Finite Group Databasebeta

← #22611894

Subgroups — #22611894

Order 9344.

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

normal subgroups only

This group has 210 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, complemented
2#17989023C211yesmaximal, characteristic, complemented
3#17988854C211yesmaximal, characteristic, complemented
4#17988403C211yesmaximal, characteristic, complemented
5#17988395C211yesmaximal, characteristic, complemented
6#17988370C211yesmaximal, characteristic, complemented
7C2×SD32×C73C211yesmaximal, characteristic, complemented
8#14556639—21no—
9#14556623—22no—
10#14556622—21no—
11#14556617—21no—
12#14556614—21no—
13#14556613C2211yescharacteristic
14Q16×D73—21no—
15#14556597C2211yescharacteristic
16#14556535—21no—
17#14556532—21no—
18#14556531C2211yescharacteristic
19#14556527C2211yescharacteristic
20#14556508—21no—
21C2×Q16×C73C2211yescharacteristic
22C2×D8×C73C2211yescharacteristic
23SD32×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#11924017—21no—
35#11924016—41no—
36#11924015—22no—
37D584D411yescharacteristic
38#11924013—41no—
39#11924012—21no—
40#11924012D411yescharacteristic
41#11924011—21no—
42C8×D73—21no—
43#11924003—21no—
44C2×Q8×C73—21no—
45C2×D4×C73—21no—
46Q16×C73—21no—
47Q16×C73D412yes—
48D8×C73—21no—
49D8×C73—21no—
50C2×C8×C73C2311yescharacteristic
51C16×C73—21no—
52C23×C73—41no—
53Q8×C73—22no—
54Q8×C73—41no—
55D4×C73—41no—
56D4×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×C73—81no—
76C22×C73—161no—
77C22×C73AGL(1,ℤ/8)11yescharacteristic
78C2×D73—21no—
79C2×D73—41no—
80C4×C73—42no—
81C4×C73#12011yescharacteristic
82C4×C73C2×D811yescharacteristic
83Dic73—21no—
84Dic73—41no—
85C2×C73—21no—
86C2×C73—161no—
87C2×C73#44711yescharacteristic
88D73—41no—
89D73—81no—
90#2193—731nomaximal, Sylow
91C73#219311yescharacteristic, complemented, Sylow
92#578—731no—
93#509—731no—
94C2×SD32D7311yescharacteristic, complemented
95#472—731no—
96#362—731no—
97#359—731no—
98#350—731no—
992−1+4—1461no—
100#137—1461no—
101#137—1462no—
102AGL(1,ℤ/8)—1461no—
103#135—731no—
104#135—1461no—
105C2×Q16—1461no—
106C2×Q16C2×D7311yescharacteristic
107C2×D8C2×D7311yescharacteristic
108#131—731no—
109SD32—22no—
110SD32—1461no—
111D16—1461no—
112M32—731no—
113C2×C16C2×D7311yescharacteristic
114#108—731no—
115#100—1461no—
116#41—2922no—
117#41—2921no—
118#41—731no—
119#41—1462no—
120#41—1461no—
121C2×Q8—21no—
122C2×Q8—2921no—
123C2×Q8—1462no—
124C2×D4—21no—
125Q16—21no—
126Q16—731no—
127Q16—1462no—
128Q16C22⋊D7312yes—
129SD16—2921no—
130SD16—1462no—
131SD16—1461no—
132D8—21no—
133D8—21no—
134D8—2921no—
135D8—731no—
136M16—731no—
137M16—1461no—
138M16—1461no—
139C2×C8—1461no—
140C2×C8C22×D7311yescharacteristic
141C16—21no—
142C16—1461no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—2922no—
147Q8—731no—
148Q8—1461no—
149D4—41no—
150D4—41no—
151D4—2922no—
152D4—2921no—
153D4—731no—
154D4—1461no—
155D4—1461no—
156C2×C4—41no—
157C2×C4—2922no—
158C2×C4—2922no—
159C2×C4—2921no—
160C2×C4—1461no—
161C2×C4D4×D7311yescharacteristic
162C8—2921no—
163C8—1461no—
164C8D4×D7311yescharacteristic
165C8C2×C22⋊D7311yescharacteristic
166C22—81no—
167C22—161no—
168C22—2921no—
169C22—1461no—
170C22#1455661511yescharacteristic
171C4—42no—
172C4—2921no—
173C4—1461no—
174C4#1455655911yescharacteristic
175C4D8×D7311yescharacteristic
176C2—21no—
177C2—161no—
178C2—2921no—
179C2—5841no—
180C2#1798871911yescharacteristic
subgroupG/H
centerC2#17988719
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×SD32×C73C2
socleC2×C73#447
hypercenterC2×SD32D73
hypocenterC73#2193
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #17989400C2semidirect
2. #17989023C2semidirect
3. #17988854C2semidirect
4. #17988403C2semidirect
5. #17988395C2semidirect
6. #17988370C2semidirect
7. C2×SD32×C73C2semidirect
91. C73#2193semidirect
94. C2×SD32D73semidirect