Finite Group Databasebeta

← C107×#8744 #41034708

Subgroups — C107×#8744 #41034708

Order 27392.

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

normal subgroups only

This group has 384 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×#2298C211yesmaximal, characteristic
2C107×#1464C212yesmaximal
3C107×#1285C214yesmaximal, complemented
4C2×#117×C107C2211yescharacteristic
5#432×C107C2214yes—
6#388×C107—22no—
7#387×C107—22no—
8C4×C4⋊C4×C107C2212yes—
9C4×C22⋊C4×C107C412yes—
10#376×C107C411yescharacteristic
11C43×C107C411yescharacteristic
12#324×C107—22no—
13#323×C107—22no—
14C23×C4×C107C2×C411yescharacteristic
15#117×C107—24no—
16C2×C4⋊C4×C107—22no—
17C2×C4⋊C4×C107D412yes—
18C2×C22⋊C4×C107—22no—
19C2×C22⋊C4×C107D412yes—
20C2×C42×C107—22no—
21C2×C42×C107C2×C411yescharacteristic
22C2×C42×C107C2×C412yes—
23C2×C42×C107C2×C412yes—
24C2×C42×C107C2311yescharacteristic
25C4⋊C8×C107—24no—
26C22⋊C8×C107—24no—
27#97×C107—24no—
28#95×C107—22no—
29#95×C107—22no—
30#95×C107—22no—
31C24×C107C22⋊C411yescharacteristic
32C22×C4×C107—22no—
33C22×C4×C107—22no—
34C22×C4×C107—22no—
35C22×C4×C107—42no—
36C22×C4×C107C22⋊C411yescharacteristic
37C22×C4×C107C22⋊C412yes—
38C22×C4×C107C22×C411yescharacteristic
39C22×C4×C107C2×D412yes—
40C2×C8×C107—44no—
41C4⋊C4×C107—24no—
42C4⋊C4×C107—44no—
43C22⋊C4×C107—24no—
44C22⋊C4×C107—44no—
45C42×C107—22no—
46C42×C107—42no—
47C42×C107—42no—
48C42×C107—44no—
49C42×C107#4114yes—
50C23×C107—21no—
51C23×C107—22no—
52C23×C107—42no—
53C23×C107C2×C22⋊C411yescharacteristic
54C2×C4×C107—22no—
55C2×C4×C107—24no—
56C2×C4×C107—22no—
57C2×C4×C107—21no—
58C2×C4×C107—22no—
59C2×C4×C107—42no—
60C2×C4×C107—44no—
61C2×C4×C107—42no—
62C2×C4×C107—42no—
63C2×C4×C107—42no—
64C2×C4×C107—42no—
65C2×C4×C107—42no—
66C2×C4×C107—42no—
67C2×C4×C107#11712yes—
68C2×C4×C107#12314yes—
69C8×C107—84no—
70C22×C107—22no—
71C22×C107—41no—
72C22×C107—42no—
73C22×C107—82no—
74C22×C107#38111yescharacteristic
75C22×C107#41312yes—
76C4×C107—22no—
77C4×C107—24no—
78C4×C107—44no—
79C4×C107—41no—
80C4×C107—42no—
81C4×C107—82no—
82#8744C10711yesmaximal, characteristic, direct product factor, Sylow
83C2×C107—22no—
84C2×C107—81no—
85C2×C107#182211yescharacteristic
86C2×C107#182712yes—
87#2298C2×C10711yescharacteristic
88#1464C2×C10712yes—
89#1285C2×C10714yescomplemented
90C107#874411yescharacteristic, direct product factor, Sylow
91C2×#117C22×C10711yescharacteristic
92#432C22×C10714yes—
93#388—22no—
94#387—22no—
95C4×C4⋊C4C22×C10712yes—
96C4×C22⋊C4C4×C10712yes—
97#376C4×C10711yescharacteristic
98C43C4×C10711yescharacteristic
99#324—22no—
100#323—22no—
101C23×C4C2×C4×C10711yescharacteristic
102#117—24no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4D4×C10712yes—
105C2×C22⋊C4—22no—
106C2×C22⋊C4D4×C10712yes—
107C2×C42—22no—
108C2×C42C2×C4×C10711yescharacteristic
109C2×C42C2×C4×C10712yes—
110C2×C42C2×C4×C10712yes—
111C2×C42C23×C10711yescharacteristic
112C4⋊C8—24no—
113C22⋊C8—24no—
114#97—24no—
115#95—22no—
116#95—22no—
117#95—22no—
118C24C22⋊C4×C10711yescharacteristic
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—42no—
123C22×C4C22⋊C4×C10711yescharacteristic
124C22×C4C22⋊C4×C10712yes—
125C22×C4C22×C4×C10711yescharacteristic
126C22×C4C2×D4×C10712yes—
127C2×C8—44no—
128C4⋊C4—24no—
129C4⋊C4—44no—
130C22⋊C4—24no—
131C22⋊C4—44no—
132C42—22no—
133C42—42no—
134C42—42no—
135C42—44no—
136C42#41×C10714yes—
137C23—21no—
138C23—22no—
139C23—42no—
140C23C2×C22⋊C4×C10711yescharacteristic
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4#117×C10712yes—
155C2×C4#123×C10714yes—
156C8—84no—
157C22—22no—
158C22—41no—
159C22—42no—
160C22—82no—
161C22#381×C10711yescharacteristic
162C22#413×C10712yes—
163C4—22no—
164C4—24no—
165C4—44no—
166C4—41no—
167C4—42no—
168C4—82no—
169C2—22no—
170C2—81no—
171C2C107×#182211yescharacteristic
172C2C107×#182712yes—
subgroupG/H
center, socleC22×C107#381
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC24×C107C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1285C2semidirect
82. #8744C107direct (N × H)
89. #1285C2×C107semidirect
90. C107#8744direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#22982
C107×#14642
C107×#12852
#8744107