Finite Group Databasebeta

← #21448015

Subgroups — #21448015

Order 7808.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#16840000C211yesmaximal, characteristic
2#107×D61C211yesmaximal, characteristic
3#16839590C211yesmaximal, characteristic, complemented
4#16839589C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic
7C61×#358C211yesmaximal, characteristic, complemented
8C2×C8×D61C2211yescharacteristic
9#14519753—21no—
10C4⋊C4×D61—21no—
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519710—21no—
15#14519701—21no—
16C2×Q16×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×Q8×C61—21no—
20C2×C4×D61—41no—
21C2×C4×D61D411yescharacteristic
22Q16×C61—21no—
23Q16×C61—21no—
24C2×C8×C61C2311yescharacteristic
25C4⋊C4×C61—21no—
26#11758198—41no—
27C4⋊Dic61—21no—
28C4⋊Dic61—21no—
29#11758196—41no—
30#11758196—41no—
31C2×#92418D411yescharacteristic
32C8×D61—21no—
33C8×D61—21no—
34C16×C61—21no—
35#11758185—21no—
36C22×D61D811yescharacteristic
37Q8×C61—41no—
38Q8×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61D811yescharacteristic
45C4×D61—21no—
46C4×D61—21no—
47C4×D61—82no—
48C8×C61#4111yescharacteristic
49C8×C61#4111yescharacteristic
50#92418—21no—
51C22×C61C2×D811yescharacteristic
52C2×D61—21no—
53C2×D61—21no—
54C2×D61SD3212yes—
55C4×C61—81no—
56C4×C61—81no—
57C4×C61#12311yescharacteristic
58C4×C61#13711yescharacteristic
59Dic61—21no—
60Dic61—81no—
61Dic61—81no—
62#2235—611nomaximal, Sylow
63C2×C61#48011yescharacteristic
64C2×C61C2×SD3211yescharacteristic
65C2×C61#51011yescharacteristic
66D61—22no—
67#467—611no—
68C2×#107—611no—
69#367—611no—
70#367—611no—
71#358—611no—
72#358D6111yescharacteristic, complemented
73C22⋊C16—611no—
74C61#223511yescharacteristic, complemented, Sylow
75C2×Q16C2×D6111yescharacteristic
76C22×C8—611no—
77C22⋊Q8—1221no—
78C2×C4⋊C4—1221no—
79C2×C16—611no—
80C2×C16C2×D6111yescharacteristic
81#107—611no—
82#107—611no—
83#107—1221no—
84#107C2×D6111yescharacteristic
85#103—1221no—
86C2×Q8—21no—
87C22×C4—611no—
88C22×C4—2441no—
89Q16—21no—
90Q16—21no—
91C2×C8—611no—
92C2×C8—1221no—
93C2×C8—1221no—
94C2×C8C22×D6111yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—1221no—
97C4⋊C4—1221no—
98C4⋊C4—2441no—
99C4⋊C4—2441no—
100C22⋊C4—2441no—
101C16—21no—
102C16—1221no—
103C23—611no—
104Q8—41no—
105Q8—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—611no—
109C2×C4—1221no—
110C2×C4—1221no—
111C2×C4—4882no—
112C2×C4—2441no—
113C2×C4—2441no—
114C2×C4D4×D6111yescharacteristic
115C8—1221no—
116C8#1175822211yescharacteristic
117C8#1175822411yescharacteristic
118C22—612no—
119C22—1221no—
120C22—1221no—
121C22D8×D6111yescharacteristic
122C4—81no—
123C4—81no—
124C4—1221no—
125C4—4881no—
126C4—4881no—
127C4#1451975911yescharacteristic
128C4#1451980611yescharacteristic
129C2—1222no—
130C2#1684007411yescharacteristic
131C2SD32×D6111yescharacteristic
132C2#1684020411yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2235
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. #16839590C2semidirect
4. #16839589C2semidirect
5. #16839566C2semidirect
7. C61×#358C2semidirect
72. #358D61semidirect
74. C61#2235semidirect