Finite Group Databasebeta

← #358×D73 #22611631

Subgroups — #358×D73 #22611631

Order 9344.

232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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×Q16×D73C211yesmaximal, characteristic
2C2×C16×D73C211yesmaximal, characteristic
3#107×D73C211yesmaximal, characteristic
4#17988392C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988390C211yesmaximal, characteristic, complemented
7#358×C73C211yesmaximal, characteristic, complemented
8C2×Q8×D73—21no—
9C2×Dic292C2211yescharacteristic
10C2×#11924018—21no—
11Q16×D73—22no—
12Q16×D73C414yescomplemented
13C2×C8×D73C2211yescharacteristic
14C4⋊C4×D73—21no—
15C2×#11924003C2211yescharacteristic
16C16×D73—22no—
17#14556525C2211yescharacteristic
18#14556524—21no—
19C2×Q16×C73C2211yescharacteristic
20C2×C16×C73C2211yescharacteristic
21#107×C73C2211yescharacteristic
22C2×Dic146—21no—
23C2×Dic146—41no—
24Q8×D73—24no—
25Q8×D73—42no—
26C2×C4×D73—41no—
27C2×C4×D73—41no—
28C2×C4×D73D411yescharacteristic
29Dic292—21no—
30Dic292C2×C412yescomplemented
31#11924018—24no—
32C2×#10596831D411yescharacteristic
33C8×D73C2×C412yes—
34C8×D73D412yes—
35C4⋊Dic73—21no—
36#11924007—41no—
37#11924003—21no—
38C2×Q8×C73—21no—
39Q16×C73—21no—
40Q16×C73C2×C412yescomplemented
41C2×C8×C73C2311yescharacteristic
42C4⋊C4×C73—21no—
43C16×C73—21no—
44C22×D73D811yescharacteristic
45Q8×C73—22no—
46Q8×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73—41no—
49C2×C4×C73C2×D411yescharacteristic
50C2×Dic73—41no—
51C2×Dic73—41no—
52C2×Dic73D811yescharacteristic
53C4×D73—44no—
54C4×D73—82no—
55C4×D73C22⋊C412yes—
56C4×D73SD1612yes—
57Dic146—22no—
58Dic146—41no—
59Dic146—44no—
60C8×C73C22×C411yescharacteristic
61C8×C73C2×D411yescharacteristic
62#10596831C22⋊C412yes—
63C22×C73C2×D811yescharacteristic
64C2×D73#10212yes—
65C2×D73SD3212yes—
66C2×D73Q3212yes—
67C4×C73—42no—
68C4×C73—81no—
69C4×C73C2×C22⋊C411yescharacteristic
70C4×C73C2×SD1611yescharacteristic
71Dic73—42no—
72Dic73—81no—
73Dic73#10212yes—
74C2×C73C2×#10211yescharacteristic
75C2×C73C2×SD3211yescharacteristic
76C2×C73C2×Q3211yescharacteristic
77D73#35814yesdirect product factor
78C2×#358—731nomaximal, Sylow
79C73C2×#35811yescharacteristic, complemented, Sylow
80C22×Q16—731no—
81C22×C16—731no—
82C2×#107—731no—
83#358—731no—
84#358—731no—
85#358—731no—
86#358D7311yescharacteristic, direct product factor
87C22×Q8—1461no—
88C2×Q16—734no—
89C2×Q16—731no—
90C2×Q16—1462no—
91C2×Q16—1461no—
92C2×Q16C2×D7311yescharacteristic
93C22×C8—731no—
94C2×C4⋊C4—1461no—
95C2×C16—731no—
96C2×C16—1462no—
97C2×C16C2×D7311yescharacteristic
98#107—731no—
99#107—1461no—
100#107C2×D7311yescharacteristic
101C2×Q8—21no—
102C2×Q8—2921no—
103C2×Q8—2922no—
104C2×Q8—1464no—
105C2×Q8—1461no—
106C22×C4—2921no—
107C22×C4—2921no—
108C22×C4—731no—
109Q16—21no—
110Q16—732no—
111Q16—1464no—
112Q16—1461no—
113Q16C4×D7312yescomplemented
114C2×C8—731no—
115C2×C8—732no—
116C2×C8—732no—
117C2×C8C22×D7311yescharacteristic
118C4⋊C4—21no—
119C4⋊C4—2921no—
120C4⋊C4—1461no—
121C16—21no—
122C16—1461no—
123C23—731no—
124Q8—22no—
125Q8—41no—
126Q8—2924no—
127Q8—2921no—
128Q8—1462no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—2924no—
132C2×C4—2921no—
133C2×C4—2921no—
134C2×C4—5842no—
135C2×C4—731no—
136C2×C4—732no—
137C2×C4—732no—
138C2×C4D4×D7311yescharacteristic
139C8—732no—
140C8C2×C4×D7311yescharacteristic
141C8D4×D7311yescharacteristic
142C22—732no—
143C22—732no—
144C22—732no—
145C22D8×D7311yescharacteristic
146C4—42no—
147C4—81no—
148C4—2922no—
149C4—5841no—
150C4—732no—
151C4C22⋊C4×D7311yescharacteristic
152C4SD16×D7311yescharacteristic
153C2—734no—
154C2#102×D7311yescharacteristic
155C2SD32×D7311yescharacteristic
156C2Q32×D7311yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73C2×#358
LCSG ▷ 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
4. #17988392C2semidirect
5. #17988391C2semidirect
6. #17988390C2semidirect
7. #358×C73C2semidirect
12. Q16×D73C4semidirect
30. Dic292C2×C4semidirect
40. Q16×C73C2×C4semidirect
77. D73#358direct (N × H)
79. C73C2×#358semidirect
86. #358D73direct (N × H)
113. Q16C4×D73semidirect