Finite Group Databasebeta

← C127×#12530 #44576203

Subgroups — C127×#12530 #44576203

Order 32512.

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

normal subgroups only

This group has 284 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×#2248C211yesmaximal, characteristic
2C127×#2247C211yesmaximal, characteristic, complemented
3C127×#2241C211yesmaximal, characteristic, complemented
4C127×#2240C211yesmaximal, characteristic
5C127×#1709C211yesmaximal, characteristic
6C127×#1707C211yesmaximal, characteristic, complemented
7C127×#1312C211yesmaximal, characteristic, complemented
8C2×Q32×C127—22no—
9C2×SD32×C127—22no—
10#500×C127C2211yescharacteristic
11#498×C127—21no—
12#494×C127C2211yescharacteristic
13#494×C127C2211yescharacteristic
14#493×C127C2211yescharacteristic
15#487×C127—21no—
16#486×C127—21no—
17#486×C127—21no—
18#358×C127—22no—
19#357×C127—22no—
20C4×C16×C127C2211yescharacteristic
21C4×C16×C127C2211yescharacteristic
22C82×C127C2211yescharacteristic
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×Q16×C127—21no—
26C2×Q16×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C4⋊Q8×C127—21no—
30C4⋊Q8×C127—21no—
31C4⋊Q8×C127—21no—
32#127×C127—21no—
33Q32×C127—44no—
34SD32×C127—44no—
35C2×C16×C127D412yes—
36C2×C16×C127D412yes—
37#107×C127—21no—
38#107×C127—21no—
39#106×C127—42no—
40#103×C127—42no—
41#102×C127—42no—
42#102×C127—42no—
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
46C2×Q8×C127—41no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×D4×C127—41no—
50C2×D4×C127—41no—
51C2×D4×C127—41no—
52Q16×C127—42no—
53Q16×C127—42no—
54Q16×C127—42no—
55Q16×C127—42no—
56D8×C127—42no—
57D8×C127—42no—
58C2×C8×C127D812yes—
59C2×C8×C127D812yes—
60C2×C8×C127C2×D411yescharacteristic
61C2×C8×C127C2×D411yescharacteristic
62C4⋊C4×C127—41no—
63C4⋊C4×C127—41no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—41no—
68C42×C127C2×D411yescharacteristic
69C16×C127—22no—
70C16×C127—22no—
71C23×C127—81no—
72Q8×C127—81no—
73Q8×C127—81no—
74Q8×C127—81no—
75Q8×C127—81no—
76Q8×C127—82no—
77D4×C127—81no—
78D4×C127—81no—
79D4×C127—82no—
80D4×C127—82no—
81C2×C4×C127—81no—
82C2×C4×C127—81no—
83C2×C4×C127—81no—
84C2×C4×C127#12711yescharacteristic
85C2×C4×C127C2×D811yescharacteristic
86C2×C4×C127C2×D811yescharacteristic
87C8×C127—22no—
88C8×C127—22no—
89C8×C127AGL(1,ℤ/8)12yes—
90C8×C127AGL(1,ℤ/8)12yes—
91C22×C127—161no—
92C22×C127—161no—
93C22×C127—161no—
94C22×C127#49311yescharacteristic
95C4×C127—161no—
96C4×C127—161no—
97C4×C127—161no—
98C4×C127#49611yescharacteristic
99C4×C127#49611yescharacteristic
100C4×C127#50812yes—
101C4×C127#51012yes—
102#12530C12711yesmaximal, characteristic, direct product factor, Sylow
103C2×C127—321no—
104C2×C127#172111yescharacteristic
105C2×C127#224911yescharacteristic
106C2×C127#225111yescharacteristic
107#2248C2×C12711yescharacteristic
108#2247C2×C12711yescharacteristic, complemented
109#2241C2×C12711yescharacteristic, complemented
110#2240C2×C12711yescharacteristic
111#1709C2×C12711yescharacteristic
112#1707C2×C12711yescharacteristic, complemented
113#1312C2×C12711yescharacteristic, complemented
114C127#1253011yescharacteristic, direct product factor, Sylow
115C2×Q32—22no—
116C2×SD32—22no—
117#500C22×C12711yescharacteristic
118#498—21no—
119#494C22×C12711yescharacteristic
120#494C22×C12711yescharacteristic
121#493C22×C12711yescharacteristic
122#487—21no—
123#486—21no—
124#486—21no—
125#358—22no—
126#357—22no—
127C4×C16C22×C12711yescharacteristic
128C4×C16C22×C12711yescharacteristic
129C82C22×C12711yescharacteristic
130C2×Q16—21no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—21no—
135C2×D8—21no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139#127—21no—
140Q32—44no—
141SD32—44no—
142C2×C16D4×C12712yes—
143C2×C16D4×C12712yes—
144#107—21no—
145#107—21no—
146#106—42no—
147#103—42no—
148#102—42no—
149#102—42no—
150C4×C8D4×C12711yescharacteristic
151C4×C8D4×C12711yescharacteristic
152C4×C8C23×C12711yescharacteristic
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—42no—
160Q16—42no—
161Q16—42no—
162Q16—42no—
163D8—42no—
164D8—42no—
165C2×C8D8×C12712yes—
166C2×C8D8×C12712yes—
167C2×C8C2×D4×C12711yescharacteristic
168C2×C8C2×D4×C12711yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C42C2×D4×C12711yescharacteristic
176C16—22no—
177C16—22no—
178C23—81no—
179Q8—81no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—82no—
184D4—81no—
185D4—81no—
186D4—82no—
187D4—82no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#127×C12711yescharacteristic
192C2×C4C2×D8×C12711yescharacteristic
193C2×C4C2×D8×C12711yescharacteristic
194C8—22no—
195C8—22no—
196C8AGL(1,ℤ/8)×C12712yes—
197C8AGL(1,ℤ/8)×C12712yes—
198C22—161no—
199C22—161no—
200C22—161no—
201C22#493×C12711yescharacteristic
202C4—161no—
203C4—161no—
204C4—161no—
205C4#496×C12711yescharacteristic
206C4#496×C12711yescharacteristic
207C4#508×C12712yes—
208C4#510×C12712yes—
209C2—321no—
210C2C127×#172111yescharacteristic
211C2C127×#224911yescharacteristic
212C2C127×#225111yescharacteristic
subgroupG/H
center, socleC22×C127#493
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
2. C127×#2247C2semidirect
3. C127×#2241C2semidirect
6. C127×#1707C2semidirect
7. C127×#1312C2semidirect
102. #12530C127direct (N × H)
108. #2247C2×C127semidirect
109. #2241C2×C127semidirect
112. #1707C2×C127semidirect
113. #1312C2×C127semidirect
114. C127#12530direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22482
C127×#22472
C127×#22412
C127×#22402
C127×#17092
C127×#17072
C127×#13122
#12530127