Finite Group Databasebeta

← C127×#13531 #44577204

Subgroups — C127×#13531 #44577204

Order 32512.

358 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×#367×C127C212yesmaximal
2C2×#358×C127C212yesmaximal
3C127×#1969C211yesmaximal, characteristic
4C127×#1845C211yesmaximal, characteristic
5C127×#1374C211yesmaximal, characteristic
6C22×Q16×C127C2211yescharacteristic
7C22×C16×C127C2212yes—
8C2×#107×C127—21no—
9C2×#107×C127C2212yes—
10C2×#107×C127C2211yescharacteristic
11C2×#103×C127—21no—
12C2×C4×C8×C127C2211yescharacteristic
13#391×C127—21no—
14#384×C127—21no—
15#367×C127—24no—
16#358×C127—24no—
17C22×Q8×C127—21no—
18C2×Q16×C127—22no—
19C2×Q16×C127—22no—
20C2×Q16×C127—21no—
21C2×Q16×C127Q812yes—
22C22×C8×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24C2×C4⋊C4×C127—22no—
25C2×C4⋊C4×C127—21no—
26C2×C4⋊C4×C127—42no—
27C2×C42×C127D411yescharacteristic
28C2×C16×C127—22no—
29C2×C16×C127—22no—
30C2×C16×C127D414yes—
31#107×C127—22no—
32#107×C127—22no—
33#107×C127—22no—
34#107×C127—42no—
35#103×C127—42no—
36C4×C8×C127—22no—
37#95×C127—42no—
38C2×Q8×C127—22no—
39C2×Q8×C127—41no—
40C2×Q8×C127—41no—
41C2×Q8×C127—41no—
42C2×Q8×C127—41no—
43C2×Q8×C127—41no—
44C22×C4×C127—41no—
45C22×C4×C127—41no—
46C22×C4×C127—42no—
47C22×C4×C127D812yes—
48C22×C4×C127C2×D411yescharacteristic
49Q16×C127—24no—
50Q16×C127—42no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127D812yes—
54C2×C8×C127C2×D412yes—
55C2×C8×C127C2×Q811yescharacteristic
56C2×C8×C127#4112yes—
57C2×C8×C127#4111yescharacteristic
58C4⋊C4×C127—42no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—41no—
61C4⋊C4×C127—42no—
62C4⋊C4×C127—84no—
63C42×C127—21no—
64C42×C127—21no—
65C16×C127—24no—
66C23×C127C2×D811yescharacteristic
67Q8×C127—42no—
68Q8×C127—42no—
69Q8×C127—81no—
70Q8×C127—81no—
71C2×C4×C127—22no—
72C2×C4×C127—22no—
73C2×C4×C127—42no—
74C2×C4×C127—81no—
75C2×C4×C127—81no—
76C2×C4×C127—82no—
77C2×C4×C127—81no—
78C2×C4×C127—84no—
79C2×C4×C127—82no—
80C2×C4×C127SD3214yes—
81C2×C4×C127C22⋊Q811yescharacteristic
82C2×C4×C127#12311yescharacteristic
83C2×C4×C127#12711yescharacteristic
84C2×C4×C127C2×D811yescharacteristic
85C2×C4×C127#13711yescharacteristic
86C2×C4×C127#13711yescharacteristic
87C8×C127—22no—
88C8×C127C22⋊Q812yes—
89C8×C127#12312yes—
90C22×C127#47411yescharacteristic
91C22×C127#48011yescharacteristic
92C22×C127#49311yescharacteristic
93C22×C127C2×SD3212yes—
94C22×C127#51012yes—
95C4×C127—24no—
96C4×C127—82no—
97C4×C127—162no—
98C4×C127—161no—
99C4×C127#39911yescharacteristic
100C4×C127#47411yescharacteristic
101C4×C127#48011yescharacteristic
102C4×C127#49711yescharacteristic
103#13531C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127#209311yescharacteristic
105C2×C127#222512yes—
106C2×C127#223512yes—
107C2×C127#224811yescharacteristic
108C2×C127#225111yescharacteristic
109C2×#367C2×C12712yes—
110C2×#358C2×C12712yes—
111#1969C2×C12711yescharacteristic
112#1845C2×C12711yescharacteristic
113#1374C2×C12711yescharacteristic
114C127#1353111yescharacteristic, direct product factor, Sylow
115C22×Q16C22×C12711yescharacteristic
116C22×C16C22×C12712yes—
117C2×#107—21no—
118C2×#107C22×C12712yes—
119C2×#107C22×C12711yescharacteristic
120C2×#103—21no—
121C2×C4×C8C22×C12711yescharacteristic
122#391—21no—
123#384—21no—
124#367—24no—
125#358—24no—
126C22×Q8—21no—
127C2×Q16—22no—
128C2×Q16—22no—
129C2×Q16—21no—
130C2×Q16Q8×C12712yes—
131C22×C8D4×C12711yescharacteristic
132C22×C8C23×C12711yescharacteristic
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—42no—
136C2×C42D4×C12711yescharacteristic
137C2×C16—22no—
138C2×C16—22no—
139C2×C16D4×C12714yes—
140#107—22no—
141#107—22no—
142#107—22no—
143#107—42no—
144#103—42no—
145C4×C8—22no—
146#95—42no—
147C2×Q8—22no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—42no—
156C22×C4D8×C12712yes—
157C22×C4C2×D4×C12711yescharacteristic
158Q16—24no—
159Q16—42no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8D8×C12712yes—
163C2×C8C2×D4×C12712yes—
164C2×C8C2×Q8×C12711yescharacteristic
165C2×C8#41×C12712yes—
166C2×C8#41×C12711yescharacteristic
167C4⋊C4—42no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—84no—
172C42—21no—
173C42—21no—
174C16—24no—
175C23C2×D8×C12711yescharacteristic
176Q8—42no—
177Q8—42no—
178Q8—81no—
179Q8—81no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—84no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—81no—
189C2×C4SD32×C12714yes—
190C2×C4C22⋊Q8×C12711yescharacteristic
191C2×C4#123×C12711yescharacteristic
192C2×C4#127×C12711yescharacteristic
193C2×C4C2×D8×C12711yescharacteristic
194C2×C4#137×C12711yescharacteristic
195C2×C4#137×C12711yescharacteristic
196C8—22no—
197C8C22⋊Q8×C12712yes—
198C8#123×C12712yes—
199C22#474×C12711yescharacteristic
200C22#480×C12711yescharacteristic
201C22#493×C12711yescharacteristic
202C22C2×SD32×C12712yes—
203C22#510×C12712yes—
204C4—24no—
205C4—82no—
206C4—162no—
207C4—161no—
208C4#399×C12711yescharacteristic
209C4#474×C12711yescharacteristic
210C4#480×C12711yescharacteristic
211C4#497×C12711yescharacteristic
212C2C127×#209311yescharacteristic
213C2C127×#222512yes—
214C2C127×#223512yes—
215C2C127×#224811yescharacteristic
216C2C127×#225111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
103. #13531C127direct (N × H)
114. C127#13531direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#367×C1272
C2×#358×C1272
C127×#19692
C127×#18452
C127×#13742
#13531127