Finite Group Databasebeta

← #20253244

Subgroups — #20253244

Order 6016.

376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689754C211yesmaximal, characteristic, complemented
2#15689604C211yesmaximal, characteristic
3#15689429C212yesmaximal, complemented
4#15689426C212yesmaximal, complemented
5#15689417C212yesmaximal, complemented
6#15689402C212yesmaximal, complemented
7#15689163C211yesmaximal, characteristic, complemented
8#15689149C211yesmaximal, characteristic, complemented
9#15689122C211yesmaximal, characteristic
10#15689120C211yesmaximal, characteristic
11C2×#107×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094015—21no—
17#13094015C2212yes—
18#13094003—22no—
19#13093989C2212yes—
20#13093986C2212yes—
21C4×C22⋊D47—22no—
22#13093983C2211yescharacteristic
23#13093983C2211yescharacteristic
24#13093982—21no—
25C4⋊C4×D47—21no—
26#13093957C2212yes—
27#13093955C2212yes—
28Dic47⋊C8C2212yes—
29Dic47⋊C8C2212yes—
30#13093949C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093946C2211yescharacteristic
35#13093944C2212yes—
36C22×C8×C47C2211yescharacteristic
37C2×C4⋊C4×C47C2211yescharacteristic
38C2×C4⋊C4×C47C2211yescharacteristic
39#107×C47C2212yes—
40#107×C47C2212yes—
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—21no—
45#10625350—22no—
46#10625350Q814yescomplemented
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×C4×D47—22no—
50C2×Dic94—22no—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47—22no—
53C2×C8×C47C2311yescharacteristic
54C2×C8×C47C2311yescharacteristic
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2312yes—
58C4⋊C4×C47C2312yes—
59C22⋊Dic47—21no—
60C22⋊Dic47D412yes—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47D411yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70C4×Dic47—21no—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73#10625329—22no—
74C2×C47⋊C8C2312yes—
75C23×C47C2×D411yescharacteristic
76C22×D47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—81no—
80C2×C4×C47—81no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×Q812yes—
83C2×C4×C47#4112yes—
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—24no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91D188—21no—
92D188C2×Q812yes—
93C4×D47—24no—
94C4×D47—82no—
95Dic94—21no—
96Dic94—82no—
97Dic94C2×Q812yes—
98C8×C47—21no—
99C8×C47—21no—
100C47⋊C8—22no—
101C22×C47—21no—
102C22×C47—21no—
103C22×C47C22⋊Q812yes—
104C22×C47C22×D411yescharacteristic
105C2×D47—22no—
106C2×D47—41no—
107C2×D47—41no—
108C4×C47—42no—
109C4×C47—42no—
110C4×C47C22⋊Q812yes—
111C4×C47C22×Q811yescharacteristic
112C4×C47C2×#4111yescharacteristic
113Dic47—22no—
114Dic47—22no—
115Dic47—22no—
116Dic47—41no—
117Dic47—41no—
118#3083—471nomaximal, Sylow
119C2×C47—22no—
120C2×C47C2×C22⋊Q811yescharacteristic
121C2×C47#57611yescharacteristic
122C2×C47#57811yescharacteristic
123D47—42no—
124#544—471no—
125#520—471no—
126#479—472no—
127#478—472no—
128#477—472no—
129#474—472no—
130#428—471no—
131C2×#107D4711yescharacteristic, complemented
132#424—471no—
133#417—471no—
134#416—471no—
135C47#308311yescharacteristic, complemented, Sylow
136C2×#41—471no—
137C2×M16—471no—
138C22×C8C2×D4711yescharacteristic
139C4⋊Q8—472no—
140C4⋊Q8—941no—
141#125—472no—
142#125—941no—
143C22⋊Q8—942no—
144C4×Q8—472no—
145C4×D4—472no—
146C4×D4—942no—
147#117—471no—
148#117—471no—
149#117—941no—
150C2×C4⋊C4—941no—
151C2×C4⋊C4C2×D4711yescharacteristic
152C2×C4⋊C4C2×D4711yescharacteristic
153#107—472no—
154#107C2×D4712yes—
155#107C2×D4712yes—
156#106—472no—
157C4⋊C8—472no—
158C4⋊C8—472no—
159#103—471no—
160#103—471no—
161#103—472no—
162#102—471no—
163#102—471no—
164#102—472no—
165#41—474no—
166#41—942no—
167C2×Q8—471no—
168C2×Q8—942no—
169C2×D4—471no—
170C2×D4—941no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—942no—
174C22×C4—941no—
175C22×C4C22×D4711yescharacteristic
176M16—942no—
177C2×C8—22no—
178C2×C8—472no—
179C2×C8C22×D4711yescharacteristic
180C2×C8C22×D4711yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—471no—
184C4⋊C4—471no—
185C4⋊C4—471no—
186C4⋊C4—471no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4C22×D4712yes—
192C4⋊C4C22×D4712yes—
193C22⋊C4—472no—
194C22⋊C4—942no—
195C22⋊C4—941no—
196C42—472no—
197C42—942no—
198C42—941no—
199C23—941no—
200C23D4×D4711yescharacteristic
201Q8—472no—
202Q8—941no—
203Q8—3762no—
204D4—472no—
205D4—944no—
206D4—941no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—472no—
212C2×C4—472no—
213C2×C4—941no—
214C2×C4—944no—
215C2×C4—941no—
216C2×C4—941no—
217C2×C4—3762no—
218C2×C4#1062535012yes—
219C2×C4D4×D4711yescharacteristic
220C2×C4Q8×D4712yes—
221C2×C4C23×D4711yescharacteristic
222C8—21no—
223C8—21no—
224C8—942no—
225C22—21no—
226C22—21no—
227C22—942no—
228C22—1881no—
229C22—1881no—
230C22#1309400212yes—
231C22C2×D4×D4711yescharacteristic
232C4—42no—
233C4—42no—
234C4—942no—
235C4—942no—
236C4—942no—
237C4—1881no—
238C4—1881no—
239C4#1309400212yes—
240C4C2×Q8×D4711yescharacteristic
241C4C2×#1062535011yescharacteristic
242C2—22no—
243C2—1882no—
244C2C2×#1309400211yescharacteristic
245C2#1568992411yescharacteristic
246C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#107×C47C2
socleC22×C47C22×D4
hypercenterC2×#107D47
hypocenterC47#3083
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #15689754C2semidirect
3. #15689429C2semidirect
4. #15689426C2semidirect
5. #15689417C2semidirect
6. #15689402C2semidirect
7. #15689163C2semidirect
8. #15689149C2semidirect
11. C2×#107×C47C2semidirect
46. #10625350Q8semidirect
131. C2×#107D47semidirect
135. C47#3083semidirect