Finite Group Databasebeta

← C127×#12076 #44575749

Subgroups — C127×#12076 #44575749

Order 32512.

210 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×Q32×C127C211yesmaximal, characteristic
2C127×#1591C211yesmaximal, characteristic
3C8×Q16×C127C211yesmaximal, characteristic
4C127×#1372C211yesmaximal, characteristic
5C127×#1332C211yesmaximal, characteristic
6C127×#1332C211yesmaximal, characteristic
7C127×#1312C211yesmaximal, characteristic
8C2×Q32×C127C411yescharacteristic
9#446×C127—21no—
10C8×Q8×C127—21no—
11C4×Q16×C127C2211yescharacteristic
12C4×Q16×C127C2211yescharacteristic
13#366×C127C411yescharacteristic
14#358×C127C411yescharacteristic
15#358×C127C411yescharacteristic
16C4×C16×C127C2211yescharacteristic
17C4×C16×C127C2211yescharacteristic
18#335×C127C2211yescharacteristic
19#335×C127C2211yescharacteristic
20Q8⋊C8×C127—21no—
21Q8⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×Q16×C127C2×C411yescharacteristic
24C2×Q16×C127C2×C411yescharacteristic
25C4×Q8×C127—21no—
26C4×Q8×C127—21no—
27Q32×C127—22no—
28C2×C16×C127—21no—
29C2×C16×C127C2×C411yescharacteristic
30C2×C16×C127C2×C411yescharacteristic
31#107×C127C2×C411yescharacteristic
32#107×C127C2×C411yescharacteristic
33C4⋊C8×C127—21no—
34C4⋊C8×C127—21no—
35C4⋊C8×C127—41no—
36C4⋊C8×C127—41no—
37#103×C127—21no—
38#103×C127—21no—
39#97×C127—41no—
40C4×C8×C127—41no—
41C4×C8×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127C2311yescharacteristic
44C2×Q8×C127—21no—
45C2×Q8×C127—21no—
46Q16×C127—21no—
47Q16×C127—21no—
48Q16×C127—21no—
49Q16×C127M1612yes—
50C2×C8×C127—21no—
51C2×C8×C127—41no—
52C2×C8×C127—41no—
53C2×C8×C127D811yescharacteristic
54C2×C8×C127D811yescharacteristic
55C2×C8×C127C22×C411yescharacteristic
56C2×C8×C127#4111yescharacteristic
57C4⋊C4×C127—21no—
58C4⋊C4×C127—21no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C42×C127—41no—
62C42×C127—41no—
63C42×C127C2×D411yescharacteristic
64C16×C127—21no—
65C16×C127—21no—
66C16×C127—41no—
67Q8×C127—22no—
68Q8×C127—41no—
69Q8×C127—41no—
70Q8×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127C4×D411yescharacteristic
76C2×C4×C127C2×D811yescharacteristic
77C2×C4×C127#13511yescharacteristic
78C8×C127—22no—
79C8×C127—21no—
80C8×C127—21no—
81C8×C127—21no—
82C8×C127—81no—
83C8×C127—81no—
84C8×C127C2×M1611yescharacteristic
85C8×C127#13111yescharacteristic
86C22×C127C4×D811yescharacteristic
87C4×C127—21no—
88C4×C127—42no—
89C4×C127—81no—
90C4×C127—81no—
91C4×C127—81no—
92C4×C127#43511yescharacteristic
93C4×C127#44411yescharacteristic
94C4×C127#51011yescharacteristic
95C4×C127#51011yescharacteristic
96#12076C12711yesmaximal, characteristic, direct product factor, Sylow
97C2×C127#158111yescharacteristic
98C2×C127#217611yescharacteristic
99C2×C127#217811yescharacteristic
100C4×Q32C2×C12711yescharacteristic
101#1591C2×C12711yescharacteristic
102C8×Q16C2×C12711yescharacteristic
103#1372C2×C12711yescharacteristic
104#1332C2×C12711yescharacteristic
105#1332C2×C12711yescharacteristic
106#1312C2×C12711yescharacteristic
107C127#1207611yescharacteristic, direct product factor, Sylow
108C2×Q32C4×C12711yescharacteristic
109#446—21no—
110C8×Q8—21no—
111C4×Q16C22×C12711yescharacteristic
112C4×Q16C22×C12711yescharacteristic
113#366C4×C12711yescharacteristic
114#358C4×C12711yescharacteristic
115#358C4×C12711yescharacteristic
116C4×C16C22×C12711yescharacteristic
117C4×C16C22×C12711yescharacteristic
118#335C22×C12711yescharacteristic
119#335C22×C12711yescharacteristic
120Q8⋊C8—21no—
121Q8⋊C8—21no—
122C82C22×C12711yescharacteristic
123C2×Q16C2×C4×C12711yescharacteristic
124C2×Q16C2×C4×C12711yescharacteristic
125C4×Q8—21no—
126C4×Q8—21no—
127Q32—22no—
128C2×C16—21no—
129C2×C16C2×C4×C12711yescharacteristic
130C2×C16C2×C4×C12711yescharacteristic
131#107C2×C4×C12711yescharacteristic
132#107C2×C4×C12711yescharacteristic
133C4⋊C8—21no—
134C4⋊C8—21no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137#103—21no—
138#103—21no—
139#97—41no—
140C4×C8—41no—
141C4×C8D4×C12711yescharacteristic
142C4×C8D4×C12711yescharacteristic
143C4×C8C23×C12711yescharacteristic
144C2×Q8—21no—
145C2×Q8—21no—
146Q16—21no—
147Q16—21no—
148Q16—21no—
149Q16M16×C12712yes—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8D8×C12711yescharacteristic
154C2×C8D8×C12711yescharacteristic
155C2×C8C22×C4×C12711yescharacteristic
156C2×C8#41×C12711yescharacteristic
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C42—41no—
162C42—41no—
163C42C2×D4×C12711yescharacteristic
164C16—21no—
165C16—21no—
166C16—41no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4C4×D4×C12711yescharacteristic
176C2×C4C2×D8×C12711yescharacteristic
177C2×C4#135×C12711yescharacteristic
178C8—22no—
179C8—21no—
180C8—21no—
181C8—21no—
182C8—81no—
183C8—81no—
184C8C2×M16×C12711yescharacteristic
185C8#131×C12711yescharacteristic
186C22C4×D8×C12711yescharacteristic
187C4—21no—
188C4—42no—
189C4—81no—
190C4—81no—
191C4—81no—
192C4#435×C12711yescharacteristic
193C4#444×C12711yescharacteristic
194C4#510×C12711yescharacteristic
195C4#510×C12711yescharacteristic
196C2C127×#158111yescharacteristic
197C2C127×#217611yescharacteristic
198C2C127×#217811yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socle, prime radicalC22×C127C4×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
96. #12076C127direct (N × H)
107. C127#12076direct (N × H)

Maximal subgroups

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

subgroupindex
C4×Q32×C1272
C127×#15912
C8×Q16×C1272
C127×#13722
C127×#13322
C127×#13122
#12076127