Finite Group Databasebeta

← C109×#2403 #28359657

Subgroups — C109×#2403 #28359657

Order 13952.

1564 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 280 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
1C23×D4×C109C212yesmaximal, complemented
2C2×#120×C109C214yesmaximal, complemented
3#392×C109C214yesmaximal, complemented
4#386×C109C214yesmaximal, complemented
5#379×C109C211yesmaximal, characteristic, complemented
6C25×C109C2211yescharacteristic
7C25×C109C2212yescomplemented
8C22×D4×C109—28no—
9C22×D4×C109—216no—
10C22×D4×C109C2214yes—
11C22×D4×C109C2214yescomplemented
12C22×D4×C109C2214yescomplemented
13C23×C4×C109C2212yescomplemented
14#120×C109—216no—
15C2×C22⋊C4×C109C2214yescomplemented
16C2×C22⋊C4×C109C2218yescomplemented
17C2×C22⋊C4×C109C2212yescomplemented
18#95×C109C2214yescomplemented
19C24×C109—28no—
20C24×C109—24no—
21C24×C109—28no—
22C24×C109—28no—
23C24×C109—42no—
24C24×C109—44no—
25C24×C109D414yescomplemented
26C24×C109C2311yescharacteristic
27C24×C109C2314yes—
28C24×C109C2312yes—
29C2×D4×C109—264no—
30C2×D4×C109—28no—
31C2×D4×C109—28no—
32C2×D4×C109—28no—
33C2×D4×C109—28no—
34C2×D4×C109—216no—
35C2×D4×C109—28no—
36C2×D4×C109—44no—
37C2×D4×C109D4116yescomplemented
38C22×C4×C109—24no—
39C22×C4×C109—28no—
40C22×C4×C109C2314yes—
41C22×C4×C109C2314yes—
42C22⋊C4×C109—28no—
43C22⋊C4×C109—216no—
44C22⋊C4×C109—42no—
45C23×C109—24no—
46C23×C109—24no—
47C23×C109—216no—
48C23×C109—216no—
49C23×C109—28no—
50C23×C109—24no—
51C23×C109—24no—
52C23×C109—24no—
53C23×C109—22no—
54C23×C109—28no—
55C23×C109—44no—
56C23×C109—416no—
57C23×C109—432no—
58C23×C109—48no—
59C23×C109—48no—
60C23×C109C2×D412yes—
61C23×C109C2×D418yes—
62C23×C109C2×D414yes—
63C23×C109C2×D418yescomplemented
64C23×C109C2411yescharacteristic
65D4×C109—232no—
66D4×C109—232no—
67D4×C109—416no—
68C2×C4×C109—216no—
69C2×C4×C109—24no—
70C2×C4×C109—24no—
71C2×C4×C109—28no—
72C2×C4×C109—24no—
73C2×C4×C109C2×D418yescomplemented
74C22×C109—24no—
75C22×C109—24no—
76C22×C109—216no—
77C22×C109—24no—
78C22×C109—28no—
79C22×C109—22no—
80C22×C109—216no—
81C22×C109—416no—
82C22×C109—432no—
83C22×C109—44no—
84C22×C109—44no—
85C22×C109—48no—
86C22×C109—44no—
87C22×C109#12018yescomplemented
88C22×C109C22×D411yescharacteristic
89C22×C109C22×D414yes—
90C22×C109H(5,𝔽2)12yes—
91C4×C109—28no—
92C4×C109—44no—
93C2×C109—28no—
94C2×C109—42no—
95C2×C109—48no—
96C2×C109C2×#12012yes—
97C2×C109#53411yescharacteristic
98C2×C109D4214yes—
99#2403C10911yesmaximal, characteristic, direct product factor, Sylow
100C109#240311yescharacteristic, direct product factor, Sylow
101C23×D4C2×C10912yescomplemented
102C2×#120C2×C10914yescomplemented
103#392C2×C10914yescomplemented
104#386C2×C10914yescomplemented
105#379C2×C10911yescharacteristic, complemented
106C25C22×C10911yescharacteristic
107C25C22×C10912yescomplemented
108C22×D4—28no—
109C22×D4—216no—
110C22×D4C22×C10914yes—
111C22×D4C22×C10914yescomplemented
112C22×D4C22×C10914yescomplemented
