Finite Group Databasebeta

← #21445879

Subgroups — #21445879

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×#14519713C211yesmaximal, characteristic, complemented
3#16839761C212yesmaximal
4#16839531C212yesmaximal, complemented
5C2×#106×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7#14519783—22no—
8#14519783C414yescomplemented
9C2×#11758194C2212yes—
10C2×#11758194C2211yescharacteristic
11C2×#11758189—21no—
12C2×C8×D61—21no—
13#14519713—22no—
14#14519700—22no—
15#14519697—22no—
16C22×C8×C61C2211yescharacteristic
17C2×C4⋊C4×C61C2212yes—
18#106×C61—21no—
19#106×C61—21no—
20C22×C4×C61—22no—
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—21no—
23#11758222—21no—
24#11758222—21no—
25#11758222C2×C412yes—
26#11758222Q812yes—
27C2×D244D411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122D411yescharacteristic
30C2×C8×C61C2×C412yes—
31C2×C8×C61D412yes—
32C2×C8×C61D411yescharacteristic
33C2×C8×C61D411yescharacteristic
34C4⋊C4×C61—22no—
35C4⋊C4×C61—22no—
36#11758194—21no—
37#11758194—22no—
38#11758194—22no—
39#11758194C2×C412yes—
40C2×#92418—21no—
41C2×#92418—22no—
42#11758189—24no—
43C8×D61—24no—
44C23×C61#4111yescharacteristic
45C22×D61—21no—
46C2×C4×C61—42no—
47C2×C4×C61—82no—
48C2×C4×C61C22×C411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×Q811yescharacteristic
53C2×C4×C61#4111yescharacteristic
54C22⋊D61—22no—
55C22⋊D61—22no—
56C2×Dic61—21no—
57D244—21no—
58D244C4⋊C412yes—
59C4×D61—22no—
60C4×D61—22no—
61Dic122—21no—
62Dic122C4⋊C412yes—
63C8×C61C22⋊C412yes—
64C8×C61C22⋊C412yes—
65#92418—22no—
66#92418—42no—
67C22×C61—22no—
68C22×C61#11711yescharacteristic
69C22×C61#12111yescharacteristic
70C22×C61C22⋊Q811yescharacteristic
71C2×D61—22no—
72C2×D61—42no—
73C4×C61—82no—
74C4×C61C2×C22⋊C411yescharacteristic
75C4×C61C2×C4⋊C411yescharacteristic
76C4×C61#12111yescharacteristic
77C4×C61C22⋊Q811yescharacteristic
78Dic61—22no—
79#1815—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61#38011yescharacteristic
83C2×C61#47112yes—
84D61—42no—
85C2×#131—611no—
86C2×#108—611no—
87C2×#106D6111yescharacteristic, complemented
88#417—612no—
89#343—612no—
90C61#181511yescharacteristic, complemented, Sylow
91C2×#41—611no—
92#131—614no—
93#131—1222no—
94C2×M16—611no—
95C2×M16—612no—
96C2×M16—1221no—
97C22×C8—1221no—
98C22×C8C2×D6111yescharacteristic
99C2×C4⋊C4C2×D6112yes—
100#108—1222no—
101#106—21no—
102#106—21no—
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—22no—
113C22×C4—1221no—
114C22×C4C22×D6111yescharacteristic
115M16—612no—
116M16—1221no—
117M16—1224no—
118M16—1222no—
119M16—1222no—
120C2×C8—1221no—
121C2×C8—1224no—
122C2×C8—1222no—
123C2×C8C4×D6112yes—
124C2×C8D24412yes—
125C2×C8C22⋊D6111yescharacteristic
126C2×C8C22⋊D6111yescharacteristic
127C4⋊C4—22no—
128C4⋊C4—22no—
129C23—1221no—
130C23#1175822411yescharacteristic
131Q8—612no—
132Q8—1221no—
133D4—612no—
134D4—1222no—
135D4—1222no—
136D4—1221no—
137C2×C4—42no—
138C2×C4—82no—
139C2×C4—1221no—
140C2×C4—1222no—
141C2×C4—1222no—
142C2×C4C2×C4×D6111yescharacteristic
143C2×C4C2×D24411yescharacteristic
144C2×C4D4×D6111yescharacteristic
145C2×C4Q8×D6111yescharacteristic
146C2×C4#1175822611yescharacteristic
147C2×C4C2×C22⋊D6111yescharacteristic
148C8—1222no—
149C8—2442no—
150C8#1175819812yes—
151C8#1175819812yes—
152C22—22no—
153C22—1222no—
154C22—2442no—
155C22#1451973511yescharacteristic
156C22#1451974811yescharacteristic
157C22#1451975711yescharacteristic
158C4—82no—
159C4—1222no—
160C4C2×#1175819811yescharacteristic
161C4C4⋊C4×D6111yescharacteristic
162C4#1451975211yescharacteristic
163C4#1451975311yescharacteristic
164C2—21no—
165C2—21no—
166C2—2442no—
167C2#1683961911yescharacteristic
168C2#1684002212yes—
subgroupG/H
centerC22#14519748
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#106×C61C2
socleC22×C61#121
hypercenterC2×#106D61
hypocenterC61#1815
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#14519713C2semidirect
4. #16839531C2semidirect
5. C2×#106×C61C2semidirect
8. #14519783C4semidirect
87. C2×#106D61semidirect
90. C61#1815semidirect