Finite Group Databasebeta

← #22612044

Subgroups — #22612044

Order 9344.

160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14556536C211yesmaximal, characteristic, complemented
2#17988828C211yesmaximal, characteristic, complemented
3#17988823C211yesmaximal, characteristic
4#17988413C211yesmaximal, characteristic, complemented
5#17988392C211yesmaximal, characteristic, complemented
6#17988389C211yesmaximal, characteristic, complemented
7C2×M32×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×D584C2211yescharacteristic
10#14556570—21no—
11#14556565—21no—
12#14556536—22no—
13#14556525C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556516—21no—
16#14556513—21no—
17C22×C8×C73C2211yescharacteristic
18M32×C73—22no—
19C2×C16×C73C2211yescharacteristic
20C2×C16×C73C2211yescharacteristic
21C2×Dic146—21no—
22C2×D292—21no—
23C2×C22⋊D73—41no—
24Dic292—21no—
25Dic292—21no—
26D584—21no—
27D584—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30#11924007—41no—
31C22⋊Dic73—41no—
32#11924005—41no—
33C22×C4×C73D411yescharacteristic
34C2×C8×C73—21no—
35C2×C8×C73—21no—
36C2×C8×C73D411yescharacteristic
37C2×C8×C73C2311yescharacteristic
38C16×C73—21no—
39C16×C73D412yescomplemented
40C23×C73D811yescharacteristic
41C22×D73—41no—
42C2×C4×C73—21no—
43C2×C4×C73—21no—
44C2×C4×C73D811yescharacteristic
45C2×C4×C73C2×D411yescharacteristic
46C22⋊D73—82no—
47C2×Dic73—41no—
48C2×Dic73—41no—
49C2×Dic73—41no—
50D292—41no—
51D292—41no—
52Dic146—41no—
53Dic146—41no—
54C8×C73—21no—
55C8×C73C2×D411yescharacteristic
56C8×C73#4111yescharacteristic
57C22×C73—21no—
58C22×C73—21no—
59C22×C73—21no—
60C22×C73C2×D811yescharacteristic
61C2×D73—81no—
62C2×D73—81no—
63C2×D73—81no—
64C4×C73—21no—
65C4×C73#12111yescharacteristic
66C4×C73#13511yescharacteristic
67Dic73—81no—
68Dic73—81no—
69Dic73—81no—
70C2×C73—41no—
71C2×C73#46611yescharacteristic
72C2×C73#50911yescharacteristic
73C2×C73#51011yescharacteristic
74D73—161no—
75#2220—731nomaximal, Sylow
76C73#222011yescharacteristic, complemented, Sylow
77C2×SD32—731no—
78C2×M32D7311yescharacteristic, complemented
79#467—731no—
80#466—731no—
81#366—731no—
82#358—731no—
83#357—731no—
84C2×Q16—731no—
85C2×D8—731no—
86C22×C8C2×D7311yescharacteristic
87C22⋊Q8—1461no—
88#121—1461no—
89SD32—1462no—
90M32—22no—
91C2×C16C2×D7311yescharacteristic
92C2×C16C2×D7311yescharacteristic
93#107—731no—
94#107—731no—
95#103—1461no—
96#102—1461no—
97C2×Q8—1461no—
98C2×D4—2921no—
99C2×D4—1461no—
100C22×C4D29211yescharacteristic
101Q16—1461no—
102Q16—1461no—
103D8—1461no—
104D8—1461no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8D29211yescharacteristic
108C2×C8C22×D7311yescharacteristic
109C4⋊C4—2921no—
110C4⋊C4—1461no—
111C4⋊C4—1461no—
112C22⋊C4—2921no—
113C22⋊C4—2921no—
114C16—21no—
115C16C22⋊D7312yescomplemented
116C23—2921no—
117C23D58411yescharacteristic
118Q8—2921no—
119Q8—2921no—
120D4—2921no—
121D4—2921no—
122D4—5842no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—2921no—
126C2×C4—2921no—
127C2×C4—2921no—
128C2×C4D58411yescharacteristic
129C2×C4C2×D29211yescharacteristic
130C8—21no—
131C8C2×C22⋊D7311yescharacteristic
132C8#1192402811yescharacteristic
133C22—21no—
134C22—21no—
135C22—21no—
136C22—5841no—
137C22—5841no—
138C22—5841no—
139C22C2×D58411yescharacteristic
140C4—21no—
141C4—5841no—
142C4—5841no—
143C4—5841no—
144C4#1455656511yescharacteristic
145C4#1455661311yescharacteristic
146C2—41no—
147C2—11681no—
148C2#1798882311yescharacteristic
149C2#1798902511yescharacteristic
150C2#1798903011yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×M32×C73C2
socleC22×C73C2×D8
hypercenterC2×M32D73
hypocenterC73#2220
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
1. C2×#14556536C2semidirect
2. #17988828C2semidirect
4. #17988413C2semidirect
5. #17988392C2semidirect
6. #17988389C2semidirect
7. C2×M32×C73C2semidirect
39. C16×C73D4semidirect
76. C73#2220semidirect
78. C2×M32D73semidirect
115. C16C22⋊D73semidirect