Finite Group Databasebeta

← C127×#12483 #44576156

Subgroups — C127×#12483 #44576156

Order 32512.

248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2224C211yesmaximal, characteristic, complemented
2C127×#2206C211yesmaximal, characteristic
3C127×#1706C211yesmaximal, characteristic, complemented
4C127×#1589C211yesmaximal, characteristic, complemented
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1364C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic, complemented
8C2×D16×C127—21no—
9#500×C127C2211yescharacteristic
10#493×C127C2211yescharacteristic
11#492×C127—21no—
12#486×C127—21no—
13C4×D8×C127C2211yescharacteristic
14#436×C127—21no—
15#366×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#357×C127—21no—
19#357×C127—21no—
20#335×C127C2211yescharacteristic
21D4⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×SD16×C127—41no—
24C2×SD16×C127—41no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127D411yescharacteristic
28C2×M16×C127—41no—
29C4⋊Q8×C127—21no—
30#127×C127—21no—
31C4×D4×C127—21no—
32D16×C127—42no—
33C2×C16×C127—21no—
34C2×C16×C127—21no—
35#107×C127—21no—
36#107×C127—21no—
37#107×C127D411yescharacteristic
38C4⋊C8×C127—21no—
39#102×C127—21no—
40#102×C127—42no—
41C22⋊C8×C127—41no—
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—41no—
46C2×D4×C127—21no—
47C2×D4×C127—41no—
48C2×D4×C127—41no—
49C2×D4×C127—41no—
50C22×C4×C127—41no—
51SD16×C127—82no—
52SD16×C127—82no—
53D8×C127—21no—
54D8×C127—21no—
55D8×C127—41no—
56D8×C127—41no—
57D8×C127—81no—
58M16×C127—82no—
59C2×C8×C127—21no—
60C2×C8×C127—41no—
61C2×C8×C127D811yescharacteristic
62C2×C8×C127D811yescharacteristic
63C2×C8×C127C2×D411yescharacteristic
64C2×C8×C127#4111yescharacteristic
65C4⋊C4×C127—21no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—41no—
68C22⋊C4×C127—41no—
69C42×C127C2×D411yescharacteristic
70C16×C127—41no—
71C16×C127—41no—
72C23×C127—41no—
73C23×C127—81no—
74Q8×C127—81no—
75Q8×C127—81no—
76D4×C127—41no—
77D4×C127—41no—
78D4×C127—82no—
79D4×C127—81no—
80D4×C127—81no—
81D4×C127—81no—
82D4×C127—81no—
83C2×C4×C127—41no—
84C2×C4×C127—81no—
85C2×C4×C127—81no—
86C2×C4×C127—81no—
87C2×C4×C127#12111yescharacteristic
88C2×C4×C127C2×D811yescharacteristic
89C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
90C8×C127—21no—
91C8×C127—21no—
92C8×C127—41no—
93C8×C127—81no—
94C8×C127D1612yescomplemented
95C8×C127AGL(1,ℤ/8)11yescharacteristic
96C8×C127#13711yescharacteristic
97C22×C127—81no—
98C22×C127—81no—
99C22×C127—81no—
100C22×C127—161no—
101C22×C127—161no—
102C22×C127—161no—
103C22×C127#45911yescharacteristic
104C4×C127—21no—
105C4×C127—81no—
106C4×C127—161no—
107C4×C127#46811yescharacteristic
108C4×C127#47111yescharacteristic
109C4×C127C2×D1611yescharacteristic
110C4×C127#50911yescharacteristic
111#12483C12711yesmaximal, characteristic, direct product factor, Sylow
112C2×C127—161no—
113C2×C127—321no—
114C2×C127#168511yescharacteristic
115C2×C127#220611yescharacteristic
116C2×C127#221211yescharacteristic
117#2224C2×C12711yescharacteristic, complemented
118#2206C2×C12711yescharacteristic
119#1706C2×C12711yescharacteristic, complemented
