Finite Group Databasebeta

← C127×#1879 #30634831

Subgroups — C127×#1879 #30634831

Order 16256.

438 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×C127C211yesmaximal, characteristic
2C2×C4×D4×C127C211yesmaximal, characteristic, complemented
3C2×#102×C127C211yesmaximal, characteristic, complemented
4C2×#102×C127C211yesmaximal, characteristic, complemented
5#390×C127C211yesmaximal, characteristic, complemented
6#340×C127C211yesmaximal, characteristic, complemented
7#336×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127—21no—
11C2×D8×C127—22no—
12C2×D8×C127—22no—
13C2×D8×C127C414yescomplemented
14C22×C8×C127C2211yescharacteristic
15C22×C8×C127C2211yescharacteristic
16C4×D4×C127—22no—
17C4×D4×C127—22no—
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C22⋊C4×C127—21no—
21C2×C22⋊C4×C127—21no—
22C2×C22⋊C4×C127—21no—
23C2×C42×C127C2211yescharacteristic
24#102×C127—22no—
25#102×C127—22no—
26C24×C127—21no—
27C24×C127—21no—
28C2×D4×C127—21no—
29C2×D4×C127—21no—
30C2×D4×C127—21no—
31C2×D4×C127—21no—
32C2×D4×C127—21no—
33C2×D4×C127—21no—
34C2×D4×C127—21no—
35C2×D4×C127—21no—
36C2×D4×C127C2×C412yes—
37C2×D4×C127C2×C412yescomplemented
38C2×D4×C127D412yes—
39C2×D4×C127D412yes—
40C22×C4×C127—24no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—42no—
44C22×C4×C127—42no—
45C22×C4×C127D411yescharacteristic
46C22×C4×C127D411yescharacteristic
47C22×C4×C127C2311yescharacteristic
48D8×C127—28no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C2×C8×C127—21no—
54C2×C8×C127C2×C412yescomplemented
55C4⋊C4×C127—21no—
56C4⋊C4×C127—21no—
57C4⋊C4×C127—21no—
58C4⋊C4×C127D412yes—
59C22⋊C4×C127—24no—
60C22⋊C4×C127—42no—
61C22⋊C4×C127—42no—
62C42×C127—21no—
63C42×C127—21no—
64C23×C127—22no—
65C23×C127—22no—
66C23×C127—22no—
67C23×C127—22no—
68C23×C127—41no—
69C23×C127—41no—
70C23×C127—41no—
71C23×C127—41no—
72C23×C127—41no—
73C23×C127—41no—
74C23×C127—41no—
75C23×C127—41no—
76C23×C127—41no—
77C23×C127—41no—
78C23×C127C2×D411yescharacteristic
79D4×C127—22no—
80D4×C127—22no—
81D4×C127—22no—
82D4×C127—22no—
83D4×C127—22no—
84D4×C127—41no—
85D4×C127—41no—
86D4×C127C22⋊C414yescomplemented
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—22no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—48no—
94C2×C4×C127—41no—
95C2×C4×C127—41no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—41no—
99C2×C4×C127D812yescomplemented
100C2×C4×C127C22×C411yescharacteristic
101C2×C4×C127C2×D411yescharacteristic
102C2×C4×C127C2×D411yescharacteristic
103C2×C4×C127C2×D411yescharacteristic
104C2×C4×C127#4111yescharacteristic
105C2×C4×C127#4111yescharacteristic
106C8×C127—22no—
107C8×C127—41no—
108C22×C127—24no—
109C22×C127—42no—
110C22×C127—42no—
111C22×C127—42no—
112C22×C127—42no—
113C22×C127—42no—
114C22×C127—42no—
115C22×C127—42no—
116C22×C127—42no—
117C22×C127—42no—
118C22×C127—81no—
119C22×C127—81no—
120C22×C127—81no—
121C22×C127—81no—
122C22×C127C4×D411yescharacteristic
123C22×C127#12011yescharacteristic
124C22×C127#12111yescharacteristic
125C22×C127C2×D811yescharacteristic
126C22×C127#13511yescharacteristic
127C22×C127AGL(1,ℤ/8)11yescharacteristic
128C22×C127AGL(1,ℤ/8)11yescharacteristic
129C4×C127—22no—
130C4×C127—42no—
131C4×C127—41no—
132C4×C127—81no—
133C4×C127C2×C22⋊C411yescharacteristic
134C4×C127C4×D411yescharacteristic
135C4×C127#12111yescharacteristic
136C4×C127#12311yescharacteristic
137C2×C127—44no—
138C2×C127—82no—
139C2×C127#38611yescharacteristic
140C2×C127C4×D811yescharacteristic
141C2×C127#44211yescharacteristic
142C2×C127#44711yescharacteristic
143C2×C127#44911yescharacteristic
144C2×C127#45911yescharacteristic
145C2×C127#46311yescharacteristic
146#1879C12711yesmaximal, characteristic, direct product factor, Sylow
147C127#187911yescharacteristic, direct product factor, Sylow
