Finite Group Databasebeta

← C127×#12487 #44576160

Subgroups — C127×#12487 #44576160

Order 32512.

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

normal subgroups only

This group has 226 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×#2226C211yesmaximal, characteristic
2C127×#2208C211yesmaximal, characteristic
3C127×#1707C211yesmaximal, characteristic, complemented
4C127×#1589C211yesmaximal, characteristic
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1365C211yesmaximal, characteristic, complemented
7C127×#1362C211yesmaximal, characteristic, complemented
8C2×SD32×C127—21no—
9#500×C127C2211yescharacteristic
10#498×C127—21no—
11#494×C127C2211yescharacteristic
12#487×C127—21no—
13C4×D8×C127C2211yescharacteristic
14#436×C127—21no—
15#367×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#358×C127—21no—
19#357×C127—21no—
20#335×C127C2211yescharacteristic
21D4⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×D8×C127D411yescharacteristic
26C2×M16×C127—41no—
27C4⋊Q8×C127—21no—
28C4⋊Q8×C127—21no—
29C4×D4×C127—21no—
30SD32×C127—42no—
31C2×C16×C127—21no—
32C2×C16×C127—21no—
33#107×C127—21no—
34#107×C127—21no—
35#107×C127D411yescharacteristic
36#106×C127—41no—
37#106×C127—41no—
38C4⋊C8×C127—21no—
39#103×C127—42no—
40#102×C127—21no—
41C22⋊C8×C127—41no—
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—41no—
46C2×Q8×C127—41no—
47C2×D4×C127—21no—
48C22×C4×C127—41no—
49Q16×C127—41no—
50Q16×C127—41no—
51Q16×C127—81no—
52D8×C127—21no—
53D8×C127—21no—
54M16×C127—82no—
55C2×C8×C127—21no—
56C2×C8×C127—41no—
57C2×C8×C127D811yescharacteristic
58C2×C8×C127D811yescharacteristic
59C2×C8×C127C2×D411yescharacteristic
60C2×C8×C127#4111yescharacteristic
61C4⋊C4×C127—21no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C22⋊C4×C127—41no—
67C42×C127C2×D411yescharacteristic
68C16×C127—41no—
69C16×C127—41no—
70C23×C127—41no—
71Q8×C127—82no—
72Q8×C127—81no—
73Q8×C127—81no—
74D4×C127—41no—
75D4×C127—41no—
76C2×C4×C127—41no—
77C2×C4×C127—81no—
78C2×C4×C127—81no—
79C2×C4×C127—81no—
80C2×C4×C127—81no—
81C2×C4×C127#12111yescharacteristic
82C2×C4×C127C2×D811yescharacteristic
83C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
84C8×C127—21no—
85C8×C127—21no—
86C8×C127—41no—
87C8×C127—81no—
88C8×C127SD3212yescomplemented
89C8×C127AGL(1,ℤ/8)11yescharacteristic
90C8×C127#13711yescharacteristic
91C22×C127—81no—
92C22×C127—81no—
93C22×C127—81no—
94C22×C127#45911yescharacteristic
95C4×C127—21no—
96C4×C127—81no—
97C4×C127—161no—
98C4×C127—161no—
99C4×C127#46811yescharacteristic
100C4×C127#47111yescharacteristic
101C4×C127C2×SD3211yescharacteristic
102C4×C127#51011yescharacteristic
103#12487C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—161no—
105C2×C127#168511yescharacteristic
106C2×C127#220811yescharacteristic
107C2×C127#221211yescharacteristic
108#2226C2×C12711yescharacteristic
109#2208C2×C12711yescharacteristic
110#1707C2×C12711yescharacteristic, complemented
111#1589C2×C12711yescharacteristic
112#1370C2×C12711yescharacteristic, complemented
113#1365C2×C12711yescharacteristic, complemented
114#1362C2×C12711yescharacteristic, complemented
115C127#1248711yescharacteristic, direct product factor, Sylow
116C2×SD32—21no—
117#500C22×C12711yescharacteristic
118#498—21no—
119#494C22×C12711yescharacteristic
120#487—21no—
121C4×D8C22×C12711yescharacteristic
122#436—21no—
123#367—21no—
124C4⋊C16C22×C12711yescharacteristic
125C4⋊C16C22×C12711yescharacteristic
126#358—21no—
127#357—21no—
128#335C22×C12711yescharacteristic
129D4⋊C8—21no—
130C82C22×C12711yescharacteristic
131C2×Q16—21no—
132C2×Q16—21no—
133C2×D8D4×C12711yescharacteristic
134C2×M16—41no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4×D4—21no—
138SD32—42no—
139C2×C16—21no—
140C2×C16—21no—
141#107—21no—
142#107—21no—
143#107D4×C12711yescharacteristic
144#106—41no—
145#106—41no—
146C4⋊C8—21no—
147#103—42no—
148#102—21no—
149C22⋊C8—41no—
150C4×C8D4×C12711yescharacteristic
151C4×C8D4×C12711yescharacteristic
152C4×C8C23×C12711yescharacteristic
153C2×Q8—41no—
154C2×Q8—41no—
155C2×D4—21no—
156C22×C4—41no—
157Q16—41no—
158Q16—41no—
159Q16—81no—
160D8—21no—
161D8—21no—
162M16—82no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8D8×C12711yescharacteristic
166C2×C8D8×C12711yescharacteristic
167C2×C8C2×D4×C12711yescharacteristic
168C2×C8#41×C12711yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C22⋊C4—41no—
175C42C2×D4×C12711yescharacteristic
176C16—41no—
177C16—41no—
178C23—41no—
179Q8—82no—
180Q8—81no—
181Q8—81no—
182D4—41no—
183D4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4#121×C12711yescharacteristic
190C2×C4C2×D8×C12711yescharacteristic
191C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
192C8—21no—
193C8—21no—
194C8—41no—
195C8—81no—
196C8SD32×C12712yescomplemented
197C8AGL(1,ℤ/8)×C12711yescharacteristic
198C8#137×C12711yescharacteristic
199C22—81no—
200C22—81no—
201C22—81no—
202C22#459×C12711yescharacteristic
203C4—21no—
204C4—81no—
205C4—161no—
206C4—161no—
207C4#468×C12711yescharacteristic
208C4#471×C12711yescharacteristic
209C4C2×SD32×C12711yescharacteristic
210C4#510×C12711yescharacteristic
211C2—161no—
212C2C127×#168511yescharacteristic
213C2C127×#220811yescharacteristic
214C2C127×#221211yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D8×C127D4
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
3. C127×#1707C2semidirect
5. C127×#1370C2semidirect
6. C127×#1365C2semidirect
7. C127×#1362C2semidirect
88. C8×C127SD32semidirect
103. #12487C127direct (N × H)
110. #1707C2×C127semidirect
112. #1370C2×C127semidirect
113. #1365C2×C127semidirect
114. #1362C2×C127semidirect
115. C127#12487direct (N × H)
196. C8SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22262
C127×#22082
C127×#17072
C127×#15892
C127×#13702
C127×#13652
C127×#13622
#12487127