120#1589C2×C12711yescharacteristic, complemented
121#1370C2×C12711yescharacteristic, complemented
122#1364C2×C12711yescharacteristic, complemented
123#1361C2×C12711yescharacteristic, complemented
124C127#1248311yescharacteristic, direct product factor, Sylow
125C2×D16—21no—
126#500C22×C12711yescharacteristic
127#493C22×C12711yescharacteristic
128#492—21no—
129#486—21no—
130C4×D8C22×C12711yescharacteristic
131#436—21no—
132#366—21no—
133C4⋊C16C22×C12711yescharacteristic
134C4⋊C16C22×C12711yescharacteristic
135#357—21no—
136#357—21no—
137#335C22×C12711yescharacteristic
138D4⋊C8—21no—
139C82C22×C12711yescharacteristic
140C2×SD16—41no—
141C2×SD16—41no—
142C2×D8—21no—
143C2×D8—21no—
144C2×D8D4×C12711yescharacteristic
145C2×M16—41no—
146C4⋊Q8—21no—
147#127—21no—
148C4×D4—21no—
149D16—42no—
150C2×C16—21no—
151C2×C16—21no—
152#107—21no—
153#107—21no—
154#107D4×C12711yescharacteristic
155C4⋊C8—21no—
156#102—21no—
157#102—42no—
158C22⋊C8—41no—
159C4×C8D4×C12711yescharacteristic
160C4×C8D4×C12711yescharacteristic
161C4×C8C23×C12711yescharacteristic
162C2×Q8—41no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C22×C4—41no—
168SD16—82no—
169SD16—82no—
170D8—21no—
171D8—21no—
172D8—41no—
173D8—41no—
174D8—81no—
175M16—82no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8D8×C12711yescharacteristic
179C2×C8D8×C12711yescharacteristic
180C2×C8C2×D4×C12711yescharacteristic
181C2×C8#41×C12711yescharacteristic
182C4⋊C4—21no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C22⋊C4—41no—
186C42C2×D4×C12711yescharacteristic
187C16—41no—
188C16—41no—
189C23—41no—
190C23—81no—
191Q8—81no—
192Q8—81no—
193D4—41no—
194D4—41no—
195D4—82no—
196D4—81no—
197D4—81no—
198D4—81no—
199D4—81no—
200C2×C4—41no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4#121×C12711yescharacteristic
205C2×C4C2×D8×C12711yescharacteristic
206C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
207C8—21no—
208C8—21no—
209C8—41no—
210C8—81no—
211C8D16×C12712yescomplemented
212C8AGL(1,ℤ/8)×C12711yescharacteristic
213C8#137×C12711yescharacteristic
214C22—81no—
215C22—81no—
216C22—81no—
217C22—161no—
218C22—161no—
219C22—161no—
220C22#459×C12711yescharacteristic
221C4—21no—
222C4—81no—
223C4—161no—
224C4#468×C12711yescharacteristic
225C4#471×C12711yescharacteristic
226C4C2×D16×C12711yescharacteristic
227C4#509×C12711yescharacteristic
228C2—161no—
229C2—321no—
230C2C127×#168511yescharacteristic
231C2C127×#220611yescharacteristic
232C2C127×#221211yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2206C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2224C2semidirect
3. C127×#1706C2semidirect
4. C127×#1589C2semidirect
5. C127×#1370C2semidirect
6. C127×#1364C2semidirect
7. C127×#1361C2semidirect
94. C8×C127D16semidirect
111. #12483C127direct (N × H)
117. #2224C2×C127semidirect
119. #1706C2×C127semidirect
120. #1589C2×C127semidirect
121. #1370C2×C127semidirect
122. #1364C2×C127semidirect
123. #1361C2×C127semidirect
124. C127#12483direct (N × H)
211. C8D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22242
C127×#22062
C127×#17062
C127×#15892
C127×#13702
C127×#13642
C127×#13612
#12483127