Finite Group Databasebeta

← C127×#11770 #44575443

Subgroups — C127×#11770 #44575443

Order 32512.

316 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3176C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic, complemented
3C127×#1747C211yesmaximal, characteristic, complemented
4C127×#1341C212yesmaximal, complemented
5C127×#1339C212yesmaximal, complemented
6#540×C127—21no—
7#499×C127C411yescharacteristic, complemented
8#493×C127C411yescharacteristic, complemented
9#490×C127—21no—
10#469×C127C2212yes—
11#466×C127—21no—
12#442×C127C412yescomplemented
13C4×D8×C127—21no—
14#405×C127—21no—
15#405×C127C2211yescharacteristic
16#364×C127—21no—
17#349×C127C2212yes—
18#347×C127—21no—
19#338×C127C2211yescharacteristic
20H(3,ℤ/4)×C127—21no—
21H(3,ℤ/4)×C127C2211yescharacteristic
22C2×D8×C127—21no—
23C2×D8×C127C2×C412yes—
24C2×M16×C127—21no—
25C2×M16×C127C2311yescharacteristic
26C22×C8×C127D411yescharacteristic
27#127×C127—21no—
28#125×C127—21no—
29#123×C127—42no—
30#121×C127—22no—
31#121×C127—42no—
32C4×D4×C127—22no—
33#117×C127—21no—
34#117×C127D411yescharacteristic
35M32×C127—22no—
36#107×C127—21no—
37#106×C127C2×C412yes—
38#102×C127—22no—
39#102×C127—22no—
40#97×C127—22no—
41#97×C127C2×C411yescharacteristic
42#97×C127D411yescharacteristic
43C4×C8×C127—22no—
44C4×C8×C127C2×C411yescharacteristic
45C4×C8×C127D411yescharacteristic
46C2×D4×C127—22no—
47C2×D4×C127—42no—
48C2×D4×C127—42no—
49C22×C4×C127—42no—
50C22×C4×C127C2×D411yescharacteristic
51D8×C127—42no—
52D8×C127—41no—
53D8×C127—41no—
54M16×C127—41no—
55M16×C127—41no—
56M16×C127—41no—
57C2×C8×C127—21no—
58C2×C8×C127—21no—
59C2×C8×C127—22no—
60C2×C8×C127C22⋊C411yescharacteristic
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22×C411yescharacteristic
63C2×C8×C127C2×D411yescharacteristic
64C4⋊C4×C127—21no—
65C4⋊C4×C127—22no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—42no—
68C22⋊C4×C127—21no—
69C22⋊C4×C127—42no—
70C22⋊C4×C127—41no—
71C22⋊C4×C127—42no—
72C42×C127—22no—
73C42×C127C22⋊C411yescharacteristic
74C42×C127C22⋊C411yescharacteristic
75C16×C127—42no—
76C23×C127—42no—
77C23×C127AGL(1,ℤ/8)11yescharacteristic
78D4×C127—42no—
79D4×C127—42no—
80D4×C127—162no—
81D4×C127—162no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—42no—
87C2×C4×C127—42no—
88C2×C4×C127—162no—
89C2×C4×C127C2×C22⋊C411yescharacteristic
90C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
91C8×C127—21no—
92C8×C127—21no—
93C8×C127—21no—
94C8×C127—42no—
95C8×C127#10411yescharacteristic
96C8×C127#10411yescharacteristic
97C22×C127—21no—
98C22×C127—41no—
99C22×C127—82no—
100C22×C127—82no—
101C22×C127—82no—
102C22×C127#41811yescharacteristic
103C4×C127—21no—
104C4×C127—41no—
105C4×C127—41no—
106C4×C127—82no—
107C4×C127—82no—
108C4×C127#41011yescharacteristic
109C4×C127C2×#10411yescharacteristic
110#11770C12711yesmaximal, characteristic, direct product factor, Sylow
111C2×C127—21no—
112C2×C127—41no—
113C2×C127—162no—
114C2×C127#150511yescharacteristic
115#3176C2×C12711yescharacteristic
