Finite Group Databasebeta

← C127×#13491 #44577164

Subgroups — C127×#13491 #44577164

Order 32512.

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

normal subgroups only

This group has 272 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
1C2×#362×C127C211yesmaximal, characteristic
2C127×#2141C211yesmaximal, characteristic
3C127×#1979C211yesmaximal, characteristic
4C127×#1833C211yesmaximal, characteristic
5C127×#1389C211yesmaximal, characteristic
6C127×#1388C211yesmaximal, characteristic
7C127×#1378C211yesmaximal, characteristic
8C22×Q16×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13#427×C127C2211yescharacteristic
14#419×C127—21no—
15C2×#101×C127—21no—
16#405×C127C2211yescharacteristic
17#362×C127—22no—
18#358×C127—22no—
19#344×C127—21no—
20H(3,ℤ/4)×C127—21no—
21C22×Q8×C127—21no—
22C2×Q16×C127—21no—
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×Q16×C127—21no—
26C2×Q16×C127—21no—
27C2×Q16×C127D412yes—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C2×M16×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#117×C127—21no—
33#117×C127D411yescharacteristic
34M32×C127—21no—
35M32×C127—21no—
36M32×C127—21no—
37M32×C127—21no—
38C2×C16×C127—21no—
39C2×C16×C127—21no—
40#108×C127—21no—
41#108×C127—21no—
42#108×C127—21no—
43#108×C127—21no—
44#107×C127—21no—
45#106×C127—21no—
46#103×C127—42no—
47#101×C127—42no—
48#97×C127—21no—
49C4×C8×C127—21no—
50C2×Q8×C127—22no—
51C2×Q8×C127—41no—
52C2×Q8×C127—41no—
53C2×Q8×C127—41no—
54C2×Q8×C127—41no—
55C2×Q8×C127—41no—
56C22×C4×C127—41no—
57C22×C4×C127C2×D411yescharacteristic
58Q16×C127—22no—
59Q16×C127—22no—
60Q16×C127—41no—
61Q16×C127—41no—
62M16×C127—21no—
63M16×C127—21no—
64M16×C127—41no—
65M16×C127—41no—
66M16×C127—41no—
67M16×C127—41no—
68C2×C8×C127—21no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127C2×D411yescharacteristic
72C2×C8×C127#4111yescharacteristic
73C2×C8×C127#4111yescharacteristic
74C2×C8×C127#4111yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C4⋊C4×C127—21no—
78C4⋊C4×C127—41no—
79C22⋊C4×C127—21no—
80C22⋊C4×C127—41no—
81C42×C127—21no—
82C42×C127—41no—
83C16×C127—41no—
84C16×C127—41no—
85C23×C127#13511yescharacteristic
86Q8×C127—42no—
87Q8×C127—42no—
88Q8×C127—81no—
89Q8×C127—81no—
90C2×C4×C127—42no—
91C2×C4×C127—41no—
92C2×C4×C127—81no—
93C2×C4×C127—81no—
94C2×C4×C127—81no—
95C2×C4×C127#12111yescharacteristic
96C2×C4×C127#12311yescharacteristic
97C2×C4×C127#12411yescharacteristic
98C2×C4×C127#13511yescharacteristic
99C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
101C8×C127—41no—
102C8×C127—81no—
103C8×C127—81no—
104C8×C127#12311yescharacteristic
105C8×C127#12311yescharacteristic
106C8×C127#12611yescharacteristic
107C8×C127#12611yescharacteristic
108C22×C127—41no—
109C22×C127#46311yescharacteristic
110C22×C127#48211yescharacteristic
111C22×C127#48811yescharacteristic
112C4×C127—81no—
113C4×C127—82no—
114C4×C127—161no—
115C4×C127#39711yescharacteristic
116C4×C127#46311yescharacteristic
117C4×C127#48211yescharacteristic
118C4×C127#49011yescharacteristic
119#13491C12711yesmaximal, characteristic, direct product factor, Sylow
120C2×C127—21no—
121C2×C127—21no—
122C2×C127—21no—
123C2×C127#207311yescharacteristic
124C2×#362C2×C12711yescharacteristic
125#2141C2×C12711yescharacteristic
126#1979C2×C12711yescharacteristic
127#1833C2×C12711yescharacteristic
128#1389C2×C12711yescharacteristic
129#1388C2×C12711yescharacteristic
130#1378C2×C12711yescharacteristic
131C127#1349111yescharacteristic, direct product factor, Sylow
132C22×Q16C22×C12711yescharacteristic
133C2×M32C22×C12711yescharacteristic
134C2×M32C22×C12711yescharacteristic
135C2×#108C22×C12711yescharacteristic
136C2×#108C22×C12711yescharacteristic
137#427C22×C12711yescharacteristic
138#419—21no—
139C2×#101—21no—
140#405C22×C12711yescharacteristic
141#362—22no—
142#358—22no—
143#344—21no—
144H(3,ℤ/4)—21no—
145C22×Q8—21no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×Q16—21no—
149C2×Q16—21no—
150C2×Q16—21no—
151C2×Q16D4×C12712yes—
152C2×M16—21no—
153C2×M16—21no—
154C2×M16D4×C12711yescharacteristic
155C22×C8C23×C12711yescharacteristic
156#117—21no—
157#117D4×C12711yescharacteristic
158M32—21no—
159M32—21no—
160M32—21no—
161M32—21no—
162C2×C16—21no—
163C2×C16—21no—
164#108—21no—
165#108—21no—
166#108—21no—
167#108—21no—
168#107—21no—
169#106—21no—
170#103—42no—
171#101—42no—
172#97—21no—
173C4×C8—21no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C22×C4—41no—
181C22×C4C2×D4×C12711yescharacteristic
182Q16—22no—
183Q16—22no—
184Q16—41no—
185Q16—41no—
186M16—21no—
187M16—21no—
188M16—41no—
189M16—41no—
190M16—41no—
191M16—41no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8C2×D4×C12711yescharacteristic
196C2×C8#41×C12711yescharacteristic
197C2×C8#41×C12711yescharacteristic
198C2×C8#41×C12711yescharacteristic
199C2×C8#41×C12711yescharacteristic
200C2×C8#41×C12711yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—41no—
203C22⋊C4—21no—
204C22⋊C4—41no—
205C42—21no—
206C42—41no—
207C16—41no—
208C16—41no—
209C23#135×C12711yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—81no—
213Q8—81no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4#121×C12711yescharacteristic
220C2×C4#123×C12711yescharacteristic
221C2×C4#124×C12711yescharacteristic
222C2×C4#135×C12711yescharacteristic
223C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
224C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
225C8—41no—
226C8—81no—
227C8—81no—
228C8#123×C12711yescharacteristic
229C8#123×C12711yescharacteristic
230C8#126×C12711yescharacteristic
231C8#126×C12711yescharacteristic
232C22—41no—
233C22#463×C12711yescharacteristic
234C22#482×C12711yescharacteristic
235C22#488×C12711yescharacteristic
236C4—81no—
237C4—82no—
238C4—161no—
239C4#397×C12711yescharacteristic
240C4#463×C12711yescharacteristic
241C4#482×C12711yescharacteristic
242C4#490×C12711yescharacteristic
243C2—21no—
244C2—21no—
245C2—21no—
246C2C127×#207311yescharacteristic
subgroupG/H
center, socleC2×C127#2073
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127#135
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
119. #13491C127direct (N × H)
131. C127#13491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#362×C1272
C127×#21412
C127×#19792
C127×#18332
C127×#13892
C127×#13882
C127×#13782
#13491127