Finite Group Databasebeta

← C127×#13439 #44577112

Subgroups — C127×#13439 #44577112

Order 32512.

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

normal subgroups only

This group has 418 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×D16×C127C211yesmaximal, characteristic
2C127×#2151C211yesmaximal, characteristic, complemented
3C2×#361×C127C212yesmaximal, complemented
4C127×#1978C212yesmaximal, complemented
5C127×#1381C211yesmaximal, characteristic, complemented
6C22×D8×C127C2212yes—
7C2×D16×C127—24no—
8C2×D16×C127—22no—
9C2×M32×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#108×C127C2212yes—
12#418×C127—22no—
13C2×#100×C127—22no—
14#405×C127C2211yescharacteristic
15C4⋊C16×C127—22no—
16#361×C127—24no—
17C22×D4×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—22no—
21C2×D8×C127—22no—
22C2×D8×C127—22no—
23C2×D8×C127D414yes—
24C2×M16×C127—22no—
25C2×M16×C127D411yescharacteristic
26C22×C8×C127C2311yescharacteristic
27#117×C127D411yescharacteristic
28D16×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#102×C127—44no—
36#100×C127—44no—
37#97×C127—21no—
38C4×C8×C127—21no—
39C24×C127—42no—
40C2×D4×C127—24no—
41C2×D4×C127—42no—
42C2×D4×C127—42no—
43C2×D4×C127—42no—
44C2×D4×C127—42no—
45C2×D4×C127—42no—
46C22×C4×C127C2×D411yescharacteristic
47D8×C127—24no—
48D8×C127—24no—
49D8×C127—42no—
50D8×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—44no—
66C23×C127—82no—
67C23×C127—82no—
68C23×C127—164no—
69C23×C127#13511yescharacteristic
70D4×C127—44no—
71D4×C127—44no—
72D4×C127—82no—
73D4×C127—82no—
74C2×C4×C127—22no—
75C2×C4×C127#12112yes—
76C2×C4×C127#12111yescharacteristic
77C2×C4×C127C2×D811yescharacteristic
78C2×C4×C127AGL(1,ℤ/8)12yes—
79C8×C127—41no—
80C8×C127—82no—
81C8×C127#12011yescharacteristic
82C8×C127#12312yes—
83C8×C127#12411yescharacteristic
84C22×C127—22no—
85C22×C127—84no—
86C22×C127—164no—
87C22×C127—164no—
88C22×C127—164no—
89C22×C127#46312yes—
90C22×C127#46611yescharacteristic
91C4×C127—42no—
92C4×C127#39411yescharacteristic
93C4×C127#45912yes—
94C4×C127#46911yescharacteristic
95#13439C12711yesmaximal, characteristic, direct product factor, Sylow
96C2×C127—22no—
97C2×C127—164no—
98C2×C127#205411yescharacteristic
99C2×C127#222112yes—
100C22×D16C2×C12711yescharacteristic
101#2151C2×C12711yescharacteristic, complemented
102C2×#361C2×C12712yescomplemented
103#1978C2×C12712yescomplemented
104#1381C2×C12711yescharacteristic, complemented
105C127#1343911yescharacteristic, direct product factor, Sylow
106C22×D8C22×C12712yes—
107C2×D16—24no—
108C2×D16—22no—
109C2×M32C22×C12711yescharacteristic
110C22×C16C22×C12711yescharacteristic
111C2×#108C22×C12712yes—
112#418—22no—
113C2×#100—22no—
114#405C22×C12711yescharacteristic
115C4⋊C16—22no—
116#361—24no—
117C22×D4—22no—
118C2×D8—22no—
119C2×D8—22no—
120C2×D8—22no—
121C2×D8—22no—
122C2×D8—22no—
123C2×D8D4×C12714yes—
124C2×M16—22no—
125C2×M16D4×C12711yescharacteristic
126C22×C8C23×C12711yescharacteristic
127#117D4×C12711yescharacteristic
128D16—28no—
129M32—22no—
130C2×C16—22no—
131C2×C16—21no—
132C2×C16D4×C12712yes—
133#108—22no—
134#108—22no—
135#102—44no—
136#100—44no—
137#97—21no—
138C4×C8—21no—
139C24—42no—
140C2×D4—24no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—42no—
146C22×C4C2×D4×C12711yescharacteristic
147D8—24no—
148D8—24no—
149D8—42no—
150D8—42no—
151M16—22no—
152M16—42no—
153M16—42no—
154C2×C8—21no—
155C2×C8—42no—
156C2×C8C2×D4×C12712yes—
157C2×C8C2×D4×C12711yescharacteristic
158C2×C8#41×C12711yescharacteristic
159C2×C8#41×C12712yes—
160C4⋊C4D8×C12712yes—
161C22⋊C4—21no—
162C42—21no—
163C16—22no—
164C16—41no—
165C23—44no—
166C23—82no—
167C23—82no—
168C23—164no—
169C23#135×C12711yescharacteristic
170D4—44no—
171D4—44no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4#121×C12712yes—
176C2×C4#121×C12711yescharacteristic
177C2×C4C2×D8×C12711yescharacteristic
178C2×C4AGL(1,ℤ/8)×C12712yes—
179C8—41no—
180C8—82no—
181C8#120×C12711yescharacteristic
182C8#123×C12712yes—
183C8#124×C12711yescharacteristic
184C22—22no—
185C22—84no—
186C22—164no—
187C22—164no—
188C22—164no—
189C22#463×C12712yes—
190C22#466×C12711yescharacteristic
191C4—42no—
192C4#394×C12711yescharacteristic
193C4#459×C12712yes—
194C4#469×C12711yescharacteristic
195C2—22no—
196C2—164no—
197C2C127×#205411yescharacteristic
198C2C127×#222112yes—
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D16×C127C2
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
2. C127×#2151C2semidirect
3. C2×#361×C127C2semidirect
4. C127×#1978C2semidirect
5. C127×#1381C2semidirect
95. #13439C127direct (N × H)
101. #2151C2×C127semidirect
102. C2×#361C2×C127semidirect
103. #1978C2×C127semidirect
104. #1381C2×C127semidirect
105. C127#13439direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D16×C1272
C127×#21512
C2×#361×C1272
C127×#19782
C127×#13812
#13439127