Finite Group Databasebeta

← C127×#11744 #44575417

Subgroups — C127×#11744 #44575417

Order 32512.

390 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3169C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C4×#106×C127C211yesmaximal, characteristic, complemented
4C127×#1347C214yesmaximal, complemented
5#532×C127—21no—
6#500×C127C411yescharacteristic, complemented
7#493×C127C411yescharacteristic, complemented
8#486×C127—21no—
9#466×C127—21no—
10#466×C127C2212yes—
11C4×D8×C127—21no—
12C4×D8×C127C412yescomplemented
13C2×#106×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4×C4⋊C4×C127—21no—
16C4⋊C16×C127—21no—
17C22⋊C16×C127C2212yes—
18#346×C127—21no—
19#340×C127C2212yes—
20C2×#41×C127—41no—
21C2×D8×C127—21no—
22C2×D8×C127C2×C412yes—
23C22×C8×C127D411yescharacteristic
24C22×C8×C127C2311yescharacteristic
25C4⋊Q8×C127—21no—
26#127×C127—21no—
27#124×C127—41no—
28#121×C127—22no—
29#121×C127—41no—
30C4×D4×C127—22no—
31C4×D4×C127—41no—
32C2×C4⋊C4×C127—22no—
33C2×C42×C127—41no—
34C2×C42×C127D411yescharacteristic
35C2×C16×C127—22no—
36#107×C127—21no—
37#107×C127C2×C412yes—
38#106×C127—24no—
39#102×C127—22no—
40#102×C127—22no—
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45#95×C127—41no—
46#41×C127—84no—
47C2×Q8×C127—41no—
48C2×D4×C127—22no—
49C2×D4×C127—42no—
50C2×D4×C127—41no—
51C2×D4×C127—41no—
52C22×C4×C127—42no—
53C22×C4×C127—42no—
54C22×C4×C127D811yescharacteristic
55C22×C4×C127D811yescharacteristic
56C22×C4×C127C2×D411yescharacteristic
57D8×C127—42no—
58D8×C127—42no—
59C2×C8×C127—22no—
60C2×C8×C127—41no—
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22⋊C411yescharacteristic
63C2×C8×C127C22×C411yescharacteristic
64C2×C8×C127C2×D411yescharacteristic
65C4⋊C4×C127—24no—
66C4⋊C4×C127—22no—
67C4⋊C4×C127—42no—
68C4⋊C4×C127—41no—
69C22⋊C4×C127—42no—
70C22⋊C4×C127—42no—
71C42×C127—82no—
72C42×C127C22⋊C411yescharacteristic
73C42×C127C22⋊C411yescharacteristic
74C42×C127SD1611yescharacteristic
75C42×C127SD1611yescharacteristic
76C16×C127—42no—
77C23×C127—42no—
78C23×C127C2×D811yescharacteristic
79Q8×C127—82no—
80D4×C127—42no—
81D4×C127—42no—
82D4×C127—82no—
83D4×C127—84no—
84D4×C127—82no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—44no—
90C2×C4×C127—42no—
91C2×C4×C127—84no—
92C2×C4×C127—82no—
93C2×C4×C127—82no—
94C2×C4×C127#10211yescharacteristic
95C2×C4×C127#10211yescharacteristic
96C2×C4×C127#10211yescharacteristic
97C2×C4×C127#10211yescharacteristic
98C2×C4×C127C2×C22⋊C411yescharacteristic
99C2×C4×C127C2×SD1611yescharacteristic
100C8×C127—21no—
101C8×C127—21no—
102C8×C127—21no—
103C8×C127#10412yes—
104C22×C127—21no—
105C22×C127—21no—
106C22×C127—82no—
107C22×C127—82no—
108C22×C127—82no—
109C22×C127C2×#10211yescharacteristic
110C22×C127#50912yes—
111C4×C127—21no—
112C4×C127—21no—
113C4×C127—21no—
114C4×C127—21no—
115C4×C127—84no—
116C4×C127—82no—
117C4×C127#36012yes—
118C4×C127#41011yescharacteristic
119C4×C127C2×#10411yescharacteristic
120#11744C12711yesmaximal, characteristic, direct product factor, Sylow
121C2×C127—22no—
122C2×C127—162no—
123C2×C127#150211yescharacteristic
124C2×C127#214011yescharacteristic
125C2×C127C2×#36011yescharacteristic
126#3169C2×C12711yescharacteristic
127#2163C2×C12711yescharacteristic, complemented
