Finite Group Databasebeta

← C127×#12488 #44576161

Subgroups — C127×#12488 #44576161

Order 32512.

212 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2227C211yesmaximal, characteristic
2C127×#2209C211yesmaximal, characteristic
3C127×#1707C211yesmaximal, characteristic
4C127×#1591C211yesmaximal, characteristic
5C127×#1370C211yesmaximal, characteristic
6C127×#1365C211yesmaximal, characteristic
7C127×#1362C211yesmaximal, characteristic
8C2×Q32×C127—21no—
9#500×C127C2211yescharacteristic
10#498×C127—21no—
11#494×C127C2211yescharacteristic
12#487×C127—21no—
13#446×C127—21no—
14C4×Q16×C127C2211yescharacteristic
15#366×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#358×C127—21no—
19#358×C127—21no—
20#335×C127C2211yescharacteristic
21Q8⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×Q16×C127D411yescharacteristic
26C4⋊Q8×C127—21no—
27C4⋊Q8×C127—21no—
28C4×Q8×C127—21no—
29Q32×C127—42no—
30C2×C16×C127—21no—
31C2×C16×C127—21no—
32#107×C127—21no—
33#107×C127—21no—
34#107×C127D411yescharacteristic
35#106×C127—41no—
36#106×C127—41no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127—41no—
39#103×C127—21no—
40#103×C127—42no—
41#97×C127—41no—
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—21no—
46C2×Q8×C127—41no—
47C2×Q8×C127—41no—
48Q16×C127—21no—
49Q16×C127—21no—
50Q16×C127—41no—
51Q16×C127—41no—
52Q16×C127—81no—
53C2×C8×C127—21no—
54C2×C8×C127—41no—
55C2×C8×C127D811yescharacteristic
56C2×C8×C127D811yescharacteristic
57C2×C8×C127C2×D411yescharacteristic
58C2×C8×C127#4111yescharacteristic
59C4⋊C4×C127—21no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—41no—
65C42×C127—41no—
66C42×C127C2×D411yescharacteristic
67C16×C127—41no—
68C16×C127—41no—
69Q8×C127—41no—
70Q8×C127—41no—
71Q8×C127—82no—
72Q8×C127—81no—
73Q8×C127—81no—
74C2×C4×C127—41no—
75C2×C4×C127—41no—
76C2×C4×C127—81no—
77C2×C4×C127—81no—
78C2×C4×C127#12111yescharacteristic
79C2×C4×C127C2×D811yescharacteristic
80C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
81C8×C127—21no—
82C8×C127—21no—
83C8×C127—41no—
84C8×C127—81no—
85C8×C127Q3212yescomplemented
86C8×C127AGL(1,ℤ/8)11yescharacteristic
87C8×C127#13711yescharacteristic
88C22×C127#45911yescharacteristic
89C4×C127—21no—
90C4×C127—81no—
91C4×C127—81no—
92C4×C127—161no—
93C4×C127—161no—
94C4×C127#46811yescharacteristic
95C4×C127#47111yescharacteristic
96C4×C127C2×Q3211yescharacteristic
97C4×C127#51011yescharacteristic
98#12488C12711yesmaximal, characteristic, direct product factor, Sylow
99C2×C127#168511yescharacteristic
100C2×C127#220911yescharacteristic
101C2×C127#221211yescharacteristic
102#2227C2×C12711yescharacteristic
103#2209C2×C12711yescharacteristic
104#1707C2×C12711yescharacteristic
105#1591C2×C12711yescharacteristic
106#1370C2×C12711yescharacteristic
107#1365C2×C12711yescharacteristic
108#1362C2×C12711yescharacteristic
109C127#1248811yescharacteristic, direct product factor, Sylow
110C2×Q32—21no—
111#500C22×C12711yescharacteristic
112#498—21no—
113#494C22×C12711yescharacteristic
114#487—21no—
115#446—21no—
116C4×Q16C22×C12711yescharacteristic
117#366—21no—
118C4⋊C16C22×C12711yescharacteristic
119C4⋊C16C22×C12711yescharacteristic
120#358—21no—
121#358—21no—
122#335C22×C12711yescharacteristic
123Q8⋊C8—21no—
124C82C22×C12711yescharacteristic
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16D4×C12711yescharacteristic
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4×Q8—21no—
131Q32—42no—
132C2×C16—21no—
133C2×C16—21no—
134#107—21no—
135#107—21no—
136#107D4×C12711yescharacteristic
137#106—41no—
138#106—41no—
139C4⋊C8—21no—
140C4⋊C8—41no—
141#103—21no—
142#103—42no—
143#97—41no—
144C4×C8D4×C12711yescharacteristic
145C4×C8D4×C12711yescharacteristic
146C4×C8C23×C12711yescharacteristic
147C2×Q8—21no—
148C2×Q8—41no—
149C2×Q8—41no—
150Q16—21no—
151Q16—21no—
152Q16—41no—
153Q16—41no—
154Q16—81no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8D8×C12711yescharacteristic
158C2×C8D8×C12711yescharacteristic
159C2×C8C2×D4×C12711yescharacteristic
160C2×C8#41×C12711yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C42—41no—
168C42C2×D4×C12711yescharacteristic
169C16—41no—
170C16—41no—
171Q8—41no—
172Q8—41no—
173Q8—82no—
174Q8—81no—
175Q8—81no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4#121×C12711yescharacteristic
181C2×C4C2×D8×C12711yescharacteristic
182C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—81no—
187C8Q32×C12712yescomplemented
188C8AGL(1,ℤ/8)×C12711yescharacteristic
189C8#137×C12711yescharacteristic
190C22#459×C12711yescharacteristic
191C4—21no—
192C4—81no—
193C4—81no—
194C4—161no—
195C4—161no—
196C4#468×C12711yescharacteristic
197C4#471×C12711yescharacteristic
198C4C2×Q32×C12711yescharacteristic
199C4#510×C12711yescharacteristic
200C2C127×#168511yescharacteristic
201C2C127×#220911yescharacteristic
202C2C127×#221211yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
85. C8×C127Q32semidirect
98. #12488C127direct (N × H)
109. C127#12488direct (N × H)
187. C8Q32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22272
C127×#22092
C127×#17072
C127×#15912
C127×#13702
C127×#13652
C127×#13622
#12488127