Finite Group Databasebeta

← C127×#13431 #44577104

Subgroups — C127×#13431 #44577104

Order 32512.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3202C211yesmaximal, characteristic
2C127×#2135C212yesmaximal
3C127×#1915C212yesmaximal
4C127×#1858C211yesmaximal, characteristic
5C127×#1392C211yesmaximal, characteristic
6#568×C127C2211yescharacteristic
7#536×C127C2212yes—
8#485×C127—22no—
9#470×C127—21no—
10#467×C127—21no—
11#451×C127—22no—
12#430×C127—21no—
13#413×C127C2212yes—
14#413×C127C2211yescharacteristic
15C2×#101×C127—22no—
16#408×C127C2211yescharacteristic
17#356×C127—24no—
18#344×C127—22no—
19#341×C127—21no—
20C2×#41×C127C2311yescharacteristic
21C22×Q8×C127D412yes—
22C2×Q16×C127—21no—
23C2×Q16×C127—21no—
24#131×C127—42no—
25C2×M16×C127—21no—
26C2×M16×C127—22no—
27C2×M16×C127—21no—
28C2×M16×C127—22no—
29C2×M16×C127D411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C4⋊Q8×C127—22no—
32#124×C127—22no—
33#123×C127—22no—
34#123×C127—22no—
35C22⋊Q8×C127—22no—
36C22⋊Q8×C127—22no—
37#117×C127D412yes—
38#108×C127—42no—
39#107×C127—21no—
40#106×C127—21no—
41#103×C127—22no—
42#103×C127—22no—
43#101×C127—22no—
44#101×C127—44no—
45#101×C127D412yes—
46#100×C127—21no—
47#100×C127—22no—
48C22⋊C8×C127—22no—
49#41×C127—41no—
50#41×C127—41no—
51C2×Q8×C127—22no—
52C2×Q8×C127—22no—
53C2×Q8×C127—42no—
54C2×Q8×C127—42no—
55C2×Q8×C127C2×D411yescharacteristic
56C2×D4×C127#4111yescharacteristic
57C2×D4×C127#4112yes—
58C22×C4×C127—22no—
59C22×C4×C127C2×D412yes—
60C22×C4×C127C2×D411yescharacteristic
61Q16×C127—81no—
62Q16×C127—81no—
63M16×C127—24no—
64M16×C127—22no—
65M16×C127—22no—
66M16×C127—41no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127—42no—
70M16×C127—42no—
71C2×C8×C127—21no—
72C2×C8×C127—21no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—42no—
76C2×C8×C127—41no—
77C2×C8×C127—42no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—42no—
81C22⋊C4×C127—22no—
82C22⋊C4×C127—42no—
83C22⋊C4×C127—42no—
84C42×C127—22no—
85C23×C127#12312yes—
86C23×C127#12411yescharacteristic
87Q8×C127—41no—
88Q8×C127—42no—
89Q8×C127—42no—
90Q8×C127—82no—
91D4×C127—41no—
92D4×C127—42no—
93C2×C4×C127—21no—
94C2×C4×C127—22no—
95C2×C4×C127—21no—
96C2×C4×C127—22no—
97C2×C4×C127—44no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127#12011yescharacteristic
101C2×C4×C127#12112yes—
102C2×C4×C127#12111yescharacteristic
103C8×C127—42no—
104C8×C127—41no—
105C8×C127—42no—
106C8×C127—41no—
107C8×C127—82no—
108C22×C127—22no—
109C22×C127—21no—
110C22×C127—42no—
111C22×C127—41no—
112C22×C127#39411yescharacteristic
113C4×C127—21no—
114C4×C127—22no—
115C4×C127—82no—
116C4×C127—82no—
117C4×C127B(4,𝔽2)11yescharacteristic
118C4×C127#45811yescharacteristic
119#13431C12711yesmaximal, characteristic, direct product factor, Sylow
120C2×C127—21no—
121C2×C127—42no—
122C2×C127—41no—
123C2×C127#204411yescharacteristic
124#3202C2×C12711yescharacteristic
125#2135C2×C12712yes—
126#1915C2×C12712yes—
127#1858C2×C12711yescharacteristic
128#1392C2×C12711yescharacteristic
129C127#1343111yescharacteristic, direct product factor, Sylow
130#568C22×C12711yescharacteristic
131#536C22×C12712yes—
132#485—22no—
133#470—21no—
134#467—21no—
135#451—22no—
136#430—21no—
137#413C22×C12712yes—
138#413C22×C12711yescharacteristic
139C2×#101—22no—
140#408C22×C12711yescharacteristic
141#356—24no—
142#344—22no—
143#341—21no—
144C2×#41C23×C12711yescharacteristic
145C22×Q8D4×C12712yes—
146C2×Q16—21no—
147C2×Q16—21no—
148#131—42no—
149C2×M16—21no—
150C2×M16—22no—
151C2×M16—21no—
152C2×M16—22no—
153C2×M16D4×C12711yescharacteristic
154C22×C8D4×C12711yescharacteristic
155C4⋊Q8—22no—
156#124—22no—
157#123—22no—
158#123—22no—
159C22⋊Q8—22no—
160C22⋊Q8—22no—
161#117D4×C12712yes—
162#108—42no—
163#107—21no—
164#106—21no—
165#103—22no—
166#103—22no—
167#101—22no—
168#101—44no—
169#101D4×C12712yes—
170#100—21no—
171#100—22no—
172C22⋊C8—22no—
173#41—41no—
174#41—41no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8C2×D4×C12711yescharacteristic
180C2×D4#41×C12711yescharacteristic
181C2×D4#41×C12712yes—
182C22×C4—22no—
183C22×C4C2×D4×C12712yes—
184C22×C4C2×D4×C12711yescharacteristic
185Q16—81no—
186Q16—81no—
187M16—24no—
188M16—22no—
189M16—22no—
190M16—41no—
191M16—41no—
192M16—41no—
193M16—42no—
194M16—42no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—42no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—22no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—22no—
209C23#123×C12712yes—
210C23#124×C12711yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—42no—
214Q8—82no—
215D4—41no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#120×C12711yescharacteristic
225C2×C4#121×C12712yes—
226C2×C4#121×C12711yescharacteristic
227C8—42no—
228C8—41no—
229C8—42no—
230C8—41no—
231C8—82no—
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22#394×C12711yescharacteristic
237C4—21no—
238C4—22no—
239C4—82no—
240C4—82no—
241C4B(4,𝔽2)×C12711yescharacteristic
242C4#458×C12711yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2C127×#204411yescharacteristic
subgroupG/H
center, socleC2×C127#2044
commutator, Frattini, cosocleC2×#41C23×C127
prime radicalC2×#41×C127C23
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
119. #13431C127direct (N × H)
129. C127#13431direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32022
C127×#21352
C127×#19152
C127×#18582
C127×#13922
#13431127