Finite Group Databasebeta

← C127×#11837 #44575510

Subgroups — C127×#11837 #44575510

Order 32512.

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

normal subgroups only

This group has 324 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×#3184C211yesmaximal, characteristic
2C127×#2165C211yesmaximal, characteristic, complemented
3C127×#1841C211yesmaximal, characteristic, complemented
4C127×#1341C212yesmaximal, complemented
5C127×#1339C212yesmaximal, complemented
6#532×C127—21no—
7#498×C127C411yescharacteristic, complemented
8#493×C127C411yescharacteristic, complemented
9#486×C127—21no—
10#469×C127—21no—
11#469×C127C2212yes—
12#442×C127—21no—
13#442×C127C412yescomplemented
14C4×M16×C127C2211yescharacteristic
15#364×C127—21no—
16#349×C127C2212yes—
17#347×C127—21no—
18#344×C127—21no—
19#339×C127—21no—
20#338×C127C2211yescharacteristic
21H(3,ℤ/4)×C127C2211yescharacteristic
22C2×#41×C127—41no—
23C2×D8×C127—21no—
24C2×D8×C127C2×C412yes—
25C2×M16×C127—21no—
26C2×M16×C127D411yescharacteristic
27C2×M16×C127C2311yescharacteristic
28C4⋊Q8×C127—21no—
29#127×C127—21no—
30#124×C127—41no—
31#121×C127—22no—
32#121×C127—41no—
33C4×D4×C127—22no—
34C4×D4×C127—41no—
35#117×C127—21no—
36C2×C42×C127D411yescharacteristic
37M32×C127—22no—
38#106×C127—21no—
39#106×C127C2×C412yes—
40#102×C127—22no—
41#102×C127—22no—
42#97×C127C2×C411yescharacteristic
43#97×C127D411yescharacteristic
44C4×C8×C127C2×C411yescharacteristic
45C4×C8×C127D411yescharacteristic
46#41×C127—84no—
47C2×Q8×C127—41no—
48C2×D4×C127—22no—
49C2×D4×C127—41no—
50C2×D4×C127—41no—
51C2×D4×C127—42no—
52C22×C4×C127—21no—
53C22×C4×C127—42no—
54C22×C4×C127C2×D411yescharacteristic
55D8×C127—42no—
56D8×C127—42no—
57M16×C127—41no—
58M16×C127—41no—
59M16×C127—41no—
60M16×C127—41no—
61C2×C8×C127—41no—
62C2×C8×C127C22⋊C411yescharacteristic
63C2×C8×C127C22⋊C411yescharacteristic
64C2×C8×C127C22×C411yescharacteristic
65C2×C8×C127C2×D411yescharacteristic
66C4⋊C4×C127—22no—
67C4⋊C4×C127—41no—
68C4⋊C4×C127—41no—
69C22⋊C4×C127—42no—
70C22⋊C4×C127—42no—
71C22⋊C4×C127—41no—
72C42×C127—21no—
73C42×C127—41no—
74C42×C127C22⋊C411yescharacteristic
75C42×C127C22⋊C411yescharacteristic
76C16×C127—42no—
77C23×C127—42no—
78C23×C127AGL(1,ℤ/8)11yescharacteristic
79Q8×C127—82no—
80D4×C127—42no—
81D4×C127—42no—
82D4×C127—82no—
83D4×C127—82no—
84D4×C127—84no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—42no—
90C2×C4×C127—42no—
91C2×C4×C127—84no—
92C2×C4×C127—81no—
93C2×C4×C127C2×C22⋊C411yescharacteristic
94C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
95C8×C127—21no—
96C8×C127—21no—
97C8×C127—21no—
98C8×C127—21no—
99C8×C127—81no—
100C22×C127—21no—
101C22×C127—41no—
102C22×C127—82no—
103C22×C127—82no—
104C22×C127—82no—
105C22×C127#41811yescharacteristic
106C4×C127—22no—
107C4×C127—21no—
108C4×C127—41no—
109C4×C127—82no—
110C4×C127—161no—
111C4×C127#41011yescharacteristic
112C4×C127#42111yescharacteristic
113#11837C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—21no—
115C2×C127—41no—
116C2×C127—162no—
117C2×C127#151411yescharacteristic
