Finite Group Databasebeta

← #22611989

Subgroups — #22611989

Order 9344.

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

normal subgroups only

This group has 170 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×#14556534C211yesmaximal, characteristic, complemented
2C2×D1168C211yesmaximal, characteristic
3#17988972C211yesmaximal, characteristic, complemented
4#17988669C211yesmaximal, characteristic, complemented
5#17988405C211yesmaximal, characteristic, complemented
6#17988387C211yesmaximal, characteristic, complemented
7#358×C73C211yesmaximal, characteristic, complemented
8C2×#11924015—21no—
9C2×D584C2211yescharacteristic
10C2×D584C2211yescharacteristic
11#14556580—21no—
12#14556553—21no—
13#14556534—22no—
14D1168—22no—
15C2×#11924003C2211yescharacteristic
16#14556511—21no—
17C8×Dic73C2211yescharacteristic
18C2×Q16×C73C2211yescharacteristic
19C2×C16×C73C2211yescharacteristic
20#107×C73C2211yescharacteristic
21C2×D292—21no—
22C2×D292—21no—
23C2×C4×D73—41no—
24#11924015—42no—
25D584—21no—
26D584—21no—
27D584—21no—
28D584D412yes—
29C2×#10596831D411yescharacteristic
30#11924005—41no—
31#11924005—41no—
32#11924005—41no—
33C4×Dic73D411yescharacteristic
34#11924003—21no—
35C2×Q8×C73—21no—
36Q16×C73—21no—
37Q16×C73—21no—
38C2×C8×C73C2311yescharacteristic
39C4⋊C4×C73—21no—
40C16×C73—21no—
41C22×D73—41no—
42C22×D73—41no—
43Q8×C73—41no—
44Q8×C73—41no—
45C2×C4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73C2×D411yescharacteristic
48C2×Dic73D811yescharacteristic
49C2×Dic73D811yescharacteristic
50D292—22no—
51D292—41no—
52D292—41no—
53D292—41no—
54C4×D73—82no—
55C8×C73C2×D411yescharacteristic
56C8×C73#4111yescharacteristic
57#10596831—21no—
58C22×C73C2×D811yescharacteristic
59C2×D73—42no—
60C2×D73—81no—
61C2×D73—81no—
62C2×D73—81no—
63C2×D73—81no—
64C2×D73—81no—
65C4×C73—81no—
66C4×C73—81no—
67C4×C73#12111yescharacteristic
68C4×C73AGL(1,ℤ/8)11yescharacteristic
69Dic73—21no—
70Dic73—21no—
71C2×C73#45911yescharacteristic
72C2×C73#50811yescharacteristic
73C2×C73#50911yescharacteristic
74D73—82no—
75D73—161no—
76#2210—731nomaximal, Sylow
77C73#221011yescharacteristic, complemented, Sylow
78C2×SD32—731no—
79C2×D16—731no—
80#495—731no—
81C4×D8—731no—
82C4⋊C16—731no—
83#358D7311yescharacteristic, complemented
84#357—731no—
85C2×Q16C2×D7311yescharacteristic
86C2×SD16—1461no—
87C2×D8—731no—
88C2×D8—731no—
89#124—1461no—
90C4×D4—1461no—
91SD32—1462no—
92D16—1462no—
93C2×C16—731no—
94C2×C16C2×D7311yescharacteristic
95#107C2×D7311yescharacteristic
96#102—1461no—
97C4×C8—731no—
98C2×Q8—21no—
99C2×D4—1461no—
100C2×D4—1461no—
101C22×C4—2921no—
102Q16—21no—
103Q16—21no—
104SD16—2922no—
105D8—732no—
106D8—1461no—
107D8—1461no—
108D8—1461no—
109C2×C8—731no—
110C2×C8C22×D7311yescharacteristic
111C4⋊C4—21no—
112C22⋊C4—2921no—
113C22⋊C4—2921no—
114C22⋊C4—2921no—
115C42—731no—
116C16—21no—
117C16—1461no—
118C23—2921no—
119C23—2921no—
120Q8—41no—
121Q8—41no—
122D4—2921no—
123D4—2921no—
124D4—2921no—
125D4—1462no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—5842no—
129C2×C4—731no—
130C2×C4—731no—
131C2×C4D4×D7311yescharacteristic
132C8—1461no—
133C8D4×D7311yescharacteristic
134C8#1192402811yescharacteristic
135C22—2922no—
136C22—5841no—
137C22—5841no—
138C22—5841no—
139C22—5841no—
140C22—5841no—
141C22D8×D7311yescharacteristic
142C4—81no—
143C4—81no—
144C4—1461no—
145C4—1461no—
146C4#1455656411yescharacteristic
147C4#1455661811yescharacteristic
148C2—5842no—
149C2—11681no—
150C2#1798878111yescharacteristic
151C2#1798902011yescharacteristic
152C2#1798902411yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73#2210
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×#14556534C2semidirect
3. #17988972C2semidirect
4. #17988669C2semidirect
5. #17988405C2semidirect
6. #17988387C2semidirect
7. #358×C73C2semidirect
77. C73#2210semidirect
83. #358D73semidirect