Finite Group Databasebeta

← C127×#12480 #44576153

Subgroups — C127×#12480 #44576153

Order 32512.

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

normal subgroups only

This group has 210 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×#2240C211yesmaximal, characteristic
2C127×#2183C211yesmaximal, characteristic, complemented
3C127×#1676C211yesmaximal, characteristic, complemented
4C127×#1668C211yesmaximal, characteristic
5C127×#1371C211yesmaximal, characteristic, complemented
6C127×#1365C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic
8#500×C127C2211yescharacteristic
9#493×C127C2211yescharacteristic
10#477×C127—21no—
11#460×C127—21no—
12C8×Q8×C127C2211yescharacteristic
13C4⋊C16×C127—21no—
14C4⋊C16×C127C2211yescharacteristic
15#357×C127—21no—
16#357×C127—21no—
17#346×C127—21no—
18C4×C16×C127C2211yescharacteristic
19#335×C127C2211yescharacteristic
20#335×C127C2211yescharacteristic
21#333×C127—21no—
22#331×C127—21no—
23C2×SD16×C127—41no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C4⋊Q8×C127—21no—
27#127×C127—21no—
28C4×Q8×C127D411yescharacteristic
29C2×C16×C127—21no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127D411yescharacteristic
32#107×C127—21no—
33#107×C127—21no—
34#107×C127—41no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127D411yescharacteristic
39#103×C127—41no—
40#102×C127—41no—
41C4×C8×C127—21no—
42C4×C8×C127C2311yescharacteristic
43C2×Q8×C127—41no—
44C2×Q8×C127D811yescharacteristic
45C2×D4×C127—41no—
46C2×D4×C127—41no—
47C2×D4×C127—41no—
48SD16×C127—82no—
49D8×C127—41no—
50D8×C127—41no—
51D8×C127—81no—
52C2×C8×C127—21no—
53C2×C8×C127—41no—
54C2×C8×C127—41no—
55C2×C8×C127C2×D411yescharacteristic
56C2×C8×C127#4111yescharacteristic
57C4⋊C4×C127—21no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127D811yescharacteristic
61C42×C127—21no—
62C42×C127C2×D411yescharacteristic
63C16×C127—21no—
64C16×C127—21no—
65C16×C127—41no—
66C23×C127—81no—
67Q8×C127—21no—
68Q8×C127—21no—
69Q8×C127—161no—
70D4×C127—81no—
71D4×C127—81no—
72D4×C127—81no—
73D4×C127—81no—
74D4×C127—161no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—81no—
78C2×C4×C127#12111yescharacteristic
79C2×C4×C127C2×D811yescharacteristic
80C2×C4×C127#13511yescharacteristic
81C8×C127—21no—
82C8×C127—41no—
83C8×C127—81no—
84C8×C127—81no—
85C8×C127#13511yescharacteristic
86C8×C127#13711yescharacteristic
87C22×C127—161no—
88C22×C127—161no—
89C22×C127—161no—
90C22×C127#46611yescharacteristic
91C4×C127—21no—
92C4×C127—41no—
93C4×C127—41no—
94C4×C127—161no—
95C4×C127#46411yescharacteristic
96C4×C127#47111yescharacteristic
97C4×C127#50911yescharacteristic
98C4×C127#51011yescharacteristic
99#12480C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127—321no—
101C2×C127#168211yescharacteristic
102C2×C127#222011yescharacteristic
103C2×C127#222111yescharacteristic
104#2240C2×C12711yescharacteristic
105#2183C2×C12711yescharacteristic, complemented
106#1676C2×C12711yescharacteristic, complemented
107#1668C2×C12711yescharacteristic
108#1371C2×C12711yescharacteristic, complemented
109#1365C2×C12711yescharacteristic, complemented
110#1361C2×C12711yescharacteristic
111C127#1248011yescharacteristic, direct product factor, Sylow
112#500C22×C12711yescharacteristic
113#493C22×C12711yescharacteristic
114#477—21no—
115#460—21no—
116C8×Q8C22×C12711yescharacteristic
117C4⋊C16—21no—
118C4⋊C16C22×C12711yescharacteristic
119#357—21no—
120#357—21no—
121#346—21no—
122C4×C16C22×C12711yescharacteristic
123#335C22×C12711yescharacteristic
124#335C22×C12711yescharacteristic
125#333—21no—
126#331—21no—
127C2×SD16—41no—
128C2×D8—21no—
129C2×D8—21no—
130C4⋊Q8—21no—
131#127—21no—
132C4×Q8D4×C12711yescharacteristic
133C2×C16—21no—
134C2×C16D4×C12711yescharacteristic
135C2×C16D4×C12711yescharacteristic
136#107—21no—
137#107—21no—
138#107—41no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8D4×C12711yescharacteristic
143#103—41no—
144#102—41no—
145C4×C8—21no—
146C4×C8C23×C12711yescharacteristic
147C2×Q8—41no—
148C2×Q8D8×C12711yescharacteristic
149C2×D4—41no—
150C2×D4—41no—
151C2×D4—41no—
152SD16—82no—
153D8—41no—
154D8—41no—
155D8—81no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8C2×D4×C12711yescharacteristic
160C2×C8#41×C12711yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4D8×C12711yescharacteristic
165C42—21no—
166C42C2×D4×C12711yescharacteristic
167C16—21no—
168C16—21no—
169C16—41no—
170C23—81no—
171Q8—21no—
172Q8—21no—
173Q8—161no—
174D4—81no—
175D4—81no—
176D4—81no—
177D4—81no—
178D4—161no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—81no—
182C2×C4#121×C12711yescharacteristic
183C2×C4C2×D8×C12711yescharacteristic
184C2×C4#135×C12711yescharacteristic
185C8—21no—
186C8—41no—
187C8—81no—
188C8—81no—
189C8#135×C12711yescharacteristic
190C8#137×C12711yescharacteristic
191C22—161no—
192C22—161no—
193C22—161no—
194C22#466×C12711yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—161no—
199C4#464×C12711yescharacteristic
200C4#471×C12711yescharacteristic
201C4#509×C12711yescharacteristic
202C4#510×C12711yescharacteristic
203C2—321no—
204C2C127×#168211yescharacteristic
205C2C127×#222011yescharacteristic
206C2C127×#222111yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2183C2semidirect
3. C127×#1676C2semidirect
5. C127×#1371C2semidirect
6. C127×#1365C2semidirect
99. #12480C127direct (N × H)
105. #2183C2×C127semidirect
106. #1676C2×C127semidirect
108. #1371C2×C127semidirect
109. #1365C2×C127semidirect
111. C127#12480direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22402
C127×#21832
C127×#16762
C127×#16682
C127×#13712
C127×#13652
C127×#13612
#12480127