Finite Group Databasebeta

← C107×#8759 #41034723

Subgroups — C107×#8759 #41034723

Order 27392.

474 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C107×#2312C211yesmaximal, characteristic
2C107×#1462C212yesmaximal
3C107×#1305C214yesmaximal, complemented
4C22×C22⋊C4×C107C2211yescharacteristic
5#407×C107C2214yes—
6#388×C107—24no—
7#380×C107C2212yes—
8#379×C107C412yes—
9C4×C22⋊C4×C107C412yes—
10#323×C107—24no—
11C25×C107C2×C411yescharacteristic
12C23×C4×C107C2×C411yescharacteristic
13C23×C4×C107C2311yescharacteristic
14C2×M16×C107—24no—
15C2×C4⋊C4×C107—22no—
16C2×C22⋊C4×C107—24no—
17C2×C22⋊C4×C107—22no—
18C2×C22⋊C4×C107—22no—
19C2×C22⋊C4×C107C2×C414yes—
20C2×C22⋊C4×C107D414yes—
21C2×C42×C107—22no—
22C22⋊C8×C107—24no—
23C22⋊C8×C107—24no—
24#95×C107—22no—
25#95×C107—22no—
26C24×C107—22no—
27C24×C107—42no—
28C24×C107—81no—
29C24×C107—81no—
30C24×C107C22⋊C412yes—
31C24×C107C22×C411yescharacteristic
32C22×C4×C107—22no—
33C22×C4×C107—24no—
34C22×C4×C107—81no—
35C22×C4×C107—81no—
36C22×C4×C107C22⋊C412yes—
37C22×C4×C107C2×D412yes—
38C22×C4×C107#4114yes—
39M16×C107—84no—
40C2×C8×C107—44no—
41C4⋊C4×C107—82no—
42C22⋊C4×C107—28no—
43C22⋊C4×C107—44no—
44C22⋊C4×C107—82no—
45C22⋊C4×C107—82no—
46C42×C107—82no—
47C23×C107—22no—
48C23×C107—22no—
49C23×C107—24no—
50C23×C107—41no—
51C23×C107—41no—
52C23×C107—44no—
53C23×C107—42no—
54C23×C107—42no—
55C23×C107—82no—
56C23×C107—82no—
57C23×C107—88no—
58C23×C107C2×C22⋊C411yescharacteristic
59C23×C107#11712yes—
60C2×C4×C107—22no—
61C2×C4×C107—42no—
62C2×C4×C107—44no—
63C2×C4×C107—42no—
64C2×C4×C107—44no—
65C2×C4×C107—44no—
66C2×C4×C107—44no—
67C2×C4×C107—82no—
68C2×C4×C107#12314yes—
69C8×C107—84no—
70C22×C107—21no—
71C22×C107—21no—
72C22×C107—22no—
73C22×C107—22no—
74C22×C107—22no—
75C22×C107—44no—
76C22×C107—42no—
77C22×C107—42no—
78C22×C107—42no—
79C22×C107—84no—
80C22×C107—88no—
81C22×C107#38111yescharacteristic
82C22×C107#41312yes—
83C4×C107—24no—
84C4×C107—42no—
85C4×C107—84no—
86#8759C10711yesmaximal, characteristic, direct product factor, Sylow
87C2×C107—22no—
88C2×C107—42no—
89C2×C107—82no—
90C2×C107#182211yescharacteristic
91C2×C107#182811yescharacteristic
92C2×C107#182911yescharacteristic
93#2312C2×C10711yescharacteristic
94#1462C2×C10712yes—
95#1305C2×C10714yescomplemented
96C107#875911yescharacteristic, direct product factor, Sylow
97C22×C22⋊C4C22×C10711yescharacteristic
98#407C22×C10714yes—
99#388—24no—
100#380C22×C10712yes—
101#379C4×C10712yes—
102C4×C22⋊C4C4×C10712yes—
103#323—24no—
104C25C2×C4×C10711yescharacteristic
105C23×C4C2×C4×C10711yescharacteristic
106C23×C4C23×C10711yescharacteristic
107C2×M16—24no—
108C2×C4⋊C4—22no—
109C2×C22⋊C4—24no—
110C2×C22⋊C4—22no—
111C2×C22⋊C4—22no—
112C2×C22⋊C4C2×C4×C10714yes—
113C2×C22⋊C4D4×C10714yes—
114C2×C42—22no—
115C22⋊C8—24no—
116C22⋊C8—24no—
117#95—22no—
118#95—22no—
119C24—22no—
120C24—42no—
121C24—81no—
122C24—81no—
123C24C22⋊C4×C10712yes—
124C24C22×C4×C10711yescharacteristic
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4C22⋊C4×C10712yes—
130C22×C4C2×D4×C10712yes—
131C22×C4#41×C10714yes—
132M16—84no—
133C2×C8—44no—
134C4⋊C4—82no—
135C22⋊C4—28no—
136C22⋊C4—44no—
137C22⋊C4—82no—
138C22⋊C4—82no—
139C42—82no—
140C23—22no—
141C23—22no—
142C23—24no—
143C23—41no—
144C23—41no—
145C23—44no—
146C23—42no—
147C23—42no—
148C23—82no—
149C23—82no—
150C23—88no—
151C23C2×C22⋊C4×C10711yescharacteristic
152C23#117×C10712yes—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—82no—
161C2×C4#123×C10714yes—
162C8—84no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—84no—
173C22—88no—
174C22#381×C10711yescharacteristic
175C22#413×C10712yes—
176C4—24no—
177C4—42no—
178C4—84no—
179C2—22no—
180C2—42no—
181C2—82no—
182C2C107×#182211yescharacteristic
183C2C107×#182811yescharacteristic
184C2C107×#182911yescharacteristic
subgroupG/H
center, socleC22×C107#381
commutatorC24C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC25×C107C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1305C2semidirect
86. #8759C107direct (N × H)
95. #1305C2×C107semidirect
96. C107#8759direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#23122
C107×#14622
C107×#13052
#8759107