Finite Group Databasebeta

← #21445883

Subgroups — #21445883

Order 7808.

264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14519713C211yesmaximal, characteristic, complemented
2C2×#14519711C211yesmaximal, characteristic, complemented
3#16839763C212yesmaximal
4#16839530C212yesmaximal, complemented
5C2×#131×C61C211yesmaximal, characteristic
6C2×#11758194C2212yes—
7C2×C4⋊Dic61C2212yes—
8#14519713—22no—
9#14519711—21no—
10#14519711—21no—
11#14519701—22no—
12#14519698—22no—
13C2×#41×C61C2211yescharacteristic
14#131×C61—22no—
15#131×C61C414yescomplemented
16C2×M16×C61—21no—
17C2×M16×C61C2211yescharacteristic
18C22×C8×C61—21no—
19C22×C8×C61C2211yescharacteristic
20#41×C61—21no—
21#41×C61—21no—
22#41×C61C2×C412yes—
23#41×C61Q812yes—
24C2×Q8×C61D411yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—22no—
30M16×C61—21no—
31M16×C61—24no—
32M16×C61C2×C412yes—
33C2×C8×C61—21no—
34C2×C8×C61—24no—
35C2×C8×C61C2×C412yes—
36C2×C8×C61D411yescharacteristic
37C2×C8×C61D411yescharacteristic
38C2×C8×C61D412yes—
39C4⋊Dic61—22no—
40C4⋊Dic61—22no—
41#11758194—22no—
42#11758194—22no—
43C2×#92418—22no—
44C23×C61—21no—
45C23×C61#4111yescharacteristic
46Q8×C61—21no—
47Q8×C61C4⋊C412yes—
48D4×C61—22no—
49D4×C61—22no—
50D4×C61—21no—
51D4×C61C4⋊C412yes—
52C2×C4×C61—21no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×Dic61—42no—
62C2×Dic61—82no—
63C8×C61—22no—
64C8×C61C22⋊C412yes—
65C8×C61C22⋊C412yes—
66#92418—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—22no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61#11711yescharacteristic
73C22×C61#12111yescharacteristic
74C22×C61C22⋊Q811yescharacteristic
75C4×C61—22no—
76C4×C61C2×C22⋊C411yescharacteristic
77C4×C61C2×C4⋊C411yescharacteristic
78C4×C61#12111yescharacteristic
79C4×C61C22⋊Q811yescharacteristic
80Dic61—82no—
81#1816—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—21no—
84C2×C61—42no—
85C2×C61#38011yescharacteristic
86C2×C61#47211yescharacteristic
87C2×C61#47311yescharacteristic
88C2×#131D6111yescharacteristic
89C2×#108—611no—
90C2×#107—611no—
91#417—612no—
92#343—612no—
93C61#181611yescharacteristic, complemented, Sylow
94C2×#41C2×D6111yescharacteristic
95#131—22no—
96#131Dic6114yescomplemented
97C2×M16—21no—
98C2×M16—612no—
99C2×M16C2×D6111yescharacteristic
100C22×C8—21no—
101C22×C8C2×D6111yescharacteristic
102C2×C4⋊C4—612no—
103#108—1222no—
104#107—1221no—
105#107—1221no—
106#103—1222no—
107#102—1222no—
108#41—21no—
109#41—21no—
110#41Dic12212yes—
111#41C2×Dic6112yes—
112C2×Q8D24411yescharacteristic
113C2×D4—21no—
114C2×D4D24411yescharacteristic
115C22×C4—21no—
116C22×C4—1222no—
117C22×C4C22×D6111yescharacteristic
118M16—21no—
119M16—24no—
120M16—1222no—
121M16—1222no—
122M16C2×Dic6112yes—
123C2×C8—21no—
124C2×C8—24no—
125C2×C8—1222no—
126C2×C8C2×Dic6112yes—
127C2×C8C22⋊D6111yescharacteristic
128C2×C8C22⋊D6111yescharacteristic
129C2×C8C22⋊D6112yes—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C23—21no—
133C23#1175822211yescharacteristic
134Q8—21no—
135Q8C4⋊Dic6112yes—
136D4—22no—
137D4—22no—
138D4—21no—
139D4C4⋊Dic6112yes—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—4882no—
144C2×C4—2442no—
145C2×C4C2×Dic12211yescharacteristic
146C2×C4C2×D24411yescharacteristic
147C2×C4#1175822211yescharacteristic
148C2×C4C22×Dic6111yescharacteristic
149C2×C4C2×C22⋊D6111yescharacteristic
150C2×C4C2×C22⋊D6111yescharacteristic
151C8—22no—
152C8—2442no—
153C8C22⋊Dic6112yes—
154C8C22⋊Dic6112yes—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1451973611yescharacteristic
161C22#1451975111yescharacteristic
162C22#1451975611yescharacteristic
163C4—22no—
164C4—4882no—
165C4C2×C22⋊Dic6111yescharacteristic
166C4C2×C4⋊Dic6111yescharacteristic
167C4#1451975111yescharacteristic
168C4#1451975611yescharacteristic
169C2—21no—
170C2—21no—
171C2—42no—
172C2#1683962211yescharacteristic
173C2#1684003211yescharacteristic
174C2#1684003711yescharacteristic
subgroupG/H
centerC22#14519751
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#131×C61C2
socleC22×C61#121
hypercenterC2×#131D61
hypocenterC61#1816
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#14519713C2semidirect
2. C2×#14519711C2semidirect
4. #16839530C2semidirect
15. #131×C61C4semidirect
93. C61#1816semidirect
96. #131Dic61semidirect