Finite Group Databasebeta

← C127×#1880 #30634832

Subgroups — C127×#1880 #30634832

Order 16256.

374 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×C127C211yesmaximal, characteristic
2C2×C4×Q8×C127C211yesmaximal, characteristic, complemented
3C2×#103×C127C211yesmaximal, characteristic, complemented
4C2×#102×C127C211yesmaximal, characteristic
5#390×C127C211yesmaximal, characteristic
6#340×C127C211yesmaximal, characteristic, complemented
7#336×C127C211yesmaximal, characteristic, complemented
8C22×Q8×C127C2211yescharacteristic
9C22×D4×C127C2211yescharacteristic
10C2×SD16×C127—22no—
11C2×SD16×C127—22no—
12C2×SD16×C127C414yescomplemented
13C22×C8×C127C2211yescharacteristic
14C22×C8×C127C2211yescharacteristic
15C4×Q8×C127—22no—
16C4×Q8×C127—22no—
17C2×C4⋊C4×C127—21no—
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C22⋊C4×C127—21no—
21C2×C22⋊C4×C127—21no—
22C2×C42×C127—21no—
23C2×C42×C127C2211yescharacteristic
24#103×C127—22no—
25#102×C127—22no—
26C24×C127—21no—
27C2×Q8×C127—21no—
28C2×Q8×C127—21no—
29C2×Q8×C127—21no—
30C2×Q8×C127C2×C412yes—
31C2×Q8×C127D412yes—
32C2×Q8×C127D412yes—
33C2×D4×C127—21no—
34C2×D4×C127—21no—
35C2×D4×C127—21no—
36C2×D4×C127—21no—
37C2×D4×C127—21no—
38C2×D4×C127C2×C412yes—
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127D411yescharacteristic
43C22×C4×C127D411yescharacteristic
44C22×C4×C127C2311yescharacteristic
45SD16×C127—28no—
46C2×C8×C127—21no—
47C2×C8×C127—21no—
48C2×C8×C127—21no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127C2×C412yes—
52C4⋊C4×C127—24no—
53C4⋊C4×C127—21no—
54C4⋊C4×C127—21no—
55C4⋊C4×C127—21no—
56C4⋊C4×C127D412yes—
57C22⋊C4×C127—42no—
58C22⋊C4×C127—42no—
59C42×C127—24no—
60C42×C127—21no—
61C42×C127—21no—
62C23×C127—22no—
63C23×C127—41no—
64C23×C127—41no—
65C23×C127—41no—
66C23×C127—41no—
67C23×C127—41no—
68C23×C127—41no—
69C23×C127C2×D411yescharacteristic
70Q8×C127—22no—
71Q8×C127—22no—
72Q8×C127—22no—
73Q8×C127C22⋊C414yescomplemented
74D4×C127—22no—
75D4×C127—22no—
76D4×C127—41no—
77D4×C127—41no—
78C2×C4×C127—22no—
79C2×C4×C127—21no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—22no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127SD1612yescomplemented
93C2×C4×C127C22×C411yescharacteristic
94C2×C4×C127C2×D411yescharacteristic
95C2×C4×C127C2×D411yescharacteristic
96C2×C4×C127C2×D411yescharacteristic
97C2×C4×C127#4111yescharacteristic
98C2×C4×C127#4111yescharacteristic
99C8×C127—22no—
100C8×C127—41no—
101C22×C127—42no—
102C22×C127—42no—
103C22×C127—42no—
104C22×C127—81no—
105C22×C127—81no—
106C22×C127—81no—
107C22×C127—81no—
108C22×C127C4×D411yescharacteristic
109C22×C127#12011yescharacteristic
110C22×C127#12111yescharacteristic
111C22×C127C2×SD1611yescharacteristic
112C22×C127#13511yescharacteristic
113C22×C127AGL(1,ℤ/8)11yescharacteristic
114C22×C127#13711yescharacteristic
115C4×C127—24no—
116C4×C127—22no—
117C4×C127—41no—
118C4×C127—42no—
119C4×C127—81no—
120C4×C127C2×C22⋊C411yescharacteristic
121C4×C127C4×D411yescharacteristic
122C4×C127#12111yescharacteristic
123C4×C127#12311yescharacteristic
124C2×C127—82no—
125C2×C127#38611yescharacteristic
126C2×C127C4×SD1611yescharacteristic
127C2×C127#44011yescharacteristic
128C2×C127#44811yescharacteristic
129C2×C127#44911yescharacteristic
130C2×C127#46011yescharacteristic
131C2×C127#46411yescharacteristic
