Finite Group Databasebeta

← C127×#13488 #44577161

Subgroups — C127×#13488 #44577161

Order 32512.

302 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 106 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×#362×C127C212yesmaximal
2C127×#1971C211yesmaximal, characteristic
3C127×#1849C211yesmaximal, characteristic
4C127×#1383C212yesmaximal
5C127×#1377C211yesmaximal, characteristic
6C22×Q16×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127—21no—
9C2×#108×C127C2212yes—
10C2×#106×C127C2211yescharacteristic
11#423×C127—21no—
12C2×#103×C127—21no—
13C2×#97×C127C2211yescharacteristic
14#391×C127—21no—
15#362×C127—24no—
16C22×Q8×C127—21no—
17C2×Q16×C127—22no—
18C2×Q16×C127—22no—
19C2×Q16×C127—21no—
20C2×Q16×C127D412yes—
21C2×M16×C127—22no—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24C2×C4⋊C4×C127—21no—
25C2×C42×C127D411yescharacteristic
26M32×C127—22no—
27M32×C127—22no—
28C2×C16×C127—22no—
29#108×C127—22no—
30#108×C127—22no—
31#108×C127—42no—
32#106×C127—22no—
33C4⋊C8×C127—42no—
34#103×C127—42no—
35#97×C127—22no—
36#95×C127—42no—
37C2×Q8×C127—22no—
38C2×Q8×C127—41no—
39C2×Q8×C127—41no—
40C2×Q8×C127—41no—
41C2×Q8×C127—41no—
42C2×Q8×C127—41no—
43C22×C4×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127SD1612yes—
46C22×C4×C127C2×D411yescharacteristic
47Q16×C127—24no—
48Q16×C127—42no—
49M16×C127—42no—
50M16×C127—42no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127—42no—
54C2×C8×C127D812yes—
55C2×C8×C127C2×D411yescharacteristic
56C2×C8×C127#4112yes—
57C2×C8×C127#4112yes—
58C2×C8×C127#4111yescharacteristic
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C42×C127—21no—
62C42×C127—21no—
63C16×C127—42no—
64C23×C127C2×SD1611yescharacteristic
65Q8×C127—42no—
66Q8×C127—42no—
67Q8×C127—81no—
68Q8×C127—81no—
69C2×C4×C127—22no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127—81no—
73C2×C4×C127—81no—
74C2×C4×C127—82no—
75C2×C4×C127—81no—
76C2×C4×C127#12111yescharacteristic
77C2×C4×C127#12311yescharacteristic
78C2×C4×C127#12411yescharacteristic
79C2×C4×C127C2×D811yescharacteristic
80C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
81C2×C4×C127#13711yescharacteristic
82C8×C127—22no—
83C8×C127—82no—
84C8×C127#12312yes—
85C8×C127#12612yes—
86C22×C127—22no—
87C22×C127#46111yescharacteristic
88C22×C127#48111yescharacteristic
89C22×C127#48611yescharacteristic
90C4×C127—42no—
91C4×C127—82no—
92C4×C127—161no—
93C4×C127#39711yescharacteristic
94C4×C127#45911yescharacteristic
95C4×C127#48011yescharacteristic
96C4×C127#48911yescharacteristic
97#13488C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—21no—
99C2×C127—21no—
100C2×C127#207111yescharacteristic
101C2×C127#223912yes—
102C2×#362C2×C12712yes—
103#1971C2×C12711yescharacteristic
104#1849C2×C12711yescharacteristic
105#1383C2×C12712yes—
106#1377C2×C12711yescharacteristic
107C127#1348811yescharacteristic, direct product factor, Sylow
108C22×Q16C22×C12711yescharacteristic
109C2×M32C22×C12712yes—
110C2×#108—21no—
111C2×#108C22×C12712yes—
112C2×#106C22×C12711yescharacteristic
113#423—21no—
114C2×#103—21no—
115C2×#97C22×C12711yescharacteristic
116#391—21no—
117#362—24no—
118C22×Q8—21no—
119C2×Q16—22no—
120C2×Q16—22no—
121C2×Q16—21no—
122C2×Q16D4×C12712yes—
123C2×M16—22no—
124C22×C8D4×C12711yescharacteristic
125C22×C8C23×C12711yescharacteristic
126C2×C4⋊C4—21no—
127C2×C42D4×C12711yescharacteristic
128M32—22no—
129M32—22no—
130C2×C16—22no—
131#108—22no—
132#108—22no—
133#108—42no—
134#106—22no—
135C4⋊C8—42no—
136#103—42no—
137#97—22no—
138#95—42no—
139C2×Q8—22no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4SD16×C12712yes—
148C22×C4C2×D4×C12711yescharacteristic
149Q16—24no—
150Q16—42no—
151M16—42no—
152M16—42no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—42no—
156C2×C8D8×C12712yes—
157C2×C8C2×D4×C12711yescharacteristic
158C2×C8#41×C12712yes—
159C2×C8#41×C12712yes—
160C2×C8#41×C12711yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C42—21no—
164C42—21no—
165C16—42no—
166C23C2×SD16×C12711yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—81no—
170Q8—81no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4—81no—
178C2×C4#121×C12711yescharacteristic
179C2×C4#123×C12711yescharacteristic
180C2×C4#124×C12711yescharacteristic
181C2×C4C2×D8×C12711yescharacteristic
182C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
183C2×C4#137×C12711yescharacteristic
184C8—22no—
185C8—82no—
186C8#123×C12712yes—
187C8#126×C12712yes—
188C22—22no—
189C22#461×C12711yescharacteristic
190C22#481×C12711yescharacteristic
191C22#486×C12711yescharacteristic
192C4—42no—
193C4—82no—
194C4—161no—
195C4#397×C12711yescharacteristic
196C4#459×C12711yescharacteristic
197C4#480×C12711yescharacteristic
198C4#489×C12711yescharacteristic
199C2—21no—
200C2—21no—
201C2C127×#207111yescharacteristic
202C2C127×#223912yes—
subgroupG/H
center, socleC22×C127#481
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127C2×SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
97. #13488C127direct (N × H)
107. C127#13488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#362×C1272
C127×#19712
C127×#18492
C127×#13832
C127×#13772
#13488127