Finite Group Databasebeta

← C127×#13473 #44577146

Subgroups — C127×#13473 #44577146

Order 32512.

296 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2161C211yesmaximal, characteristic
2C127×#2153C211yesmaximal, characteristic
3C2×#362×C127C211yesmaximal, characteristic
4C2×#362×C127C211yesmaximal, characteristic
5C127×#1979C211yesmaximal, characteristic
6C127×#1953C211yesmaximal, characteristic
7C127×#1385C211yesmaximal, characteristic
8C22×Q16×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11#430×C127—21no—
12C2×#108×C127C2211yescharacteristic
13C2×#108×C127C2211yescharacteristic
14C2×#108×C127C2211yescharacteristic
15#419×C127—21no—
16C2×#101×C127—21no—
17#405×C127C2211yescharacteristic
18#368×C127—22no—
19#364×C127—22no—
20#362×C127—22no—
21#362×C127—22no—
22#344×C127—21no—
23C22×Q8×C127—21no—
24C2×Q16×C127—21no—
25C2×Q16×C127—21no—
26C2×Q16×C127—21no—
27C2×Q16×C127—21no—
28C2×Q16×C127—21no—
29C2×Q16×C127Q812yes—
30C2×M16×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127D411yescharacteristic
34C22×C8×C127C2311yescharacteristic
35#117×C127D411yescharacteristic
36M32×C127—21no—
37M32×C127—21no—
38M32×C127—21no—
39M32×C127D412yes—
40C2×C16×C127—21no—
41C2×C16×C127—21no—
42#108×C127—21no—
43#108×C127—21no—
44#108×C127—21no—
45#108×C127—21no—
46#108×C127—21no—
47#108×C127—42no—
48#108×C127D412yes—
49#103×C127—42no—
50#101×C127—42no—
51#97×C127—21no—
52C4×C8×C127—21no—
53C2×Q8×C127—22no—
54C2×Q8×C127—41no—
55C2×Q8×C127—41no—
56C2×Q8×C127—41no—
57C2×Q8×C127—41no—
58C2×Q8×C127—41no—
59C22×C4×C127—41no—
60C22×C4×C127C2×D411yescharacteristic
61Q16×C127—22no—
62Q16×C127—22no—
63Q16×C127—41no—
64Q16×C127—41no—
65M16×C127—21no—
66M16×C127—22no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127—41no—
70M16×C127—41no—
71M16×C127—41no—
72M16×C127D812yes—
73C2×C8×C127—21no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127C2×D411yescharacteristic
78C2×C8×C127C2×D411yescharacteristic
79C2×C8×C127C2×Q811yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C2×C8×C127#4111yescharacteristic
82C2×C8×C127#4111yescharacteristic
83C4⋊C4×C127—21no—
84C22⋊C4×C127—21no—
85C42×C127—21no—
86C16×C127—22no—
87C16×C127—41no—
88C23×C127#13711yescharacteristic
89Q8×C127—42no—
90Q8×C127—42no—
91Q8×C127—81no—
92Q8×C127—81no—
93C2×C4×C127—41no—
94C2×C4×C127—42no—
95C2×C4×C127—81no—
96C2×C4×C127—81no—
97C2×C4×C127#12111yescharacteristic
98C2×C4×C127#12111yescharacteristic
99C2×C4×C127C22⋊Q811yescharacteristic
100C2×C4×C127C2×D811yescharacteristic
101C2×C4×C127#13511yescharacteristic
102C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
103C8×C127—22no—
104C8×C127—42no—
105C8×C127—81no—
106C8×C127—81no—
107C8×C127#12111yescharacteristic
108C8×C127C22⋊Q811yescharacteristic
109C8×C127C22⋊Q811yescharacteristic
110C8×C127#12611yescharacteristic
111C22×C127—41no—
112C22×C127#46411yescharacteristic
113C22×C127#46811yescharacteristic
114C22×C127#47411yescharacteristic
115C4×C127—81no—
116C4×C127—82no—
117C4×C127#39611yescharacteristic
118C4×C127#45911yescharacteristic
119C4×C127#46611yescharacteristic
120C4×C127#47811yescharacteristic
121#13473C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—21no—
