Finite Group Databasebeta

← C107×#2501 #28333184

Subgroups — C107×#2501 #28333184

Order 13696.

708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 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
1C2×#123×C107C214yesmaximal, complemented
2C2×#121×C107C211yesmaximal, characteristic
3C22×C4⋊C4×C107C211yesmaximal, characteristic, complemented
4#399×C107C214yesmaximal, complemented
5#390×C107C212yesmaximal, complemented
6#384×C107C212yesmaximal, complemented
7C4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
8C22×D4×C107C2211yescharacteristic
9C22×D4×C107C2212yes—
10C23×C4×C107C2212yes—
11C23×C4×C107C2211yescharacteristic
12#123×C107—216no—
13#121×C107—24no—
14C2×C4⋊C4×C107—24no—
15C2×C4⋊C4×C107C2211yescharacteristic
16C2×C4⋊C4×C107C2212yes—
17C2×C4⋊C4×C107C2218yes—
18C2×C4⋊C4×C107C2212yes—
19C2×C22⋊C4×C107C2218yes—
20C2×C22⋊C4×C107C2212yes—
21C2×C22⋊C4×C107C2212yes—
22C2×C42×C107C2212yes—
23#95×C107C2212yes—
24C24×C107C2312yes—
25C24×C107C2311yescharacteristic
26C2×D4×C107—24no—
27C2×D4×C107—28no—
28C2×D4×C107—22no—
29C2×D4×C107—24no—
30C22×C4×C107—24no—
31C22×C4×C107—24no—
32C22×C4×C107—28no—
33C22×C4×C107D414yes—
34C22×C4×C107C2314yes—
35C22×C4×C107C2312yes—
36C22×C4×C107C2311yescharacteristic
37C22×C4×C107C2314yes—
38C22×C4×C107C2311yescharacteristic
39C4⋊C4×C107—24no—
40C4⋊C4×C107—24no—
41C4⋊C4×C107—22no—
42C4⋊C4×C107—216no—
43C22⋊C4×C107—24no—
44C22⋊C4×C107—216no—
45C22⋊C4×C107D418yescomplemented
46C42×C107—24no—
47C23×C107—22no—
48C23×C107—22no—
49C23×C107—24no—
50C23×C107—22no—
51C23×C107—24no—
52C23×C107—24no—
53C23×C107C2×D414yes—
54C23×C107C2×D412yes—
55C23×C107C2411yescharacteristic
56D4×C107—48no—
57D4×C107—44no—
58C2×C4×C107—24no—
59C2×C4×C107—22no—
60C2×C4×C107—24no—
61C2×C4×C107—28no—
62C2×C4×C107—28no—
63C2×C4×C107—22no—
64C2×C4×C107—24no—
65C2×C4×C107—24no—
66C2×C4×C107—48no—
67C2×C4×C107C2×D418yes—
68C2×C4×C107C2×D412yes—
69C2×C4×C107C2×D412yes—
70C2×C4×C107#4114yes—
71C22×C107—22no—
72C22×C107—22no—
73C22×C107—28no—
74C22×C107—42no—
75C22×C107—42no—
76C22×C107—42no—
77C22×C107—48no—
78C22×C107#12714yes—
79C22×C107C22×D411yescharacteristic
80C22×C107C22×D412yes—
81C22×C107C2×#4112yes—
82C22×C1072−1+412yes—
83C4×C107—22no—
84C4×C107—28no—
85C4×C107—44no—
86C4×C107—42no—
87C4×C107#12314yescomplemented
88C2×C107—24no—
89C2×C107—82no—
90C2×C107C2×#12311yescharacteristic
91C2×C107C2×#12711yescharacteristic
92C2×C107#53611yescharacteristic
93C2×C107#54714yes—
94#2501C10711yesmaximal, characteristic, direct product factor, Sylow
95C107#250111yescharacteristic, direct product factor, Sylow
96C2×#123C2×C10714yescomplemented
97C2×#121C2×C10711yescharacteristic
98C22×C4⋊C4C2×C10711yescharacteristic, complemented
99#399C2×C10714yescomplemented
