Finite Group Databasebeta

← #21445875

Subgroups — #21445875

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×#14519709C211yesmaximal, 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#14519709—21no—
14#14519709—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—22no—
68C22×C61#11711yescharacteristic
69C22×C61#12111yescharacteristic
70C22×C61C22⋊Q811yescharacteristic
71C2×D61—22no—
72C2×D61—42no—
73C4×C61C2×C22⋊C411yescharacteristic
74C4×C61C2×C4⋊C411yescharacteristic
75C4×C61#12111yescharacteristic
76C4×C61C22⋊Q811yescharacteristic
77Dic61—22no—
78Dic61—82no—
79#1815—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61#38011yescharacteristic
83C2×C61#47112yes—
84D61—42no—
85C2×#131—611no—
86C2×#108D6111yescharacteristic, complemented
87C2×#106—611no—
88#417—612no—
89#343—612no—
90C61#181511yescharacteristic, complemented, Sylow
91C2×#41—611no—
92#131—614no—
93#131—1222no—
94C2×M16—611no—
95C2×M16—1221no—
96C2×M16C2×D6112yes—
97C22×C8—1221no—
98C22×C8C2×D6111yescharacteristic
99C2×C4⋊C4—612no—
100#108—22no—
101#106—1221no—
102#106—1221no—
103#103—1222no—
104#102—1222no—
105#41—612no—
106#41—612no—
107#41—1221no—
108#41—1221no—
109C2×Q8—611no—
110C2×D4—611no—
111C2×D4—1221no—
112C22×C4—1221no—
113C22×C4—1222no—
114C22×C4C22×D6111yescharacteristic
115M16—22no—
116M16—22no—
117M16—612no—
118M16—1221no—
119M16—1224no—
120C2×C8—22no—
121C2×C8—1221no—
122C2×C8—1224no—
123C2×C8C4×D6112yes—
124C2×C8D24411yescharacteristic
125C2×C8D24411yescharacteristic
126C2×C8C22⋊D6112yes—
127C4⋊C4—1222no—
128C4⋊C4—1222no—
129C23—1221no—
130C23#1175822611yescharacteristic
131Q8—612no—
132Q8—1221no—
133D4—612no—
134D4—1222no—
135D4—1222no—
136D4—1221no—
137C2×C4—1221no—
138C2×C4—1222no—
139C2×C4—1222no—
140C2×C4—4882no—
141C2×C4—2442no—
142C2×C4C2×C4×D6111yescharacteristic
143C2×C4C2×D24411yescharacteristic
144C2×C4D4×D6111yescharacteristic
145C2×C4#1175822411yescharacteristic
146C2×C4Q8×D6111yescharacteristic
147C2×C4C2×C22⋊D6111yescharacteristic
148C8—42no—
149C8—1222no—
150C8#1175819812yes—
151C8#1175819812yes—
152C22—22no—
153C22—1222no—
154C22—2442no—
155C22#1451973511yescharacteristic
156C22#1451975211yescharacteristic
157C22#1451975311yescharacteristic
158C4—1222no—
159C4—4882no—
160C4C2×#1175819811yescharacteristic
161C4C4⋊C4×D6111yescharacteristic
162C4#1451974811yescharacteristic
163C4#1451975711yescharacteristic
164C2—21no—
165C2—21no—
166C2—2442no—
167C2#1683961911yescharacteristic
168C2#1684002612yes—
subgroupG/H
centerC22#14519752
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#108×C61C2
socleC22×C61#121
hypercenterC2×#108D61
hypocenterC61#1815
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×#14519709C2semidirect
4. #16839530C2semidirect
5. C2×#108×C61C2semidirect
8. #14519783C4semidirect
86. C2×#108D61semidirect
90. C61#1815semidirect