Finite Group Databasebeta

← C127×#13512 #44577185

Subgroups — C127×#13512 #44577185

Order 32512.

232 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2161C211yesmaximal, characteristic
2C127×#2155C211yesmaximal, characteristic
3C127×#1951C211yesmaximal, characteristic
4C127×#1833C211yesmaximal, characteristic
5C127×#1386C211yesmaximal, characteristic
6C127×#1383C211yesmaximal, characteristic
7C127×#1378C211yesmaximal, characteristic
8C2×M32×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×#108×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#428×C127—21no—
13#427×C127C2211yescharacteristic
14C2×#106×C127C2211yescharacteristic
15#405×C127C2211yescharacteristic
16#368×C127—22no—
17#365×C127—22no—
18#344×C127—21no—
19#343×C127—21no—
20H(3,ℤ/4)×C127—21no—
21C2×M16×C127—21no—
22C2×M16×C127—21no—
23C2×M16×C127D411yescharacteristic
24C22×C8×C127C2311yescharacteristic
25#117×C127—21no—
26#117×C127D411yescharacteristic
27C2×C4⋊C4×C127—21no—
28M32×C127—21no—
29M32×C127—21no—
30M32×C127—21no—
31M32×C127Q812yes—
32C2×C16×C127—21no—
33C2×C16×C127Q812yes—
34#108×C127—21no—
35#108×C127—21no—
36#108×C127—21no—
37#108×C127D412yes—
38#107×C127—21no—
39#107×C127—41no—
40#106×C127—21no—
41#106×C127—21no—
42#106×C127—21no—
43#106×C127—41no—
44#97×C127—21no—
45C4×C8×C127—21no—
46C22×C4×C127—41no—
47C22×C4×C127C2×D411yescharacteristic
48M16×C127—22no—
49M16×C127—21no—
50M16×C127—21no—
51M16×C127—41no—
52M16×C127—41no—
53M16×C127—41no—
54C2×C8×C127—21no—
55C2×C8×C127—41no—
56C2×C8×C127—41no—
57C2×C8×C127C2×D411yescharacteristic
58C2×C8×C127C2×Q811yescharacteristic
59C2×C8×C127C2×Q811yescharacteristic
60C2×C8×C127#4111yescharacteristic
61C2×C8×C127#4111yescharacteristic
62C2×C8×C127#4111yescharacteristic
63C4⋊C4×C127—21no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C22⋊C4×C127—21no—
68C22⋊C4×C127—41no—
69C42×C127—21no—
70C42×C127—41no—
71C16×C127—22no—
72C16×C127—22no—
73C23×C127#13511yescharacteristic
74C2×C4×C127—41no—
75C2×C4×C127—81no—
76C2×C4×C127—81no—
77C2×C4×C127—161no—
78C2×C4×C127#12111yescharacteristic
79C2×C4×C127#12311yescharacteristic
80C2×C4×C127C4⋊Q811yescharacteristic
81C2×C4×C127#13511yescharacteristic
82C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C127#13711yescharacteristic
84C8×C127—42no—
85C8×C127—41no—
86C8×C127—81no—
87C8×C127C22⋊Q811yescharacteristic
88C8×C127C22⋊Q811yescharacteristic
89C8×C127#12511yescharacteristic
90C8×C127#12511yescharacteristic
91C22×C127—41no—
92C22×C127#46411yescharacteristic
93C22×C127#48211yescharacteristic
94C22×C127#49911yescharacteristic
95C4×C127—81no—
96C4×C127—161no—
97C4×C127—161no—
98C4×C127#39811yescharacteristic
99C4×C127#46311yescharacteristic
100C4×C127#48511yescharacteristic
101C4×C127#50111yescharacteristic
102#13512C12711yesmaximal, characteristic, direct product factor, Sylow
103C2×C127—21no—
104C2×C127—21no—
105C2×C127—21no—
106C2×C127#208511yescharacteristic
107#2161C2×C12711yescharacteristic
108#2155C2×C12711yescharacteristic
109#1951C2×C12711yescharacteristic
110#1833C2×C12711yescharacteristic
111#1386C2×C12711yescharacteristic
112#1383C2×C12711yescharacteristic
113#1378C2×C12711yescharacteristic
114C127#1351211yescharacteristic, direct product factor, Sylow
115C2×M32C22×C12711yescharacteristic
116C2×M32C22×C12711yescharacteristic
117C2×#108C22×C12711yescharacteristic
118C2×#108C22×C12711yescharacteristic
119#428—21no—
120#427C22×C12711yescharacteristic
121C2×#106C22×C12711yescharacteristic
122#405C22×C12711yescharacteristic
123#368—22no—
124#365—22no—
125#344—21no—
126#343—21no—
127H(3,ℤ/4)—21no—
128C2×M16—21no—
129C2×M16—21no—
130C2×M16D4×C12711yescharacteristic
131C22×C8C23×C12711yescharacteristic
132#117—21no—
133#117D4×C12711yescharacteristic
134C2×C4⋊C4—21no—
135M32—21no—
136M32—21no—
137M32—21no—
138M32Q8×C12712yes—
139C2×C16—21no—
140C2×C16Q8×C12712yes—
141#108—21no—
142#108—21no—
143#108—21no—
144#108D4×C12712yes—
145#107—21no—
146#107—41no—
147#106—21no—
148#106—21no—
149#106—21no—
150#106—41no—
151#97—21no—
152C4×C8—21no—
153C22×C4—41no—
154C22×C4C2×D4×C12711yescharacteristic
155M16—22no—
156M16—21no—
157M16—21no—
158M16—41no—
159M16—41no—
160M16—41no—
161C2×C8—21no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8C2×D4×C12711yescharacteristic
165C2×C8C2×Q8×C12711yescharacteristic
166C2×C8C2×Q8×C12711yescharacteristic
167C2×C8#41×C12711yescharacteristic
168C2×C8#41×C12711yescharacteristic
169C2×C8#41×C12711yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C22⋊C4—21no—
175C22⋊C4—41no—
176C42—21no—
177C42—41no—
178C16—22no—
179C16—22no—
180C23#135×C12711yescharacteristic
181C2×C4—41no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4—161no—
185C2×C4#121×C12711yescharacteristic
186C2×C4#123×C12711yescharacteristic
187C2×C4C4⋊Q8×C12711yescharacteristic
188C2×C4#135×C12711yescharacteristic
189C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
190C2×C4#137×C12711yescharacteristic
191C8—42no—
192C8—41no—
193C8—81no—
194C8C22⋊Q8×C12711yescharacteristic
195C8C22⋊Q8×C12711yescharacteristic
196C8#125×C12711yescharacteristic
197C8#125×C12711yescharacteristic
198C22—41no—
199C22#464×C12711yescharacteristic
200C22#482×C12711yescharacteristic
201C22#499×C12711yescharacteristic
202C4—81no—
203C4—161no—
204C4—161no—
205C4#398×C12711yescharacteristic
206C4#463×C12711yescharacteristic
207C4#485×C12711yescharacteristic
208C4#501×C12711yescharacteristic
209C2—21no—
210C2—21no—
211C2—21no—
212C2C127×#208511yescharacteristic
subgroupG/H
center, socleC2×C127#2085
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127#135
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
102. #13512C127direct (N × H)
114. C127#13512direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21612
C127×#21552
C127×#19512
C127×#18332
C127×#13862
C127×#13832
C127×#13782
#13512127