Finite Group Databasebeta

← #22611908

Subgroups — #22611908

Order 9344.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#17989400C211yesmaximal, characteristic
2#17989028C211yesmaximal, characteristic, complemented
3#17988859C211yesmaximal, characteristic, complemented
4#17988403C211yesmaximal, characteristic, complemented
5#17988395C211yesmaximal, characteristic, complemented
6#17988370C211yesmaximal, characteristic, complemented
7C2×Q32×C73C211yesmaximal, characteristic, complemented
8#14556639—21no—
9#14556623—22no—
10#14556622—21no—
11#14556622—21no—
12#14556614—21no—
13#14556613C2211yescharacteristic
14Q16×D73—21no—
15#14556597C2211yescharacteristic
16#14556537—21no—
17#14556534—21no—
18#14556531C2211yescharacteristic
19#14556527C2211yescharacteristic
20#14556510—21no—
21C2×Q16×C73C2211yescharacteristic
22C2×Q16×C73C2211yescharacteristic
23Q32×C73—22no—
24C2×C16×C73C2211yescharacteristic
25#11924029—22no—
26#11924029—41no—
27#11924028—21no—
28#11924028—42no—
29#11924028D411yescharacteristic
30Q8×D73—22no—
31Q8×D73—41no—
32Dic292D411yescharacteristic
33#11924018—22no—
34#11924018—41no—
35#11924017—21no—
36#11924015—22no—
37#11924015—41no—
38D584D411yescharacteristic
39#11924012—21no—
40#11924012D411yescharacteristic
41#11924011—21no—
42C8×D73—21no—
43#11924003—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46Q16×C73—21no—
47Q16×C73—21no—
48Q16×C73—21no—
49Q16×C73D412yes—
50C2×C8×C73C2311yescharacteristic
51C16×C73—21no—
52Q8×C73—22no—
53Q8×C73—41no—
54Q8×C73—41no—
55Q8×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73C2×D411yescharacteristic
59C22⋊D73—21no—
60C22⋊D73—41no—
61D292—21no—
62D292—42no—
63D292D811yescharacteristic
64C4×D73—21no—
65C4×D73—42no—
66C4×D73—42no—
67C4×D73—41no—
68Dic146—21no—
69Dic146—42no—
70Dic146D811yescharacteristic
71C8×C73C2×D411yescharacteristic
72C8×C73C2×D411yescharacteristic
73#10596831—21no—
74#10596831—41no—
75C22×C73AGL(1,ℤ/8)11yescharacteristic
76C2×D73—21no—
77C2×D73—41no—
78C4×C73—42no—
79C4×C73—81no—
80C4×C73#12011yescharacteristic
81C4×C73C2×D811yescharacteristic
82Dic73—21no—
83Dic73—41no—
84C2×C73—21no—
85C2×C73#44711yescharacteristic
86D73—41no—
87D73—81no—
88#2195—731nomaximal, Sylow
89C73#219511yescharacteristic, complemented, Sylow
90#578—731no—
91#510—731no—
92C2×Q32D7311yescharacteristic, complemented
93#473—731no—
94#362—731no—
95#359—731no—
96#350—731no—
972−1+4—1461no—
98#137—1461no—
99#137—1461no—
100#137—1462no—
101#135—731no—
102#135—1461no—
103C2×Q16—1461no—
104C2×Q16C2×D7311yescharacteristic
105C2×Q16C2×D7311yescharacteristic
106#131—731no—
107Q32—22no—
108Q32—1461no—
109SD32—1461no—
110M32—731no—
111C2×C16C2×D7311yescharacteristic
112#108—731no—
113#101—1461no—
114#41—2922no—
115#41—2921no—
116#41—731no—
117#41—1462no—
118#41—1461no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—2921no—
122C2×Q8—1462no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—2921no—
127Q16—731no—
128Q16—1462no—
129Q16C22⋊D7312yes—
130SD16—2921no—
131SD16—1462no—
132SD16—1461no—
133D8—731no—
134M16—731no—
135M16—1461no—
136M16—1461no—
137C2×C8—1461no—
138C2×C8C22×D7311yescharacteristic
139C16—21no—
140C16—1461no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—2922no—
146Q8—731no—
147Q8—1461no—
148D4—2922no—
149D4—2921no—
150D4—731no—
151D4—1461no—
152D4—1461no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—2922no—
156C2×C4—2922no—
157C2×C4—2921no—
158C2×C4—1461no—
159C2×C4D4×D7311yescharacteristic
160C8—2921no—
161C8—1461no—
162C8D4×D7311yescharacteristic
163C8C2×C22⋊D7311yescharacteristic
164C22—2921no—
165C22—1461no—
166C22#1455661511yescharacteristic
167C4—42no—
168C4—81no—
169C4—2921no—
170C4—1461no—
171C4#1455655911yescharacteristic
172C4D8×D7311yescharacteristic
173C2—21no—
174C2—2921no—
175C2—5841no—
176C2#1798871911yescharacteristic
subgroupG/H
centerC2#17988719
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×Q32×C73C2
socleC2×C73#447
hypercenterC2×Q32D73
hypocenterC73#2195
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #17989028C2semidirect
3. #17988859C2semidirect
4. #17988403C2semidirect
5. #17988395C2semidirect
6. #17988370C2semidirect
7. C2×Q32×C73C2semidirect
89. C73#2195semidirect
92. C2×Q32D73semidirect