Finite Group Databasebeta

← #21447568

Subgroups — #21447568

Order 7808.

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

normal subgroups only

This group has 220 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
1C2×#14519717C211yesmaximal, characteristic, complemented
2C2×#14519713C211yesmaximal, characteristic, complemented
3#16839578C212yesmaximal, complemented
4#16839575C212yesmaximal, complemented
5C2×#135×C61C211yesmaximal, characteristic
6C2×#11758194—21no—
7#14519717—21no—
8#14519717C2212yes—
9C2×#11758185—21no—
10#14519713—21no—
11#14519713C2212yes—
12C2×#41×C61—21no—
13#135×C61—21no—
14#135×C61—21no—
15#135×C61C412yes—
16#135×C61C412yes—
17C2×Q16×C61C2211yescharacteristic
18C2×SD16×C61—21no—
19C2×D8×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21#41×C61—22no—
22#41×C61—22no—
23#41×C61—41no—
24#41×C61—41no—
25C2×Q8×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—41no—
28C22×C4×C61—41no—
29C22×C4×C61D411yescharacteristic
30Q16×C61—21no—
31Q16×C61C2×C412yes—
32SD16×C61—22no—
33SD16×C61—22no—
34D8×C61—21no—
35D8×C61C2×C412yes—
36C2×C8×C61C2×C411yescharacteristic
37C2×C8×C61C2×C411yescharacteristic
38C2×C8×C61D411yescharacteristic
39C2×C8×C61D411yescharacteristic
40C2×C8×C61D411yescharacteristic
41C2×C8×C61C2311yescharacteristic
42#11758194—22no—
43#11758194—41no—
44C2×#92418—41no—
45#11758185—22no—
46C23×C61—41no—
47C23×C61SD1611yescharacteristic
48Q8×C61—22no—
49Q8×C61—41no—
50D4×C61—22no—
51D4×C61—42no—
52D4×C61—42no—
53D4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—42no—
56C2×C4×C61—42no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61D811yescharacteristic
60C2×C4×C61D811yescharacteristic
61C2×C4×C61SD1611yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C8×C61C22⋊C411yescharacteristic
64C8×C61C22⋊C411yescharacteristic
65C8×C61C22×C411yescharacteristic
66C8×C61C2×D411yescharacteristic
67#92418—42no—
68C22×C61—41no—
69C22×C61—42no—
70C22×C61—82no—
71C22×C61#10211yescharacteristic
72C22×C61#10211yescharacteristic
73C22×C61C2×SD1611yescharacteristic
74C4×C61—42no—
75C4×C61#10211yescharacteristic
76C4×C61#10211yescharacteristic
77C4×C61C2×C22⋊C411yescharacteristic
78C4×C61C2×D811yescharacteristic
79#2148—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61—21no—
83C2×C61—82no—
84C2×C61C2×#10211yescharacteristic
85C2×#135D6111yescharacteristic
86C2×M32—611no—
87C2×#108—611no—
88#362—612no—
89#361—612no—
90C61#214811yescharacteristic, complemented, Sylow
91C2×#41—21no—
92#135—21no—
93#135—21no—
94#135Dic6112yes—
95#135Dic6112yes—
96C2×Q16C2×D6111yescharacteristic
97C2×SD16—21no—
98C2×D8C2×D6111yescharacteristic
99C2×M16—1221no—
100C22×C8C2×D6111yescharacteristic
101M32—612no—
102M32—1221no—
103C2×C16—1221no—
104#108—612no—
105#108—1221no—
106#41—22no—
107#41—22no—
108#41—41no—
109#41—41no—
110C2×Q8—21no—
111C2×D4—21no—
112C2×D4—41no—
113C22×C4—41no—
114C22×C4C22⋊D6111yescharacteristic
115Q16—21no—
116Q16C2×Dic6112yes—
117SD16—22no—
118SD16—22no—
119D8—21no—
120D8C2×Dic6112yes—
121M16—1222no—
122M16—2441no—
123C2×C8—2441no—
124C2×C8C2×Dic6111yescharacteristic
125C2×C8C2×Dic6111yescharacteristic
126C2×C8C22⋊D6111yescharacteristic
127C2×C8C22⋊D6111yescharacteristic
128C2×C8C22⋊D6111yescharacteristic
129C2×C8C22×D6111yescharacteristic
130C16—1222no—
131C23—41no—
132C23#1175820011yescharacteristic
133Q8—22no—
134Q8—41no—
135D4—22no—
136D4—42no—
137D4—42no—
138D4—41no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4#1175819911yescharacteristic
143C2×C4#1175819911yescharacteristic
144C2×C4#1175820011yescharacteristic
145C2×C4C22⋊Dic6111yescharacteristic
146C2×C4C22⋊Dic6111yescharacteristic
147C2×C4C2×C22⋊D6111yescharacteristic
148C8—2442no—
149C8C22⋊Dic6111yescharacteristic
150C8C22⋊Dic6111yescharacteristic
151C8C22×Dic6111yescharacteristic
152C8C2×C22⋊D6111yescharacteristic
153C22—41no—
154C22—42no—
155C22—82no—
156C22#1451969811yescharacteristic
157C22#1451969811yescharacteristic
158C22C2×#1175820011yescharacteristic
159C4—42no—
160C4#1451969811yescharacteristic
161C4#1451969811yescharacteristic
162C4C2×C22⋊Dic6111yescharacteristic
163C4C2×#1175819911yescharacteristic
164C2—21no—
165C2—21no—
166C2—21no—
167C2—82no—
168C2C2×#1451969811yescharacteristic
subgroupG/H
centerC4#14519698
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC2×#135×C61C2
socleC2×C61C2×#102
hypercenterC2×#135D61
hypocenterC61#2148
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519717C2semidirect
2. C2×#14519713C2semidirect
3. #16839578C2semidirect
4. #16839575C2semidirect
90. C61#2148semidirect