Finite Group Databasebeta

← #21444497

Subgroups — #21444497

Order 7808.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840312C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3#16839509C212yesmaximal, complemented
4#16839505C212yesmaximal, complemented
5C61×#423C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7C22×#92418—21no—
8#14519777C2211yescharacteristic
9#14519774C2211yescharacteristic
10#14519765—21no—
11#14519751—21no—
12#14519751C412yes—
13C4×D244—21no—
14C4×D244C412yes—
15C4⋊#92418—21no—
16C4⋊#92418C2212yes—
17C2×M16×C61—21no—
18C2×C42×C61C2211yescharacteristic
19C4⋊C8×C61—21no—
20C4⋊C8×C61C2212yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244C2×C412yes—
30C2×C4×D61—22no—
31C2×Dic122—21no—
32M16×C61—42no—
33C2×C8×C61—22no—
34C42×C61C2×C411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61C2311yescharacteristic
38#11758198—22no—
39#11758198—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C412yes—
42C2×#92418—22no—
43C2×#92418—42no—
44C23×C61C22⋊C411yescharacteristic
45C22×D61—22no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—41no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61D812yes—
53C2×C4×C61SD1612yes—
54C2×C4×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C22⋊D61—44no—
58C2×Dic61—22no—
59D244—42no—
60D244—41no—
61D244—41no—
62D244—41no—
63D244—41no—
64C4×D61—44no—
65Dic122—41no—
66Dic122—41no—
67C8×C61—42no—
68#92418—42no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#10212yes—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61#10212yes—
80C4×C61C2×D811yescharacteristic
81C4×C61C2×SD1611yescharacteristic
82C4×C61AGL(1,ℤ/8)11yescharacteristic
83C4×C61#13711yescharacteristic
84Dic61—42no—
85#1547—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61#41311yescharacteristic
88C2×C61C2×#10211yescharacteristic
89C2×C61#41711yescharacteristic
90D61—82no—
91#532—611no—
92#423D6111yescharacteristic, complemented
93C2×C4⋊C8—611no—
94#332—612no—
95#331—612no—
96C61#154711yescharacteristic, complemented, Sylow
97C2×#41—1221no—
98C2×M16—21no—
99C22×C8—1221no—
100C4⋊Q8—611no—
101#127—611no—
102#124—1221no—
103#121—612no—
104#121—1221no—
105C4×D4—612no—
106C4×D4—1221no—
107C2×C42C2×D6111yescharacteristic
108C4⋊C8—21no—
109C4⋊C8—612no—
110C4⋊C8—1221no—
111C4⋊C8C2×D6112yes—
112#41—2442no—
113#41—2442no—
114C2×Q8—1221no—
115C2×D4—612no—
116C2×D4—1222no—
117C2×D4—1221no—
118C2×D4—1221no—
119C22×C4—1222no—
120C22×C4C4×D6111yescharacteristic
121C22×C4D24411yescharacteristic
122C22×C4C22⋊D6111yescharacteristic
123M16—42no—
124C2×C8—22no—
125C2×C8—1222no—
126C2×C8—2442no—
127C4⋊C4—612no—
128C4⋊C4—1221no—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C42C4×D6111yescharacteristic
132C42D24411yescharacteristic
133C42C22⋊D6111yescharacteristic
134C42C22×D6111yescharacteristic
135C23—1222no—
136C23#1175819811yescharacteristic
137Q8—2441no—
138Q8—2441no—
139D4—2442no—
140D4—2444no—
141D4—2441no—
142D4—2441no—
143D4—2441no—
144D4—2441no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—1222no—
149C2×C4—2444no—
150C2×C4#1175819811yescharacteristic
151C2×C4#1175819811yescharacteristic
152C2×C4#1175819811yescharacteristic
153C2×C4#1175819912yes—
154C2×C4#1175820112yes—
155C2×C4C2×C4×D6111yescharacteristic
156C2×C4C2×D24411yescharacteristic
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—42no—
159C8—2442no—
160C22—21no—
161C22—21no—
162C22—2442no—
163C22—2442no—
164C22—2442no—
165C22#1451969712yes—
166C22C2×#1175819811yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—2442no—
171C4#1451969712yes—
172C4C2×#1175819911yescharacteristic
173C4C2×#1175820111yescharacteristic
174C4#1451980511yescharacteristic
175C4#1451981011yescharacteristic
176C2—22no—
177C2—4882no—
178C2#1683974411yescharacteristic
179C2C2×#1451969711yescharacteristic
180C2#1683976411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#92418C2semidirect
3. #16839509C2semidirect
4. #16839505C2semidirect
5. C61×#423C2semidirect
92. #423D61semidirect
96. C61#1547semidirect