Finite Group Databasebeta

← C127×#13441 #44577114

Subgroups — C127×#13441 #44577114

Order 32512.

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

normal subgroups only

This group has 378 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
1C22×Q32×C127C211yesmaximal, characteristic
2C127×#2151C211yesmaximal, characteristic
3C2×#362×C127C212yesmaximal
4C127×#1979C212yesmaximal
5C127×#1381C211yesmaximal, characteristic
6C22×Q16×C127C2212yes—
7C2×Q32×C127—24no—
8C2×Q32×C127—22no—
9C2×M32×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#108×C127C2212yes—
12#419×C127—22no—
13C2×#101×C127—22no—
14#405×C127C2211yescharacteristic
15C4⋊C16×C127—22no—
16#362×C127—24no—
17C22×Q8×C127—22no—
18C2×Q16×C127—22no—
19C2×Q16×C127—22no—
20C2×Q16×C127—22no—
21C2×Q16×C127—22no—
22C2×Q16×C127—22no—
23C2×Q16×C127D414yes—
24C2×M16×C127—22no—
25C2×M16×C127D411yescharacteristic
26C22×C8×C127C2311yescharacteristic
27#117×C127D411yescharacteristic
28Q32×C127—28no—
29M32×C127—22no—
30C2×C16×C127—22no—
31C2×C16×C127—21no—
32C2×C16×C127D412yes—
33#108×C127—22no—
34#108×C127—22no—
35#103×C127—44no—
36#101×C127—44no—
37#97×C127—21no—
38C4×C8×C127—21no—
39C2×Q8×C127—24no—
40C2×Q8×C127—42no—
41C2×Q8×C127—42no—
42C2×Q8×C127—42no—
43C2×Q8×C127—42no—
44C2×Q8×C127—42no—
45C22×C4×C127—42no—
46C22×C4×C127C2×D411yescharacteristic
47Q16×C127—24no—
48Q16×C127—24no—
49Q16×C127—42no—
50Q16×C127—42no—
51M16×C127—22no—
52M16×C127—42no—
53M16×C127—42no—
54C2×C8×C127—21no—
55C2×C8×C127—42no—
56C2×C8×C127C2×D412yes—
57C2×C8×C127C2×D411yescharacteristic
58C2×C8×C127#4111yescharacteristic
59C2×C8×C127#4112yes—
60C4⋊C4×C127D812yes—
61C22⋊C4×C127—21no—
62C42×C127—21no—
63C16×C127—22no—
64C16×C127—41no—
65C23×C127#13511yescharacteristic
66Q8×C127—44no—
67Q8×C127—44no—
68Q8×C127—82no—
69Q8×C127—82no—
70C2×C4×C127—22no—
71C2×C4×C127—44no—
72C2×C4×C127—82no—
73C2×C4×C127—82no—
74C2×C4×C127#12112yes—
75C2×C4×C127#12111yescharacteristic
76C2×C4×C127C2×D811yescharacteristic
77C2×C4×C127AGL(1,ℤ/8)12yes—
78C8×C127—41no—
79C8×C127—82no—
80C8×C127#12011yescharacteristic
81C8×C127#12312yes—
82C8×C127#12411yescharacteristic
83C22×C127—22no—
84C22×C127#46312yes—
85C22×C127#46611yescharacteristic
86C4×C127—42no—
87C4×C127—84no—
88C4×C127#39411yescharacteristic
89C4×C127#45912yes—
90C4×C127#46911yescharacteristic
91#13441C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—22no—
93C2×C127#205411yescharacteristic
94C2×C127#222212yes—
95C22×Q32C2×C12711yescharacteristic
96#2151C2×C12711yescharacteristic
97C2×#362C2×C12712yes—
98#1979C2×C12712yes—
99#1381C2×C12711yescharacteristic
100C127#1344111yescharacteristic, direct product factor, Sylow
101C22×Q16C22×C12712yes—
102C2×Q32—24no—
103C2×Q32—22no—
104C2×M32C22×C12711yescharacteristic
105C22×C16C22×C12711yescharacteristic
106C2×#108C22×C12712yes—
107#419—22no—
108C2×#101—22no—
109#405C22×C12711yescharacteristic
110C4⋊C16—22no—
111#362—24no—
112C22×Q8—22no—
113C2×Q16—22no—
114C2×Q16—22no—
115C2×Q16—22no—
116C2×Q16—22no—
117C2×Q16—22no—
118C2×Q16D4×C12714yes—
119C2×M16—22no—
120C2×M16D4×C12711yescharacteristic
121C22×C8C23×C12711yescharacteristic
122#117D4×C12711yescharacteristic
123Q32—28no—
124M32—22no—
125C2×C16—22no—
126C2×C16—21no—
127C2×C16D4×C12712yes—
128#108—22no—
129#108—22no—
130#103—44no—
131#101—44no—
132#97—21no—
133C4×C8—21no—
134C2×Q8—24no—
135C2×Q8—42no—
136C2×Q8—42no—
137C2×Q8—42no—
138C2×Q8—42no—
139C2×Q8—42no—
140C22×C4—42no—
141C22×C4C2×D4×C12711yescharacteristic
142Q16—24no—
143Q16—24no—
144Q16—42no—
145Q16—42no—
146M16—22no—
147M16—42no—
148M16—42no—
149C2×C8—21no—
150C2×C8—42no—
151C2×C8C2×D4×C12712yes—
152C2×C8C2×D4×C12711yescharacteristic
153C2×C8#41×C12711yescharacteristic
154C2×C8#41×C12712yes—
155C4⋊C4D8×C12712yes—
156C22⋊C4—21no—
157C42—21no—
158C16—22no—
159C16—41no—
160C23#135×C12711yescharacteristic
161Q8—44no—
162Q8—44no—
163Q8—82no—
164Q8—82no—
165C2×C4—22no—
166C2×C4—44no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4#121×C12712yes—
170C2×C4#121×C12711yescharacteristic
171C2×C4C2×D8×C12711yescharacteristic
172C2×C4AGL(1,ℤ/8)×C12712yes—
173C8—41no—
174C8—82no—
175C8#120×C12711yescharacteristic
176C8#123×C12712yes—
177C8#124×C12711yescharacteristic
178C22—22no—
179C22#463×C12712yes—
180C22#466×C12711yescharacteristic
181C4—42no—
182C4—84no—
183C4#394×C12711yescharacteristic
184C4#459×C12712yes—
185C4#469×C12711yescharacteristic
186C2—22no—
187C2C127×#205411yescharacteristic
188C2C127×#222212yes—
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127#135
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
91. #13441C127direct (N × H)
100. C127#13441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q32×C1272
C127×#21512
C2×#362×C1272
C127×#19792
C127×#13812
#13441127