118#3184C2×C12711yescharacteristic
119#2165C2×C12711yescharacteristic, complemented
120#1841C2×C12711yescharacteristic, complemented
121#1341C2×C12712yescomplemented
122#1339C2×C12712yescomplemented
123C127#1183711yescharacteristic, direct product factor, Sylow
124#532—21no—
125#498C4×C12711yescharacteristic, complemented
126#493C4×C12711yescharacteristic, complemented
127#486—21no—
128#469—21no—
129#469C22×C12712yes—
130#442—21no—
131#442C4×C12712yescomplemented
132C4×M16C22×C12711yescharacteristic
133#364—21no—
134#349C22×C12712yes—
135#347—21no—
136#344—21no—
137#339—21no—
138#338C22×C12711yescharacteristic
139H(3,ℤ/4)C22×C12711yescharacteristic
140C2×#41—41no—
141C2×D8—21no—
142C2×D8C2×C4×C12712yes—
143C2×M16—21no—
144C2×M16D4×C12711yescharacteristic
145C2×M16C23×C12711yescharacteristic
146C4⋊Q8—21no—
147#127—21no—
148#124—41no—
149#121—22no—
150#121—41no—
151C4×D4—22no—
152C4×D4—41no—
153#117—21no—
154C2×C42D4×C12711yescharacteristic
155M32—22no—
156#106—21no—
157#106C2×C4×C12712yes—
158#102—22no—
159#102—22no—
160#97C2×C4×C12711yescharacteristic
161#97D4×C12711yescharacteristic
162C4×C8C2×C4×C12711yescharacteristic
163C4×C8D4×C12711yescharacteristic
164#41—84no—
165C2×Q8—41no—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—42no—
170C22×C4—21no—
171C22×C4—42no—
172C22×C4C2×D4×C12711yescharacteristic
173D8—42no—
174D8—42no—
175M16—41no—
176M16—41no—
177M16—41no—
178M16—41no—
179C2×C8—41no—
180C2×C8C22⋊C4×C12711yescharacteristic
181C2×C8C22⋊C4×C12711yescharacteristic
182C2×C8C22×C4×C12711yescharacteristic
183C2×C8C2×D4×C12711yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C22⋊C4—42no—
188C22⋊C4—42no—
189C22⋊C4—41no—
190C42—21no—
191C42—41no—
192C42C22⋊C4×C12711yescharacteristic
193C42C22⋊C4×C12711yescharacteristic
194C16—42no—
195C23—42no—
196C23AGL(1,ℤ/8)×C12711yescharacteristic
197Q8—82no—
198D4—42no—
199D4—42no—
200D4—82no—
201D4—82no—
202D4—84no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—84no—
210C2×C4—81no—
211C2×C4C2×C22⋊C4×C12711yescharacteristic
212C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—81no—
218C22—21no—
219C22—41no—
220C22—82no—
221C22—82no—
222C22—82no—
223C22#418×C12711yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—82no—
228C4—161no—
229C4#410×C12711yescharacteristic
230C4#421×C12711yescharacteristic
231C2—21no—
232C2—41no—
233C2—162no—
234C2C127×#151411yescharacteristic
subgroupG/H
center, socleC2×C127#1514
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC127×#3184C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2165C2semidirect
3. C127×#1841C2semidirect
4. C127×#1341C2semidirect
5. C127×#1339C2semidirect
7. #498×C127C4semidirect
8. #493×C127C4semidirect
13. #442×C127C4semidirect
113. #11837C127direct (N × H)
119. #2165C2×C127semidirect
120. #1841C2×C127semidirect
121. #1341C2×C127semidirect
122. #1339C2×C127semidirect
123. C127#11837direct (N × H)
125. #498C4×C127semidirect
126. #493C4×C127semidirect
131. #442C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31842
C127×#21652
C127×#18412
C127×#13412
C127×#13392
#11837127