Finite Group Databasebeta

← C127×#12490 #44576163

Subgroups — C127×#12490 #44576163

Order 32512.

212 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 78 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×#2225C211yesmaximal, characteristic
2C127×#2209C211yesmaximal, characteristic
3C127×#1707C211yesmaximal, characteristic
4C127×#1591C211yesmaximal, characteristic
5C127×#1370C211yesmaximal, characteristic
6C127×#1364C211yesmaximal, 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#367×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—42no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—41no—
38#103×C127—21no—
39#103×C127—41no—
40#103×C127—41no—
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—81no—
72Q8×C127—81no—
73Q8×C127—81no—
74Q8×C127—81no—
75C2×C4×C127—41no—
76C2×C4×C127—41no—
77C2×C4×C127—81no—
78C2×C4×C127—81no—
79C2×C4×C127#12111yescharacteristic
80C2×C4×C127C2×D811yescharacteristic
81C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
82C8×C127—22no—
83C8×C127—21no—
84C8×C127—21no—
85C8×C127—21no—
86C8×C127—81no—
87C8×C127AGL(1,ℤ/8)11yescharacteristic
88C8×C127#13711yescharacteristic
89C22×C127#45911yescharacteristic
90C4×C127—21no—
91C4×C127—81no—
92C4×C127—81no—
93C4×C127—161no—
94C4×C127—161no—
95C4×C127#46811yescharacteristic
96C4×C127#47111yescharacteristic
97C4×C127#50811yescharacteristic
98C4×C127#51011yescharacteristic
99#12490C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127#168511yescharacteristic
101C2×C127#221111yescharacteristic
102C2×C127#221411yescharacteristic
103#2225C2×C12711yescharacteristic
104#2209C2×C12711yescharacteristic
105#1707C2×C12711yescharacteristic
106#1591C2×C12711yescharacteristic
107#1370C2×C12711yescharacteristic
108#1364C2×C12711yescharacteristic
109#1362C2×C12711yescharacteristic
110C127#1249011yescharacteristic, direct product factor, Sylow
111C2×Q32—21no—
112#500C22×C12711yescharacteristic
113#498—21no—
114#494C22×C12711yescharacteristic
115#487—21no—
116#446—21no—
117C4×Q16C22×C12711yescharacteristic
118#367—21no—
119C4⋊C16C22×C12711yescharacteristic
120C4⋊C16C22×C12711yescharacteristic
121#358—21no—
122#358—21no—
123#335C22×C12711yescharacteristic
124Q8⋊C8—21no—
125C82C22×C12711yescharacteristic
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16D4×C12711yescharacteristic
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4×Q8—21no—
132Q32—42no—
133C2×C16—21no—
134C2×C16—21no—
135#107—21no—
136#107—21no—
137#107D4×C12711yescharacteristic
138#106—42no—
139C4⋊C8—21no—
140C4⋊C8—41no—
141#103—21no—
142#103—41no—
143#103—41no—
144#97—41no—
145C4×C8D4×C12711yescharacteristic
146C4×C8D4×C12711yescharacteristic
147C4×C8C23×C12711yescharacteristic
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151Q16—21no—
152Q16—21no—
153Q16—41no—
154Q16—41no—
155Q16—81no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8D8×C12711yescharacteristic
159C2×C8D8×C12711yescharacteristic
160C2×C8C2×D4×C12711yescharacteristic
161C2×C8#41×C12711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C42—41no—
169C42C2×D4×C12711yescharacteristic
170C16—41no—
171C16—41no—
172Q8—41no—
173Q8—41no—
174Q8—81no—
175Q8—81no—
176Q8—81no—
177Q8—81no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4#121×C12711yescharacteristic
183C2×C4C2×D8×C12711yescharacteristic
184C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
185C8—22no—
186C8—21no—
187C8—21no—
188C8—21no—
189C8—81no—
190C8AGL(1,ℤ/8)×C12711yescharacteristic
191C8#137×C12711yescharacteristic
192C22#459×C12711yescharacteristic
193C4—21no—
194C4—81no—
195C4—81no—
196C4—161no—
197C4—161no—
198C4#468×C12711yescharacteristic
199C4#471×C12711yescharacteristic
200C4#508×C12711yescharacteristic
201C4#510×C12711yescharacteristic
202C2C127×#168511yescharacteristic
203C2C127×#221111yescharacteristic
204C2C127×#221411yescharacteristic
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
99. #12490C127direct (N × H)
110. C127#12490direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22252
C127×#22092
C127×#17072
C127×#15912
C127×#13702
C127×#13642
C127×#13622
#12490127