Finite Group Databasebeta

← #20253231

Subgroups — #20253231

Order 6016.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689751C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic
3#15689431C212yesmaximal, complemented
4#15689431C212yesmaximal, complemented
5#15689419C212yesmaximal, complemented
6#15689409C212yesmaximal, complemented
7#15689165C211yesmaximal, characteristic
8#15689161C211yesmaximal, characteristic
9#15689133C211yesmaximal, characteristic
10C2×#13093949C211yesmaximal, characteristic
11C47×#424C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094024C2212yes—
14#13094023—21no—
15#13094016C2212yes—
16#13094015—21no—
17#13094001—22no—
18C4×Dic94C2212yes—
19C4×Dic94C2212yes—
20#13093989—21no—
21#13093989—21no—
22#13093983C2211yescharacteristic
23#13093983C2211yescharacteristic
24#13093980—22no—
25C2×C4⋊Dic47C2211yescharacteristic
26#13093958C2211yescharacteristic
27#13093958C2211yescharacteristic
28#13093958C2212yes—
29#13093956C2211yescharacteristic
30#13093956C2212yes—
31#13093956C2211yescharacteristic
32#13093949C2212yes—
33#13093949C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36C2×M16×C47C2211yescharacteristic
37C22×C8×C47C2211yescharacteristic
38#117×C47C2211yescharacteristic
39C4⋊C8×C47C2212yes—
40C4⋊C8×C47C2212yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—21no—
43C22×Dic47—21no—
44C2×Dic94—21no—
45C2×Dic94—22no—
46C2×Dic94—22no—
47C2×Dic94Q814yescomplemented
48C2×Dic94C2312yes—
49M16×C47—22no—
50C2×C8×C47—22no—
51C2×C8×C47C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2312yes—
54C4⋊C4×C47D411yescharacteristic
55C4⋊C4×C47D411yescharacteristic
56C22⋊C4×C47D412yes—
57C42×C47C2312yes—
58C22⋊Dic47—21no—
59C22⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47C2312yes—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71C4×Dic47—22no—
72C4×Dic47—22no—
73C4×Dic47—21no—
74C4×Dic47—21no—
75C23×C47C2×D411yescharacteristic
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×Q812yes—
80C2×C4×C47#4112yes—
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—24no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—81no—
90Dic94—24no—
91Dic94—22no—
92Dic94—82no—
93Dic94C2×Q814yes—
94C8×C47—21no—
95C8×C47—21no—
96C8×C47—22no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47C22⋊Q812yes—
100C22×C47C22×D411yescharacteristic
101C4×C47—22no—
102C4×C47—22no—
103C4×C47C22⋊Q812yes—
104C4×C47C22×Q811yescharacteristic
105C4×C47C2×#4111yescharacteristic
106Dic47—24no—
107Dic47—41no—
108Dic47—42no—
109Dic47—41no—
110Dic47—41no—
111Dic47—41no—
112#3082—471nomaximal, Sylow
113C2×C47—22no—
114C2×C47C2×C22⋊Q811yescharacteristic
115C2×C47#57711yescharacteristic
116C2×C47#57811yescharacteristic
117#544—471no—
118#519—471no—
119#479—472no—
120#479—472no—
121#477—472no—
122#475—472no—
123#428—471no—
124#427—471no—
125#424D4711yescharacteristic
126#419—471no—
127C2×#103—471no—
128C47#308211yescharacteristic, complemented, Sylow
129C22×Q8—471no—
130C2×M16C2×D4711yescharacteristic
131C22×C8C2×D4711yescharacteristic
132C4⋊Q8—472no—
133C4⋊Q8—941no—
134#125—472no—
135#125—941no—
136C22⋊Q8—942no—
137C4×Q8—472no—
138C4×Q8—472no—
139C4×Q8—941no—
140C4×Q8—941no—
141#117—471no—
142#117—471no—
143#117—942no—
144#117C2×D4711yescharacteristic
145C2×C4⋊C4—471no—
146#107—471no—
147#107—471no—
148#107—472no—
149#106—471no—
150#106—471no—
151#106—472no—
152C4⋊C8C2×D4712yes—
153C4⋊C8C2×D4712yes—
154#103—472no—
155#103—472no—
156#103—472no—
157#103—472no—
158C2×Q8—474no—
159C2×Q8—472no—
160C2×Q8—941no—
161C2×Q8—942no—
162C2×Q8—942no—
163C22×C4—941no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166M16—22no—
167C2×C8—22no—
168C2×C8C22×D4711yescharacteristic
169C2×C8C22×D4712yes—
170C2×C8C22×D4711yescharacteristic
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—471no—
174C4⋊C4—471no—
175C4⋊C4—471no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—941no—
181C4⋊C4—942no—
182C4⋊C4D18811yescharacteristic
183C4⋊C4D18811yescharacteristic
184C22⋊C4—941no—
185C22⋊C4—941no—
186C22⋊C4D18812yes—
187C42—941no—
188C42—941no—
189C42—942no—
190C42—942no—
191C42C22×D4712yes—
192C23C2×D18811yescharacteristic
193Q8—474no—
194Q8—944no—
195Q8—942no—
196Q8—3762no—
197C2×C4—944no—
198C2×C4—942no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—3761no—
205C2×C4C2×D18812yes—
206C2×C4C2×D18812yes—
207C2×C4C2×D18811yescharacteristic
208C2×C4#1062535212yes—
209C2×C4Q8×D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—21no—
212C8—21no—
213C8—22no—
214C22—21no—
215C22—21no—
216C22#1309400412yes—
217C22C22×D18811yescharacteristic
218C4—22no—
219C4—22no—
220C4—944no—
221C4—1882no—
222C4—1881no—
223C4—1881no—
224C4—1881no—
225C4—1881no—
226C4#1309400412yes—
227C4C2×Q8×D4711yescharacteristic
228C4C2×#1062535211yescharacteristic
229C2—22no—
230C2C2×#1309400411yescharacteristic
231C2#1568993511yescharacteristic
232C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#424C2
socleC22×C47C22×D4
hypercenter#424D47
hypocenterC47#3082
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #15689431C2semidirect
4. #15689431C2semidirect
5. #15689419C2semidirect
6. #15689409C2semidirect
47. C2×Dic94Q8semidirect
128. C47#3082semidirect