Finite Group Databasebeta

← #21447054

Subgroups — #21447054

Order 7808.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14519774C211yesmaximal, characteristic
2C2×#14519699C212yesmaximal, complemented
3C2×#14519699C212yesmaximal, complemented
4#16839660C211yesmaximal, characteristic, complemented
5C61×#336C211yesmaximal, characteristic, complemented
6C22×D244—21no—
7C22×D244—21no—
8C22×D244C2212yes—
9#14519774—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519699—24no—
14#14519699—24no—
15#14519684—21no—
16C22×C8×C61C2212yes—
17C2×C42×C61C2211yescharacteristic
18C23×D61—22no—
19C22×C4×C61D411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61C2311yescharacteristic
22C22×Dic61—21no—
23C22×Dic61—21no—
24C2×D244—22no—
25C2×D244—22no—
26C2×D244—22no—
27C2×D244—22no—
28C2×D244—24no—
29C2×D244—24no—
30C2×D244—22no—
31C2×D244—42no—
32C2×D244—42no—
33C2×D244—42no—
34C2×D244—42no—
35C2×D244D414yes—
36C2×C8×C61—22no—
37C2×C8×C61—22no—
38C2×C8×C61—22no—
39C42×C61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—22no—
42C4⋊Dic61D412yescomplemented
43#11758196—42no—
44C23×C61C2×D411yescharacteristic
45C22×D61—24no—
46C22×D61—42no—
47C22×D61—42no—
48C22×D61—42no—
49C22×D61—42no—
50C22×D61—42no—
51C22×D61—42no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61D812yes—
57C2×C4×C61SD1612yes—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D412yes—
60C2×C4×C61#4112yes—
61C2×C4×C61#4111yescharacteristic
62C2×Dic61—22no—
63C2×Dic61—41no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68D244—24no—
69D244—24no—
70D244—48no—
71D244—48no—
72D244—42no—
73D244—42no—
74C8×C61—42no—
75C22×C61#12011yescharacteristic
76C22×C61#12111yescharacteristic
77C22×C61#12411yescharacteristic
78C22×C61C2×D811yescharacteristic
79C22×C61C2×SD1611yescharacteristic
80C22×C61AGL(1,ℤ/8)11yescharacteristic
81C22×C61AGL(1,ℤ/8)11yescharacteristic
82C2×D61—44no—
83C2×D61—44no—
84C2×D61—44no—
85C2×D61—82no—
86C2×D61—82no—
87C2×D61—82no—
88C2×D61—82no—
89C4×C61—22no—
90C4×C61—22no—
91C4×C61#12112yes—
92C4×C61#12312yes—
93Dic61—42no—
94Dic61—81no—
95#2041—611nomaximal, Sylow
96C2×C61#39411yescharacteristic
97C2×C61#44711yescharacteristic
98C2×C61#45011yescharacteristic
99C2×C61#45911yescharacteristic
100C2×C61#46011yescharacteristic
101C2×C61#48611yescharacteristic
102C2×C61#49011yescharacteristic
103D61—84no—
104C2×#127—611no—
105C2×#102—612no—
106C2×#102—612no—
107#389—611no—
108#336D6111yescharacteristic, complemented
109C61#204111yescharacteristic, complemented, Sylow
110C22×D4—612no—
111C22×D4—1221no—
112C22×D4—1221no—
113C22×C8C2×D6112yes—
114#127—1224no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—1221no—
118C2×C42C2×D6111yescharacteristic
119#102—1224no—
120#102—1224no—
121#95—1221no—
122C24—1222no—
123C2×D4—614no—
124C2×D4—1224no—
125C2×D4—1224no—
126C2×D4—1222no—
127C2×D4—1222no—
128C2×D4—1222no—
129C2×D4—1222no—
130C2×D4—1222no—
131C2×D4—2442no—
132C2×D4—2442no—
133C2×D4—2442no—
134C2×D4—2442no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4D24411yescharacteristic
138C22×C4D24411yescharacteristic
139C22×C4C22×D6111yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C4⋊C4—612no—
144C4⋊C4—1221no—
145C4⋊C4—1222no—
146C4⋊C4—2442no—
147C42—22no—
148C23—1224no—
149C23—2442no—
150C23—2442no—
151C23—2442no—
152C23—2442no—
153C23—2442no—
154C23—2442no—
155C23C2×D24411yescharacteristic
156D4—1224no—
157D4—1224no—
158D4—2448no—
159D4—2448no—
160D4—2442no—
161D4—2442no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1222no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4#1175819012yes—
173C2×C4D48812yes—
174C2×C4#1175822212yes—
175C2×C4D4×D6111yescharacteristic
176C2×C4D4×D6112yes—
177C2×C4#1175822611yescharacteristic
178C8—42no—
179C22—4882no—
180C22—4882no—
181C22—4882no—
182C22—4882no—
183C22—2444no—
184C22—2444no—
185C22—2444no—
186C22#1451974711yescharacteristic
187C22#1451975211yescharacteristic
188C22#1451976511yescharacteristic
189C22C2×D48811yescharacteristic
190C22C2×#1175819011yescharacteristic
191C22#1451980511yescharacteristic
192C22#1451980511yescharacteristic
193C4—22no—
194C4—22no—
195C4—4881no—
196C4—2442no—
197C4#1451975012yes—
198C4#1451976212yes—
199C2—4884no—
200C2#1683968011yescharacteristic
201C2#1683989811yescharacteristic
202C2#1683991511yescharacteristic
203C2#1683995811yescharacteristic
204C2#1683996311yescharacteristic
205C2#1684010911yescharacteristic
206C2#1684012711yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#2041
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×#14519699C2semidirect
3. C2×#14519699C2semidirect
4. #16839660C2semidirect
5. C61×#336C2semidirect
42. C4⋊Dic61D4semidirect
108. #336D61semidirect
109. C61#2041semidirect