Finite Group Databasebeta

← C109×#2010 #28359264

Subgroups — C109×#2010 #28359264

Order 13952.

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×C109C211yesmaximal, characteristic, complemented
2#525×C109C212yesmaximal, complemented
3#421×C109C212yesmaximal, complemented
4#407×C109C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C109C211yesmaximal, characteristic, complemented
6C2×#41×C109C2212yes—
7C23×C4×C109C2211yescharacteristic
8#137×C109—22no—
9AGL(1,ℤ/8)×C109—22no—
10#135×C109—22no—
11C2×M16×C109C2211yescharacteristic
12C2×M16×C109C2211yescharacteristic
13#123×C109—22no—
14C22⋊Q8×C109—22no—
15#121×C109—22no—
16#120×C109—22no—
17C4×D4×C109—24no—
18#117×C109C2212yes—
19#104×C109—24no—
20C22⋊C8×C109—22no—
21C24×C109D411yescharacteristic
22#41×C109—22no—
23#41×C109—22no—
24#41×C109—22no—
25#41×C109—22no—
26C2×Q8×C109D412yescomplemented
27C2×D4×C109—24no—
28C2×D4×C109—22no—
29C2×D4×C109D412yescomplemented
30C22×C4×C109—21no—
31C22×C4×C109—22no—
32C22×C4×C109—22no—
33C22×C4×C109—22no—
34C22×C4×C109—21no—
35C22×C4×C109D411yescharacteristic
36C22×C4×C109C2311yescharacteristic
37Q16×C109—22no—
38SD16×C109—24no—
39D8×C109—22no—
40M16×C109—22no—
41M16×C109—22no—
42C2×C8×C109—21no—
43C2×C8×C109D412yescomplemented
44C4⋊C4×C109—24no—
45C4⋊C4×C109—22no—
46C22⋊C4×C109—24no—
47C22⋊C4×C109—24no—
48C22⋊C4×C109—22no—
49C42×C109D414yescomplemented
50C23×C109—22no—
51C23×C109—21no—
52C23×C109—22no—
53C23×C109—42no—
54C23×C109C2×D411yescharacteristic
55Q8×C109—22no—
56Q8×C109—22no—
57D4×C109—22no—
58D4×C109—22no—
59D4×C109—48no—
60D4×C109—42no—
61D4×C109—42no—
62C2×C4×C109—24no—
63C2×C4×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—21no—
66C2×C4×C109—41no—
67C2×C4×C109—42no—
68C2×C4×C109—42no—
69C2×C4×C109—41no—
70C2×C4×C109—42no—
71C2×C4×C109C2×D412yes—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2×D412yes—
74C2×C4×C109#4111yescharacteristic
75C8×C109—22no—
76C8×C109—41no—
77C22×C109—24no—
78C22×C109—22no—
79C22×C109—41no—
80C22×C109—42no—
81C22×C109—41no—
82C22×C109—44no—
83C22×C109—41no—
84C22×C109—42no—
85C22×C109#12012yes—
86C22×C109#12111yescharacteristic
87C4×C109—44no—
88C4×C109—41no—
89C4×C109—42no—
90C4×C109#12011yescharacteristic
91C4×C109#12112yes—
92C4×C109#12711yescharacteristic
93C2×C109—22no—
94C2×C109—21no—
95C2×C109—42no—
96C2×C109—82no—
97C2×C109#39211yescharacteristic
98#2010C10911yesmaximal, characteristic, direct product factor, Sylow
99C109#201011yescharacteristic, direct product factor, Sylow
100#575C2×C10911yescharacteristic, complemented
101#525C2×C10912yescomplemented
102#421C2×C10912yescomplemented
103#407C2×C10911yescharacteristic, complemented
104H(3,ℤ/4)C2×C10911yescharacteristic, complemented
105C2×#41C22×C10912yes—
106C23×C4C22×C10911yescharacteristic
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16C22×C10911yescharacteristic
111C2×M16C22×C10911yescharacteristic
112#123—22no—
113C22⋊Q8—22no—
114#121—22no—
115#120—22no—
116C4×D4—24no—
117#117C22×C10912yes—
118#104—24no—
119C22⋊C8—22no—
120C24D4×C10911yescharacteristic
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8D4×C10912yescomplemented
126C2×D4—24no—
127C2×D4—22no—
128C2×D4D4×C10912yescomplemented
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4D4×C10911yescharacteristic
135C22×C4C23×C10911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8D4×C10912yescomplemented
143C4⋊C4—24no—
144C4⋊C4—22no—
145C22⋊C4—24no—
146C22⋊C4—24no—
147C22⋊C4—22no—
148C42D4×C10914yescomplemented
149C23—22no—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×D4×C10911yescharacteristic
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×C10912yes—
171C2×C4C2×D4×C10911yescharacteristic
172C2×C4C2×D4×C10912yes—
173C2×C4#41×C10911yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—44no—
182C22—41no—
183C22—42no—
184C22#120×C10912yes—
185C22#121×C10911yescharacteristic
186C4—44no—
187C4—41no—
188C4—42no—
189C4#120×C10911yescharacteristic
190C4#121×C10912yes—
191C4#127×C10911yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—82no—
196C2#392×C10911yescharacteristic
subgroupG/H
centerC4×C109#127
commutator, Frattini, cosocleC22×C4C23×C109
socleC2×C109#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C109 ◁ C22×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. #575×C109C2semidirect
2. #525×C109C2semidirect
3. #421×C109C2semidirect
4. #407×C109C2semidirect
5. H(3,ℤ/4)×C109C2semidirect
26. C2×Q8×C109D4semidirect
29. C2×D4×C109D4semidirect
43. C2×C8×C109D4semidirect
49. C42×C109D4semidirect
98. #2010C109direct (N × H)
99. C109#2010direct (N × H)
100. #575C2×C109semidirect
101. #525C2×C109semidirect
102. #421C2×C109semidirect
103. #407C2×C109semidirect
104. H(3,ℤ/4)C2×C109semidirect
125. C2×Q8D4×C109semidirect
128. C2×D4D4×C109semidirect
142. C2×C8D4×C109semidirect
148. C42D4×C109semidirect

Maximal subgroups

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

subgroupindex
#575×C1092
#525×C1092
#421×C1092
#407×C1092
H(3,ℤ/4)×C1092
#2010109