Finite Group Databasebeta

← #21455307

Subgroups — #21455307

Order 7808.

480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519810C212yesmaximal
2C2×#14519777C211yesmaximal, characteristic, complemented
3C4×#11758222C211yesmaximal, characteristic
4#16839973C214yesmaximal, complemented
5#16839968C214yesmaximal, complemented
6#16839772C212yesmaximal, complemented
7C61×#423C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2212yes—
10#14519810—28no—
11C2×Dic244C2214yes—
12C2×#11758190C2214yes—
13#14519777—21no—
14#14519777—21no—
15#14519777C2214yes—
16C4×Dic122C2212yes—
17C4×D244C2212yes—
18C4×C22⋊D61—22no—
19#14519736C2211yescharacteristic
20#14519734—21no—
21C2×C4⋊Dic61—22no—
22C42×D61—21no—
23#14519702C2218yes—
24C2×M16×C61C2212yes—
25C2×C42×C61C2211yescharacteristic
26C4⋊C8×C61C2214yes—
27C22×C4×C61D412yes—
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—21no—
30C22×Dic61—22no—
31#11758222—22no—
32#11758222D414yes—
33C2×D244C2311yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61—22no—
36C2×Dic122—24no—
37C2×Dic122—24no—
38C2×Dic122—22no—
39C2×Dic122C2314yes—
40C2×Dic122C2311yescharacteristic
41M16×C61—24no—
42C2×C8×C61C2314yes—
43C42×C61D411yescharacteristic
44C42×C61D411yescharacteristic
45C42×C61C2312yes—
46C22⋊Dic61—21no—
47#11758198—22no—
48C4⋊Dic61—24no—
49C4⋊Dic61—24no—
50C4⋊Dic61C2312yes—
51#11758196—22no—
52C4×Dic61—21no—
53C4×Dic61—22no—
54Dic244—28no—
55#11758190—28no—
56C23×C61C2×D411yescharacteristic
57C22×D61—21no—
58C2×C4×C61—24no—
59C2×C4×C61C2×D412yes—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D412yes—
62C2×C4×C61C2×D412yes—
63C2×C4×C61#4112yes—
64C2×C4×C61C2411yescharacteristic
65C22⋊D61—24no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—24no—
69C2×Dic61—44no—
70D244—21no—
71D244C2×D412yes—
72C4×D61—24no—
73C4×D61—44no—
74Dic122—21no—
75Dic122—24no—
76Dic122—24no—
77Dic122—44no—
78Dic122C2×D412yes—
79C8×C61—24no—
80C22×C61—22no—
81C22×C61#12112yes—
82C22×C61C22×D411yescharacteristic
83C2×D61—22no—
84C2×D61—42no—
85C4×C61—22no—
86C4×C61#12112yes—
87C4×C61#13714yescomplemented
88C4×C61C22×D411yescharacteristic
89C4×C61C2×#4111yescharacteristic
90Dic61—22no—
91Dic61—44no—
92Dic61—42no—
93#3039—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61C2×#12111yescharacteristic
96C2×C61C2×#13712yes—
97D61—42no—
98C2×#137—612no—
99C2×C4⋊Q8—611no—
100C4×#41—611no—
101#462—614no—
102#461—614no—
103#423D6111yescharacteristic, complemented
104#419—612no—
105C61#303911yescharacteristic, complemented, Sylow
106C2×#41—611no—
107C22×Q8—612no—
108#137—1228no—
109C2×Q16—614no—
110C2×SD16—614no—
111C2×M16C2×D6112yes—
112C4⋊Q8—614no—
113C4⋊Q8—1221no—
114C4⋊Q8—1221no—
115C4×Q8—612no—
116C4×D4—612no—
117C4×D4—1222no—
118#117—611no—
119#117—1221no—
120C2×C4⋊C4—1222no—
121C2×C42—1221no—
122C2×C42C2×D6111yescharacteristic
123C4⋊C8C2×D6114yes—
124#103—618no—
125#41—614no—
126#41—1222no—
127C2×Q8—611no—
128C2×Q8—614no—
129C2×Q8—1222no—
130C2×Q8—1224no—
131C2×Q8—1224no—
132C2×D4—611no—
133C2×D4—1221no—
134C22×C4—1221no—
135C22×C4—1222no—
136C22×C4—1222no—
137C22×C4D24412yes—
138C22×C4C22×D6111yescharacteristic
139Q16—1228no—
140SD16—1228no—
141M16—24no—
142C2×C8C22×D6114yes—
143C4⋊C4—612no—
144C4⋊C4—1224no—
145C4⋊C4—1224no—
146C4⋊C4—1222no—
147C22⋊C4—1221no—
148C22⋊C4—1222no—
149C42—1221no—
150C42—1222no—
151C42D24411yescharacteristic
152C42D24411yescharacteristic
153C42C22×D6112yes—
154C23—1221no—
155C23C2×D24411yescharacteristic
156Q8—612no—
157Q8—1221no—
158Q8—1224no—
159Q8—1224no—
160Q8—2444no—
161D4—612no—
162D4—1224no—
163D4—1221no—
164C2×C4—24no—
165C2×C4—1221no—
166C2×C4—1224no—
167C2×C4—1222no—
168C2×C4—1224no—
169C2×C4—2444no—
170C2×C4—2444no—
171C2×C4C2×D24412yes—
172C2×C4C2×D24412yes—
173C2×C4C2×D24411yescharacteristic
174C2×C4D4×D6112yes—
175C2×C4#1175822612yes—
176C2×C4C23×D6111yescharacteristic
177C8—24no—
178C22—22no—
179C22—1222no—
180C22—2442no—
181C22#1451975212yes—
182C22C22×D24411yescharacteristic
183C4—22no—
184C4—1222no—
185C4—2444no—
186C4—2442no—
187C4#1451975212yes—
188C4#1451981014yescomplemented
189C4C2×D4×D6111yescharacteristic
190C4C2×#1175822611yescharacteristic
191C2—22no—
192C2—2442no—
193C2C2×#1451975211yescharacteristic
194C2C2×#1451981012yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#423C2
socleC22×C61C22×D4
hypercenter#423D61
hypocenterC61#3039
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C2×#14519777C2semidirect
4. #16839973C2semidirect
5. #16839968C2semidirect
6. #16839772C2semidirect
7. C61×#423C2semidirect
87. C4×C61#137semidirect
103. #423D61semidirect
105. C61#3039semidirect
188. C4#14519810semidirect