Finite Group Databasebeta

← C127×#7238 #44570911

Subgroups — C127×#7238 #44570911

Order 32512.

280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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×#1984C211yesmaximal, characteristic
2C127×#1801C212yesmaximal
3C2×C4×Q8×C127C2211yescharacteristic
4#423×C127—22no—
5C2×C4⋊C8×C127C411yescharacteristic
6C2×#101×C127—22no—
7C2×C4×C8×C127C411yescharacteristic
8#343×C127C414yes—
9#336×C127—22no—
10C22×Q8×C127D411yescharacteristic
11C2×M16×C127—24no—
12C22×C8×C127—21no—
13C22×C8×C127—21no—
14C4×Q8×C127—41no—
15C4×Q8×C127—41no—
16C2×C4⋊C4×C127C2×C412yes—
17C2×C4⋊C4×C127Q811yescharacteristic
18C2×C42×C127C2×C411yescharacteristic
19C2×C42×C127D412yes—
20C4⋊C8×C127—42no—
21C4⋊C8×C127—42no—
22C4⋊C8×C127—41no—
23#101×C127—42no—
24#101×C127—42no—
25C4×C8×C127—41no—
26C2×Q8×C127—41no—
27C2×Q8×C127—41no—
28C2×Q8×C127D811yescharacteristic
29C2×Q8×C127SD1612yes—
30C2×Q8×C127Q1611yescharacteristic
31C22×C4×C127C4211yescharacteristic
32C22×C4×C127C22⋊C412yes—
33C22×C4×C127C22⋊C411yescharacteristic
34C22×C4×C127C4⋊C411yescharacteristic
35C22×C4×C127C4⋊C412yes—
36M16×C127—44no—
37M16×C127—44no—
38C2×C8×C127—22no—
39C2×C8×C127—41no—
40C2×C8×C127—41no—
41C2×C8×C127—44no—
42C2×C8×C127—42no—
43C2×C8×C127—41no—
44C4⋊C4×C127—42no—
45C4⋊C4×C127—41no—
46C42×C127—21no—
47C42×C127—21no—
48C42×C127—22no—
49C42×C127—22no—
50C23×C127#9511yescharacteristic
51Q8×C127—41no—
52Q8×C127—42no—
53Q8×C127—41no—
54C2×C4×C127—22no—
55C2×C4×C127—21no—
56C2×C4×C127—22no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—22no—
62C2×C4×C127—41no—
63C2×C4×C127—42no—
64C2×C4×C127#9911yescharacteristic
65C2×C4×C127#9911yescharacteristic
66C2×C4×C127#10212yes—
67C2×C4×C127#10312yes—
68C2×C4×C127#10611yescharacteristic
69C2×C4×C127#10711yescharacteristic
70C8×C127—42no—
71C8×C127—84no—
72C8×C127—81no—
73C22×C127—21no—
74C22×C127—21no—
75C22×C127H(3,ℤ/4)11yescharacteristic
76C22×C127#34011yescharacteristic
77C22×C127#34211yescharacteristic
78C4×C127—22no—
79C4×C127—22no—
80C4×C127—21no—
81C4×C127—21no—
82C4×C127—21no—
83C4×C127—41no—
84C4×C127—42no—
85C4×C127#35511yescharacteristic
86C4×C127#35611yescharacteristic
87#7238C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—21no—
90C2×C127#128911yescharacteristic
91C2×C127#139211yescharacteristic
92C2×C127#139411yescharacteristic
93#1984C2×C12711yescharacteristic
94#1801C2×C12712yes—
95C127#723811yescharacteristic, direct product factor, Sylow
96C2×C4×Q8C22×C12711yescharacteristic
97#423—22no—
98C2×C4⋊C8C4×C12711yescharacteristic
99C2×#101—22no—
100C2×C4×C8C4×C12711yescharacteristic
101#343C4×C12714yes—
102#336—22no—
103C22×Q8D4×C12711yescharacteristic
104C2×M16—24no—
105C22×C8—21no—
106C22×C8—21no—
107C4×Q8—41no—
108C4×Q8—41no—
109C2×C4⋊C4C2×C4×C12712yes—
110C2×C4⋊C4Q8×C12711yescharacteristic
111C2×C42C2×C4×C12711yescharacteristic
112C2×C42D4×C12712yes—
113C4⋊C8—41no—
114C4⋊C8—42no—
115C4⋊C8—42no—
116#101—42no—
117#101—42no—
118C4×C8—41no—
119C2×Q8—41no—
120C2×Q8—41no—
121C2×Q8D8×C12711yescharacteristic
122C2×Q8SD16×C12712yes—
123C2×Q8Q16×C12711yescharacteristic
124C22×C4C42×C12711yescharacteristic
125C22×C4C22⋊C4×C12711yescharacteristic
126C22×C4C22⋊C4×C12712yes—
127C22×C4C4⋊C4×C12711yescharacteristic
128C22×C4C4⋊C4×C12712yes—
129M16—44no—
130M16—44no—
131C2×C8—22no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8—44no—
135C2×C8—42no—
136C2×C8—41no—
137C4⋊C4—42no—
138C4⋊C4—41no—
139C42—21no—
140C42—21no—
141C42—22no—
142C42—22no—
143C23#95×C12711yescharacteristic
144Q8—41no—
145Q8—42no—
146Q8—41no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4#99×C12711yescharacteristic
158C2×C4#99×C12711yescharacteristic
159C2×C4#102×C12712yes—
160C2×C4#103×C12712yes—
161C2×C4#106×C12711yescharacteristic
162C2×C4#107×C12711yescharacteristic
163C8—42no—
164C8—84no—
165C8—81no—
166C22—21no—
167C22—21no—
168C22H(3,ℤ/4)×C12711yescharacteristic
169C22#340×C12711yescharacteristic
170C22#342×C12711yescharacteristic
171C4—22no—
172C4—22no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—42no—
178C4#355×C12711yescharacteristic
179C4#356×C12711yescharacteristic
180C2—21no—
181C2—21no—
182C2C127×#128911yescharacteristic
183C2C127×#139211yescharacteristic
184C2C127×#139411yescharacteristic
subgroupG/H
center, socleC22×C127#342
commutatorC22×C4C42×C127
Frattini, cosocleC2×C4×Q8C22×C127
prime radicalC23×C127#95
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
87. #7238C127direct (N × H)
95. C127#7238direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19842
C127×#18012
#7238127