Finite Group Databasebeta

← #22612171

Subgroups — #22612171

Order 9344.

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

normal subgroups only

This group has 152 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#17988988C211yesmaximal, characteristic, complemented
2#17988962C211yesmaximal, characteristic
3#17988389C211yesmaximal, characteristic, complemented
4#17988388C211yesmaximal, characteristic, complemented
5#17988387C211yesmaximal, characteristic, complemented
6#17988362C211yesmaximal, characteristic, complemented
7#357×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9C2×#11924013—21no—
10#14556587—21no—
11#14556582—21no—
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556522—21no—
15C8×Dic73C2211yescharacteristic
16C2×D8×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19C2×D292—21no—
20C2×C22⋊D73—41no—
21C2×C22⋊D73—41no—
22D584—21no—
23D584—21no—
24#11924013—42no—
25C2×#10596831D411yescharacteristic
26C4⋊Dic73—21no—
27C4⋊Dic73—41no—
28#11924007—41no—
29C4×Dic73D411yescharacteristic
30#11924003—21no—
31C2×D4×C73—21no—
32D8×C73—21no—
33D8×C73—21no—
34C2×C8×C73C2311yescharacteristic
35C4⋊C4×C73—21no—
36C16×C73—21no—
37C23×C73—41no—
38C22×D73—41no—
39D4×C73—41no—
40D4×C73—41no—
41C2×C4×C73—41no—
42C2×C4×C73C2×D411yescharacteristic
43C22⋊D73—82no—
44C22⋊D73—82no—
45C2×Dic73—41no—
46C2×Dic73D811yescharacteristic
47C2×Dic73D811yescharacteristic
48D292—41no—
49D292—41no—
50C8×C73#4111yescharacteristic
51C8×C73#4111yescharacteristic
52#10596831SD1612yes—
53C22×C73—81no—
54C22×C73—81no—
55C22×C73—81no—
56C22×C73C2×D811yescharacteristic
57C2×D73—81no—
58C2×D73—81no—
59C2×D73—81no—
60C4×C73—81no—
61C4×C73#12411yescharacteristic
62C4×C73C2×SD1611yescharacteristic
63Dic73—21no—
64Dic73—21no—
65Dic73—81no—
66C2×C73—161no—
67C2×C73#48611yescharacteristic
68C2×C73#50911yescharacteristic
69C2×C73#50911yescharacteristic
70D73—161no—
71#2244—731nomaximal, Sylow
72C73#224411yescharacteristic, complemented, Sylow
73#499—731no—
74#493—731no—
75#357—731no—
76#357—731no—
77#357—731no—
78#357D7311yescharacteristic, complemented
79#346—731no—
80C2×D8—731no—
81C2×D8—1461no—
82C2×D8C2×D7311yescharacteristic
83#127—1461no—
84#125—1461no—
85C2×C16—731no—
86C2×C16C2×D7311yescharacteristic
87#107—731no—
88#107C2×D7311yescharacteristic
89#106—1461no—
90C4×C8—731no—
91C2×D4—21no—
92C2×D4—2921no—
93C2×D4—2921no—
94C2×D4—1461no—
95D8—21no—
96D8—21no—
97D8—2922no—
98D8—1461no—
99D8—1461no—
100C2×C8—731no—
101C2×C8C22×D7311yescharacteristic
102C4⋊C4—21no—
103C4⋊C4—2921no—
104C4⋊C4—2921no—
105C4⋊C4—1461no—
106C42—731no—
107C16—21no—
108C16—1461no—
109C23—41no—
110C23—2921no—
111D4—41no—
112D4—41no—
113D4—2921no—
114D4—2921no—
115D4—5842no—
116D4—5842no—
117C2×C4—41no—
118C2×C4—2921no—
119C2×C4—731no—
120C2×C4—731no—
121C2×C4D4×D7311yescharacteristic
122C8—732no—
123C8#1192402711yescharacteristic
124C8#1192402811yescharacteristic
125C22—81no—
126C22—81no—
127C22—81no—
128C22—5841no—
129C22—5841no—
130C22—5841no—
131C22D8×D7311yescharacteristic
132C4—81no—
133C4—5841no—
134C4—1461no—
135C4—1461no—
136C4#1455657711yescharacteristic
137C4SD16×D7311yescharacteristic
138C2—161no—
139C2—11681no—
140C2#1798893211yescharacteristic
141C2#1798902111yescharacteristic
142C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#357×C73C2
socleC22×C73C2×D8
hypercenter#357D73
hypocenterC73#2244
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #17988988C2semidirect
3. #17988389C2semidirect
4. #17988388C2semidirect
5. #17988387C2semidirect
6. #17988362C2semidirect
7. #357×C73C2semidirect
72. C73#2244semidirect
78. #357D73semidirect