Finite Group Databasebeta

← #21447863

Subgroups — #21447863

Order 7808.

166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14519722C211yesmaximal, characteristic
2C2×#14519720C211yesmaximal, characteristic
3#16840140C211yesmaximal, characteristic, complemented
4#16839844C211yesmaximal, characteristic
5#16839580C211yesmaximal, characteristic, complemented
6#16839565C211yesmaximal, characteristic, complemented
7C61×#358C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×#11758202—21no—
10C2×D488C2211yescharacteristic
11#14519775—21no—
12#14519739—21no—
13#14519722—22no—
14#14519720—22no—
15C2×#11758185C2211yescharacteristic
16#14519697—21no—
17C8×Dic61C2211yescharacteristic
18C2×Q16×C61C2211yescharacteristic
19C2×C16×C61C2211yescharacteristic
20#107×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×D244—21no—
23C2×C4×D61—41no—
24C2×Dic122—21no—
25Q16×C61—21no—
26Q16×C61—21no—
27C2×C8×C61C2311yescharacteristic
28C4⋊C4×C61—21no—
29#11758202—42no—
30#11758198—41no—
31#11758196—41no—
32#11758196—41no—
33C4×Dic61D411yescharacteristic
34C2×#92418D411yescharacteristic
35Dic244—21no—
36Dic244—21no—
37D488—21no—
38D488D412yes—
39C16×C61—21no—
40#11758185—21no—
41C22×D61—41no—
42Q8×C61—41no—
43Q8×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C2×D411yescharacteristic
47C2×Dic61—41no—
48C2×Dic61D811yescharacteristic
49C2×Dic61D811yescharacteristic
50D244—22no—
51D244—41no—
52C4×D61—82no—
53Dic122—41no—
54Dic122—41no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57#92418—21no—
58C22×C61C2×D811yescharacteristic
59C2×D61—42no—
60C2×D61—81no—
61C2×D61—81no—
62C4×C61—81no—
63C4×C61—81no—
64C4×C61#12111yescharacteristic
65C4×C61AGL(1,ℤ/8)11yescharacteristic
66Dic61—21no—
67Dic61—81no—
68Dic61SD3212yescomplemented
69#2208—611nomaximal, Sylow
70C2×C61#45911yescharacteristic
71C2×C61C2×SD3211yescharacteristic
72C2×C61#51011yescharacteristic
73D61—82no—
74C2×SD32—611no—
75C2×SD32—611no—
76#494—611no—
77C4×D8—611no—
78C4⋊C16—611no—
79#358—611no—
80#358D6111yescharacteristic, complemented
81C61#220811yescharacteristic, complemented, Sylow
82C2×Q16—611no—
83C2×Q16—1221no—
84C2×Q16C2×D6111yescharacteristic
85C2×D8—611no—
86C4⋊Q8—1221no—
87C4×D4—1221no—
88SD32—1222no—
89SD32—1222no—
90C2×C16—611no—
91C2×C16C2×D6111yescharacteristic
92#107C2×D6111yescharacteristic
93#102—1221no—
94C4×C8—611no—
95C2×Q8—21no—
96C2×Q8—1221no—
97C2×D4—1221no—
98C22×C4—2441no—
99Q16—21no—
100Q16—21no—
101Q16—1221no—
102Q16—1221no—
103Q16—2442no—
104D8—612no—
105D8—1221no—
106C2×C8—611no—
107C2×C8C22×D6111yescharacteristic
108C4⋊C4—21no—
109C4⋊C4—2441no—
110C4⋊C4—2441no—
111C22⋊C4—2441no—
112C42—611no—
113C16—21no—
114C16—1221no—
115C23—2441no—
116Q8—41no—
117Q8—41no—
118Q8—2441no—
119Q8—2441no—
120D4—1222no—
121D4—2441no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—611no—
125C2×C4—611no—
126C2×C4—4882no—
127C2×C4—2441no—
128C2×C4D4×D6111yescharacteristic
129C8—1221no—
130C8#1175822211yescharacteristic
131C8D4×D6111yescharacteristic
132C22—4881no—
133C22—4881no—
134C22—2442no—
135C22D8×D6111yescharacteristic
136C4—81no—
137C4—81no—
138C4—612no—
139C4—1221no—
140C4—4881no—
141C4#1451975011yescharacteristic
142C4#1451980411yescharacteristic
143C2—4882no—
144C2#1683995611yescharacteristic
145C2SD32×D6111yescharacteristic
146C2#1684020411yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2208
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
3. #16840140C2semidirect
5. #16839580C2semidirect
6. #16839565C2semidirect
7. C61×#358C2semidirect
68. Dic61SD32semidirect
80. #358D61semidirect
81. C61#2208semidirect