100#390C2×C10712yescomplemented
101#384C2×C10712yescomplemented
102C4×C22⋊C4C2×C10711yescharacteristic, complemented
103C22×D4C22×C10712yes—
104C22×D4C22×C10711yescharacteristic
105C23×C4C22×C10712yes—
106C23×C4C22×C10711yescharacteristic
107#123—216no—
108#121—24no—
109C2×C4⋊C4—24no—
110C2×C4⋊C4C22×C10712yes—
111C2×C4⋊C4C22×C10712yes—
112C2×C4⋊C4C22×C10711yescharacteristic
113C2×C4⋊C4C22×C10718yes—
114C2×C22⋊C4C22×C10712yes—
115C2×C22⋊C4C22×C10718yes—
116C2×C22⋊C4C22×C10712yes—
117C2×C42C22×C10712yes—
118#95C22×C10712yes—
119C24C23×C10712yes—
120C24C23×C10711yescharacteristic
121C2×D4—24no—
122C2×D4—28no—
123C2×D4—22no—
124C2×D4—24no—
125C22×C4—24no—
126C22×C4—24no—
127C22×C4—28no—
128C22×C4D4×C10714yes—
129C22×C4C23×C10714yes—
130C22×C4C23×C10712yes—
131C22×C4C23×C10711yescharacteristic
132C22×C4C23×C10714yes—
133C22×C4C23×C10711yescharacteristic
134C4⋊C4—24no—
135C4⋊C4—24no—
136C4⋊C4—22no—
137C4⋊C4—216no—
138C22⋊C4—24no—
139C22⋊C4—216no—
140C22⋊C4D4×C10718yescomplemented
141C42—24no—
142C23—22no—
143C23—22no—
144C23—24no—
145C23—22no—
146C23—24no—
147C23—24no—
148C23C2×D4×C10714yes—
149C23C2×D4×C10712yes—
150C23C24×C10711yescharacteristic
151D4—48no—
152D4—44no—
153C2×C4—24no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—28no—
157C2×C4—28no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—24no—
161C2×C4—48no—
162C2×C4C2×D4×C10718yes—
163C2×C4C2×D4×C10712yes—
164C2×C4C2×D4×C10712yes—
165C2×C4#41×C10714yes—
166C22—22no—
167C22—22no—
168C22—28no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—48no—
173C22#127×C10714yes—
174C22C22×D4×C10711yescharacteristic
175C22C22×D4×C10712yes—
176C22C2×#41×C10712yes—
177C222−1+4×C10712yes—
178C4—22no—
179C4—28no—
180C4—44no—
181C4—42no—
182C4#123×C10714yescomplemented
183C2—24no—
184C2—82no—
185C2C2×#123×C10711yescharacteristic
186C2C2×#127×C10711yescharacteristic
187C2#536×C10711yescharacteristic
188C2#547×C10714yes—
subgroupG/H
center, socleC23×C107C24
commutator, Frattini, cosocleC23C24×C107
prime radicalC2×#121×C107C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#123×C107C2semidirect
3. C22×C4⋊C4×C107C2semidirect
4. #399×C107C2semidirect
5. #390×C107C2semidirect
6. #384×C107C2semidirect
7. C4×C22⋊C4×C107C2semidirect
45. C22⋊C4×C107D4semidirect
87. C4×C107#123semidirect
94. #2501C107direct (N × H)
95. C107#2501direct (N × H)
96. C2×#123C2×C107semidirect
98. C22×C4⋊C4C2×C107semidirect
99. #399C2×C107semidirect
100. #390C2×C107semidirect
101. #384C2×C107semidirect
102. C4×C22⋊C4C2×C107semidirect
140. C22⋊C4D4×C107semidirect
182. C4#123×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1072
C2×#121×C1072
C22×C4⋊C4×C1072
#399×C1072
#390×C1072
#384×C1072
C4×C22⋊C4×C1072
#2501107