Finite Group Databasebeta

← C127×#12536 #44576209

Subgroups — C127×#12536 #44576209

Order 32512.

260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2254C211yesmaximal, characteristic, complemented
2C127×#2252C211yesmaximal, characteristic, complemented
3C127×#2240C211yesmaximal, characteristic
4C127×#2240C211yesmaximal, characteristic
5C127×#1710C211yesmaximal, characteristic, complemented
6C127×#1706C211yesmaximal, characteristic
7C127×#1312C211yesmaximal, characteristic, complemented
8#500×C127C2211yescharacteristic
9#500×C127C2211yescharacteristic
10#500×C127C2211yescharacteristic
11#493×C127C2211yescharacteristic
12#492×C127—21no—
13#487×C127—21no—
14#487×C127—21no—
15#486×C127—21no—
16#367×C127—22no—
17#366×C127—22no—
18#357×C127—22no—
19#357×C127—22no—
20C4×C16×C127C2211yescharacteristic
21C4×C16×C127C2211yescharacteristic
22C82×C127C2211yescharacteristic
23C2×SD16×C127—42no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C4⋊Q8×C127—21no—
27C4⋊Q8×C127—21no—
28C4⋊Q8×C127—21no—
29#127×C127—21no—
30C2×C16×C127D412yes—
31C2×C16×C127D412yes—
32#107×C127—21no—
33#107×C127—21no—
34#107×C127—21no—
35#107×C127—21no—
36#107×C127—21no—
37#107×C127—21no—
38#103×C127—42no—
39#103×C127—42no—
40#102×C127—42no—
41C4×C8×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127C2311yescharacteristic
44C2×Q8×C127—41no—
45C2×Q8×C127—41no—
46C2×Q8×C127—41no—
47C2×D4×C127—41no—
48C2×D4×C127—41no—
49C2×D4×C127—41no—
50SD16×C127—84no—
51D8×C127—42no—
52D8×C127—42no—
53C2×C8×C127D812yes—
54C2×C8×C127D812yes—
55C2×C8×C127C2×D411yescharacteristic
56C2×C8×C127C2×D411yescharacteristic
57C4⋊C4×C127—41no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—41no—
63C42×C127C2×D411yescharacteristic
64C16×C127—22no—
65C16×C127—22no—
66C23×C127—81no—
67Q8×C127—82no—
68Q8×C127—82no—
69Q8×C127—82no—
70D4×C127—81no—
71D4×C127—81no—
72D4×C127—82no—
73D4×C127—82no—
74C2×C4×C127—81no—
75C2×C4×C127—81no—
76C2×C4×C127—81no—
77C2×C4×C127#12711yescharacteristic
78C2×C4×C127C2×D811yescharacteristic
79C2×C4×C127C2×D811yescharacteristic
80C8×C127—22no—
81C8×C127—22no—
82C8×C127#13712yes—
83C8×C127#13712yes—
84C22×C127—161no—
85C22×C127—161no—
86C22×C127—161no—
87C22×C127#49311yescharacteristic
88C4×C127—161no—
89C4×C127—161no—
90C4×C127—161no—
91C4×C127#49711yescharacteristic
92C4×C127#49711yescharacteristic
93C4×C127#50812yes—
94C4×C127#50912yes—
95#12536C12711yesmaximal, characteristic, direct product factor, Sylow
96C2×C127—321no—
97C2×C127#172211yescharacteristic
98C2×C127#224911yescharacteristic
99C2×C127#225011yescharacteristic
100#2254C2×C12711yescharacteristic, complemented
101#2252C2×C12711yescharacteristic, complemented
102#2240C2×C12711yescharacteristic
103#2240C2×C12711yescharacteristic
104#1710C2×C12711yescharacteristic, complemented
105#1706C2×C12711yescharacteristic
106#1312C2×C12711yescharacteristic, complemented
107C127#1253611yescharacteristic, direct product factor, Sylow
108#500C22×C12711yescharacteristic
109#500C22×C12711yescharacteristic
110#500C22×C12711yescharacteristic
111#493C22×C12711yescharacteristic
112#492—21no—
113#487—21no—
114#487—21no—
115#486—21no—
116#367—22no—
117#366—22no—
118#357—22no—
119#357—22no—
120C4×C16C22×C12711yescharacteristic
121C4×C16C22×C12711yescharacteristic
122C82C22×C12711yescharacteristic
123C2×SD16—42no—
124C2×D8—21no—
125C2×D8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129#127—21no—
130C2×C16D4×C12712yes—
131C2×C16D4×C12712yes—
132#107—21no—
133#107—21no—
134#107—21no—
135#107—21no—
136#107—21no—
137#107—21no—
138#103—42no—
139#103—42no—
140#102—42no—
141C4×C8D4×C12711yescharacteristic
142C4×C8D4×C12711yescharacteristic
143C4×C8C23×C12711yescharacteristic
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×D4—41no—
148C2×D4—41no—
149C2×D4—41no—
150SD16—84no—
151D8—42no—
152D8—42no—
153C2×C8D8×C12712yes—
154C2×C8D8×C12712yes—
155C2×C8C2×D4×C12711yescharacteristic
156C2×C8C2×D4×C12711yescharacteristic
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C42C2×D4×C12711yescharacteristic
164C16—22no—
165C16—22no—
166C23—81no—
167Q8—82no—
168Q8—82no—
169Q8—82no—
170D4—81no—
171D4—81no—
172D4—82no—
173D4—82no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4#127×C12711yescharacteristic
178C2×C4C2×D8×C12711yescharacteristic
179C2×C4C2×D8×C12711yescharacteristic
180C8—22no—
181C8—22no—
182C8#137×C12712yes—
183C8#137×C12712yes—
184C22—161no—
185C22—161no—
186C22—161no—
187C22#493×C12711yescharacteristic
188C4—161no—
189C4—161no—
190C4—161no—
191C4#497×C12711yescharacteristic
192C4#497×C12711yescharacteristic
193C4#508×C12712yes—
194C4#509×C12712yes—
195C2—321no—
196C2C127×#172211yescharacteristic
197C2C127×#224911yescharacteristic
198C2C127×#225011yescharacteristic
subgroupG/H
center, socleC22×C127#493
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
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
1. C127×#2254C2semidirect
2. C127×#2252C2semidirect
5. C127×#1710C2semidirect
7. C127×#1312C2semidirect
95. #12536C127direct (N × H)
100. #2254C2×C127semidirect
101. #2252C2×C127semidirect
104. #1710C2×C127semidirect
106. #1312C2×C127semidirect
107. C127#12536direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22542
C127×#22522
C127×#22402
C127×#17102
C127×#17062
C127×#13122
#12536127