Finite Group Databasebeta

← #21455350

Subgroups — #21455350

Order 7808.

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

normal subgroups only

This group has 458 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
1C2×#14519810C211yesmaximal, characteristic
2C22×Dic244C211yesmaximal, characteristic, complemented
3#16840338C211yesmaximal, characteristic
4#16840239C211yesmaximal, characteristic, complemented
5#16839985C214yesmaximal, complemented
6#16839973C214yesmaximal, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic
9C61×#424C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C22×Dic122C2211yescharacteristic
13#14519810—24no—
14C2×Dic244—24no—
15C2×Dic244C2212yes—
16C2×Dic244C2214yes—
17C2×#11758190C2212yes—
18#14519777C2212yes—
19#14519765C2212yes—
20#14519761—22no—
21#14519757—22no—
22C4×Dic122C2214yes—
23#14519742—22no—
24#14519736C2211yescharacteristic
25#14519733—22no—
26#14519702C2212yes—
27#14519702C2214yes—
28#14519699C2212yes—
29C2×M16×C61C2211yescharacteristic
30C22×C8×C61C2211yescharacteristic
31#117×C61C2211yescharacteristic
32C4⋊C8×C61C2214yes—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35C22×Dic61—21no—
36C22×Dic61—21no—
37#11758222—22no—
38#11758222—22no—
39C2×D244C2311yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122—21no—
42C2×Dic122—22no—
43C2×Dic122—22no—
44C2×Dic122—22no—
45C2×Dic122—21no—
46C2×Dic122D414yes—
47C2×Dic122C2312yes—
48C2×Dic122C2311yescharacteristic
49C2×Dic122C2312yes—
50M16×C61—22no—
51C2×C8×C61—22no—
52C2×C8×C61C2312yes—
53C2×C8×C61C2312yes—
54C4⋊C4×C61D412yes—
55C22⋊C4×C61D412yes—
56C42×C61C2312yes—
57C22⋊Dic61—21no—
58#11758198—24no—
59C4⋊Dic61—24no—
60C4⋊Dic61C2312yes—
61#11758196—24no—
62C4×Dic61—24no—
63C4×Dic61—21no—
64Dic244—24no—
65Dic244—28no—
66#11758190—24no—
67C23×C61C2×D411yescharacteristic
68C22×D61—21no—
69C2×C4×C61C2×D414yes—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D412yes—
72C2×C4×C61#4112yes—
73C2×C4×C61C2411yescharacteristic
74C22⋊D61—42no—
75C2×Dic61—24no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61—42no—
81D244—21no—
82D244—21no—
83C4×D61—42no—
84Dic122—24no—
85Dic122—22no—
86Dic122—22no—
87Dic122—21no—
88Dic122—22no—
89Dic122—21no—
90Dic122—42no—
91Dic122C2×D414yes—
92C8×C61—22no—
93C8×C61—22no—
94C22×C61—22no—
95C22×C61#12112yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—42no—
99C4×C61—24no—
100C4×C61#12112yes—
101C4×C61C22×D411yescharacteristic
102C4×C61C2×#4111yescharacteristic
103Dic61—24no—
104Dic61—42no—
105Dic61—41no—
106Dic61—42no—
107#3044—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61C2×#12111yescharacteristic
110C2×C61#57812yes—
111D61—81no—
112C2×#137—611no—
113C22×Q16—611no—
114#536—611no—
115#519—611no—
116#464—614no—
117#462—614no—
118#424D6111yescharacteristic, complemented
119#419—611no—
120#416—611no—
121C61#304411yescharacteristic, complemented, Sylow
122C2×#41—611no—
123C22×Q8—611no—
124C22×Q8—611no—
125#137—1224no—
126C2×Q16—614no—
127C2×Q16—612no—
128C2×Q16—1224no—
129C2×SD16—612no—
130C2×M16C2×D6111yescharacteristic
131C22×C8C2×D6111yescharacteristic
132C4⋊Q8—612no—
133#124—612no—
134#123—1222no—
135C22⋊Q8—1222no—
136C4×Q8—614no—
137C4×Q8—1222no—
138#117—611no—
139#117—1222no—
140#117C2×D6111yescharacteristic
141C4⋊C8C2×D6114yes—
142#103—612no—
143#103—614no—
144#102—612no—
145#41—1222no—
146#41—1222no—
147C2×Q8—614no—
148C2×Q8—612no—
149C2×Q8—612no—
150C2×Q8—611no—
151C2×Q8—1221no—
152C2×Q8—1221no—
153C2×Q8—1222no—
154C2×Q8—1222no—
155C2×Q8—1222no—
156C2×D4—611no—
157C2×D4—1221no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162Q16—1228no—
163Q16—1224no—
164SD16—1224no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D6112yes—
168C2×C8C22×D6112yes—
169C4⋊C4—612no—
170C4⋊C4—1224no—
171C4⋊C4—1224no—
172C4⋊C4D24412yes—
173C22⋊C4—1221no—
174C22⋊C4—1224no—
175C22⋊C4D24412yes—
176C42—1221no—
177C42—1224no—
178C42C22×D6112yes—
179C23—1221no—
180C23C2×D24411yescharacteristic
181Q8—614no—
182Q8—1222no—
183Q8—1224no—
184Q8—1222no—
185Q8—1221no—
186Q8—1222no—
187Q8—1221no—
188Q8—2442no—
189D4—1221no—
190D4—1221no—
191D4—2442no—
192C2×C4—1222no—
193C2×C4—1224no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4C2×D24414yes—
200C2×C4C2×D24411yescharacteristic
201C2×C4D4×D6112yes—
202C2×C4#1175822612yes—
203C2×C4C23×D6111yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—2441no—
208C22—2442no—
209C22#1451975212yes—
210C22C22×D24411yescharacteristic
211C4—24no—
212C4—1224no—
213C4—2441no—
214C4—2442no—
215C4—2442no—
216C4#1451975212yes—
217C4C2×D4×D6111yescharacteristic
218C4C2×#1175822611yescharacteristic
219C2—22no—
220C2—4881no—
221C2C2×#1451975211yescharacteristic
222C2#1684057912yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3044
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic244C2semidirect
4. #16840239C2semidirect
5. #16839985C2semidirect
6. #16839973C2semidirect
7. #16839772C2semidirect
9. C61×#424C2semidirect
118. #424D61semidirect
121. C61#3044semidirect