Finite Group Databasebeta

← #22612001

Subgroups — #22612001

Order 9344.

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

normal subgroups only

This group has 154 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#17989030C211yesmaximal, characteristic, complemented
2#17989025C211yesmaximal, characteristic
3#17988971C211yesmaximal, characteristic, complemented
4#17988705C211yesmaximal, characteristic, complemented
5#17988404C211yesmaximal, characteristic, complemented
6#17988401C211yesmaximal, characteristic, complemented
7#364×C73C211yesmaximal, characteristic, complemented
8#14556613C2211yescharacteristic
9C2×Dic292C2211yescharacteristic
10C2×#11924017—21no—
11C2×D584C2211yescharacteristic
12#14556597—21no—
13#14556579—21no—
14Dic584—21no—
15#14556536—21no—
16#14556536—21no—
17D1168—21no—
18#14556527C2211yescharacteristic
19#14556519—21no—
20M32×C73C2211yescharacteristic
21M32×C73C2211yescharacteristic
22C4×C8×C73C2211yescharacteristic
23#11924028—21no—
24C2×Dic146—21no—
25C2×D292—21no—
26Dic292—21no—
27Dic292—21no—
28Dic292D411yescharacteristic
29#11924017—21no—
30#11924017—41no—
31#11924017—41no—
32D584—21no—
33D584—21no—
34D584D411yescharacteristic
35#11924012—21no—
36#11924011—41no—
37C8×D73—41no—
38#11924005—42no—
39C2×C8×C73D411yescharacteristic
40C2×C8×C73C2311yescharacteristic
41C42×C73D411yescharacteristic
42C16×C73—21no—
43C16×C73—21no—
44C22×D73—41no—
45C2×C4×C73—21no—
46C2×C4×C73C2×D411yescharacteristic
47C22⋊D73—41no—
48C2×Dic73—41no—
49D292—21no—
50D292—41no—
51D292—41no—
52C4×D73—41no—
53Dic146—21no—
54Dic146—41no—
55Dic146—41no—
56C8×C73D811yescharacteristic
57C8×C73D811yescharacteristic
58C8×C73C2×D411yescharacteristic
59C8×C73#4111yescharacteristic
60#10596831—41no—
61C22×C73AGL(1,ℤ/8)11yescharacteristic
62C2×D73—41no—
63C2×D73—82no—
64C2×D73—81no—
65C4×C73—41no—
66C4×C73#12111yescharacteristic
67C4×C73C2×D811yescharacteristic
68Dic73—41no—
69Dic73—81no—
70C2×C73—21no—
71C2×C73#45911yescharacteristic
72D73—81no—
73D73—161no—
74#2212—731nomaximal, Sylow
75C73#221211yescharacteristic, complemented, Sylow
76#510—731no—
77#509—731no—
78#495—731no—
79#443—731no—
80#364D7311yescharacteristic, complemented
81#362—731no—
82#361—731no—
83#135—731no—
84C2×Q16—731no—
85C2×SD16—1461no—
86C2×D8—731no—
87#131—1461no—
88#124—1461no—
89Q32—1461no—
90SD32—1461no—
91SD32—1461no—
92D16—1461no—
93M32C2×D7311yescharacteristic
94M32C2×D7311yescharacteristic
95#108—731no—
96#104—1461no—
97C4×C8C2×D7311yescharacteristic
98#41—1461no—
99C2×Q8—1461no—
100C2×D4—1461no—
101Q16—731no—
102Q16—1461no—
103Q16—1461no—
104SD16—2921no—
105SD16—2921no—
106SD16—1461no—
107D8—731no—
108D8—1461no—
109D8—1461no—
110M16—2921no—
111M16—1461no—
112C2×C8—2921no—
113C2×C8D29211yescharacteristic
114C2×C8C22×D7311yescharacteristic
115C22⋊C4—2922no—
116C42D29211yescharacteristic
117C16—21no—
118C16—21no—
119C23—2921no—
120Q8—2921no—
121Q8—2921no—
122Q8—1461no—
123D4—2921no—
124D4—2921no—
125D4—2921no—
126D4—1461no—
127C2×C4—21no—
128C2×C4—2921no—
129C2×C4—2921no—
130C2×C4C2×D29211yescharacteristic
131C8—2921no—
132C8D58411yescharacteristic
133C8D58411yescharacteristic
134C8D4×D7311yescharacteristic
135C8#1192402911yescharacteristic
136C22—2921no—
137C22—5842no—
138C22—5841no—
139C22#1455661911yescharacteristic
140C4—41no—
141C4—2921no—
142C4—5841no—
143C4#1455656611yescharacteristic
144C4C2×D58411yescharacteristic
145C2—21no—
146C2—5841no—
147C2—11681no—
148C2#1798878311yescharacteristic
subgroupG/H
centerC2#17988783
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#364×C73C2
socleC2×C73#459
hypercenter#364D73
hypocenterC73#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #17989030C2semidirect
3. #17988971C2semidirect
4. #17988705C2semidirect
5. #17988404C2semidirect
6. #17988401C2semidirect
7. #364×C73C2semidirect
75. C73#2212semidirect
80. #364D73semidirect