Finite Group Databasebeta

← C127×#13510 #44577183

Subgroups — C127×#13510 #44577183

Order 32512.

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

normal subgroups only

This group has 270 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
1C2×#365×C127C212yesmaximal
2C127×#1944C211yesmaximal, characteristic
3C127×#1849C211yesmaximal, characteristic
4C127×#1387C212yesmaximal
5C127×#1377C211yesmaximal, characteristic
6C2×M32×C127C2212yes—
7C2×#108×C127—21no—
8C2×#108×C127C2212yes—
9C2×#107×C127C2211yescharacteristic
10C2×#106×C127C2211yescharacteristic
11#423×C127—21no—
12C2×#97×C127C2211yescharacteristic
13#389×C127—21no—
14#365×C127—24no—
15#340×C127—21no—
16C2×M16×C127—22no—
17C22×C8×C127D411yescharacteristic
18C22×C8×C127C2311yescharacteristic
19C2×C4⋊C4×C127—21no—
20C2×C4⋊C4×C127—21no—
21C2×C4⋊C4×C127—41no—
22C2×C42×C127D411yescharacteristic
23M32×C127—22no—
24M32×C127Q814yes—
25C2×C16×C127—22no—
26#108×C127—22no—
27#108×C127—22no—
28#108×C127—42no—
29#107×C127—22no—
30#106×C127—21no—
31#106×C127D412yes—
32C4⋊C8×C127—42no—
33#97×C127—22no—
34#95×C127—41no—
35C22×C4×C127—41no—
36C22×C4×C127—41no—
37C22×C4×C127SD1611yescharacteristic
38C22×C4×C127SD1611yescharacteristic
39C22×C4×C127C2×D411yescharacteristic
40M16×C127—42no—
41M16×C127—42no—
42C2×C8×C127—21no—
43C2×C8×C127—21no—
44C2×C8×C127—42no—
45C2×C8×C127SD1612yes—
46C2×C8×C127C2×D411yescharacteristic
47C2×C8×C127C2×Q812yes—
48C2×C8×C127#4112yes—
49C2×C8×C127#4111yescharacteristic
50C4⋊C4×C127—22no—
51C4⋊C4×C127—41no—
52C4⋊C4×C127—41no—
53C4⋊C4×C127—41no—
54C4⋊C4×C127—82no—
55C42×C127—21no—
56C42×C127—21no—
57C16×C127—24no—
58C23×C127C2×SD1611yescharacteristic
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—41no—
62C2×C4×C127—41no—
63C2×C4×C127—42no—
64C2×C4×C127—81no—
65C2×C4×C127—81no—
66C2×C4×C127—81no—
67C2×C4×C127—81no—
68C2×C4×C127—81no—
69C2×C4×C127#12111yescharacteristic
70C2×C4×C127#12311yescharacteristic
71C2×C4×C127C4⋊Q811yescharacteristic
72C2×C4×C127C2×SD1611yescharacteristic
73C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
74C2×C4×C127#13711yescharacteristic
75C8×C127—22no—
76C8×C127—82no—
77C8×C127C22⋊Q812yes—
78C8×C127#12512yes—
79C22×C127—21no—
80C22×C127—21no—
81C22×C127#46111yescharacteristic
82C22×C127#48111yescharacteristic
83C22×C127#49811yescharacteristic
84C4×C127—41no—
85C4×C127—41no—
86C4×C127—82no—
87C4×C127—161no—
88C4×C127#39811yescharacteristic
89C4×C127#46011yescharacteristic
90C4×C127#48311yescharacteristic
91C4×C127#50111yescharacteristic
92#13510C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127—21no—
94C2×C127—21no—
95C2×C127#208411yescharacteristic
96C2×C127#223811yescharacteristic
97C2×C127#223911yescharacteristic
98C2×#365C2×C12712yes—
99#1944C2×C12711yescharacteristic
100#1849C2×C12711yescharacteristic
101#1387C2×C12712yes—
102#1377C2×C12711yescharacteristic
103C127#1351011yescharacteristic, direct product factor, Sylow
104C2×M32C22×C12712yes—
105C2×#108—21no—
106C2×#108C22×C12712yes—
107C2×#107C22×C12711yescharacteristic
108C2×#106C22×C12711yescharacteristic
109#423—21no—
110C2×#97C22×C12711yescharacteristic
111#389—21no—
112#365—24no—
113#340—21no—
114C2×M16—22no—
115C22×C8D4×C12711yescharacteristic
116C22×C8C23×C12711yescharacteristic
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42D4×C12711yescharacteristic
121M32—22no—
122M32Q8×C12714yes—
123C2×C16—22no—
124#108—22no—
125#108—22no—
126#108—42no—
127#107—22no—
128#106—21no—
129#106D4×C12712yes—
130C4⋊C8—42no—
131#97—22no—
132#95—41no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4SD16×C12711yescharacteristic
136C22×C4SD16×C12711yescharacteristic
137C22×C4C2×D4×C12711yescharacteristic
138M16—42no—
139M16—42no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—42no—
143C2×C8SD16×C12712yes—
144C2×C8C2×D4×C12711yescharacteristic
145C2×C8C2×Q8×C12712yes—
146C2×C8#41×C12712yes—
147C2×C8#41×C12711yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—82no—
153C42—21no—
154C42—21no—
155C16—24no—
156C23C2×SD16×C12711yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4#121×C12711yescharacteristic
168C2×C4#123×C12711yescharacteristic
169C2×C4C4⋊Q8×C12711yescharacteristic
170C2×C4C2×SD16×C12711yescharacteristic
171C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
172C2×C4#137×C12711yescharacteristic
173C8—22no—
174C8—82no—
175C8C22⋊Q8×C12712yes—
176C8#125×C12712yes—
177C22—21no—
178C22—21no—
179C22#461×C12711yescharacteristic
180C22#481×C12711yescharacteristic
181C22#498×C12711yescharacteristic
182C4—41no—
183C4—41no—
184C4—82no—
185C4—161no—
186C4#398×C12711yescharacteristic
187C4#460×C12711yescharacteristic
188C4#483×C12711yescharacteristic
189C4#501×C12711yescharacteristic
190C2—21no—
191C2—21no—
192C2C127×#208411yescharacteristic
193C2C127×#223811yescharacteristic
194C2C127×#223911yescharacteristic
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
92. #13510C127direct (N × H)
103. C127#13510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#365×C1272
C127×#19442
C127×#18492
C127×#13872
C127×#13772
#13510127