123C2×C127—21no—
124C2×C127—21no—
125C2×C127#206711yescharacteristic
126#2161C2×C12711yescharacteristic
127#2153C2×C12711yescharacteristic
128C2×#362C2×C12711yescharacteristic
129C2×#362C2×C12711yescharacteristic
130#1979C2×C12711yescharacteristic
131#1953C2×C12711yescharacteristic
132#1385C2×C12711yescharacteristic
133C127#1347311yescharacteristic, direct product factor, Sylow
134C22×Q16C22×C12711yescharacteristic
135C2×M32C22×C12711yescharacteristic
136C2×M32C22×C12711yescharacteristic
137#430—21no—
138C2×#108C22×C12711yescharacteristic
139C2×#108C22×C12711yescharacteristic
140C2×#108C22×C12711yescharacteristic
141#419—21no—
142C2×#101—21no—
143#405C22×C12711yescharacteristic
144#368—22no—
145#364—22no—
146#362—22no—
147#362—22no—
148#344—21no—
149C22×Q8—21no—
150C2×Q16—21no—
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—21no—
154C2×Q16—21no—
155C2×Q16Q8×C12712yes—
156C2×M16—21no—
157C2×M16—21no—
158C2×M16—21no—
159C2×M16D4×C12711yescharacteristic
160C22×C8C23×C12711yescharacteristic
161#117D4×C12711yescharacteristic
162M32—21no—
163M32—21no—
164M32—21no—
165M32D4×C12712yes—
166C2×C16—21no—
167C2×C16—21no—
168#108—21no—
169#108—21no—
170#108—21no—
171#108—21no—
172#108—21no—
173#108—42no—
174#108D4×C12712yes—
175#103—42no—
176#101—42no—
177#97—21no—
178C4×C8—21no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C22×C4—41no—
186C22×C4C2×D4×C12711yescharacteristic
187Q16—22no—
188Q16—22no—
189Q16—41no—
190Q16—41no—
191M16—21no—
192M16—22no—
193M16—41no—
194M16—41no—
195M16—41no—
196M16—41no—
197M16—41no—
198M16D8×C12712yes—
199C2×C8—21no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8C2×D4×C12711yescharacteristic
204C2×C8C2×D4×C12711yescharacteristic
205C2×C8C2×Q8×C12711yescharacteristic
206C2×C8#41×C12711yescharacteristic
207C2×C8#41×C12711yescharacteristic
208C2×C8#41×C12711yescharacteristic
209C4⋊C4—21no—
210C22⋊C4—21no—
211C42—21no—
212C16—22no—
213C16—41no—
214C23#137×C12711yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—81no—
218Q8—81no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4#121×C12711yescharacteristic
224C2×C4#121×C12711yescharacteristic
225C2×C4C22⋊Q8×C12711yescharacteristic
226C2×C4C2×D8×C12711yescharacteristic
227C2×C4#135×C12711yescharacteristic
228C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
229C8—22no—
230C8—42no—
231C8—81no—
232C8—81no—
233C8#121×C12711yescharacteristic
234C8C22⋊Q8×C12711yescharacteristic
235C8C22⋊Q8×C12711yescharacteristic
236C8#126×C12711yescharacteristic
237C22—41no—
238C22#464×C12711yescharacteristic
239C22#468×C12711yescharacteristic
240C22#474×C12711yescharacteristic
241C4—81no—
242C4—82no—
243C4#396×C12711yescharacteristic
244C4#459×C12711yescharacteristic
245C4#466×C12711yescharacteristic
246C4#478×C12711yescharacteristic
247C2—21no—
248C2—21no—
249C2—21no—
250C2C127×#206711yescharacteristic
subgroupG/H
center, socleC2×C127#2067
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127#137
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
121. #13473C127direct (N × H)
133. C127#13473direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21612
C127×#21532
C2×#362×C1272
C127×#19792
C127×#19532
C127×#13852
#13473127