Finite Group Databasebeta

← C127×#12484 #44576157

Subgroups — C127×#12484 #44576157

Order 32512.

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

normal subgroups only

This group has 234 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×#2225C211yesmaximal, characteristic, complemented
2C127×#2207C211yesmaximal, characteristic
3C127×#1706C211yesmaximal, characteristic
4C127×#1591C211yesmaximal, characteristic, complemented
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1364C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic
8C2×SD32×C127—21no—
9#500×C127C2211yescharacteristic
10#493×C127C2211yescharacteristic
11#492×C127—21no—
12#486×C127—21no—
13#446×C127—21no—
14C4×Q16×C127C2211yescharacteristic
15#367×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#358×C127—21no—
19#357×C127—21no—
20#335×C127C2211yescharacteristic
21Q8⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×Q16×C127D411yescharacteristic
24C2×SD16×C127—41no—
25C2×SD16×C127—41no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C4⋊Q8×C127—21no—
29#127×C127—21no—
30C4×Q8×C127—21no—
31SD32×C127—42no—
32C2×C16×C127—21no—
33C2×C16×C127—21no—
34#107×C127—21no—
35#107×C127—21no—
36#107×C127D411yescharacteristic
37C4⋊C8×C127—21no—
38C4⋊C8×C127—41no—
39#103×C127—21no—
40#102×C127—42no—
41#97×C127—41no—
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—21no—
46C2×Q8×C127—41no—
47C2×D4×C127—41no—
48C2×D4×C127—41no—
49C2×D4×C127—41no—
50Q16×C127—21no—
51Q16×C127—21no—
52SD16×C127—82no—
53SD16×C127—82no—
54D8×C127—41no—
55D8×C127—41no—
56D8×C127—81no—
57C2×C8×C127—21no—
58C2×C8×C127—41no—
59C2×C8×C127D811yescharacteristic
60C2×C8×C127D811yescharacteristic
61C2×C8×C127C2×D411yescharacteristic
62C2×C8×C127#4111yescharacteristic
63C4⋊C4×C127—21no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C42×C127—41no—
68C42×C127C2×D411yescharacteristic
69C16×C127—41no—
70C16×C127—41no—
71C23×C127—81no—
72Q8×C127—41no—
73Q8×C127—41no—
74Q8×C127—81no—
75Q8×C127—81no—
76D4×C127—82no—
77D4×C127—81no—
78D4×C127—81no—
79D4×C127—81no—
80D4×C127—81no—
81C2×C4×C127—41no—
82C2×C4×C127—41no—
83C2×C4×C127—81no—
84C2×C4×C127#12111yescharacteristic
85C2×C4×C127C2×D811yescharacteristic
86C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
87C8×C127—21no—
88C8×C127—21no—
89C8×C127—41no—
90C8×C127—81no—
91C8×C127SD3212yescomplemented
92C8×C127AGL(1,ℤ/8)11yescharacteristic
93C8×C127#13711yescharacteristic
94C22×C127—161no—
95C22×C127—161no—
96C22×C127—161no—
97C22×C127#45911yescharacteristic
98C4×C127—21no—
99C4×C127—81no—
100C4×C127—81no—
101C4×C127—161no—
102C4×C127#46811yescharacteristic
103C4×C127#47111yescharacteristic
104C4×C127C2×SD3211yescharacteristic
105C4×C127#50911yescharacteristic
106#12484C12711yesmaximal, characteristic, direct product factor, Sylow
107C2×C127—321no—
108C2×C127#168511yescharacteristic
109C2×C127#220711yescharacteristic
110C2×C127#221211yescharacteristic
111#2225C2×C12711yescharacteristic, complemented
112#2207C2×C12711yescharacteristic
113#1706C2×C12711yescharacteristic
114#1591C2×C12711yescharacteristic, complemented
115#1370C2×C12711yescharacteristic, complemented
116#1364C2×C12711yescharacteristic, complemented
117#1361C2×C12711yescharacteristic
118C127#1248411yescharacteristic, direct product factor, Sylow
119C2×SD32—21no—
120#500C22×C12711yescharacteristic
121#493C22×C12711yescharacteristic
122#492—21no—
123#486—21no—
124#446—21no—
125C4×Q16C22×C12711yescharacteristic
126#367—21no—
127C4⋊C16C22×C12711yescharacteristic
128C4⋊C16C22×C12711yescharacteristic
129#358—21no—
130#357—21no—
131#335C22×C12711yescharacteristic
132Q8⋊C8—21no—
133C82C22×C12711yescharacteristic
134C2×Q16D4×C12711yescharacteristic
135C2×SD16—41no—
136C2×SD16—41no—
137C2×D8—21no—
138C2×D8—21no—
139C4⋊Q8—21no—
140#127—21no—
141C4×Q8—21no—
142SD32—42no—
143C2×C16—21no—
144C2×C16—21no—
145#107—21no—
146#107—21no—
147#107D4×C12711yescharacteristic
148C4⋊C8—21no—
149C4⋊C8—41no—
150#103—21no—
151#102—42no—
152#97—41no—
153C4×C8D4×C12711yescharacteristic
154C4×C8D4×C12711yescharacteristic
155C4×C8C23×C12711yescharacteristic
156C2×Q8—21no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161Q16—21no—
162Q16—21no—
163SD16—82no—
164SD16—82no—
165D8—41no—
166D8—41no—
167D8—81no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8D8×C12711yescharacteristic
171C2×C8D8×C12711yescharacteristic
172C2×C8C2×D4×C12711yescharacteristic
173C2×C8#41×C12711yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C42—41no—
179C42C2×D4×C12711yescharacteristic
180C16—41no—
181C16—41no—
182C23—81no—
183Q8—41no—
184Q8—41no—
185Q8—81no—
186Q8—81no—
187D4—82no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4#121×C12711yescharacteristic
196C2×C4C2×D8×C12711yescharacteristic
197C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
198C8—21no—
199C8—21no—
200C8—41no—
201C8—81no—
202C8SD32×C12712yescomplemented
203C8AGL(1,ℤ/8)×C12711yescharacteristic
204C8#137×C12711yescharacteristic
205C22—161no—
206C22—161no—
207C22—161no—
208C22#459×C12711yescharacteristic
209C4—21no—
210C4—81no—
211C4—81no—
212C4—161no—
213C4#468×C12711yescharacteristic
214C4#471×C12711yescharacteristic
215C4C2×SD32×C12711yescharacteristic
216C4#509×C12711yescharacteristic
217C2—321no—
218C2C127×#168511yescharacteristic
219C2C127×#220711yescharacteristic
220C2C127×#221211yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
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×#2225C2semidirect
4. C127×#1591C2semidirect
5. C127×#1370C2semidirect
6. C127×#1364C2semidirect
91. C8×C127SD32semidirect
106. #12484C127direct (N × H)
111. #2225C2×C127semidirect
114. #1591C2×C127semidirect
115. #1370C2×C127semidirect
116. #1364C2×C127semidirect
118. C127#12484direct (N × H)
202. C8SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22252
C127×#22072
C127×#17062
C127×#15912
C127×#13702
C127×#13642
C127×#13612
#12484127