41no—
102C4×C43C2×Q1612yes—
103C4×C43C2×#4111yescharacteristic
104C4×C432−1+411yescharacteristic
105Dic43—22no—
106Dic43—42no—
107Dic43—42no—
108Dic43C2×Q1614yes—
109#3363—431nomaximal, Sylow
110C2×C43#54811yescharacteristic
111C2×C43C22×Q1611yescharacteristic
112C2×C43#57711yescharacteristic
113Q82—431no—
114#557—431no—
115#487—432no—
116#487—431no—
117#477—431no—
118#477—432no—
119#462—432no—
120#462—431no—
121C8×Q8—431no—
122C4×Q16—432no—
123C4×Q16D4311yescharacteristic
124C43#336311yescharacteristic, complemented, Sylow
125C2×Q16—432no—
126C2×Q16C2×D4311yescharacteristic
127C4⋊Q8—432no—
128C4⋊Q8—432no—
129C4⋊Q8—431no—
130C4⋊Q8—431no—
131C4⋊Q8—861no—
132C4⋊Q8—862no—
133#125—861no—
134#125—862no—
135C4×Q8—431no—
136C4×Q8—432no—
137C4×Q8—432no—
138C4×Q8—861no—
139C4×Q8—861no—
140C4×Q8C2×D4311yescharacteristic
141C4×Q8C2×D4311yescharacteristic
142#107—432no—
143#107C2×D4311yescharacteristic
144C4⋊C8—432no—
145C4⋊C8—431no—
146#103—432no—
147#103—432no—
148#103—432no—
149#103—432no—
150#103C2×D4311yescharacteristic
151#103C2×D4311yescharacteristic
152C4×C8—432no—
153C4×C8C2×D4311yescharacteristic
154C2×Q8—431no—
155C2×Q8—432no—
156C2×Q8—862no—
157C2×Q8—861no—
158C2×Q8C22×D4311yescharacteristic
159C2×Q8C22×D4311yescharacteristic
160Q16—22no—
161Q16—864no—
162C2×C8—432no—
163C2×C8C22×D4311yescharacteristic
164C2×C8C22×D4311yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—432no—
168C4⋊C4—431no—
169C4⋊C4—432no—
170C4⋊C4—862no—
171C4⋊C4—862no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—861no—
178C4⋊C4C22×D4311yescharacteristic
179C4⋊C4C22×D4311yescharacteristic
180C42—21no—
181C42—21no—
182C42—432no—
183C42—862no—
184C42—862no—
185C42C22×D4311yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—434no—
190Q8—862no—
191Q8—862no—
192Q8—3441no—
193Q8—3442no—
194Q8#1062189812yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—432no—
200C2×C4—432no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4D4×D4311yescharacteristic
204C2×C4D4×D4311yescharacteristic
205C2×C4C23×D4311yescharacteristic
206C8—21no—
207C8—21no—
208C8—862no—
209C22C2×D4×D4311yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—434no—
216C4—862no—
217C4—1722no—
218C4—1722no—
219C4Q16×D4312yes—
220C4C2×#1062189811yescharacteristic
221C4#1306337211yescharacteristic
222C2#1458355811yescharacteristic
223C2C2×Q16×D4311yescharacteristic
224C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×Q16×C43C2
socleC22×C43C22×D4
hypercenterC4×Q16D43
hypocenterC43#3363
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
92. Dic86Q16semidirect
124. C43#3363semidirect