Finite Group Databasebeta

← C127×#12489 #44576162

Subgroups — C127×#12489 #44576162

Order 32512.

226 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 78 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
2C127×#2208C211yesmaximal, characteristic
3C127×#1707C211yesmaximal, characteristic, complemented
4C127×#1589C211yesmaximal, characteristic
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1364C211yesmaximal, 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#366×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—42no—
37C4⋊C8×C127—21no—
38#103×C127—41no—
39#103×C127—41no—
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—81no—
72Q8×C127—81no—
73Q8×C127—81no—
74Q8×C127—81no—
75D4×C127—41no—
76D4×C127—41no—
77C2×C4×C127—41no—
78C2×C4×C127—81no—
79C2×C4×C127—81no—
80C2×C4×C127—81no—
81C2×C4×C127—81no—
82C2×C4×C127#12111yescharacteristic
83C2×C4×C127C2×D811yescharacteristic
84C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
85C8×C127—22no—
86C8×C127—21no—
87C8×C127—21no—
88C8×C127—21no—
89C8×C127—81no—
90C8×C127AGL(1,ℤ/8)11yescharacteristic
91C8×C127#13711yescharacteristic
92C22×C127—81no—
93C22×C127—81no—
94C22×C127—81no—
95C22×C127#45911yescharacteristic
96C4×C127—21no—
97C4×C127—81no—
98C4×C127—161no—
99C4×C127—161no—
100C4×C127#46811yescharacteristic
101C4×C127#47111yescharacteristic
102C4×C127#50811yescharacteristic
103C4×C127#50911yescharacteristic
104#12489C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—161no—
106C2×C127#168511yescharacteristic
107C2×C127#221011yescharacteristic
108C2×C127#221411yescharacteristic
109#2224C2×C12711yescharacteristic
110#2208C2×C12711yescharacteristic
111#1707C2×C12711yescharacteristic, complemented
112#1589C2×C12711yescharacteristic
113#1370C2×C12711yescharacteristic, complemented
114#1364C2×C12711yescharacteristic, complemented
115#1362C2×C12711yescharacteristic, complemented
116C127#1248911yescharacteristic, direct product factor, Sylow
117C2×SD32—21no—
118#500C22×C12711yescharacteristic
119#498—21no—
120#494C22×C12711yescharacteristic
121#487—21no—
122C4×D8C22×C12711yescharacteristic
123#436—21no—
124#366—21no—
125C4⋊C16C22×C12711yescharacteristic
126C4⋊C16C22×C12711yescharacteristic
127#358—21no—
128#357—21no—
129#335C22×C12711yescharacteristic
130D4⋊C8—21no—
131C82C22×C12711yescharacteristic
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8D4×C12711yescharacteristic
135C2×M16—41no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4×D4—21no—
139SD32—42no—
140C2×C16—21no—
141C2×C16—21no—
142#107—21no—
143#107—21no—
144#107D4×C12711yescharacteristic
145#106—42no—
146C4⋊C8—21no—
147#103—41no—
148#103—41no—
149#102—21no—
150C22⋊C8—41no—
151C4×C8D4×C12711yescharacteristic
152C4×C8D4×C12711yescharacteristic
153C4×C8C23×C12711yescharacteristic
154C2×Q8—41no—
155C2×Q8—41no—
156C2×D4—21no—
157C22×C4—41no—
158Q16—41no—
159Q16—41no—
160Q16—81no—
161D8—21no—
162D8—21no—
163M16—82no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8D8×C12711yescharacteristic
167C2×C8D8×C12711yescharacteristic
168C2×C8C2×D4×C12711yescharacteristic
169C2×C8#41×C12711yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C22⋊C4—41no—
176C42C2×D4×C12711yescharacteristic
177C16—41no—
178C16—41no—
179C23—41no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—81no—
184D4—41no—
185D4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#121×C12711yescharacteristic
192C2×C4C2×D8×C12711yescharacteristic
193C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—81no—
199C8AGL(1,ℤ/8)×C12711yescharacteristic
200C8#137×C12711yescharacteristic
201C22—81no—
202C22—81no—
203C22—81no—
204C22#459×C12711yescharacteristic
205C4—21no—
206C4—81no—
207C4—161no—
208C4—161no—
209C4#468×C12711yescharacteristic
210C4#471×C12711yescharacteristic
211C4#508×C12711yescharacteristic
212C4#509×C12711yescharacteristic
213C2—161no—
214C2C127×#168511yescharacteristic
215C2C127×#221011yescharacteristic
216C2C127×#221411yescharacteristic
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×#1364C2semidirect
7. C127×#1362C2semidirect
104. #12489C127direct (N × H)
111. #1707C2×C127semidirect
113. #1370C2×C127semidirect
114. #1364C2×C127semidirect
115. #1362C2×C127semidirect
116. C127#12489direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22242
C127×#22082
C127×#17072
C127×#15892
C127×#13702
C127×#13642
C127×#13622
#12489127