Finite Group Databasebeta

← #21447858

Subgroups — #21447858

Order 7808.

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

normal subgroups only

This group has 174 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, complemented
2C2×#14519721C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic
4#16839856C211yesmaximal, characteristic, complemented
5#16839580C211yesmaximal, characteristic, complemented
6#16839562C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×D488C2211yescharacteristic
10C2×#11758199—21no—
11#14519773—21no—
12#14519742—21no—
13#14519722—22no—
14#14519721—22no—
15C2×#11758185C2211yescharacteristic
16#14519700—21no—
17C8×Dic61C2211yescharacteristic
18C2×D8×C61C2211yescharacteristic
19C2×C16×C61C2211yescharacteristic
20#107×C61C2211yescharacteristic
21C2×D4×C61—21no—
22C2×C22⋊D61—41no—
23C2×C22⋊D61—41no—
24C2×D244—21no—
25C2×Dic122—21no—
26D8×C61—21no—
27D8×C61—21no—
28C2×C8×C61C2311yescharacteristic
29C4⋊C4×C61—21no—
30#11758199—42no—
31#11758196—41no—
32C4×Dic61—41no—
33C4×Dic61D411yescharacteristic
34C2×#92418D411yescharacteristic
35Dic244—21no—
36Dic244D412yescomplemented
37D488—21no—
38D488—21no—
39C16×C61—21no—
40#11758185—21no—
41C23×C61—41no—
42C22×D61—41no—
43D4×C61—41no—
44D4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C2×D411yescharacteristic
47C22⋊D61—82no—
48C22⋊D61—82no—
49C2×Dic61—41no—
50C2×Dic61D811yescharacteristic
51C2×Dic61D811yescharacteristic
52D244—41no—
53D244—41no—
54Dic122—22no—
55Dic122—41no—
56C8×C61C2×D411yescharacteristic
57C8×C61#4111yescharacteristic
58#92418—21no—
59C22×C61—81no—
60C22×C61—81no—
61C22×C61—81no—
62C22×C61C2×D811yescharacteristic
63C2×D61—81no—
64C2×D61—81no—
65C2×D61—81no—
66C4×C61—81no—
67C4×C61#12111yescharacteristic
68C4×C61AGL(1,ℤ/8)11yescharacteristic
69Dic61—21no—
70Dic61—42no—
71Dic61SD3212yescomplemented
72#2207—611nomaximal, Sylow
73C2×C61—161no—
74C2×C61#45911yescharacteristic
75C2×C61C2×SD3211yescharacteristic
76C2×C61#50911yescharacteristic
77D61—161no—
78C2×SD32—611no—
79C2×SD32—611no—
80#493—611no—
81C4×Q16—611no—
82C4⋊C16—611no—
83#357—611no—
84#357D6111yescharacteristic, complemented
85C61#220711yescharacteristic, complemented, Sylow
86C2×Q16—611no—
87C2×D8—611no—
88C2×D8—1221no—
89C2×D8C2×D6111yescharacteristic
90#127—1221no—
91C4×Q8—1221no—
92SD32—1222no—
93SD32—1222no—
94C2×C16—611no—
95C2×C16C2×D6111yescharacteristic
96#107C2×D6111yescharacteristic
97#103—1221no—
98C4×C8—611no—
99C2×Q8—1221no—
100C2×D4—21no—
101C2×D4—1221no—
102C2×D4—2441no—
103C2×D4—2441no—
104Q16—612no—
105Q16—1221no—
106D8—21no—
107D8—21no—
108D8—1221no—
109D8—1221no—
110D8—2442no—
111C2×C8—611no—
112C2×C8C22×D6111yescharacteristic
113C4⋊C4—21no—
114C4⋊C4—2441no—
115C42—611no—
116C42—2441no—
117C16—21no—
118C16—1221no—
119C23—41no—
120C23—2441no—
121Q8—1222no—
122Q8—2441no—
123D4—41no—
124D4—41no—
125D4—4882no—
126D4—4882no—
127D4—2441no—
128D4—2441no—
129C2×C4—41no—
130C2×C4—611no—
131C2×C4—611no—
132C2×C4—2441no—
133C2×C4D4×D6111yescharacteristic
134C8—1221no—
135C8#1175822211yescharacteristic
136C8D4×D6111yescharacteristic
137C22—81no—
138C22—81no—
139C22—81no—
140C22—4881no—
141C22—4881no—
142C22—4881no—
143C22D8×D6111yescharacteristic
144C4—81no—
145C4—612no—
146C4—1221no—
147C4—2442no—
148C4#1451975011yescharacteristic
149C4#1451980411yescharacteristic
150C2—161no—
151C2—9761no—
152C2#1683995611yescharacteristic
153C2SD32×D6111yescharacteristic
154C2#1684019611yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2207
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×#14519722C2semidirect
2. C2×#14519721C2semidirect
4. #16839856C2semidirect
5. #16839580C2semidirect
6. #16839562C2semidirect
7. C61×#357C2semidirect
36. Dic244D4semidirect
71. Dic61SD32semidirect
84. #357D61semidirect
85. C61#2207semidirect