Finite Group Databasebeta

← C127×#12491 #44576164

Subgroups — C127×#12491 #44576164

Order 32512.

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

normal subgroups only

This group has 282 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×#2206C212yesmaximal, complemented
2C127×#1712C211yesmaximal, characteristic, complemented
3C127×#1589C211yesmaximal, characteristic, complemented
4C127×#1367C211yesmaximal, characteristic, complemented
5C127×#1361C212yesmaximal, complemented
6C2×D16×C127—22no—
7#493×C127—21no—
8#493×C127—21no—
9#493×C127C2212yes—
10C4×D8×C127C2211yescharacteristic
11#436×C127—21no—
12C4⋊C16×C127C2212yes—
13#357×C127—22no—
14#335×C127C2211yescharacteristic
15D4⋊C8×C127—21no—
16C82×C127C2211yescharacteristic
17C2×D8×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—42no—
20C2×D8×C127—41no—
21C2×D8×C127—41no—
22C2×D8×C127D411yescharacteristic
23C2×M16×C127—41no—
24#127×C127—22no—
25C4×D4×C127—21no—
26D16×C127—44no—
27C2×C16×C127—22no—
28#107×C127D411yescharacteristic
29C4⋊C8×C127—21no—
30#102×C127—21no—
31C22⋊C8×C127—41no—
32C4×C8×C127D411yescharacteristic
33C4×C8×C127D411yescharacteristic
34C4×C8×C127C2311yescharacteristic
35C2×D4×C127—21no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—42no—
39C22×C4×C127—41no—
40D8×C127—22no—
41D8×C127—42no—
42D8×C127—42no—
43D8×C127—82no—
44D8×C127—84no—
45D8×C127—82no—
46D8×C127—82no—
47M16×C127—82no—
48C2×C8×C127—21no—
49C2×C8×C127—41no—
50C2×C8×C127D811yescharacteristic
51C2×C8×C127D811yescharacteristic
52C2×C8×C127C2×D411yescharacteristic
53C2×C8×C127#4111yescharacteristic
54C4⋊C4×C127—21no—
55C22⋊C4×C127—41no—
56C42×C127C2×D411yescharacteristic
57C16×C127—42no—
58C23×C127—41no—
59C23×C127—82no—
60D4×C127—41no—
61D4×C127—41no—
62D4×C127—84no—
63D4×C127—82no—
64D4×C127—82no—
65D4×C127—82no—
66D4×C127—82no—
67C2×C4×C127—41no—
68C2×C4×C127—81no—
69C2×C4×C127—81no—
70C2×C4×C127#12111yescharacteristic
71C2×C4×C127C2×D811yescharacteristic
72C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
73C8×C127—22no—
74C8×C127—21no—
75C8×C127—21no—
76C8×C127—81no—
77C8×C127D1612yescomplemented
78C8×C127AGL(1,ℤ/8)12yes—
79C22×C127—81no—
80C22×C127—81no—
81C22×C127—81no—
82C22×C127—162no—
83C22×C127—162no—
84C22×C127—162no—
85C22×C127#45911yescharacteristic
86C4×C127—21no—
87C4×C127—81no—
88C4×C127#46911yescharacteristic
89C4×C127#47211yescharacteristic
90C4×C127C2×D1611yescharacteristic
91C4×C127#50911yescharacteristic
92#12491C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127—161no—
94C2×C127—322no—
95C2×C127#168711yescharacteristic
96C2×C127#220611yescharacteristic
97C2×C127#221311yescharacteristic
98#2206C2×C12712yescomplemented
99#1712C2×C12711yescharacteristic, complemented
100#1589C2×C12711yescharacteristic, complemented
101#1367C2×C12711yescharacteristic, complemented
102#1361C2×C12712yescomplemented
103C127#1249111yescharacteristic, direct product factor, Sylow
104C2×D16—22no—
105#493—21no—
106#493—21no—
107#493C22×C12712yes—
108C4×D8C22×C12711yescharacteristic
109#436—21no—
110C4⋊C16C22×C12712yes—
111#357—22no—
112#335C22×C12711yescharacteristic
113D4⋊C8—21no—
114C82C22×C12711yescharacteristic
115C2×D8—22no—
116C2×D8—22no—
117C2×D8—42no—
118C2×D8—41no—
119C2×D8—41no—
120C2×D8D4×C12711yescharacteristic
121C2×M16—41no—
122#127—22no—
123C4×D4—21no—
124D16—44no—
125C2×C16—22no—
126#107D4×C12711yescharacteristic
127C4⋊C8—21no—
128#102—21no—
129C22⋊C8—41no—
130C4×C8D4×C12711yescharacteristic
131C4×C8D4×C12711yescharacteristic
132C4×C8C23×C12711yescharacteristic
133C2×D4—21no—
134C2×D4—42no—
135C2×D4—42no—
136C2×D4—42no—
137C22×C4—41no—
138D8—22no—
139D8—42no—
140D8—42no—
141D8—82no—
142D8—84no—
143D8—82no—
144D8—82no—
145M16—82no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8D8×C12711yescharacteristic
149C2×C8D8×C12711yescharacteristic
150C2×C8C2×D4×C12711yescharacteristic
151C2×C8#41×C12711yescharacteristic
152C4⋊C4—21no—
153C22⋊C4—41no—
154C42C2×D4×C12711yescharacteristic
155C16—42no—
156C23—41no—
157C23—82no—
158D4—41no—
159D4—41no—
160D4—84no—
161D4—82no—
162D4—82no—
163D4—82no—
164D4—82no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4#121×C12711yescharacteristic
169C2×C4C2×D8×C12711yescharacteristic
170C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
171C8—22no—
172C8—21no—
173C8—21no—
174C8—81no—
175C8D16×C12712yescomplemented
176C8AGL(1,ℤ/8)×C12712yes—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—162no—
181C22—162no—
182C22—162no—
183C22#459×C12711yescharacteristic
184C4—21no—
185C4—81no—
186C4#469×C12711yescharacteristic
187C4#472×C12711yescharacteristic
188C4C2×D16×C12711yescharacteristic
189C4#509×C12711yescharacteristic
190C2—161no—
191C2—322no—
192C2C127×#168711yescharacteristic
193C2C127×#220611yescharacteristic
194C2C127×#221311yescharacteristic
subgroupG/H
center, socleC22×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
1. C127×#2206C2semidirect
2. C127×#1712C2semidirect
3. C127×#1589C2semidirect
4. C127×#1367C2semidirect
5. C127×#1361C2semidirect
77. C8×C127D16semidirect
92. #12491C127direct (N × H)
98. #2206C2×C127semidirect
99. #1712C2×C127semidirect
100. #1589C2×C127semidirect
101. #1367C2×C127semidirect
102. #1361C2×C127semidirect
103. C127#12491direct (N × H)
175. C8D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22062
C127×#17122
C127×#15892
C127×#13672
C127×#13612
#12491127