Finite Group Databasebeta

← C127×#11960 #44575633

Subgroups — C127×#11960 #44575633

Order 32512.

392 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3147C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1568C211yesmaximal, characteristic, complemented
4C127×#1360C214yesmaximal, complemented
5C2×#135×C127—21no—
6C2×#135×C127C412yes—
7#532×C127—21no—
8#495×C127—21no—
9#495×C127C2212yes—
10#494×C127C411yescharacteristic
11#493×C127C411yescharacteristic
12#492×C127—21no—
13#432×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127C2212yes—
16C22⋊C16×C127—21no—
17#346×C127—21no—
18#335×C127—21no—
19#334×C127C2212yes—
20C2×#41×C127—22no—
21#135×C127—44no—
22#135×C127—44no—
23C2×Q16×C127—21no—
24C2×Q16×C127C2×C412yes—
25C2×SD16×C127—22no—
26C2×SD16×C127—22no—
27C2×D8×C127—21no—
28C2×D8×C127C2×C412yes—
29C22×C8×C127C2×C411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C4⋊Q8×C127—21no—
32#127×C127—21no—
33#124×C127—22no—
34#121×C127—41no—
35#121×C127—41no—
36C4×D4×C127—41no—
37C4×D4×C127—41no—
38C2×C42×C127D411yescharacteristic
39C2×C16×C127—22no—
40C4⋊C8×C127—22no—
41C22⋊C8×C127—41no—
42#97×C127—41no—
43C4×C8×C127C2×C411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127D411yescharacteristic
46C4×C8×C127C2311yescharacteristic
47#41×C127—44no—
48#41×C127—44no—
49C2×Q8×C127—22no—
50C2×D4×C127—22no—
51C2×D4×C127—42no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C22×C4×C127—42no—
55C22×C4×C127C22⋊C411yescharacteristic
56C22×C4×C127D811yescharacteristic
57C22×C4×C127SD1611yescharacteristic
58Q16×C127—42no—
59Q16×C127—42no—
60SD16×C127—44no—
61SD16×C127—44no—
62D8×C127—42no—
63D8×C127—42no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—42no—
67C2×C8×C127C22⋊C411yescharacteristic
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22×C411yescharacteristic
70C2×C8×C127C2×D411yescharacteristic
71C4⋊C4×C127—41no—
72C4⋊C4×C127—41no—
73C22⋊C4×C127—42no—
74C22⋊C4×C127—42no—
75C42×C127C22⋊C411yescharacteristic
76C42×C127D811yescharacteristic
77C42×C127SD1611yescharacteristic
78C42×C127C2×D411yescharacteristic
79C16×C127—42no—
80C23×C127—42no—
81C23×C127#10211yescharacteristic
82Q8×C127—42no—
83Q8×C127—42no—
84D4×C127—42no—
85D4×C127—42no—
86D4×C127—82no—
87D4×C127—82no—
88D4×C127—84no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—42no—
94C2×C4×C127—84no—
95C2×C4×C127#10211yescharacteristic
96C2×C4×C127#10211yescharacteristic
97C2×C4×C127#10211yescharacteristic
98C2×C4×C127C2×C22⋊C411yescharacteristic
99C2×C4×C127C2×D811yescharacteristic
100C2×C4×C127C2×SD1611yescharacteristic
101C8×C127—21no—
102C8×C127—21no—
103C8×C127—82no—
104C8×C127#10012yes—
105C8×C127AGL(1,ℤ/8)12yes—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127—21no—
109C22×C127—82no—
110C22×C127—82no—
111C22×C127—82no—
112C22×C127C2×#10211yescharacteristic
113C4×C127—21no—
114C4×C127—21no—
115C4×C127—21no—
116C4×C127—21no—
117C4×C127—21no—
118C4×C127—82no—
119C4×C127C2×#10011yescharacteristic
120C4×C127#41811yescharacteristic
121#11960C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—41no—
123C2×C127—162no—
124C2×C127#154511yescharacteristic
125C2×C127#214311yescharacteristic
126C2×C127#214511yescharacteristic
