Finite Group Databasebeta

← #22626214

Subgroups — #22626214

Order 9344.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#17989568C212yesmaximal
2#17989494C212yesmaximal, complemented
3#17989493C212yesmaximal, complemented
4#17989162C211yesmaximal, characteristic
5#14556670—22no—
6#14556650—22no—
7#14556650C2214yes—
8C2×#11924029C2211yescharacteristic
9C2×Q8×D73C411yescharacteristic, complemented
10#14556589C411yescharacteristic, complemented
11#14556580C2211yescharacteristic
12#14556579C2211yescharacteristic
13#14556576—22no—
14#14556569—22no—
15#14556548C411yescharacteristic, complemented
16C4⋊Q8×C73C411yescharacteristic, complemented
17C4⋊#64408—42no—
18C22⋊#64408—24no—
19C4×#64408—42no—
20#11924029—42no—
21C2×Dic146—21no—
22C2×Dic146C2×C411yescharacteristic
23Q8×D73—42no—
24C2×D292D412yes—
25C2×D292C2311yescharacteristic
26C2×C4×D73—21no—
27C2×C4×D73C2×C411yescharacteristic
28C2×C4×D73D412yes—
29#11924007—22no—
30#11924007—21no—
31#11924005—21no—
32#11924005—22no—
33#11924005—22no—
34C4×Dic73C2×C411yescharacteristic
35C2×Q8×C73C2×C411yescharacteristic
36C2×Q8×C73C2×C411yescharacteristic
37C4⋊C4×C73—22no—
38C42×C73C2×C411yescharacteristic
39C22×D73C22⋊C411yescharacteristic
40C22×D73C2×D412yes—
41C2×#64408—44no—
42Q8×C73—41no—
43Q8×C73—41no—
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73C22⋊C412yes—
47C2×C4×C73C22×C411yescharacteristic
48C2×Dic73—21no—
49C2×Dic73—21no—
50C2×Dic73C22⋊C411yescharacteristic
51D292—42no—
52D292—41no—
53C4×D73—22no—
54C4×D73—22no—
55C4×D73—22no—
56C4×D73—42no—
57Dic146—42no—
58Dic146—41no—
59C22×C73C2×C22⋊C411yescharacteristic
60C2×D73—21no—
61C2×D73—22no—
62C2×D73—41no—
63C2×D73—42no—
64#64408—84no—
65C4×C73—21no—
66C4×C73—22no—
67C4×C73—41no—
68C4×C73—41no—
69Dic73—41no—
70Dic73—41no—
71Dic73#9912yes—
72C2×C73—21no—
73C2×C73C2×#9911yescharacteristic
74D73—42no—
75D73—41no—
76#2129—731nomaximal, Sylow
77C73#212911yescharacteristic, complemented, Sylow
78#536—731no—
79#410—732no—
80#354—732no—
81#354—732no—
82C2×#41—731no—
83C22×Q8—731no—
84C4⋊Q8—731no—
85C4⋊Q8#6440811yescharacteristic, complemented
86#124—731no—
87#124—731no—
88#123—1462no—
89C22⋊Q8—1462no—
90#117—731no—
91#117—1462no—
92#99—734no—
93#99—1462no—
94#41—2922no—
95C2×Q8—2922no—
96C2×Q8—731no—
97C2×Q8—1461no—
98C2×Q8C2×#6440811yescharacteristic
99C2×Q8C2×#6440811yescharacteristic
100C2×D4—732no—
101C2×D4—731no—
102C22×C4—732no—
103C22×C4—731no—
104C22×C4—1461no—
105C4⋊C4—22no—
106C4⋊C4—2922no—
107C4⋊C4—1461no—
108C4⋊C4—1462no—
109C22⋊C4—1461no—
110C22⋊C4—1462no—
111C22⋊C4—1462no—
112C22⋊C4—1464no—
113C42—2922no—
114C42—731no—
115C42C2×#6440811yescharacteristic
116C23—732no—
117C23—731no—
118Q8—41no—
119Q8—41no—
120Q8—2921no—
121Q8—2922no—
122D4—2922no—
123D4—2921no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—2922no—
127C2×C4—2924no—
128C2×C4—731no—
129C2×C4—1462no—
130C2×C4—1462no—
131C2×C4—1462no—
132C2×C4—1461no—
133C2×C4—1461no—
134C2×C4C22⋊#6440812yes—
135C2×C4C22×#6440811yescharacteristic
136C22—2922no—
137C22—2921no—
138C22—1462no—
139C22—1461no—
140C22C2×C22⋊#6440811yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—2921no—
146C4—2921no—
147C4—5844no—
148C4—732no—
149C2—21no—
150C2—2922no—
151C2—2921no—
152C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊Q8×C73C4
socleC2×C73C2×#99
hypercenterC4⋊Q8#64408
hypocenterC73#2129
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17989494C2semidirect
3. #17989493C2semidirect
9. C2×Q8×D73C4semidirect
10. #14556589C4semidirect
15. #14556548C4semidirect
16. C4⋊Q8×C73C4semidirect
77. C73#2129semidirect
85. C4⋊Q8#64408semidirect