Finite Group Databasebeta

← #21444217

Subgroups — #21444217

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
2#16839815C211yesmaximal, characteristic, complemented
3#16839489C214yesmaximal, complemented
4C2×C4⋊C8×C61C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6#14519777C411yescharacteristic
7#14519774C411yescharacteristic
8#14519765—21no—
9#14519751—21no—
10#14519751C412yes—
11C4×D244—21no—
12C4×D244C2212yes—
13C4⋊#92418—21no—
14C22⋊#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—22no—
32C2×C8×C61—42no—
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61D812yes—
50C2×C4×C61SD1612yes—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C22⋊D61—44no—
55C2×Dic61—22no—
56D244—24no—
57D244—42no—
58D244—42no—
59C4×D61—42no—
60C4×D61—42no—
61Dic122—42no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10212yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—42no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61#10212yes—
75C4×C61#13112yes—
76C4×C61C2×D811yescharacteristic
77C4×C61C2×SD1611yescharacteristic
78Dic61—42no—
79#1480—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61#40811yescharacteristic
82C2×C61C2×#10211yescharacteristic
83C2×C61#42111yescharacteristic
84D61—82no—
85#532—611no—
86#431—611no—
87C2×C4⋊C8D6111yescharacteristic, complemented
88D4⋊C8—614no—
89C61#148011yescharacteristic, complemented, Sylow
90C2×#41—1221no—
91C22×C8—21no—
92C4⋊Q8—611no—
93#127—611no—
94#124—1221no—
95#121—612no—
96#121—1221no—
97C4×D4—612no—
98C4×D4—1221no—
99C2×C42C2×D6111yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—1221no—
102C4⋊C8C2×D6112yes—
103C22⋊C8—1221no—
104C4×C8—612no—
105#41—2442no—
106#41—2442no—
107C2×Q8—1221no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1221no—
111C2×D4—1221no—
112C22×C4—1222no—
113C22×C4C4×D6111yescharacteristic
114C22×C4D24411yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116C2×C8—22no—
117C2×C8—42no—
118C2×C8—1222no—
119C4⋊C4—612no—
120C4⋊C4—1221no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42C4×D6111yescharacteristic
124C42D24411yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22×D6111yescharacteristic
127C23—1222no—
128C23#1175819811yescharacteristic
129Q8—2442no—
130D4—1224no—
131D4—2442no—
132D4—2444no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—1222no—
137C2×C4—2442no—
138C2×C4—2442no—
139C2×C4#1175819811yescharacteristic
140C2×C4#1175819811yescharacteristic
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819912yes—
143C2×C4#1175820112yes—
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—42no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—2442no—
152C22—2442no—
153C22—2442no—
154C22#1451969712yes—
155C22C2×#1175819811yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—2442no—
160C4#1451969712yes—
161C4#1451978312yes—
162C4C2×#1175819911yescharacteristic
163C4C2×#1175820111yescharacteristic
164C2—22no—
165C2—4882no—
166C2#1683972811yescharacteristic
167C2C2×#1451969711yescharacteristic
168C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C8D61
hypocenterC61#1480
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. #16839815C2semidirect
3. #16839489C2semidirect
4. C2×C4⋊C8×C61C2semidirect
87. C2×C4⋊C8D61semidirect
89. C61#1480semidirect