Finite Group Databasebeta

← C127×#11858 #44575531

Subgroups — C127×#11858 #44575531

Order 32512.

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

normal subgroups only

This group has 358 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×#3169C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1835C211yesmaximal, 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×C4×C8×C127C2211yescharacteristic
14#382×C127—21no—
15C4⋊C16×C127—21no—
16C22⋊C16×C127C2212yes—
17#346×C127—21no—
18#340×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×C127D411yescharacteristic
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37#102×C127—22no—
38#102×C127—22no—
39C4×C8×C127C2×C411yescharacteristic
40C4×C8×C127C2×C411yescharacteristic
41C4×C8×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43#95×C127—41no—
44#95×C127—41no—
45#41×C127—84no—
46C2×Q8×C127—41no—
47C2×D4×C127—22no—
48C2×D4×C127—42no—
49C2×D4×C127—41no—
50C2×D4×C127—41no—
51C22×C4×C127—42no—
52C22×C4×C127—42no—
53C22×C4×C127D811yescharacteristic
54C22×C4×C127D811yescharacteristic
55C22×C4×C127C2×D411yescharacteristic
56D8×C127—42no—
57D8×C127—42no—
58C2×C8×C127—41no—
59C2×C8×C127—41no—
60C2×C8×C127C22⋊C411yescharacteristic
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22×C411yescharacteristic
63C2×C8×C127C2×D411yescharacteristic
64C4⋊C4×C127—22no—
65C4⋊C4×C127—42no—
66C4⋊C4×C127—42no—
67C4⋊C4×C127—41no—
68C22⋊C4×C127—42no—
69C22⋊C4×C127—42no—
70C42×C127C22⋊C411yescharacteristic
71C42×C127C22⋊C411yescharacteristic
72C42×C127SD1611yescharacteristic
73C42×C127SD1611yescharacteristic
74C16×C127—42no—
75C23×C127—42no—
76C23×C127C2×D811yescharacteristic
77Q8×C127—82no—
78D4×C127—42no—
79D4×C127—42no—
80D4×C127—82no—
81D4×C127—82no—
82D4×C127—84no—
83C2×C4×C127—22no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—41no—
87C2×C4×C127—42no—
88C2×C4×C127—84no—
89C2×C4×C127—82no—
90C2×C4×C127—82no—
91C2×C4×C127—82no—
92C2×C4×C127#10211yescharacteristic
93C2×C4×C127#10211yescharacteristic
94C2×C4×C127#10211yescharacteristic
95C2×C4×C127#10211yescharacteristic
96C2×C4×C127C2×C22⋊C411yescharacteristic
97C2×C4×C127C2×SD1611yescharacteristic
98C8×C127—21no—
99C8×C127—21no—
100C8×C127—21no—
101C8×C127—21no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127—82no—
105C22×C127—82no—
106C22×C127—82no—
107C22×C127C2×#10211yescharacteristic
108C22×C127#50912yes—
109C4×C127—21no—
110C4×C127—21no—
111C4×C127—21no—
112C4×C127—21no—
113C4×C127—21no—
114C4×C127—82no—
115C4×C127—162no—
116C4×C127#41011yescharacteristic
117C4×C127#42111yescharacteristic
118#11858C12711yesmaximal, characteristic, direct product factor, Sylow
119C2×C127—22no—
120C2×C127—162no—
121C2×C127#151711yescharacteristic
122C2×C127#214011yescharacteristic
123C2×C127#214511yescharacteristic
124#3169C2×C12711yescharacteristic
125#2163C2×C12711yescharacteristic, complemented
126#1835C2×C12711yescharacteristic, complemented
127#1347C2×C12714yescomplemented
128C127#1185811yescharacteristic, direct product factor, Sylow
129#532—21no—
130#500C4×C12711yescharacteristic, complemented
131#493C4×C12711yescharacteristic, complemented
132#486—21no—
133#466—21no—
134#466C22×C12712yes—
135C4×D8—21no—
136C4×D8C4×C12712yescomplemented
137C2×C4×C8C22×C12711yescharacteristic
138#382—21no—
139C4⋊C16—21no—
140C22⋊C16C22×C12712yes—
141#346—21no—
142#340—21no—
143#340C22×C12712yes—
144C2×#41—41no—
145C2×D8—21no—
146C2×D8C2×C4×C12712yes—
147C22×C8D4×C12711yescharacteristic
148C22×C8C23×C12711yescharacteristic
149C4⋊Q8—21no—
150#127—21no—
151#124—41no—
152#121—22no—
153#121—41no—
154C4×D4—22no—
155C4×D4—41no—
156C2×C4⋊C4—22no—
157C2×C42D4×C12711yescharacteristic
158C2×C16—22no—
159#107—21no—
160#107C2×C4×C12712yes—
161#102—22no—
162#102—22no—
163C4×C8C2×C4×C12711yescharacteristic
164C4×C8C2×C4×C12711yescharacteristic
165C4×C8D4×C12711yescharacteristic
166C4×C8D4×C12711yescharacteristic
167#95—41no—
168#95—41no—
169#41—84no—
170C2×Q8—41no—
171C2×D4—22no—
172C2×D4—42no—
173C2×D4—41no—
174C2×D4—41no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4D8×C12711yescharacteristic
178C22×C4D8×C12711yescharacteristic
179C22×C4C2×D4×C12711yescharacteristic
180D8—42no—
181D8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8C22⋊C4×C12711yescharacteristic
185C2×C8C22⋊C4×C12711yescharacteristic
186C2×C8C22×C4×C12711yescharacteristic
187C2×C8C2×D4×C12711yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C22⋊C4—42no—
193C22⋊C4—42no—
194C42C22⋊C4×C12711yescharacteristic
195C42C22⋊C4×C12711yescharacteristic
196C42SD16×C12711yescharacteristic
197C42SD16×C12711yescharacteristic
198C16—42no—
199C23—42no—
200C23C2×D8×C12711yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—84no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—84no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4#102×C12711yescharacteristic
217C2×C4#102×C12711yescharacteristic
218C2×C4#102×C12711yescharacteristic
219C2×C4#102×C12711yescharacteristic
220C2×C4C2×C22⋊C4×C12711yescharacteristic
221C2×C4C2×SD16×C12711yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C22—21no—
227C22—21no—
228C22—82no—
229C22—82no—
230C22—82no—
231C22C2×#102×C12711yescharacteristic
232C22#509×C12712yes—
233C4—21no—
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—82no—
239C4—162no—
240C4#410×C12711yescharacteristic
241C4#421×C12711yescharacteristic
242C2—22no—
243C2—162no—
244C2C127×#151711yescharacteristic
245C2C127×#214011yescharacteristic
246C2C127×#214511yescharacteristic
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. C127×#1835C2semidirect
4. C127×#1347C2semidirect
6. #500×C127C4semidirect
7. #493×C127C4semidirect
12. C4×D8×C127C4semidirect
118. #11858C127direct (N × H)
125. #2163C2×C127semidirect
126. #1835C2×C127semidirect
127. #1347C2×C127semidirect
128. C127#11858direct (N × H)
130. #500C4×C127semidirect
131. #493C4×C127semidirect
136. 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
C127×#18352
C127×#13472
#11858127