132#1880C12711yesmaximal, characteristic, direct product factor, Sylow
133C127#188011yescharacteristic, direct product factor, Sylow
134C22×SD16C2×C12711yescharacteristic
135C2×C4×Q8C2×C12711yescharacteristic, complemented
136C2×#103C2×C12711yescharacteristic, complemented
137C2×#102C2×C12711yescharacteristic
138#390C2×C12711yescharacteristic
139#340C2×C12711yescharacteristic, complemented
140#336C2×C12711yescharacteristic, complemented
141C22×Q8C22×C12711yescharacteristic
142C22×D4C22×C12711yescharacteristic
143C2×SD16—22no—
144C2×SD16—22no—
145C2×SD16C4×C12714yescomplemented
146C22×C8C22×C12711yescharacteristic
147C22×C8C22×C12711yescharacteristic
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22×C12711yescharacteristic
152C2×C4⋊C4C22×C12711yescharacteristic
153C2×C22⋊C4—21no—
154C2×C22⋊C4—21no—
155C2×C42—21no—
156C2×C42C22×C12711yescharacteristic
157#103—22no—
158#102—22no—
159C24—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8C2×C4×C12712yes—
164C2×Q8D4×C12712yes—
165C2×Q8D4×C12712yes—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C2×C4×C12712yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4D4×C12711yescharacteristic
176C22×C4D4×C12711yescharacteristic
177C22×C4C23×C12711yescharacteristic
178SD16—28no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8C2×C4×C12712yes—
185C4⋊C4—24no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4D4×C12712yes—
190C22⋊C4—42no—
191C22⋊C4—42no—
192C42—24no—
193C42—21no—
194C42—21no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23C2×D4×C12711yescharacteristic
203Q8—22no—
204Q8—22no—
205Q8—22no—
206Q8C22⋊C4×C12714yescomplemented
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4SD16×C12712yescomplemented
226C2×C4C22×C4×C12711yescharacteristic
227C2×C4C2×D4×C12711yescharacteristic
228C2×C4C2×D4×C12711yescharacteristic
229C2×C4C2×D4×C12711yescharacteristic
230C2×C4#41×C12711yescharacteristic
231C2×C4#41×C12711yescharacteristic
232C8—22no—
233C8—41no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22C4×D4×C12711yescharacteristic
242C22#120×C12711yescharacteristic
243C22#121×C12711yescharacteristic
244C22C2×SD16×C12711yescharacteristic
245C22#135×C12711yescharacteristic
246C22AGL(1,ℤ/8)×C12711yescharacteristic
247C22#137×C12711yescharacteristic
248C4—24no—
249C4—22no—
250C4—41no—
251C4—42no—
252C4—81no—
253C4C2×C22⋊C4×C12711yescharacteristic
254C4C4×D4×C12711yescharacteristic
255C4#121×C12711yescharacteristic
256C4#123×C12711yescharacteristic
257C2—82no—
258C2#386×C12711yescharacteristic
259C2C4×SD16×C12711yescharacteristic
260C2#440×C12711yescharacteristic
261C2#448×C12711yescharacteristic
262C2#449×C12711yescharacteristic
263C2#460×C12711yescharacteristic
264C2#464×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×C127C2semidirect
3. C2×#103×C127C2semidirect
6. #340×C127C2semidirect
7. #336×C127C2semidirect
12. C2×SD16×C127C4semidirect
73. Q8×C127C22⋊C4semidirect
92. C2×C4×C127SD16semidirect
132. #1880C127direct (N × H)
133. C127#1880direct (N × H)
135. C2×C4×Q8C2×C127semidirect
136. C2×#103C2×C127semidirect
139. #340C2×C127semidirect
140. #336C2×C127semidirect
145. C2×SD16C4×C127semidirect
206. Q8C22⋊C4×C127semidirect
225. C2×C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×C1272
C2×C4×Q8×C1272
C2×#103×C1272
C2×#102×C1272
#390×C1272
#340×C1272
#336×C1272
#1880127