Finite Group Databasebeta

← C127×#10531 #44574204

Subgroups — C127×#10531 #44574204

Order 32512.

386 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1837C211yesmaximal, characteristic, complemented
3C127×#1560C212yesmaximal, complemented
4C127×#1492C212yesmaximal, complemented
5C127×#1309C211yesmaximal, characteristic, complemented
6#532×C127C2212yes—
7#476×C127—22no—
8#469×C127—22no—
9#459×C127—22no—
10#423×C127C2211yescharacteristic
11#423×C127C2212yes—
12#423×C127C2211yescharacteristic
13C2×C4×C8×C127C2211yescharacteristic
14#341×C127—22no—
15#333×C127—22no—
16#331×C127—22no—
17D4⋊C8×C127—24no—
18C2×#41×C127—22no—
19C2×D8×C127—22no—
20C2×M16×C127—21no—
21C2×M16×C127—22no—
22C2×M16×C127D412yes—
23C22×C8×C127—21no—
24C4⋊Q8×C127D412yes—
25#127×C127D412yes—
26#124×C127—22no—
27#121×C127—22no—
28#121×C127—22no—
29C4×D4×C127—22no—
30C4×D4×C127—22no—
31C2×C42×C127C2311yescharacteristic
32#106×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C4⋊C8×C127—22no—
36C4⋊C8×C127—22no—
37#102×C127—24no—
38C4×C8×C127—21no—
39C4×C8×C127D412yes—
40#41×C127—82no—
41#41×C127—82no—
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—
53M16×C127—82no—
54C2×C8×C127—22no—
55C2×C8×C127—22no—
56C2×C8×C127—41no—
57C2×C8×C127—41no—
58C2×C8×C127—41no—
59C2×C8×C127—42no—
60C4⋊C4×C127—22no—
61C4⋊C4×C127—22no—
62C22⋊C4×C127—42no—
63C22⋊C4×C127—42no—
64C42×C127C2×D412yes—
65C42×C127C2×D411yescharacteristic
66C42×C127#4111yescharacteristic
67C23×C127—42no—
68C23×C127#12411yescharacteristic
69Q8×C127—82no—
70D4×C127—42no—
71D4×C127—42no—
72D4×C127—42no—
73D4×C127—42no—
74D4×C127—82no—
75D4×C127—84no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—42no—
81C2×C4×C127—82no—
82C2×C4×C127—82no—
83C2×C4×C127#12011yescharacteristic
84C2×C4×C127#12111yescharacteristic
85C2×C4×C127#12112yes—
86C2×C4×C127#12312yes—
87C8×C127—42no—
88C8×C127—42no—
89C8×C127—81no—
90C8×C127—82no—
91C22×C127—22no—
92C22×C127—21no—
93C22×C127—82no—
94C22×C127—82no—
95C22×C127—82no—
96C22×C127#39411yescharacteristic
97C4×C127—22no—
98C4×C127—21no—
99C4×C127—82no—
100C4×C127#45411yescharacteristic
101C4×C127#45511yescharacteristic
102C4×C127#47112yes—
103C4×C127#47212yes—
104#10531C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—41no—
106C2×C127—162no—
107C2×C127#204011yescharacteristic
108C2×C127#205112yes—
109#3253C2×C12711yescharacteristic
110#1837C2×C12711yescharacteristic, complemented
111#1560C2×C12712yescomplemented
112#1492C2×C12712yescomplemented
113#1309C2×C12711yescharacteristic, complemented
114C127#1053111yescharacteristic, direct product factor, Sylow
115#532C22×C12712yes—
116#476—22no—
117#469—22no—
118#459—22no—
119#423C22×C12711yescharacteristic
120#423C22×C12712yes—
121#423C22×C12711yescharacteristic
122C2×C4×C8C22×C12711yescharacteristic
123#341—22no—
124#333—22no—
125#331—22no—
126D4⋊C8—24no—
127C2×#41—22no—
128C2×D8—22no—
129C2×M16—21no—
130C2×M16—22no—
131C2×M16D4×C12712yes—
132C22×C8—21no—
133C4⋊Q8D4×C12712yes—
134#127D4×C12712yes—
135#124—22no—
136#121—22no—
137#121—22no—
138C4×D4—22no—
139C4×D4—22no—
140C2×C42C23×C12711yescharacteristic
141#106—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146#102—24no—
147C4×C8—21no—
148C4×C8D4×C12712yes—
149#41—82no—
150#41—82no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—42no—
157C22×C4C2×D4×C12711yescharacteristic
158C22×C4#41×C12712yes—
159D8—82no—
160M16—42no—
161M16—42no—
162M16—82no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C42C2×D4×C12712yes—
174C42C2×D4×C12711yescharacteristic
175C42#41×C12711yescharacteristic
176C23—42no—
177C23#124×C12711yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—42no—
183D4—82no—
184D4—84no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4#120×C12711yescharacteristic
193C2×C4#121×C12711yescharacteristic
194C2×C4#121×C12712yes—
195C2×C4#123×C12712yes—
196C8—42no—
197C8—42no—
198C8—81no—
199C8—82no—
200C22—21no—
201C22—22no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#394×C12711yescharacteristic
206C4—21no—
207C4—22no—
208C4—82no—
209C4#454×C12711yescharacteristic
210C4#455×C12711yescharacteristic
211C4#471×C12712yes—
212C4#472×C12712yes—
213C2—41no—
214C2—162no—
215C2C127×#204011yescharacteristic
216C2C127×#205112yes—
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×#1837C2semidirect
3. C127×#1560C2semidirect
4. C127×#1492C2semidirect
5. C127×#1309C2semidirect
104. #10531C127direct (N × H)
110. #1837C2×C127semidirect
111. #1560C2×C127semidirect
112. #1492C2×C127semidirect
113. #1309C2×C127semidirect
114. C127#10531direct (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×#18372
C127×#15602
C127×#14922
C127×#13092
#10531127