127#3147C2×C12711yescharacteristic
128#2163C2×C12711yescharacteristic, complemented
129#1568C2×C12711yescharacteristic, complemented
130#1360C2×C12714yescomplemented
131C127#1196011yescharacteristic, direct product factor, Sylow
132C2×#135—21no—
133C2×#135C4×C12712yes—
134#532—21no—
135#495—21no—
136#495C22×C12712yes—
137#494C4×C12711yescharacteristic
138#493C4×C12711yescharacteristic
139#492—21no—
140#432—21no—
141C2×C4×C8C22×C12711yescharacteristic
142C4⋊C16C22×C12712yes—
143C22⋊C16—21no—
144#346—21no—
145#335—21no—
146#334C22×C12712yes—
147C2×#41—22no—
148#135—44no—
149#135—44no—
150C2×Q16—21no—
151C2×Q16C2×C4×C12712yes—
152C2×SD16—22no—
153C2×SD16—22no—
154C2×D8—21no—
155C2×D8C2×C4×C12712yes—
156C22×C8C2×C4×C12711yescharacteristic
157C22×C8D4×C12711yescharacteristic
158C4⋊Q8—21no—
159#127—21no—
160#124—22no—
161#121—41no—
162#121—41no—
163C4×D4—41no—
164C4×D4—41no—
165C2×C42D4×C12711yescharacteristic
166C2×C16—22no—
167C4⋊C8—22no—
168C22⋊C8—41no—
169#97—41no—
170C4×C8C2×C4×C12711yescharacteristic
171C4×C8D4×C12711yescharacteristic
172C4×C8D4×C12711yescharacteristic
173C4×C8C23×C12711yescharacteristic
174#41—44no—
175#41—44no—
176C2×Q8—22no—
177C2×D4—22no—
178C2×D4—42no—
179C2×D4—41no—
180C2×D4—41no—
181C22×C4—42no—
182C22×C4C22⋊C4×C12711yescharacteristic
183C22×C4D8×C12711yescharacteristic
184C22×C4SD16×C12711yescharacteristic
185Q16—42no—
186Q16—42no—
187SD16—44no—
188SD16—44no—
189D8—42no—
190D8—42no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8C22⋊C4×C12711yescharacteristic
195C2×C8C22⋊C4×C12711yescharacteristic
196C2×C8C22×C4×C12711yescharacteristic
197C2×C8C2×D4×C12711yescharacteristic
198C4⋊C4—41no—
199C4⋊C4—41no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C42C22⋊C4×C12711yescharacteristic
203C42D8×C12711yescharacteristic
204C42SD16×C12711yescharacteristic
205C42C2×D4×C12711yescharacteristic
206C16—42no—
207C23—42no—
208C23#102×C12711yescharacteristic
209Q8—42no—
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—82no—
214D4—82no—
215D4—84no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—84no—
222C2×C4#102×C12711yescharacteristic
223C2×C4#102×C12711yescharacteristic
224C2×C4#102×C12711yescharacteristic
225C2×C4C2×C22⋊C4×C12711yescharacteristic
226C2×C4C2×D8×C12711yescharacteristic
227C2×C4C2×SD16×C12711yescharacteristic
228C8—21no—
229C8—21no—
230C8—82no—
231C8#100×C12712yes—
232C8AGL(1,ℤ/8)×C12712yes—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—82no—
237C22—82no—
238C22—82no—
239C22C2×#102×C12711yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—21no—
245C4—82no—
246C4C2×#100×C12711yescharacteristic
247C4#418×C12711yescharacteristic
248C2—41no—
249C2—162no—
250C2C127×#154511yescharacteristic
251C2C127×#214311yescharacteristic
252C2C127×#214511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC127×#3147C2
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×#1568C2semidirect
4. C127×#1360C2semidirect
121. #11960C127direct (N × H)
128. #2163C2×C127semidirect
129. #1568C2×C127semidirect
130. #1360C2×C127semidirect
131. C127#11960direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31472
C127×#21632
C127×#15682
C127×#13602
#11960127