Finite Group Databasebeta

← #2010×C173 #36349795

Subgroups — #2010×C173 #36349795

Order 22144.

394 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 88 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#575×C173C211yesmaximal, characteristic, complemented
2#525×C173C212yesmaximal, complemented
3#421×C173C212yesmaximal, complemented
4#407×C173C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C173C211yesmaximal, characteristic, complemented
6C2×#41×C173C2212yes—
7C23×C4×C173C2211yescharacteristic
8#137×C173—22no—
9AGL(1,ℤ/8)×C173—22no—
10#135×C173—22no—
11C2×M16×C173C2211yescharacteristic
12C2×M16×C173C2211yescharacteristic
13#123×C173—22no—
14C22⋊Q8×C173—22no—
15#121×C173—22no—
16#120×C173—22no—
17C4×D4×C173—24no—
18#117×C173C2212yes—
19#104×C173—24no—
20C22⋊C8×C173—22no—
21C24×C173D411yescharacteristic
22#41×C173—22no—
23#41×C173—22no—
24#41×C173—22no—
25#41×C173—22no—
26C2×Q8×C173D412yescomplemented
27C2×D4×C173—24no—
28C2×D4×C173—22no—
29C2×D4×C173D412yescomplemented
30C22×C4×C173—21no—
31C22×C4×C173—22no—
32C22×C4×C173—22no—
33C22×C4×C173—22no—
34C22×C4×C173—21no—
35C22×C4×C173D411yescharacteristic
36C22×C4×C173C2311yescharacteristic
37Q16×C173—22no—
38SD16×C173—24no—
39D8×C173—22no—
40M16×C173—22no—
41M16×C173—22no—
42C2×C8×C173—21no—
43C2×C8×C173D412yescomplemented
44C4⋊C4×C173—24no—
45C4⋊C4×C173—22no—
46C22⋊C4×C173—24no—
47C22⋊C4×C173—24no—
48C22⋊C4×C173—22no—
49C42×C173D414yescomplemented
50C23×C173—22no—
51C23×C173—21no—
52C23×C173—22no—
53C23×C173—42no—
54C23×C173C2×D411yescharacteristic
55Q8×C173—22no—
56Q8×C173—22no—
57D4×C173—22no—
58D4×C173—22no—
59D4×C173—48no—
60D4×C173—42no—
61D4×C173—42no—
62C2×C4×C173—24no—
63C2×C4×C173—22no—
64C2×C4×C173—22no—
65C2×C4×C173—21no—
66C2×C4×C173—41no—
67C2×C4×C173—42no—
68C2×C4×C173—42no—
69C2×C4×C173—41no—
70C2×C4×C173—42no—
71C2×C4×C173C2×D412yes—
72C2×C4×C173C2×D411yescharacteristic
73C2×C4×C173C2×D412yes—
74C2×C4×C173#4111yescharacteristic
75C8×C173—22no—
76C8×C173—41no—
77C22×C173—24no—
78C22×C173—22no—
79C22×C173—41no—
80C22×C173—42no—
81C22×C173—41no—
82C22×C173—44no—
83C22×C173—41no—
84C22×C173—42no—
85C22×C173#12012yes—
86C22×C173#12111yescharacteristic
87C4×C173—44no—
88C4×C173—41no—
89C4×C173—42no—
90C4×C173#12011yescharacteristic
91C4×C173#12112yes—
92C4×C173#12711yescharacteristic
93C2×C173—22no—
94C2×C173—21no—
95C2×C173—42no—
96C2×C173—82no—
97C2×C173#39211yescharacteristic
98C173#201011yescharacteristic, direct product factor, Sylow
99#2010C17311yesmaximal, characteristic, direct product factor, Sylow
100#575C2×C17311yescharacteristic, complemented
101#525C2×C17312yescomplemented
102#421C2×C17312yescomplemented
103#407C2×C17311yescharacteristic, complemented
104H(3,ℤ/4)C2×C17311yescharacteristic, complemented
105C2×#41C22×C17312yes—
106C23×C4C22×C17311yescharacteristic
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16C22×C17311yescharacteristic
111C2×M16C22×C17311yescharacteristic
112#123—22no—
113C22⋊Q8—22no—
114#121—22no—
115#120—22no—
116C4×D4—24no—
117#117C22×C17312yes—
118#104—24no—
119C22⋊C8—22no—
120C24D4×C17311yescharacteristic
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8D4×C17312yescomplemented
126C2×D4—24no—
127C2×D4—22no—
128C2×D4D4×C17312yescomplemented
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4D4×C17311yescharacteristic
135C22×C4C23×C17311yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8D4×C17312yescomplemented
143C4⋊C4—24no—
144C4⋊C4—22no—
145C22⋊C4—24no—
146C22⋊C4—24no—
147C22⋊C4—22no—
148C42D4×C17314yescomplemented
149C23—22no—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×D4×C17311yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—48no—
159D4—42no—
160D4—42no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4C2×D4×C17312yes—
171C2×C4C2×D4×C17311yescharacteristic
172C2×C4C2×D4×C17312yes—
173C2×C4#41×C17311yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—44no—
182C22—41no—
183C22—42no—
184C22#120×C17312yes—
185C22#121×C17311yescharacteristic
186C4—44no—
187C4—41no—
188C4—42no—
189C4#120×C17311yescharacteristic
190C4#121×C17312yes—
191C4#127×C17311yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—82no—
196C2#392×C17311yescharacteristic
subgroupG/H
centerC4×C173#127
commutator, Frattini, cosocleC22×C4C23×C173
socleC2×C173#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C173 ◁ C22×C4×C173 ◁ G

Complements

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

NH ≅ G/Ntype
1. #575×C173C2semidirect
2. #525×C173C2semidirect
3. #421×C173C2semidirect
4. #407×C173C2semidirect
5. H(3,ℤ/4)×C173C2semidirect
26. C2×Q8×C173D4semidirect
29. C2×D4×C173D4semidirect
43. C2×C8×C173D4semidirect
49. C42×C173D4semidirect
98. C173#2010direct (N × H)
99. #2010C173direct (N × H)
100. #575C2×C173semidirect
101. #525C2×C173semidirect
102. #421C2×C173semidirect
103. #407C2×C173semidirect
104. H(3,ℤ/4)C2×C173semidirect
125. C2×Q8D4×C173semidirect
128. C2×D4D4×C173semidirect
142. C2×C8D4×C173semidirect
148. C42D4×C173semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#575×C1732
#525×C1732
#421×C1732
#407×C1732
H(3,ℤ/4)×C1732
#2010173