Finite Group Databasebeta

← #21445880

Subgroups — #21445880

Order 7808.

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

normal subgroups only

This group has 264 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
1C2×#14519783C211yesmaximal, characteristic
2C2×#14519711C211yesmaximal, characteristic, complemented
3#16839764C212yesmaximal
4#16839530C212yesmaximal, complemented
5C2×#108×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7#14519783—22no—
8#14519783C414yescomplemented
9C2×#11758194C2211yescharacteristic
10C2×#11758189—21no—
11C2×C8×D61—21no—
12C2×C4⋊Dic61C2212yes—
13#14519711—21no—
14#14519711—21no—
15#14519702—22no—
16#14519699—22no—
17C2×M16×C61C2212yes—
18C22×C8×C61C2211yescharacteristic
19#108×C61—22no—
20C22×C4×C61C2311yescharacteristic
21C2×C22⋊D61—21no—
22C22×Dic61—22no—
23#11758222—21no—
24#11758222—21no—
25#11758222C2×C412yes—
26#11758222Q812yes—
27C2×D244D411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122D411yescharacteristic
30M16×C61—22no—
31M16×C61—22no—
32C2×C8×C61—22no—
33C2×C8×C61C2×C412yes—
34C2×C8×C61D411yescharacteristic
35C2×C8×C61D411yescharacteristic
36C2×C8×C61D412yes—
37C4⋊Dic61—22no—
38C4⋊Dic61—22no—
39#11758194—21no—
40#11758194C2×C412yes—
41C2×#92418—21no—
42#11758189—24no—
43C8×D61—24no—
44C23×C61#4111yescharacteristic
45C22×D61—21no—
46C2×C4×C61C22×C411yescharacteristic
47C2×C4×C61C2×D411yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61C2×Q811yescharacteristic
51C2×C4×C61#4111yescharacteristic
52C22⋊D61—22no—
53C22⋊D61—22no—
54C2×Dic61—21no—
55C2×Dic61—42no—
56C2×Dic61—82no—
57D244—21no—
58D244C4⋊C412yes—
59C4×D61—22no—
60C4×D61—22no—
61Dic122—21no—
62Dic122C4⋊C412yes—
63C8×C61—42no—
64C8×C61C22⋊C412yes—
65C8×C61C22⋊C412yes—
66#92418—22no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61#11711yescharacteristic
70C22×C61#12111yescharacteristic
71C22×C61C22⋊Q811yescharacteristic
72C2×D61—22no—
73C2×D61—41no—
74C2×D61—41no—
75C4×C61C2×C22⋊C411yescharacteristic
76C4×C61C2×C4⋊C411yescharacteristic
77C4×C61#12111yescharacteristic
78C4×C61C22⋊Q811yescharacteristic
79Dic61—22no—
80Dic61—82no—
81#1816—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—21no—
84C2×C61#38011yescharacteristic
85C2×C61#47211yescharacteristic
86C2×C61#47311yescharacteristic
87D61—42no—
88C2×#131—611no—
89C2×#108D6111yescharacteristic, complemented
90C2×#107—611no—
91#417—612no—
92#343—612no—
93C61#181611yescharacteristic, complemented, Sylow
94C2×#41—611no—
95#131—614no—
96#131—1222no—
97C2×M16—611no—
98C2×M16—1221no—
99C2×M16C2×D6112yes—
100C22×C8—1221no—
101C22×C8C2×D6111yescharacteristic
102C2×C4⋊C4—612no—
103#108—22no—
104#107—1221no—
105#107—1221no—
106#103—1222no—
107#102—1222no—
108#41—612no—
109#41—612no—
110#41—1221no—
111#41—1221no—
112C2×Q8—611no—
113C2×D4—611no—
114C2×D4—1221no—
115C22×C4—1221no—
116C22×C4—1222no—
117C22×C4C22×D6111yescharacteristic
118M16—22no—
119M16—22no—
120M16—612no—
121M16—1221no—
122M16—1224no—
123C2×C8—22no—
124C2×C8—1221no—
125C2×C8—1224no—
126C2×C8C4×D6112yes—
127C2×C8D24411yescharacteristic
128C2×C8D24411yescharacteristic
129C2×C8C22⋊D6112yes—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C23—1221no—
133C23#1175822611yescharacteristic
134Q8—612no—
135Q8—1221no—
136D4—612no—
137D4—1222no—
138D4—1222no—
139D4—1221no—
140C2×C4—1221no—
141C2×C4—1222no—
142C2×C4—1222no—
143C2×C4—4882no—
144C2×C4—2442no—
145C2×C4C2×C4×D6111yescharacteristic
146C2×C4C2×D24411yescharacteristic
147C2×C4D4×D6111yescharacteristic
148C2×C4#1175822411yescharacteristic
149C2×C4Q8×D6111yescharacteristic
150C2×C4C2×C22⋊D6111yescharacteristic
151C8—42no—
152C8—1222no—
153C8#1175819812yes—
154C8#1175819812yes—
155C22—21no—
156C22—21no—
157C22—1222no—
158C22—2441no—
159C22—2441no—
160C22#1451973511yescharacteristic
161C22#1451975211yescharacteristic
162C22#1451975311yescharacteristic
163C4—1222no—
164C4—4882no—
165C4C2×#1175819811yescharacteristic
166C4C4⋊C4×D6111yescharacteristic
167C4#1451974811yescharacteristic
168C4#1451975711yescharacteristic
169C2—21no—
170C2—21no—
171C2—2442no—
172C2#1683961911yescharacteristic
173C2#1684003311yescharacteristic
174C2#1684003811yescharacteristic
subgroupG/H
centerC22#14519752
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#108×C61C2
socleC22×C61#121
hypercenterC2×#108D61
hypocenterC61#1816
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C2×#14519711C2semidirect
4. #16839530C2semidirect
5. C2×#108×C61C2semidirect
8. #14519783C4semidirect
89. C2×#108D61semidirect
93. C61#1816semidirect