Finite Group Databasebeta

← #22612038

Subgroups — #22612038

Order 9344.

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

normal subgroups only

This group has 150 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
1C2×#14556537C211yesmaximal, characteristic, complemented
2C2×#14556530C211yesmaximal, characteristic
3#17988829C211yesmaximal, characteristic
4#17988825C211yesmaximal, characteristic
5#17988414C211yesmaximal, characteristic, complemented
6#17988392C211yesmaximal, characteristic, complemented
7#358×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×C8×D73C2211yescharacteristic
10#14556571—21no—
11#14556567—21no—
12#14556537—22no—
13#14556530—22no—
14C2×#11924003C2211yescharacteristic
15#14556525C2211yescharacteristic
16#14556515—21no—
17#14556514—21no—
18C2×Q16×C73C2211yescharacteristic
19C2×C16×C73C2211yescharacteristic
20#107×C73C2211yescharacteristic
21C2×Dic146—21no—
22C2×C4×D73D411yescharacteristic
23Dic292—21no—
24Dic292—21no—
25C2×#10596831D411yescharacteristic
26C8×D73—21no—
27C8×D73—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—41no—
30#11924007—41no—
31#11924005—41no—
32#11924005—41no—
33#11924003D412yes—
34C2×Q8×C73—21no—
35Q16×C73—21no—
36Q16×C73—21no—
37C2×C8×C73C2311yescharacteristic
38C4⋊C4×C73—21no—
39C16×C73—21no—
40C22×D73D811yescharacteristic
41Q8×C73—41no—
42Q8×C73—41no—
43C2×C4×C73—41no—
44C2×C4×C73—41no—
45C2×C4×C73C2×D411yescharacteristic
46C2×Dic73—41no—
47C2×Dic73—41no—
48C2×Dic73D811yescharacteristic
49C4×D73—21no—
50C4×D73—21no—
51Dic146—41no—
52Dic146—41no—
53C8×C73C2×D411yescharacteristic
54C8×C73#4111yescharacteristic
55#10596831—21no—
56C22×C73C2×D811yescharacteristic
57C2×D73—21no—
58C2×D73—21no—
59C2×D73—21no—
60C4×C73—81no—
61C4×C73—81no—
62C4×C73#12111yescharacteristic
63C4×C73#13511yescharacteristic
64Dic73—21no—
65Dic73—81no—
66Dic73—81no—
67C2×C73#46611yescharacteristic
68C2×C73#51011yescharacteristic
69C2×C73#51011yescharacteristic
70D73—41no—
71#2219—731nomaximal, Sylow
72C73#221911yescharacteristic, complemented, Sylow
73C2×Q32—731no—
74C2×M32—731no—
75#467—731no—
76#467—731no—
77#367—731no—
78#358—731no—
79#358D7311yescharacteristic, complemented
80C2×Q16—731no—
81C2×Q16C2×D7311yescharacteristic
82C22×C8—731no—
83C22⋊Q8—1461no—
84C22⋊Q8—1461no—
85Q32—1462no—
86M32—1462no—
87C2×C16—731no—
88C2×C16C2×D7311yescharacteristic
89#107—731no—
90#107C2×D7311yescharacteristic
91#103—1461no—
92#103—1461no—
93C2×Q8—21no—
94C2×Q8—1461no—
95C22×C4—731no—
96Q16—21no—
97Q16—21no—
98Q16—1461no—
99Q16—1461no—
100C2×C8—731no—
101C2×C8—1461no—
102C2×C8—1461no—
103C2×C8C22×D7311yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—2921no—
106C4⋊C4—2921no—
107C4⋊C4—1461no—
108C22⋊C4—2921no—
109C22⋊C4—2921no—
110C16—21no—
111C16—732no—
112C23—731no—
113Q8—41no—
114Q8—41no—
115Q8—2921no—
116Q8—2921no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—2921no—
120C2×C4—2921no—
121C2×C4—731no—
122C2×C4—1461no—
123C2×C4—1461no—
124C2×C4D4×D7311yescharacteristic
125C8—1461no—
126C8D4×D7311yescharacteristic
127C8#1192402811yescharacteristic
128C22—1461no—
129C22—1461no—
130C22—1461no—
131C22D8×D7311yescharacteristic
132C4—81no—
133C4—81no—
134C4—5841no—
135C4—5841no—
136C4—1461no—
137C4#1455656411yescharacteristic
138C4#1455661211yescharacteristic
139C2—2921no—
140C2#1798882211yescharacteristic
141C2#1798902611yescharacteristic
142C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73#2219
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#14556537C2semidirect
5. #17988414C2semidirect
6. #17988392C2semidirect
7. #358×C73C2semidirect
72. C73#2219semidirect
79. #358D73semidirect