Finite Group Databasebeta

← C127×#10524 #44574197

Subgroups — C127×#10524 #44574197

Order 32512.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3253C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic, complemented
3C127×#1557C212yesmaximal, complemented
4C127×#1530C212yesmaximal, complemented
5C127×#1307C211yesmaximal, characteristic, complemented
6#532×C127C2212yes—
7#476×C127—22no—
8#469×C127—22no—
9#459×C127—22no—
10#432×C127C2212yes—
11C2×#108×C127—22no—
12#423×C127C2211yescharacteristic
13#423×C127C2211yescharacteristic
14C2×#97×C127C2211yescharacteristic
15#332×C127—22no—
16#331×C127—22no—
17#329×C127—24no—
18C2×#41×C127—22no—
19C2×D8×C127—22no—
20C2×M16×C127—21no—
21C2×M16×C127D412yes—
22C22×C8×C127—21no—
23C4⋊Q8×C127D412yes—
24#127×C127D412yes—
25#124×C127—22no—
26#121×C127—22no—
27#121×C127—22no—
28C4×D4×C127—22no—
29C4×D4×C127—22no—
30C2×C42×C127C2311yescharacteristic
31#108×C127—44no—
32#106×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36#102×C127—24no—
37C22⋊C8×C127—22no—
38#97×C127—22no—
39#97×C127—21no—
40#97×C127D412yes—
41#41×C127—84no—
42C2×Q8×C127—22no—
43C2×D4×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—42no—
47C22×C4×C127—42no—
48C22×C4×C127C2×D411yescharacteristic
49C22×C4×C127#4112yes—
50D8×C127—82no—
51M16×C127—42no—
52M16×C127—42no—
53C2×C8×C127—22no—
54C2×C8×C127—22no—
55C2×C8×C127—22no—
56C2×C8×C127—22no—
57C2×C8×C127—41no—
58C2×C8×C127—42no—
59C4⋊C4×C127—22no—
60C4⋊C4×C127—22no—
61C22⋊C4×C127—42no—
62C22⋊C4×C127—42no—
63C42×C127C2×D412yes—
64C42×C127C2×D411yescharacteristic
65C42×C127#4111yescharacteristic
66C23×C127—42no—
67C23×C127#12411yescharacteristic
68Q8×C127—82no—
69D4×C127—42no—
70D4×C127—42no—
71D4×C127—82no—
72D4×C127—82no—
73D4×C127—84no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127—84no—
79C2×C4×C127#12011yescharacteristic
80C2×C4×C127#12112yes—
81C2×C4×C127#12111yescharacteristic
82C2×C4×C127#12312yes—
83C8×C127—24no—
84C8×C127—42no—
85C8×C127—82no—
86C8×C127—81no—
87C22×C127—22no—
88C22×C127—21no—
89C22×C127—82no—
90C22×C127—82no—
91C22×C127—82no—
92C22×C127#39411yescharacteristic
93C4×C127—22no—
94C4×C127—22no—
95C4×C127—21no—
96C4×C127—82no—
97C4×C127#45311yescharacteristic
98C4×C127#45611yescharacteristic
99#10524C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127—41no—
101C2×C127—162no—
102C2×C127#203911yescharacteristic
103C2×C127#204812yes—
104#3253C2×C12711yescharacteristic
105#1849C2×C12711yescharacteristic, complemented
106#1557C2×C12712yescomplemented
107#1530C2×C12712yescomplemented
108#1307C2×C12711yescharacteristic, complemented
109C127#1052411yescharacteristic, direct product factor, Sylow
110#532C22×C12712yes—
111#476—22no—
112#469—22no—
113#459—22no—
114#432C22×C12712yes—
115C2×#108—22no—
116#423C22×C12711yescharacteristic
117#423C22×C12711yescharacteristic
118C2×#97C22×C12711yescharacteristic
119#332—22no—
120#331—22no—
121#329—24no—
122C2×#41—22no—
123C2×D8—22no—
124C2×M16—21no—
125C2×M16D4×C12712yes—
126C22×C8—21no—
127C4⋊Q8D4×C12712yes—
128#127D4×C12712yes—
129#124—22no—
130#121—22no—
131#121—22no—
132C4×D4—22no—
133C4×D4—22no—
134C2×C42C23×C12711yescharacteristic
135#108—44no—
136#106—22no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140#102—24no—
141C22⋊C8—22no—
142#97—22no—
143#97—21no—
144#97D4×C12712yes—
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4C2×D4×C12711yescharacteristic
153C22×C4#41×C12712yes—
154D8—82no—
155M16—42no—
156M16—42no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—42no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42C2×D4×C12712yes—
168C42C2×D4×C12711yescharacteristic
169C42#41×C12711yescharacteristic
170C23—42no—
171C23#124×C12711yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4#120×C12711yescharacteristic
184C2×C4#121×C12712yes—
185C2×C4#121×C12711yescharacteristic
186C2×C4#123×C12712yes—
187C8—24no—
188C8—42no—
189C8—82no—
190C8—81no—
191C22—21no—
192C22—22no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#394×C12711yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—82no—
201C4#453×C12711yescharacteristic
202C4#456×C12711yescharacteristic
203C2—41no—
204C2—162no—
205C2C127×#203911yescharacteristic
206C2C127×#204812yes—
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3253C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1849C2semidirect
3. C127×#1557C2semidirect
4. C127×#1530C2semidirect
5. C127×#1307C2semidirect
99. #10524C127direct (N × H)
105. #1849C2×C127semidirect
106. #1557C2×C127semidirect
107. #1530C2×C127semidirect
108. #1307C2×C127semidirect
109. C127#10524direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32532
C127×#18492
C127×#15572
C127×#15302
C127×#13072
#10524127