116#2166C2×C12711yescharacteristic, complemented
117#1747C2×C12711yescharacteristic, complemented
118#1341C2×C12712yescomplemented
119#1339C2×C12712yescomplemented
120C127#1177011yescharacteristic, direct product factor, Sylow
121#540—21no—
122#499C4×C12711yescharacteristic, complemented
123#493C4×C12711yescharacteristic, complemented
124#490—21no—
125#469C22×C12712yes—
126#466—21no—
127#442C4×C12712yescomplemented
128C4×D8—21no—
129#405—21no—
130#405C22×C12711yescharacteristic
131#364—21no—
132#349C22×C12712yes—
133#347—21no—
134#338C22×C12711yescharacteristic
135H(3,ℤ/4)—21no—
136H(3,ℤ/4)C22×C12711yescharacteristic
137C2×D8—21no—
138C2×D8C2×C4×C12712yes—
139C2×M16—21no—
140C2×M16C23×C12711yescharacteristic
141C22×C8D4×C12711yescharacteristic
142#127—21no—
143#125—21no—
144#123—42no—
145#121—22no—
146#121—42no—
147C4×D4—22no—
148#117—21no—
149#117D4×C12711yescharacteristic
150M32—22no—
151#107—21no—
152#106C2×C4×C12712yes—
153#102—22no—
154#102—22no—
155#97—22no—
156#97C2×C4×C12711yescharacteristic
157#97D4×C12711yescharacteristic
158C4×C8—22no—
159C4×C8C2×C4×C12711yescharacteristic
160C4×C8D4×C12711yescharacteristic
161C2×D4—22no—
162C2×D4—42no—
163C2×D4—42no—
164C22×C4—42no—
165C22×C4C2×D4×C12711yescharacteristic
166D8—42no—
167D8—41no—
168D8—41no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—22no—
175C2×C8C22⋊C4×C12711yescharacteristic
176C2×C8C22⋊C4×C12711yescharacteristic
177C2×C8C22×C4×C12711yescharacteristic
178C2×C8C2×D4×C12711yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C22⋊C4—21no—
184C22⋊C4—42no—
185C22⋊C4—41no—
186C22⋊C4—42no—
187C42—22no—
188C42C22⋊C4×C12711yescharacteristic
189C42C22⋊C4×C12711yescharacteristic
190C16—42no—
191C23—42no—
192C23AGL(1,ℤ/8)×C12711yescharacteristic
193D4—42no—
194D4—42no—
195D4—162no—
196D4—162no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—162no—
204C2×C4C2×C22⋊C4×C12711yescharacteristic
205C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—42no—
210C8#104×C12711yescharacteristic
211C8#104×C12711yescharacteristic
212C22—21no—
213C22—41no—
214C22—82no—
215C22—82no—
216C22—82no—
217C22#418×C12711yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—82no—
223C4#410×C12711yescharacteristic
224C4C2×#104×C12711yescharacteristic
225C2—21no—
226C2—41no—
227C2—162no—
228C2C127×#150511yescharacteristic
subgroupG/H
center, socleC2×C127#1505
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC127×#3176C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2166C2semidirect
3. C127×#1747C2semidirect
4. C127×#1341C2semidirect
5. C127×#1339C2semidirect
7. #499×C127C4semidirect
8. #493×C127C4semidirect
12. #442×C127C4semidirect
110. #11770C127direct (N × H)
116. #2166C2×C127semidirect
117. #1747C2×C127semidirect
118. #1341C2×C127semidirect
119. #1339C2×C127semidirect
120. C127#11770direct (N × H)
122. #499C4×C127semidirect
123. #493C4×C127semidirect
127. #442C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31762
C127×#21662
C127×#17472
C127×#13412
C127×#13392
#11770127