128C4×#106C2×C12711yescharacteristic, complemented
129#1347C2×C12714yescomplemented
130C127#1174411yescharacteristic, direct product factor, Sylow
131#532—21no—
132#500C4×C12711yescharacteristic, complemented
133#493C4×C12711yescharacteristic, complemented
134#486—21no—
135#466—21no—
136#466C22×C12712yes—
137C4×D8—21no—
138C4×D8C4×C12712yescomplemented
139C2×#106—21no—
140C2×C4×C8C22×C12711yescharacteristic
141C4×C4⋊C4—21no—
142C4⋊C16—21no—
143C22⋊C16C22×C12712yes—
144#346—21no—
145#340C22×C12712yes—
146C2×#41—41no—
147C2×D8—21no—
148C2×D8C2×C4×C12712yes—
149C22×C8D4×C12711yescharacteristic
150C22×C8C23×C12711yescharacteristic
151C4⋊Q8—21no—
152#127—21no—
153#124—41no—
154#121—22no—
155#121—41no—
156C4×D4—22no—
157C4×D4—41no—
158C2×C4⋊C4—22no—
159C2×C42—41no—
160C2×C42D4×C12711yescharacteristic
161C2×C16—22no—
162#107—21no—
163#107C2×C4×C12712yes—
164#106—24no—
165#102—22no—
166#102—22no—
167C4×C8C2×C4×C12711yescharacteristic
168C4×C8C2×C4×C12711yescharacteristic
169C4×C8D4×C12711yescharacteristic
170C4×C8D4×C12711yescharacteristic
171#95—41no—
172#41—84no—
173C2×Q8—41no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—41no—
177C2×D4—41no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4D8×C12711yescharacteristic
181C22×C4D8×C12711yescharacteristic
182C22×C4C2×D4×C12711yescharacteristic
183D8—42no—
184D8—42no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8C22⋊C4×C12711yescharacteristic
188C2×C8C22⋊C4×C12711yescharacteristic
189C2×C8C22×C4×C12711yescharacteristic
190C2×C8C2×D4×C12711yescharacteristic
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C42—82no—
198C42C22⋊C4×C12711yescharacteristic
199C42C22⋊C4×C12711yescharacteristic
200C42SD16×C12711yescharacteristic
201C42SD16×C12711yescharacteristic
202C16—42no—
203C23—42no—
204C23C2×D8×C12711yescharacteristic
205Q8—82no—
206D4—42no—
207D4—42no—
208D4—82no—
209D4—84no—
210D4—82no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—84no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4#102×C12711yescharacteristic
221C2×C4#102×C12711yescharacteristic
222C2×C4#102×C12711yescharacteristic
223C2×C4#102×C12711yescharacteristic
224C2×C4C2×C22⋊C4×C12711yescharacteristic
225C2×C4C2×SD16×C12711yescharacteristic
226C8—21no—
227C8—21no—
228C8—21no—
229C8#104×C12712yes—
230C22—21no—
231C22—21no—
232C22—82no—
233C22—82no—
234C22—82no—
235C22C2×#102×C12711yescharacteristic
236C22#509×C12712yes—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—21no—
241C4—84no—
242C4—82no—
243C4#360×C12712yes—
244C4#410×C12711yescharacteristic
245C4C2×#104×C12711yescharacteristic
246C2—22no—
247C2—162no—
248C2C127×#150211yescharacteristic
249C2C127×#214011yescharacteristic
250C2C2×#360×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3169C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C4×#106×C127C2semidirect
4. C127×#1347C2semidirect
6. #500×C127C4semidirect
7. #493×C127C4semidirect
12. C4×D8×C127C4semidirect
120. #11744C127direct (N × H)
127. #2163C2×C127semidirect
128. C4×#106C2×C127semidirect
129. #1347C2×C127semidirect
130. C127#11744direct (N × H)
132. #500C4×C127semidirect
133. #493C4×C127semidirect
138. C4×D8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31692
C127×#21632
C4×#106×C1272
C127×#13472
#11744127