Finite Group Databasebeta

← #21447872

Subgroups — #21447872

Order 7808.

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

normal subgroups only

This group has 170 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×#14519721C211yesmaximal, characteristic, complemented
2#16840145C211yesmaximal, characteristic, complemented
3D8×Dic61C211yesmaximal, characteristic, complemented
4#16839580C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839563C211yesmaximal, characteristic, complemented
7C2×D16×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758200—21no—
10#14519764—21no—
11D4×Dic61—21no—
12#14519721—22no—
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519698—21no—
16C8×Dic61C2211yescharacteristic
17C2×D8×C61C2211yescharacteristic
18C2×D8×C61C2211yescharacteristic
19D16×C61—22no—
20C2×C16×C61C2211yescharacteristic
21C2×D4×C61—21no—
22C2×D4×C61—21no—
23C22×Dic61—41no—
24C2×Dic122—21no—
25D8×C61—21no—
26D8×C61—21no—
27D8×C61—21no—
28D8×C61D412yes—
29C2×C8×C61C2311yescharacteristic
30C22⋊Dic61—41no—
31C22⋊Dic61—41no—
32C22⋊Dic61—41no—
33#11758200—42no—
34C4⋊Dic61—21no—
35C4×Dic61D411yescharacteristic
36C2×#92418D411yescharacteristic
37Dic244—21no—
38Dic244—21no—
39C16×C61—21no—
40#11758185—21no—
41C23×C61—41no—
42C23×C61—41no—
43D4×C61—22no—
44D4×C61—41no—
45D4×C61—41no—
46D4×C61—41no—
47C2×C4×C61C2×D411yescharacteristic
48C2×Dic61—41no—
49C2×Dic61—41no—
50C2×Dic61—82no—
51C2×Dic61D811yescharacteristic
52C2×Dic61D811yescharacteristic
53Dic122—41no—
54Dic122—41no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57#92418—21no—
58C22×C61—42no—
59C22×C61—81no—
60C22×C61—81no—
61C22×C61—81no—
62C22×C61—81no—
63C22×C61—81no—
64C22×C61C2×D811yescharacteristic
65C4×C61#12111yescharacteristic
66C4×C61AGL(1,ℤ/8)11yescharacteristic
67Dic61—21no—
68Dic61—21no—
69Dic61—81no—
70Dic61—81no—
71#2210—611nomaximal, Sylow
72C2×C61—82no—
73C2×C61—161no—
74C2×C61#45911yescharacteristic
75C2×C61#50811yescharacteristic
76C2×C61#50911yescharacteristic
77C2×SD32—611no—
78C2×D16D6111yescharacteristic
79#495—611no—
80C4×D8—611no—
81C4⋊C16—611no—
82#358—611no—
83#357—611no—
84C61#221011yescharacteristic, complemented, Sylow
85C2×Q16—611no—
86C2×SD16—1221no—
87C2×D8C2×D6111yescharacteristic
88C2×D8C2×D6111yescharacteristic
89#124—1221no—
90C4×D4—1221no—
91SD32—1222no—
92D16—22no—
93C2×C16—611no—
94C2×C16C2×D6111yescharacteristic
95#107—611no—
96#102—1221no—
97C4×C8—611no—
98C2×Q8—1221no—
99C2×D4—21no—
100C2×D4—21no—
101C22×C4—2441no—
102Q16—1221no—
103Q16—1221no—
104SD16—2442no—
105D8—21no—
106D8—21no—
107D8—21no—
108D8C22⋊D6112yes—
109C2×C8—611no—
110C2×C8C22×D6111yescharacteristic
111C4⋊C4—1221no—
112C22⋊C4—2441no—
113C22⋊C4—2441no—
114C22⋊C4—2441no—
115C42—611no—
116C16—21no—
117C16—1221no—
118C23—41no—
119C23—41no—
120Q8—2441no—
121Q8—2441no—
122D4—22no—
123D4—41no—
124D4—41no—
125D4—41no—
126C2×C4—611no—
127C2×C4—611no—
128C2×C4—4882no—
129C2×C4—2441no—
130C2×C4—2441no—
131C2×C4D4×D6111yescharacteristic
132C8—1221no—
133C8#1175822411yescharacteristic
134C8C2×C22⋊D6111yescharacteristic
135C22—42no—
136C22—81no—
137C22—81no—
138C22—81no—
139C22—81no—
140C22—81no—
141C22D8×D6111yescharacteristic
142C4—1221no—
143C4—1221no—
144C4—4881no—
145C4—4881no—
146C4#1451974911yescharacteristic
147C4#1451980111yescharacteristic
148C2—82no—
149C2—161no—
150C2#1683995511yescharacteristic
151C2#1684019111yescharacteristic
152C2#1684019611yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×D16×C61C2
socleC22×C61C2×D8
hypercenterC2×D16D61
hypocenterC61#2210
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#14519721C2semidirect
2. #16840145C2semidirect
3. D8×Dic61C2semidirect
4. #16839580C2semidirect
5. #16839567C2semidirect
6. #16839563C2semidirect
84. C61#2210semidirect