Finite Group Databasebeta

← C127×#12079 #44575752

Subgroups — C127×#12079 #44575752

Order 32512.

204 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2176C211yesmaximal, characteristic
2C127×#1593C211yesmaximal, characteristic
3C127×#1579C211yesmaximal, characteristic
4C127×#1368C211yesmaximal, characteristic
5C127×#1334C211yesmaximal, characteristic
6C127×#1334C211yesmaximal, characteristic
7C127×#1313C211yesmaximal, characteristic
8C2×Q32×C127C411yescharacteristic
9#446×C127—21no—
10C8×Q8×C127—21no—
11C4×Q16×C127C2211yescharacteristic
12C4×Q16×C127C2211yescharacteristic
13#367×C127C411yescharacteristic
14#358×C127C411yescharacteristic
15#358×C127C411yescharacteristic
16#346×C127C2211yescharacteristic
17#346×C127C2211yescharacteristic
18#334×C127C2211yescharacteristic
19#334×C127C2211yescharacteristic
20Q8⋊C8×C127—21no—
21Q8⋊C8×C127—21no—
22#322×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—21no—
52C2×C8×C127—41no—
53C2×C8×C127—41no—
54C2×C8×C127C22×C411yescharacteristic
55C2×C8×C127#4111yescharacteristic
56C4⋊C4×C127—21no—
57C4⋊C4×C127—21no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C42×C127—41no—
61C42×C127—41no—
62C42×C127C2×D411yescharacteristic
63C16×C127—22no—
64C16×C127—21no—
65C16×C127—21no—
66Q8×C127—22no—
67Q8×C127—41no—
68Q8×C127—41no—
69Q8×C127—41no—
70C2×C4×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127C4×D411yescharacteristic
75C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
76C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
77C8×C127—21no—
78C8×C127—41no—
79C8×C127—41no—
80C8×C127—81no—
81C8×C127—81no—
82C8×C127C2×M1611yescharacteristic
83C8×C127#13111yescharacteristic
84C22×C127#44211yescharacteristic
85C4×C127—21no—
86C4×C127—21no—
87C4×C127—42no—
88C4×C127—81no—
89C4×C127—81no—
90C4×C127—81no—
91C4×C127#43511yescharacteristic
92C4×C127#44311yescharacteristic
93#12079C12711yesmaximal, characteristic, direct product factor, Sylow
94C2×C127#158611yescharacteristic
95C2×C127#218011yescharacteristic
96C2×C127#218011yescharacteristic
97#2176C2×C12711yescharacteristic
98#1593C2×C12711yescharacteristic
99#1579C2×C12711yescharacteristic
100#1368C2×C12711yescharacteristic
101#1334C2×C12711yescharacteristic
102#1334C2×C12711yescharacteristic
103#1313C2×C12711yescharacteristic
104C127#1207911yescharacteristic, direct product factor, Sylow
105C2×Q32C4×C12711yescharacteristic
106#446—21no—
107C8×Q8—21no—
108C4×Q16C22×C12711yescharacteristic
109C4×Q16C22×C12711yescharacteristic
110#367C4×C12711yescharacteristic
111#358C4×C12711yescharacteristic
112#358C4×C12711yescharacteristic
113#346C22×C12711yescharacteristic
114#346C22×C12711yescharacteristic
115#334C22×C12711yescharacteristic
116#334C22×C12711yescharacteristic
117Q8⋊C8—21no—
118Q8⋊C8—21no—
119#322C22×C12711yescharacteristic
120C2×Q16C2×C4×C12711yescharacteristic
121C2×Q16C2×C4×C12711yescharacteristic
122C4×Q8—21no—
123C4×Q8—21no—
124Q32—22no—
125C2×C16—21no—
126C2×C16C2×C4×C12711yescharacteristic
127C2×C16C2×C4×C12711yescharacteristic
128#107C2×C4×C12711yescharacteristic
129#107C2×C4×C12711yescharacteristic
130C4⋊C8—21no—
131C4⋊C8—21no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134#103—21no—
135#103—21no—
136#97—41no—
137C4×C8—41no—
138C4×C8D4×C12711yescharacteristic
139C4×C8D4×C12711yescharacteristic
140C4×C8C23×C12711yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143Q16—21no—
144Q16—21no—
145Q16—21no—
146Q16M16×C12712yes—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8C22×C4×C12711yescharacteristic
152C2×C8#41×C12711yescharacteristic
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C42—41no—
158C42—41no—
159C42C2×D4×C12711yescharacteristic
160C16—22no—
161C16—21no—
162C16—21no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4C4×D4×C12711yescharacteristic
172C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
173C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
174C8—21no—
175C8—41no—
176C8—41no—
177C8—81no—
178C8—81no—
179C8C2×M16×C12711yescharacteristic
180C8#131×C12711yescharacteristic
181C22#442×C12711yescharacteristic
182C4—21no—
183C4—21no—
184C4—42no—
185C4—81no—
186C4—81no—
187C4—81no—
188C4#435×C12711yescharacteristic
189C4#443×C12711yescharacteristic
190C2C127×#158611yescharacteristic
191C2C127×#218011yescharacteristic
192C2C127×#218011yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#442
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ #322×C127 ◁ G

Complements

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

NH ≅ G/Ntype
93. #12079C127direct (N × H)
104. C127#12079direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21762
C127×#15932
C127×#15792
C127×#13682
C127×#13342
C127×#13132
#12079127