Finite Group Databasebeta

← C127×#10661 #44574334

Subgroups — C127×#10661 #44574334

Order 32512.

372 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 114 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×#1955C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic, complemented
3C127×#1570C212yesmaximal, complemented
4C127×#1486C212yesmaximal
5C127×#1275C211yesmaximal, characteristic, complemented
6C2×C4×D4×C127C2211yescharacteristic
7#431×C127C2212yes—
8C2×#108×C127—22no—
9#423×C127C2212yes—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×C22⋊C8×C127—22no—
12C2×#97×C127C2211yescharacteristic
13#334×C127—24no—
14D4⋊C8×C127—24no—
15C22×D4×C127Q811yescharacteristic
16C23×C4×C127—21no—
17C2×M16×C127—22no—
18C22×C8×C127—21no—
19C22×C8×C127D412yes—
20C4×D4×C127—22no—
21C4×D4×C127—22no—
22C2×C4⋊C4×C127Q811yescharacteristic
23C2×C22⋊C4×C127—21no—
24C2×C42×C127C2311yescharacteristic
25#108×C127—44no—
26C4⋊C8×C127—22no—
27C4⋊C8×C127—22no—
28C4⋊C8×C127—22no—
29C4⋊C8×C127—22no—
30C22⋊C8×C127—22no—
31C22⋊C8×C127—44no—
32#97×C127—22no—
33C4×C8×C127D414yes—
34C24×C127—21no—
35C2×D4×C127—22no—
36C2×D4×C127—42no—
37C22×C4×C127—21no—
38C22×C4×C127—41no—
39C22×C4×C127—41no—
40C22×C4×C127—42no—
41C22×C4×C127—42no—
42C22×C4×C127C2×D411yescharacteristic
43C22×C4×C127C2×Q811yescharacteristic
44C22×C4×C127#4111yescharacteristic
45M16×C127—44no—
46C2×C8×C127—22no—
47C2×C8×C127—22no—
48C2×C8×C127—24no—
49C2×C8×C127—41no—
50C2×C8×C127—42no—
51C2×C8×C127—42no—
52C2×C8×C127SD1614yes—
53C4⋊C4×C127—22no—
54C22⋊C4×C127—42no—
55C42×C127C2×D412yes—
56C42×C127#4112yes—
57C23×C127—22no—
58C23×C127—41no—
59C23×C127—42no—
60C23×C127—41no—
61C23×C127—42no—
62C23×C127C22⋊Q811yescharacteristic
63D4×C127—24no—
64D4×C127—42no—
65C2×C4×C127—41no—
66C2×C4×C127—41no—
67C2×C4×C127—41no—
68C2×C4×C127—42no—
69C2×C4×C127—82no—
70C2×C4×C127—81no—
71C2×C4×C127—81no—
72C2×C4×C127C22⋊Q812yes—
73C2×C4×C127#12312yes—
74C2×C4×C127#12311yescharacteristic
75C2×C4×C127#12711yescharacteristic
76C2×C4×C127C2×SD1612yes—
77C2×C4×C127AGL(1,ℤ/8)12yes—
78C8×C127—24no—
79C8×C127—44no—
80C8×C127—81no—
81C8×C127—82no—
82C22×C127—21no—
83C22×C127—21no—
84C22×C127—44no—
85C22×C127—42no—
86C22×C127—82no—
87C22×C127—81no—
88C22×C127—81no—
89C22×C127#39911yescharacteristic
90C22×C127#47612yes—
91C4×C127—22no—
92C4×C127—22no—
93C4×C127—81no—
94C4×C127#48112yes—
95C4×C127#49211yescharacteristic
96C4×C127#49611yescharacteristic
97#10661C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—22no—
99C2×C127—82no—
100C2×C127#209111yescharacteristic
101C2×C127#209411yescharacteristic
102C2×C127#209811yescharacteristic
103#1955C2×C12711yescharacteristic
104#1849C2×C12711yescharacteristic, complemented
105#1570C2×C12712yescomplemented
106#1486C2×C12712yes—
107#1275C2×C12711yescharacteristic, complemented
108C127#1066111yescharacteristic, direct product factor, Sylow
109C2×C4×D4C22×C12711yescharacteristic
110#431C22×C12712yes—
111C2×#108—22no—
112#423C22×C12712yes—
113C2×C4⋊C8C22×C12711yescharacteristic
114C2×C22⋊C8—22no—
115C2×#97C22×C12711yescharacteristic
116#334—24no—
117D4⋊C8—24no—
118C22×D4Q8×C12711yescharacteristic
119C23×C4—21no—
120C2×M16—22no—
121C22×C8—21no—
122C22×C8D4×C12712yes—
123C4×D4—22no—
124C4×D4—22no—
125C2×C4⋊C4Q8×C12711yescharacteristic
126C2×C22⋊C4—21no—
127C2×C42C23×C12711yescharacteristic
128#108—44no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C22⋊C8—22no—
134C22⋊C8—44no—
135#97—22no—
136C4×C8D4×C12714yes—
137C24—21no—
138C2×D4—22no—
139C2×D4—42no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4C2×D4×C12711yescharacteristic
146C22×C4C2×Q8×C12711yescharacteristic
147C22×C4#41×C12711yescharacteristic
148M16—44no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—24no—
152C2×C8—41no—
153C2×C8—42no—
154C2×C8—42no—
155C2×C8SD16×C12714yes—
156C4⋊C4—22no—
157C22⋊C4—42no—
158C42C2×D4×C12712yes—
159C42#41×C12712yes—
160C23—22no—
161C23—41no—
162C23—42no—
163C23—41no—
164C23—42no—
165C23C22⋊Q8×C12711yescharacteristic
166D4—24no—
167D4—42no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—81no—
173C2×C4—82no—
174C2×C4—81no—
175C2×C4C22⋊Q8×C12712yes—
176C2×C4#123×C12712yes—
177C2×C4#123×C12711yescharacteristic
178C2×C4#127×C12711yescharacteristic
179C2×C4C2×SD16×C12712yes—
180C2×C4AGL(1,ℤ/8)×C12712yes—
181C8—24no—
182C8—44no—
183C8—82no—
184C8—81no—
185C22—21no—
186C22—21no—
187C22—44no—
188C22—42no—
189C22—82no—
190C22—81no—
191C22—81no—
192C22#399×C12711yescharacteristic
193C22#476×C12712yes—
194C4—22no—
195C4—22no—
196C4—81no—
197C4#481×C12712yes—
198C4#492×C12711yescharacteristic
199C4#496×C12711yescharacteristic
200C2—22no—
201C2—82no—
202C2C127×#209111yescharacteristic
203C2C127×#209411yescharacteristic
204C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radicalC22×D4×C127Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1849C2semidirect
3. C127×#1570C2semidirect
5. C127×#1275C2semidirect
97. #10661C127direct (N × H)
104. #1849C2×C127semidirect
105. #1570C2×C127semidirect
107. #1275C2×C127semidirect
108. C127#10661direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19552
C127×#18492
C127×#15702
C127×#14862
C127×#12752
#10661127