113C23×C4C22×C10912yescomplemented
114#120—216no—
115C2×C22⋊C4C22×C10914yescomplemented
116C2×C22⋊C4C22×C10918yescomplemented
117C2×C22⋊C4C22×C10912yescomplemented
118#95C22×C10914yescomplemented
119C24—28no—
120C24—24no—
121C24—28no—
122C24—28no—
123C24—42no—
124C24—44no—
125C24D4×C10914yescomplemented
126C24C23×C10911yescharacteristic
127C24C23×C10914yes—
128C24C23×C10912yes—
129C2×D4—264no—
130C2×D4—28no—
131C2×D4—28no—
132C2×D4—28no—
133C2×D4—28no—
134C2×D4—216no—
135C2×D4—28no—
136C2×D4—44no—
137C2×D4D4×C109116yescomplemented
138C22×C4—24no—
139C22×C4—28no—
140C22×C4C23×C10914yes—
141C22×C4C23×C10914yes—
142C22⋊C4—28no—
143C22⋊C4—216no—
144C22⋊C4—42no—
145C23—24no—
146C23—24no—
147C23—216no—
148C23—216no—
149C23—28no—
150C23—24no—
151C23—24no—
152C23—24no—
153C23—22no—
154C23—28no—
155C23—44no—
156C23—416no—
157C23—432no—
158C23—48no—
159C23—48no—
160C23C2×D4×C10912yes—
161C23C2×D4×C10918yes—
162C23C2×D4×C10914yes—
163C23C2×D4×C10918yescomplemented
164C23C24×C10911yescharacteristic
165D4—232no—
166D4—232no—
167D4—416no—
168C2×C4—216no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—28no—
172C2×C4—24no—
173C2×C4C2×D4×C10918yescomplemented
174C22—24no—
175C22—24no—
176C22—216no—
177C22—24no—
178C22—28no—
179C22—22no—
180C22—216no—
181C22—416no—
182C22—432no—
183C22—44no—
184C22—44no—
185C22—48no—
186C22—44no—
187C22#120×C10918yescomplemented
188C22C22×D4×C10911yescharacteristic
189C22C22×D4×C10914yes—
190C22H(5,𝔽2)×C10912yes—
191C4—28no—
192C4—44no—
193C2—28no—
194C2—42no—
195C2—48no—
196C2C2×#120×C10912yes—
197C2#534×C10911yescharacteristic
198C2D42×C10914yes—
subgroupG/H
center, socleC23×C109C24
commutator, Frattini, cosocleC23C24×C109
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×D4×C109C2semidirect
2. C2×#120×C109C2semidirect
3. #392×C109C2semidirect
4. #386×C109C2semidirect
5. #379×C109C2semidirect
7. C25×C109C22semidirect
11. C22×D4×C109C22semidirect
12. C22×D4×C109C22semidirect
13. C23×C4×C109C22semidirect
15. C2×C22⋊C4×C109C22semidirect
16. C2×C22⋊C4×C109C22semidirect
17. C2×C22⋊C4×C109C22semidirect
18. #95×C109C22semidirect
25. C24×C109D4semidirect
37. C2×D4×C109D4semidirect
63. C23×C109C2×D4semidirect
73. C2×C4×C109C2×D4semidirect
87. C22×C109#120semidirect
99. #2403C109direct (N × H)
100. C109#2403direct (N × H)
101. C23×D4C2×C109semidirect
102. C2×#120C2×C109semidirect
103. #392C2×C109semidirect
104. #386C2×C109semidirect
105. #379C2×C109semidirect
107. C25C22×C109semidirect
111. C22×D4C22×C109semidirect
112. C22×D4C22×C109semidirect
113. C23×C4C22×C109semidirect
115. C2×C22⋊C4C22×C109semidirect
116. C2×C22⋊C4C22×C109semidirect
117. C2×C22⋊C4C22×C109semidirect
118. #95C22×C109semidirect
125. C24D4×C109semidirect
137. C2×D4D4×C109semidirect
163. C23C2×D4×C109semidirect
173. C2×C4C2×D4×C109semidirect
187. C22#120×C109semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C1092
C2×#120×C1092
#392×C1092
#386×C1092
#379×C1092
#2403109