Finite Group Databasebeta

← #21448089

Subgroups — #21448089

Order 7808.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic488C211yesmaximal, characteristic, complemented
2C2×#14519723C211yesmaximal, characteristic, complemented
3C2×#14519721C211yesmaximal, characteristic
4#16840145C211yesmaximal, characteristic
5#16840140C211yesmaximal, characteristic, complemented
6#16839537C211yesmaximal, characteristic, complemented
7C2×SD32×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×Dic244C2211yescharacteristic
10C2×#11758202—21no—
11C2×#11758200—21no—
12#14519775—21no—
13#14519764—21no—
14Dic488—22no—
15#14519723—22no—
16#14519721—22no—
17C2×#11758185C2211yescharacteristic
18C8×Dic61C2211yescharacteristic
19C2×Q16×C61C2211yescharacteristic
20C2×D8×C61C2211yescharacteristic
21SD32×C61—22no—
22C2×C16×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24C2×D4×C61—21no—
25C2×Dic122—21no—
26C2×Dic122—21no—
27Q16×C61—21no—
28Q16×C61—21no—
29D8×C61—21no—
30D8×C61—21no—
31C2×C8×C61C2311yescharacteristic
32C22⋊Dic61—42no—
33#11758202—42no—
34#11758200—42no—
35#11758196—42no—
36C4×Dic61D411yescharacteristic
37C2×#92418D411yescharacteristic
38Dic244—21no—
39Dic244—21no—
40Dic244—21no—
41Dic244—21no—
42C16×C61D412yes—
43#11758185D412yes—
44C23×C61—41no—
45Q8×C61—41no—
46Q8×C61—41no—
47D4×C61—41no—
48D4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61C2×D411yescharacteristic
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61D812yes—
54Dic122—41no—
55Dic122—41no—
56Dic122—41no—
57Dic122—41no—
58C8×C61C2×D411yescharacteristic
59C8×C61C2×D411yescharacteristic
60#92418D812yes—
61C22×C61—81no—
62C22×C61—82no—
63C22×C61C2×D811yescharacteristic
64C4×C61—81no—
65C4×C61#12711yescharacteristic
66C4×C61C2×D811yescharacteristic
67Dic61—22no—
68Dic61—81no—
69Dic61—81no—
70#2251—611nomaximal, Sylow
71C2×C61—161no—
72C2×C61#49311yescharacteristic
73C2×C61#51012yes—
74C2×Q32—611no—
75C2×Q32—611no—
76C2×SD32—611no—
77C2×SD32D6111yescharacteristic
78#495—611no—
79#494—611no—
80#346—611no—
81C61#225111yescharacteristic, complemented, Sylow
82C2×Q16—611no—
83C2×Q16—611no—
84C2×Q16—1221no—
85C2×Q16C2×D6111yescharacteristic
86C2×SD16—1221no—
87C2×D8C2×D6111yescharacteristic
88C4⋊Q8—1221no—
89#124—1221no—
90Q32—1222no—
91Q32—1222no—
92SD32—22no—
93SD32—1222no—
94C2×C16—611no—
95C2×C16C2×D6111yescharacteristic
96C4×C8—611no—
97C2×Q8—21no—
98C2×Q8—1221no—
99C2×Q8—1221no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—1221no—
104Q16—1221no—
105Q16—1221no—
106Q16—1221no—
107Q16—2442no—
108SD16—2442no—
109D8—21no—
110D8—21no—
111C2×C8—611no—
112C2×C8C22×D6111yescharacteristic
113C4⋊C4—2442no—
114C22⋊C4—2442no—
115C42—611no—
116C16—612no—
117C16C22⋊D6112yes—
118C23—41no—
119Q8—41no—
120Q8—41no—
121Q8—2441no—
122Q8—2441no—
123Q8—2441no—
124Q8—2441no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—612no—
129C2×C4—2441no—
130C2×C4—2441no—
131C2×C4D4×D6111yescharacteristic
132C8—612no—
133C8D4×D6111yescharacteristic
134C8C2×C22⋊D6111yescharacteristic
135C22—82no—
136C22—81no—
137C22D8×D6111yescharacteristic
138C4—81no—
139C4—1222no—
140C4—4881no—
141C4—4881no—
142C4#1451977311yescharacteristic
143C4D8×D6111yescharacteristic
144C2—161no—
145C2#1684013711yescharacteristic
146C2#1684020112yes—
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×SD32×C61C2
socleC22×C61C2×D8
hypercenterC2×SD32D61
hypocenterC61#2251
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Dic488C2semidirect
2. C2×#14519723C2semidirect
5. #16840140C2semidirect
6. #16839537C2semidirect
81. C61#2251semidirect