148C22×D8C2×C12711yescharacteristic
149C2×C4×D4C2×C12711yescharacteristic, complemented
150C2×#102C2×C12711yescharacteristic, complemented
151C2×#102C2×C12711yescharacteristic, complemented
152#390C2×C12711yescharacteristic, complemented
153#340C2×C12711yescharacteristic, complemented
154#336C2×C12711yescharacteristic, complemented
155C22×D4C22×C12711yescharacteristic
156C22×D4C22×C12711yescharacteristic
157C23×C4—21no—
158C2×D8—22no—
159C2×D8—22no—
160C2×D8C4×C12714yescomplemented
161C22×C8C22×C12711yescharacteristic
162C22×C8C22×C12711yescharacteristic
163C4×D4—22no—
164C4×D4—22no—
165C2×C4⋊C4C22×C12711yescharacteristic
166C2×C4⋊C4C22×C12711yescharacteristic
167C2×C22⋊C4—21no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—21no—
170C2×C42C22×C12711yescharacteristic
171#102—22no—
172#102—22no—
173C24—21no—
174C24—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4C2×C4×C12712yes—
184C2×D4C2×C4×C12712yescomplemented
185C2×D4D4×C12712yes—
186C2×D4D4×C12712yes—
187C22×C4—24no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4D4×C12711yescharacteristic
193C22×C4D4×C12711yescharacteristic
194C22×C4C23×C12711yescharacteristic
195D8—28no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8C2×C4×C12712yescomplemented
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4D4×C12712yes—
206C22⋊C4—24no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—21no—
210C42—21no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—41no—
220C23—41no—
221C23—41no—
222C23—41no—
223C23—41no—
224C23—41no—
225C23C2×D4×C12711yescharacteristic
226D4—22no—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4C22⋊C4×C12714yescomplemented
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—48no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4D8×C12712yescomplemented
247C2×C4C22×C4×C12711yescharacteristic
248C2×C4C2×D4×C12711yescharacteristic
249C2×C4C2×D4×C12711yescharacteristic
250C2×C4C2×D4×C12711yescharacteristic
251C2×C4#41×C12711yescharacteristic
252C2×C4#41×C12711yescharacteristic
253C8—22no—
254C8—41no—
255C22—24no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—81no—
269C22C4×D4×C12711yescharacteristic
270C22#120×C12711yescharacteristic
271C22#121×C12711yescharacteristic
272C22C2×D8×C12711yescharacteristic
273C22#135×C12711yescharacteristic
274C22AGL(1,ℤ/8)×C12711yescharacteristic
275C22AGL(1,ℤ/8)×C12711yescharacteristic
276C4—22no—
277C4—42no—
278C4—41no—
279C4—81no—
280C4C2×C22⋊C4×C12711yescharacteristic
281C4C4×D4×C12711yescharacteristic
282C4#121×C12711yescharacteristic
283C4#123×C12711yescharacteristic
284C2—44no—
285C2—82no—
286C2#386×C12711yescharacteristic
287C2C4×D8×C12711yescharacteristic
288C2#442×C12711yescharacteristic
289C2#447×C12711yescharacteristic
290C2#449×C12711yescharacteristic
291C2#459×C12711yescharacteristic
292C2#463×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC22×D8×C127C2
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×D4×C127C2semidirect
3. C2×#102×C127C2semidirect
4. C2×#102×C127C2semidirect
5. #390×C127C2semidirect
6. #340×C127C2semidirect
7. #336×C127C2semidirect
13. C2×D8×C127C4semidirect
37. C2×D4×C127C2×C4semidirect
54. C2×C8×C127C2×C4semidirect
86. D4×C127C22⋊C4semidirect
99. C2×C4×C127D8semidirect
146. #1879C127direct (N × H)
147. C127#1879direct (N × H)
149. C2×C4×D4C2×C127semidirect
150. C2×#102C2×C127semidirect
151. C2×#102C2×C127semidirect
152. #390C2×C127semidirect
153. #340C2×C127semidirect
154. #336C2×C127semidirect
160. C2×D8C4×C127semidirect
184. C2×D4C2×C4×C127semidirect
201. C2×C8C2×C4×C127semidirect
233. D4C22⋊C4×C127semidirect
246. C2×C4D8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D8×C1272
C2×C4×D4×C1272
C2×#102×C1272
#390×C1272
#340×C1272
#336×C1272
#1879127