Finite Group Databasebeta

← #22612046

Subgroups — #22612046

Order 9344.

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

normal subgroups only

This group has 160 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×#14556531C211yesmaximal, characteristic, complemented
3#17988823C211yesmaximal, characteristic
4#17988412C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988387C211yesmaximal, characteristic, complemented
7#467×C73C211yesmaximal, characteristic, complemented
8C2×D584C2211yescharacteristic
9#14556565—21no—
10#14556534—22no—
11#14556531—22no—
12C2×#11924003C2211yescharacteristic
13C2×#11924003C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556513—21no—
16C2×Q16×C73C2211yescharacteristic
17C22×C8×C73C2211yescharacteristic
18C22⋊Q8×C73—21no—
19#107×C73C2211yescharacteristic
20#103×C73—21no—
21C2×D292—21no—
22C2×C22⋊D73—41no—
23D584—21no—
24D584—21no—
25C4⋊Dic73—21no—
26#11924005—41no—
27#11924003—21no—
28#11924003D412yescomplemented
29C2×Q8×C73—21no—
30C22×C4×C73D411yescharacteristic
31Q16×C73—21no—
32Q16×C73—21no—
33C2×C8×C73—21no—
34C2×C8×C73—21no—
35C2×C8×C73D411yescharacteristic
36C2×C8×C73C2311yescharacteristic
37C4⋊C4×C73—21no—
38C4⋊C4×C73—41no—
39C22⋊C4×C73—41no—
40C23×C73D811yescharacteristic
41C22×D73—41no—
42Q8×C73—41no—
43Q8×C73—41no—
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73D811yescharacteristic
49C2×C4×C73C2×D411yescharacteristic
50C22⋊D73—82no—
51C2×Dic73—41no—
52D292—41no—
53D292—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—81no—
66C4×C73—81no—
67C4×C73#12111yescharacteristic
68C4×C73#13511yescharacteristic
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×M32—731no—
79#467D7311yescharacteristic, complemented
80#466—731no—
81#366—731no—
82#358—731no—
83#357—731no—
84C2×Q16C2×D7311yescharacteristic
85C2×D8—731no—
86C22×C8C2×D7311yescharacteristic
87C22⋊Q8—21no—
88#121—1461no—
89SD32—1462no—
90M32—1462no—
91C2×C16—731no—
92C2×C16—731no—
93#107—731no—
94#107C2×D7311yescharacteristic
95#103—21no—
96#102—1461no—
97C2×Q8—21no—
98C2×D4—2921no—
99C2×D4—1461no—
100C22×C4C22⋊D7311yescharacteristic
101Q16—21no—
102Q16—21no—
103D8—1461no—
104D8—1461no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8C22⋊D7311yescharacteristic
108C2×C8C22×D7311yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—1461no—
112C22⋊C4—41no—
113C22⋊C4—2921no—
114C16—732no—
115C16—1461no—
116C23—2921no—
117C23#1192401311yescharacteristic
118Q8—41no—
119Q8—41no—
120D4—2921no—
121D4—2921no—
122D4—5842no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—2921no—
128C2×C4#1192401311yescharacteristic
129C2×C4C2×C22⋊D7311yescharacteristic
130C8—21no—
131C8D4×D7311yescharacteristic
132C8#1192402711yescharacteristic
133C22—21no—
134C22—21no—
135C22—21no—
136C22—5841no—
137C22—5841no—
138C22—5841no—
139C22C2×#1192401311yescharacteristic
140C4—21no—
141C4—81no—
142C4—81no—
143C4—5841no—
144C4#1455656311yescharacteristic
145C4#1455661111yescharacteristic
146C2—41no—
147C2—11681no—
148C2#1798882111yescharacteristic
149C2#1798902211yescharacteristic
150C2#1798902811yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#467×C73C2
socleC22×C73C2×D8
hypercenter#467D73
hypocenterC73#2220
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14556534C2semidirect
2. C2×#14556531C2semidirect
4. #17988412C2semidirect
5. #17988391C2semidirect
6. #17988387C2semidirect
7. #467×C73C2semidirect
28. #11924003D4semidirect
76. C73#2220semidirect
79. #467D73semidirect