Finite Group Databasebeta

← #21447914

Subgroups — #21447914

Order 7808.

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

normal subgroups only

This group has 164 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
2C2×C16×D61C211yesmaximal, characteristic, complemented
3#16840004C211yesmaximal, characteristic, complemented
4#16839995C211yesmaximal, characteristic
5#16839589C211yesmaximal, characteristic, complemented
6#16839567C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×C8×D61C2211yescharacteristic
10#14519757—21no—
11#14519748—21no—
12#14519721—22no—
13C2×#11758185C2211yescharacteristic
14C16×D61—22no—
15#14519711C2211yescharacteristic
16#14519700—21no—
17#14519698—21no—
18C2×D8×C61C2211yescharacteristic
19C2×C16×C61C2211yescharacteristic
20#107×C61C2211yescharacteristic
21C2×D4×C61—21no—
22C2×C22⋊D61—41no—
23C2×C4×D61D411yescharacteristic
24C2×Dic122—21no—
25D8×C61—21no—
26D8×C61—21no—
27C2×C8×C61C2311yescharacteristic
28C4⋊C4×C61—21no—
29C22⋊Dic61—41no—
30#11758198—41no—
31C4⋊Dic61—21no—
32C4⋊Dic61—41no—
33C2×#92418D411yescharacteristic
34Dic244—21no—
35Dic244—21no—
36C8×D61—21no—
37C8×D61—21no—
38C16×C61—21no—
39#11758185D412yescomplemented
40C23×C61—41no—
41C22×D61D811yescharacteristic
42D4×C61—41no—
43D4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61C2×D411yescharacteristic
46C22⋊D61—82no—
47C2×Dic61—41no—
48C2×Dic61—41no—
49C2×Dic61D811yescharacteristic
50C4×D61—21no—
51C4×D61—21no—
52Dic122—41no—
53Dic122—41no—
54C8×C61C2×D411yescharacteristic
55C8×C61#4111yescharacteristic
56#92418—21no—
57C22×C61—81no—
58C22×C61—81no—
59C22×C61—81no—
60C22×C61C2×D811yescharacteristic
61C2×D61—21no—
62C2×D61—21no—
63C2×D61SD3212yescomplemented
64C4×C61—81no—
65C4×C61#12111yescharacteristic
66C4×C61#13511yescharacteristic
67Dic61—21no—
68Dic61—81no—
69Dic61—81no—
70#2217—611nomaximal, Sylow
71C2×C61—161no—
72C2×C61#46611yescharacteristic
73C2×C61C2×SD3211yescharacteristic
74C2×C61#50811yescharacteristic
75D61—22no—
76C2×SD32—611no—
77C22×C16—611no—
78#467—611no—
79#466—611no—
80#367—611no—
81#358—611no—
82#357D6111yescharacteristic, complemented
83C61#221711yescharacteristic, complemented, Sylow
84C2×Q16—611no—
85C2×D8C2×D6111yescharacteristic
86C22×C8—611no—
87C22⋊Q8—1221no—
88#121—1221no—
89SD32—1222no—
90C2×C16—611no—
91C2×C16—1222no—
92C2×C16C2×D6111yescharacteristic
93#107—611no—
94#107C2×D6111yescharacteristic
95#103—1221no—
96#102—1221no—
97C2×Q8—1221no—
98C2×D4—21no—
99C2×D4—2441no—
100C22×C4—611no—
101Q16—1221no—
102Q16—1221no—
103D8—21no—
104D8—21no—
105C2×C8—611no—
106C2×C8—1221no—
107C2×C8—1221no—
108C2×C8C22×D6111yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—1221no—
111C4⋊C4—2441no—
112C22⋊C4—2441no—
113C22⋊C4—2441no—
114C16—21no—
115C16—612no—
116C23—41no—
117C23—611no—
118Q8—2441no—
119Q8—2441no—
120D4—41no—
121D4—41no—
122D4—4882no—
123C2×C4—41no—
124C2×C4—611no—
125C2×C4—1221no—
126C2×C4—1221no—
127C2×C4—2441no—
128C2×C4—2441no—
129C2×C4D4×D6111yescharacteristic
130C8—1221no—
131C8#1175822211yescharacteristic
132C8D4×D6111yescharacteristic
133C22—81no—
134C22—81no—
135C22—81no—
136C22—612no—
137C22—1221no—
138C22—1221no—
139C22D8×D6111yescharacteristic
140C4—81no—
141C4—1221no—
142C4—4881no—
143C4—4881no—
144C4#1451975011yescharacteristic
145C4#1451979811yescharacteristic
146C2—161no—
147C2—1222no—
148C2#1683999711yescharacteristic
149C2SD32×D6111yescharacteristic
150C2#1684019111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2217
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×#14519721C2semidirect
2. C2×C16×D61C2semidirect
3. #16840004C2semidirect
5. #16839589C2semidirect
6. #16839567C2semidirect
7. C61×#357C2semidirect
39. #11758185D4semidirect
63. C2×D61SD32semidirect
82. #357D61semidirect
83. C61#2217semidirect