Finite Group Databasebeta

← #20256130

Subgroups — #20256130

Order 6016.

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

normal subgroups only

This group has 338 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
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689846C211yesmaximal, characteristic
3#15689483C212yesmaximal
4#15689474C211yesmaximal, characteristic, complemented
5#15689414C211yesmaximal, characteristic
6#15689409C212yesmaximal, complemented
7#15689346C212yesmaximal
8#15689334C211yesmaximal, characteristic, complemented
9#15689231C212yesmaximal, complemented
10C4×#10625325C211yesmaximal, characteristic
11C47×#446C211yesmaximal, characteristic, complemented
12C2×Dic188C2212yes—
13C2×#10625325C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094024C2211yescharacteristic
16#13094024C2212yes—
17#13094023—21no—
18#13094023—22no—
19#13094019—22no—
20#13094012C2212yes—
21#13094000—21no—
22Q8×Dic47—21no—
23C4×Dic94C2212yes—
24C4×Dic94C2212yes—
25C4×Dic94C2211yescharacteristic
26C4×D188C2211yescharacteristic
27#13093982—21no—
28#13093956C2212yes—
29#13093956C2211yescharacteristic
30#13093949C2212yes—
31#13093949C2212yes—
32#13093949C2212yes—
33#13093949C2211yescharacteristic
34#13093946C2211yescharacteristic
35#13093946C2212yes—
36C4×Q8×C47C2211yescharacteristic
37C4⋊C8×C47C2211yescharacteristic
38C4⋊C8×C47C2212yes—
39#97×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47D411yescharacteristic
42C2×D188C2311yescharacteristic
43C2×C4×D47—21no—
44C2×Dic94—22no—
45C2×Dic94—21no—
46C2×Dic94C2312yes—
47C2×Dic94C2311yescharacteristic
48C2×C8×C47C2312yes—
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C4⋊C4×C47D411yescharacteristic
52C4⋊C4×C47D412yes—
53C42×C47C2311yescharacteristic
54C42×C47C2312yes—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—21no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71Dic188—24no—
72#10625325—22no—
73C22×D47—21no—
74Q8×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85D188—21no—
86D188—21no—
87C4×D47—42no—
88Dic94—21no—
89Dic94—22no—
90Dic94—22no—
91Dic94—82no—
92Dic94—81no—
93Dic94#4112yes—
94C8×C47—21no—
95C8×C47—22no—
96C8×C47—21no—
97C22×C47C22×D411yescharacteristic
98C2×D47—41no—
99C2×D47—41no—
100C2×D47—41no—
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—21no—
104C4×C47#13712yes—
105C4×C47C2×#4111yescharacteristic
106C4×C472−1+411yescharacteristic
107Dic47—22no—
108Dic47—42no—
109Dic47—41no—
110Dic47—41no—
111Dic47—42no—
112#3369—471nomaximal, Sylow
113C2×C47#54811yescharacteristic
114C2×C47C2×#13711yescharacteristic
115C2×C47#57711yescharacteristic
116D47—81no—
117Q82—471no—
118#556—471no—
119#489—472no—
120#487—471no—
121#476—471no—
122#475—472no—
123#464—472no—
124#462—471no—
125#446D4711yescharacteristic, complemented
126#441—472no—
127C4×SD16—471no—
128C47#336911yescharacteristic, complemented, Sylow
129C2×Q16—472no—
130C2×SD16—471no—
131C4⋊Q8—472no—
132C4⋊Q8—471no—
133C4⋊Q8—471no—
134C4⋊Q8—941no—
135C4⋊Q8—942no—
136#126—942no—
137#124—472no—
138C22⋊Q8—941no—
139C4×Q8—472no—
140C4×Q8—471no—
141C4×Q8—472no—
142C4×Q8—941no—
143C4×Q8C2×D4711yescharacteristic
144C4×D4—471no—
145#117—941no—
146#106—471no—
147#106—472no—
148C4⋊C8C2×D4711yescharacteristic
149C4⋊C8C2×D4712yes—
150#103—471no—
151#103—472no—
152#103—472no—
153#103—472no—
154#102—471no—
155#102—472no—
156#97C2×D4712yes—
157C4×C8C2×D4711yescharacteristic
158C2×Q8—471no—
159C2×Q8—472no—
160C2×Q8—942no—
161C2×Q8—941no—
162C2×Q8D18811yescharacteristic
163C2×D4—471no—
164C22×C4—941no—
165Q16—944no—
166SD16—942no—
167C2×C8C22×D4711yescharacteristic
168C2×C8C22×D4711yescharacteristic
169C2×C8C22×D4712yes—
170C4⋊C4—471no—
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4D18811yescharacteristic
181C4⋊C4D18812yes—
182C22⋊C4—942no—
183C22⋊C4—941no—
184C22⋊C4—942no—
185C42—942no—
186C42—942no—
187C42—941no—
188C42C22×D4711yescharacteristic
189C42C22×D4712yes—
190C23—941no—
191Q8—22no—
192Q8—472no—
193Q8—941no—
194Q8—942no—
195Q8—942no—
196Q8—3762no—
197Q8—3761no—
198D4—941no—
199D4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4C2×D18812yes—
207C2×C4C2×D18812yes—
208C2×C4C2×D18811yescharacteristic
209C2×C4C2×D18811yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—21no—
212C8—22no—
213C8—21no—
214C22—1881no—
215C22—1881no—
216C22—1881no—
217C22C22×D18811yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—942no—
222C4—1882no—
223C4—1881no—
224C4—1882no—
225C4—1881no—
226C4#1309405712yes—
227C4#41×D4711yescharacteristic
228C4#1309407211yescharacteristic
229C2—3761no—
230C2#1568978511yescharacteristic
231C2C2×#1309405711yescharacteristic
232C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3369
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
4. #15689474C2semidirect
6. #15689409C2semidirect
8. #15689334C2semidirect
9. #15689231C2semidirect
11. C47×#446C2semidirect
125. #446D47semidirect
128. C47#3369semidirect