Finite Group Databasebeta

← #22611983

Subgroups — #22611983

Order 9344.

170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14556532C211yesmaximal, characteristic
3C4×D584C211yesmaximal, characteristic, complemented
4C4⋊#11924003C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988388C211yesmaximal, characteristic, complemented
7#495×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9C4×D292—21no—
10#14556534—22no—
11#14556532—22no—
12C2×#11924003C2211yescharacteristic
13C2×#11924003C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556513—21no—
16C2×Q16×C73C2211yescharacteristic
17C2×SD16×C73—21no—
18C2×D8×C73C2211yescharacteristic
19#124×C73—21no—
20C4×C8×C73C2211yescharacteristic
21C2×D292—21no—
22C2×C4×D73—41no—
23D584—21no—
24D584D412yes—
25C4⋊Dic73—21no—
26#11924005—41no—
27#11924003—21no—
28#11924003—21no—
29C2×Q8×C73—21no—
30C2×D4×C73—21no—
31Q16×C73—21no—
32Q16×C73—21no—
33SD16×C73—42no—
34D8×C73—21no—
35D8×C73—21no—
36C2×C8×C73D411yescharacteristic
37C2×C8×C73C2311yescharacteristic
38C22⋊C4×C73—41no—
39C22⋊C4×C73—41no—
40C42×C73D411yescharacteristic
41C23×C73—41no—
42C22×D73—41no—
43Q8×C73—41no—
44Q8×C73—41no—
45D4×C73—41no—
46D4×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73D811yescharacteristic
49C2×C4×C73D811yescharacteristic
50C2×C4×C73C2×D411yescharacteristic
51C2×Dic73—41no—
52D292—22no—
53D292—41no—
54C4×D73—82no—
55C8×C73—21no—
56C8×C73C2×D411yescharacteristic
57C8×C73#4111yescharacteristic
58C22×C73—81no—
59C22×C73—81no—
60C22×C73—81no—
61C22×C73C2×D811yescharacteristic
62C2×D73—42no—
63C2×D73—81no—
64C2×D73—81no—
65C4×C73—21no—
66C4×C73—21no—
67C4×C73—81no—
68C4×C73#12111yescharacteristic
69C4×C73AGL(1,ℤ/8)11yescharacteristic
70Dic73—81no—
71C2×C73—161no—
72C2×C73#45911yescharacteristic
73C2×C73#50811yescharacteristic
74C2×C73#50911yescharacteristic
75D73—82no—
76#2210—731nomaximal, Sylow
77C73#221011yescharacteristic, complemented, Sylow
78C2×SD32—731no—
79C2×D16—731no—
80#495D7311yescharacteristic, complemented
81C4×D8—731no—
82C4⋊C16—731no—
83#358—731no—
84#357—731no—
85C2×Q16C2×D7311yescharacteristic
86C2×SD16—21no—
87C2×D8—731no—
88C2×D8C2×D7311yescharacteristic
89#124—21no—
90C4×D4—1461no—
91SD32—1462no—
92D16—1462no—
93C2×C16—731no—
94C2×C16—731no—
95#107—731no—
96#102—1461no—
97C4×C8C2×D7311yescharacteristic
98C2×Q8—21no—
99C2×D4—21no—
100C2×D4—1461no—
101C22×C4—2921no—
102Q16—21no—
103Q16—21no—
104SD16—42no—
105D8—21no—
106D8—21no—
107D8—732no—
108D8—1461no—
109C2×C8C22⋊D7311yescharacteristic
110C2×C8C22×D7311yescharacteristic
111C4⋊C4—1461no—
112C22⋊C4—41no—
113C22⋊C4—41no—
114C22⋊C4—2921no—
115C42C22⋊D7311yescharacteristic
116C16—1461no—
117C16—1461no—
118C23—41no—
119C23—2921no—
120Q8—41no—
121Q8—41no—
122D4—41no—
123D4—41no—
124D4—2921no—
125D4—1462no—
126C2×C4—41no—
127C2×C4—2921no—
128C2×C4—5842no—
129C2×C4#1192401311yescharacteristic
130C2×C4#1192401311yescharacteristic
131C2×C4C2×C22⋊D7311yescharacteristic
132C8—21no—
133C8D4×D7311yescharacteristic
134C8#1192402711yescharacteristic
135C22—81no—
136C22—81no—
137C22—81no—
138C22—2922no—
139C22—5841no—
140C22—5841no—
141C22C2×#1192401311yescharacteristic
142C4—21no—
143C4—21no—
144C4—81no—
145C4—5841no—
146C4#1455656211yescharacteristic
147C4#1455661711yescharacteristic
148C2—161no—
149C2—5842no—
150C2#1798877911yescharacteristic
151C2#1798901711yescharacteristic
152C2#1798902211yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#495×C73C2
socleC22×C73C2×D8
hypercenter#495D73
hypocenterC73#2210
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14556534C2semidirect
3. C4×D584C2semidirect
4. C4⋊#11924003C2semidirect
5. #17988391C2semidirect
6. #17988388C2semidirect
7. #495×C73C2semidirect
77. C73#2210semidirect
80. #495D73semidirect