Finite Group Databasebeta

← C127×#10662 #44574335

Subgroups — C127×#10662 #44574335

Order 32512.

320 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C127×#1985C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic
3C127×#1571C212yesmaximal
4C127×#1487C212yesmaximal
5C127×#1275C211yesmaximal, characteristic
6C2×C4×Q8×C127C2211yescharacteristic
7#431×C127C2212yes—
8C2×#108×C127—22no—
9#423×C127C2212yes—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×#97×C127C2211yescharacteristic
12#336×C127—22no—
13#335×C127—24no—
14Q8⋊C8×C127—24no—
15C22×Q8×C127Q811yescharacteristic
16C2×M16×C127—22no—
17C22×C8×C127—21no—
18C22×C8×C127D412yes—
19C4×Q8×C127—22no—
20C4×Q8×C127—22no—
21C2×C4⋊C4×C127—21no—
22C2×C4⋊C4×C127Q811yescharacteristic
23C2×C42×C127—21no—
24C2×C42×C127C2311yescharacteristic
25#108×C127—44no—
26C4⋊C8×C127—22no—
27C4⋊C8×C127—22no—
28C4⋊C8×C127—22no—
29C4⋊C8×C127—22no—
30C22⋊C8×C127—22no—
31#97×C127—22no—
32C4×C8×C127D414yes—
33C2×Q8×C127—22no—
34C2×Q8×C127—42no—
35C22×C4×C127—21no—
36C22×C4×C127—21no—
37C22×C4×C127C2×D411yescharacteristic
38C22×C4×C127C2×Q811yescharacteristic
39C22×C4×C127#4111yescharacteristic
40M16×C127—44no—
41C2×C8×C127—22no—
42C2×C8×C127—22no—
43C2×C8×C127—24no—
44C2×C8×C127—41no—
45C2×C8×C127—42no—
46C2×C8×C127—42no—
47C2×C8×C127Q1614yes—
48C4⋊C4×C127—22no—
49C4⋊C4×C127—42no—
50C42×C127—41no—
51C42×C127—41no—
52C42×C127C2×D412yes—
53C42×C127#4112yes—
54C23×C127C22⋊Q811yescharacteristic
55Q8×C127—24no—
56Q8×C127—42no—
57C2×C4×C127—22no—
58C2×C4×C127—41no—
59C2×C4×C127—41no—
60C2×C4×C127—41no—
61C2×C4×C127—41no—
62C2×C4×C127—42no—
63C2×C4×C127—41no—
64C2×C4×C127C22⋊Q812yes—
65C2×C4×C127#12312yes—
66C2×C4×C127#12311yescharacteristic
67C2×C4×C127#12711yescharacteristic
68C2×C4×C127C2×Q1612yes—
69C2×C4×C127AGL(1,ℤ/8)12yes—
70C8×C127—24no—
71C8×C127—44no—
72C8×C127—81no—
73C8×C127—82no—
74C22×C127—21no—
75C22×C127—21no—
76C22×C127#39911yescharacteristic
77C22×C127#47712yes—
78C4×C127—22no—
79C4×C127—22no—
80C4×C127—42no—
81C4×C127—81no—
82C4×C127#48412yes—
83C4×C127#49411yescharacteristic
84C4×C127#49611yescharacteristic
85#10662C12711yesmaximal, characteristic, direct product factor, Sylow
86C2×C127—22no—
87C2×C127#209111yescharacteristic
88C2×C127#209511yescharacteristic
89C2×C127#209811yescharacteristic
90#1985C2×C12711yescharacteristic
91#1849C2×C12711yescharacteristic
92#1571C2×C12712yes—
93#1487C2×C12712yes—
94#1275C2×C12711yescharacteristic
95C127#1066211yescharacteristic, direct product factor, Sylow
96C2×C4×Q8C22×C12711yescharacteristic
97#431C22×C12712yes—
98C2×#108—22no—
99#423C22×C12712yes—
100C2×C4⋊C8C22×C12711yescharacteristic
101C2×#97C22×C12711yescharacteristic
102#336—22no—
103#335—24no—
104Q8⋊C8—24no—
105C22×Q8Q8×C12711yescharacteristic
106C2×M16—22no—
107C22×C8—21no—
108C22×C8D4×C12712yes—
109C4×Q8—22no—
110C4×Q8—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4Q8×C12711yescharacteristic
113C2×C42—21no—
114C2×C42C23×C12711yescharacteristic
115#108—44no—
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C22⋊C8—22no—
121#97—22no—
122C4×C8D4×C12714yes—
123C2×Q8—22no—
124C2×Q8—42no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×D4×C12711yescharacteristic
128C22×C4C2×Q8×C12711yescharacteristic
129C22×C4#41×C12711yescharacteristic
130M16—44no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8—24no—
134C2×C8—41no—
135C2×C8—42no—
136C2×C8—42no—
137C2×C8Q16×C12714yes—
138C4⋊C4—22no—
139C4⋊C4—42no—
140C42—41no—
141C42—41no—
142C42C2×D4×C12712yes—
143C42#41×C12712yes—
144C23C22⋊Q8×C12711yescharacteristic
145Q8—24no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4C22⋊Q8×C12712yes—
155C2×C4#123×C12712yes—
156C2×C4#123×C12711yescharacteristic
157C2×C4#127×C12711yescharacteristic
158C2×C4C2×Q16×C12712yes—
159C2×C4AGL(1,ℤ/8)×C12712yes—
160C8—24no—
161C8—44no—
162C8—81no—
163C8—82no—
164C22—21no—
165C22—21no—
166C22#399×C12711yescharacteristic
167C22#477×C12712yes—
168C4—22no—
169C4—22no—
170C4—42no—
171C4—81no—
172C4#484×C12712yes—
173C4#494×C12711yescharacteristic
174C4#496×C12711yescharacteristic
175C2—22no—
176C2C127×#209111yescharacteristic
177C2C127×#209511yescharacteristic
178C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radicalC23×C127C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
85. #10662C127direct (N × H)
95. C127#10662direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19852
C127×#18492
C127×#15712
C127×#14872
C127×#12752
#10662127