Finite Group Databasebeta

← #21444271

Subgroups — #21444271

Order 7808.

276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 93 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
2#16839786C211yesmaximal, characteristic, complemented
3#16839491C214yesmaximal, complemented
4C2×C4×C8×C61C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6C2×#11758194—21no—
7#14519777C411yescharacteristic
8#14519774C411yescharacteristic
9#14519765—21no—
10#14519751—21no—
11#14519751C412yes—
12C4×D244—21no—
13C4×D244C2212yes—
14C4⋊#92418—21no—
15C4⋊#92418C2212yes—
16C22×C8×C61—21no—
17C2×C42×C61C2211yescharacteristic
18C4×C8×C61—21no—
19C4×C8×C61C2212yes—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C2×C22⋊D61—22no—
24#11758222—42no—
25#11758222—42no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×Dic122—21no—
31C2×C8×C61—24no—
32C2×C8×C61—22no—
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41#11758194—42no—
42C2×#92418—22no—
43C23×C61C22⋊C411yescharacteristic
44C22×D61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—22no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61D812yes—
51C2×C4×C61SD1612yes—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C22⋊D61—44no—
56C2×Dic61—22no—
57D244—24no—
58D244—42no—
59D244—42no—
60C4×D61—42no—
61C4×D61—42no—
62Dic122—42no—
63C8×C61—24no—
64#92418—42no—
65C22×C61—21no—
66C22×C61—21no—
67C22×C61#10212yes—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61#10212yes—
75C4×C61#10412yes—
76C4×C61#13112yes—
77C4×C61C2×D811yescharacteristic
78C4×C61C2×SD1611yescharacteristic
79Dic61—42no—
80#1492—611nomaximal, Sylow
81C2×C61—22no—
82C2×C61#40811yescharacteristic
83C2×C61C2×#10211yescharacteristic
84C2×C61C2×#10411yescharacteristic
85D61—82no—
86#532—611no—
87#423—611no—
88C2×C4×C8D6111yescharacteristic, complemented
89D4⋊C8—614no—
90C61#149211yescharacteristic, complemented, Sylow
91C2×#41—1221no—
92C2×M16—1221no—
93C22×C8—21no—
94C4⋊Q8—611no—
95#127—611no—
96#124—1221no—
97#121—612no—
98#121—1221no—
99C4×D4—612no—
100C4×D4—1221no—
101C2×C42C2×D6111yescharacteristic
102C4⋊C8—612no—
103C4⋊C8—1221no—
104C4×C8—21no—
105C4×C8C2×D6112yes—
106#41—2442no—
107#41—2442no—
108C2×Q8—1221no—
109C2×D4—612no—
110C2×D4—1222no—
111C2×D4—1221no—
112C2×D4—1221no—
113C22×C4—1222no—
114C22×C4C4×D6111yescharacteristic
115C22×C4D24411yescharacteristic
116C22×C4C22⋊D6111yescharacteristic
117M16—2442no—
118C2×C8—24no—
119C2×C8—22no—
120C2×C8—1222no—
121C4⋊C4—612no—
122C4⋊C4—1221no—
123C22⋊C4—1222no—
124C22⋊C4—1222no—
125C42C4×D6111yescharacteristic
126C42D24411yescharacteristic
127C42C22⋊D6111yescharacteristic
128C42C22×D6111yescharacteristic
129C23—1222no—
130C23#1175819811yescharacteristic
131Q8—2442no—
132D4—1224no—
133D4—2444no—
134D4—2442no—
135D4—2442no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—1222no—
139C2×C4—2442no—
140C2×C4—2442no—
141C2×C4#1175819012yes—
142C2×C4D48812yes—
143C2×C4#1175819811yescharacteristic
144C2×C4#1175819811yescharacteristic
145C2×C4#1175819811yescharacteristic
146C2×C4C2×C4×D6111yescharacteristic
147C2×C4C2×D24411yescharacteristic
148C2×C4C2×C22⋊D6111yescharacteristic
149C8—24no—
150C8—2442no—
151C22—21no—
152C22—21no—
153C22—2442no—
154C22—2442no—
155C22—2442no—
156C22#1451969912yes—
157C22C2×#1175819811yescharacteristic
158C4—21no—
159C4—21no—
160C4—2442no—
161C4#1451969912yes—
162C4#1451970512yes—
163C4#1451978312yes—
164C4C2×D48811yescharacteristic
165C4C2×#1175819011yescharacteristic
166C2—22no—
167C2—4882no—
168C2#1683972811yescharacteristic
169C2C2×#1451969911yescharacteristic
170C2C2×#1451970511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4×C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4×C8D61
hypocenterC61#1492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #16839786C2semidirect
3. #16839491C2semidirect
4. C2×C4×C8×C61C2semidirect
88. C2×C4×C8D61semidirect
90. C61#1492semidirect