Finite Group Databasebeta

← C127×#13661 #44577334

Subgroups — C127×#13661 #44577334

Order 32512.

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

normal subgroups only

This group has 334 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
1C22×D16×C127C211yesmaximal, characteristic, complemented
2C2×D32×C127C212yesmaximal, complemented
3C127×#2215C211yesmaximal, characteristic, complemented
4C127×#1415C212yesmaximal, complemented
5C127×C22⋊C32C211yesmaximal, characteristic, complemented
6C22×D8×C127—21no—
7C2×D16×C127—24no—
8C2×D16×C127—21no—
9C2×D16×C127C2212yes—
10C2×D16×C127C2211yescharacteristic, complemented
11C22×C16×C127C2211yescharacteristic
12#466×C127—21no—
13D32×C127—24no—
14C2×C32×C127C2212yescomplemented
15#366×C127C2211yescharacteristic, complemented
16#357×C127—21no—
17C22×D4×C127—41no—
18C2×D8×C127—24no—
19C2×D8×C127—22no—
20C2×D8×C127—21no—
21C2×D8×C127—42no—
22C2×D8×C127—41no—
23C22×C8×C127D411yescharacteristic
24#121×C127—41no—
25D16×C127—24no—
26D16×C127—22no—
27D16×C127—22no—
28D16×C127D414yescomplemented
29C2×C16×C127—22no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127C2311yescharacteristic
32#107×C127—21no—
33#102×C127—41no—
34C32×C127—22no—
35C24×C127—81no—
36C2×D4×C127—44no—
37C2×D4×C127—42no—
38C2×D4×C127—41no—
39C2×D4×C127—82no—
40C2×D4×C127—81no—
41C2×D4×C127—81no—
42C22×C4×C127D811yescharacteristic
43D8×C127—24no—
44D8×C127—44no—
45D8×C127—41no—
46D8×C127—42no—
47D8×C127—41no—
48C2×C8×C127—21no—
49C2×C8×C127—21no—
50C2×C8×C127D811yescharacteristic
51C2×C8×C127C2×D411yescharacteristic
52C4⋊C4×C127—41no—
53C22⋊C4×C127—81no—
54C16×C127—21no—
55C16×C127C2×D412yes—
56C23×C127—84no—
57C23×C127—82no—
58C23×C127—81no—
59C23×C127—162no—
60C23×C127—162no—
61C23×C127D1611yescharacteristic
62D4×C127—44no—
63D4×C127—84no—
64D4×C127—81no—
65D4×C127—82no—
66D4×C127—81no—
67D4×C127—162no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—81no—
71C2×C4×C127D1611yescharacteristic
72C2×C4×C127C2×D811yescharacteristic
73C8×C127—21no—
74C8×C127#12011yescharacteristic
75C8×C127AGL(1,ℤ/8)11yescharacteristic
76C22×C127—21no—
77C22×C127—21no—
78C22×C127—84no—
79C22×C127—168no—
80C22×C127—162no—
81C22×C127—162no—
82C22×C127—161no—
83C22×C127—161no—
84C22×C127—161no—
85C22×C127D3212yescomplemented
86C22×C127C2×D1611yescharacteristic
87C4×C127—21no—
88C4×C127—161no—
89C4×C127#44711yescharacteristic
90C4×C127#50911yescharacteristic
91#13661C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—22no—
93C2×C127—164no—
94C2×C127—321no—
95C2×C127#218411yescharacteristic
96C2×C127C2×D3211yescharacteristic
97C2×C127#226311yescharacteristic
98C22×D16C2×C12711yescharacteristic, complemented
99C2×D32C2×C12712yescomplemented
100#2215C2×C12711yescharacteristic, complemented
101#1415C2×C12712yescomplemented
102C22⋊C32C2×C12711yescharacteristic, complemented
103C127#1366111yescharacteristic, direct product factor, Sylow
104C22×D8—21no—
105C2×D16—24no—
106C2×D16—21no—
107C2×D16C22×C12712yes—
108C2×D16C22×C12711yescharacteristic, complemented
109C22×C16C22×C12711yescharacteristic
110#466—21no—
111D32—24no—
112C2×C32C22×C12712yescomplemented
113#366C22×C12711yescharacteristic, complemented
114#357—21no—
115C22×D4—41no—
116C2×D8—24no—
117C2×D8—22no—
118C2×D8—21no—
119C2×D8—42no—
120C2×D8—41no—
121C22×C8D4×C12711yescharacteristic
122#121—41no—
123D16—24no—
124D16—22no—
125D16—22no—
126D16D4×C12714yescomplemented
127C2×C16—22no—
128C2×C16D4×C12711yescharacteristic
129C2×C16C23×C12711yescharacteristic
130#107—21no—
131#102—41no—
132C32—22no—
133C24—81no—
134C2×D4—44no—
135C2×D4—42no—
136C2×D4—41no—
137C2×D4—82no—
138C2×D4—81no—
139C2×D4—81no—
140C22×C4D8×C12711yescharacteristic
141D8—24no—
142D8—44no—
143D8—41no—
144D8—42no—
145D8—41no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8D8×C12711yescharacteristic
149C2×C8C2×D4×C12711yescharacteristic
150C4⋊C4—41no—
151C22⋊C4—81no—
152C16—21no—
153C16C2×D4×C12712yes—
154C23—84no—
155C23—82no—
156C23—81no—
157C23—162no—
158C23—162no—
159C23D16×C12711yescharacteristic
160D4—44no—
161D4—84no—
162D4—82no—
163D4—81no—
164D4—81no—
165D4—162no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4D16×C12711yescharacteristic
170C2×C4C2×D8×C12711yescharacteristic
171C8—21no—
172C8#120×C12711yescharacteristic
173C8AGL(1,ℤ/8)×C12711yescharacteristic
174C22—21no—
175C22—21no—
176C22—84no—
177C22—168no—
178C22—162no—
179C22—162no—
180C22—161no—
181C22—161no—
182C22—161no—
183C22D32×C12712yescomplemented
184C22C2×D16×C12711yescharacteristic
185C4—21no—
186C4—161no—
187C4#447×C12711yescharacteristic
188C4#509×C12711yescharacteristic
189C2—22no—
190C2—164no—
191C2—321no—
192C2C127×#218411yescharacteristic
193C2C2×D32×C12711yescharacteristic
194C2C127×#226311yescharacteristic
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×C8×C127 ◁ C22×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D16×C127C2semidirect
2. C2×D32×C127C2semidirect
3. C127×#2215C2semidirect
4. C127×#1415C2semidirect
5. C127×C22⋊C32C2semidirect
10. C2×D16×C127C22semidirect
14. C2×C32×C127C22semidirect
15. #366×C127C22semidirect
28. D16×C127D4semidirect
85. C22×C127D32semidirect
91. #13661C127direct (N × H)
98. C22×D16C2×C127semidirect
99. C2×D32C2×C127semidirect
100. #2215C2×C127semidirect
101. #1415C2×C127semidirect
102. C22⋊C32C2×C127semidirect
103. C127#13661direct (N × H)
108. C2×D16C22×C127semidirect
112. C2×C32C22×C127semidirect
113. #366C22×C127semidirect
126. D16D4×C127semidirect
183. C22D32×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D16×C1272
C2×D32×C1272
C127×#22152
C127×#14152
C127×C22⋊C322
#13661127