Finite Group Databasebeta

← C127×#13478 #44577151

Subgroups — C127×#13478 #44577151

Order 32512.

354 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
1C127×#2159C211yesmaximal, characteristic, complemented
2C2×#364×C127C211yesmaximal, characteristic, complemented
3C2×#361×C127C211yesmaximal, characteristic
4C127×#2140C211yesmaximal, characteristic
5C127×#1970C211yesmaximal, characteristic
6C127×#1945C211yesmaximal, characteristic, complemented
7C127×#1387C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#427×C127C2211yescharacteristic
13C2×#107×C127C2211yescharacteristic
14#424×C127—21no—
15C2×#102×C127—21no—
16C2×C4×C8×C127C2211yescharacteristic
17#390×C127—21no—
18#367×C127—21no—
19#366×C127—21no—
20#364×C127—22no—
21#361×C127—22no—
22#357×C127—21no—
23#357×C127—21no—
24#339×C127—21no—
25C22×D4×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C2×D8×C127—21no—
30C2×D8×C127—21no—
31C2×D8×C127Q812yes—
32C2×M16×C127—21no—
33C22×C8×C127D411yescharacteristic
34C22×C8×C127C2311yescharacteristic
35#117×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C22⋊C4×C127—42no—
38C2×C42×C127D411yescharacteristic
39M32×C127—21no—
40M32×C127—21no—
41M32×C127—21no—
42M32×C127D412yes—
43C2×C16×C127—21no—
44C2×C16×C127—21no—
45#108×C127—21no—
46#108×C127—21no—
47#107×C127—21no—
48#107×C127—21no—
49#107×C127D411yescharacteristic
50#107×C127D411yescharacteristic
51#106×C127—21no—
52C4⋊C8×C127—42no—
53#102×C127—42no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C24×C127—41no—
57C2×D4×C127—22no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C2×D4×C127—41no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C22×C4×C127—21no—
64C22×C4×C127—41no—
65C22×C4×C127C2×D411yescharacteristic
66D8×C127—22no—
67D8×C127—22no—
68D8×C127—41no—
69D8×C127—41no—
70M16×C127—41no—
71M16×C127—41no—
72C2×C8×C127—21no—
73C2×C8×C127—21no—
74C2×C8×C127—41no—
75C2×C8×C127D812yes—
76C2×C8×C127C2×D411yescharacteristic
77C2×C8×C127C2×D411yescharacteristic
78C2×C8×C127C2×Q811yescharacteristic
79C2×C8×C127#4111yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C2×C8×C127#4111yescharacteristic
82C4⋊C4×C127—21no—
83C4⋊C4×C127—21no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—84no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—41no—
91C16×C127—22no—
92C16×C127—41no—
93C23×C127—42no—
94C23×C127—82no—
95C23×C127—82no—
96C23×C127—81no—
97C23×C127—81no—
98C23×C127AGL(1,ℤ/8)11yescharacteristic
99D4×C127—42no—
100D4×C127—42no—
101D4×C127—81no—
102D4×C127—81no—
103C2×C4×C127—22no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—82no—
109C2×C4×C127—81no—
110C2×C4×C127#12111yescharacteristic
111C2×C4×C127#12111yescharacteristic
112C2×C4×C127C22⋊Q811yescharacteristic
113C2×C4×C127C2×D811yescharacteristic
114C2×C4×C127#13511yescharacteristic
115C2×C4×C127#13711yescharacteristic
116C8×C127—22no—
117C8×C127—81no—
118C8×C127#12111yescharacteristic
119C8×C127C22⋊Q811yescharacteristic
120C8×C127C22⋊Q811yescharacteristic
121C8×C127#12611yescharacteristic
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—84no—
125C22×C127—82no—
126C22×C127—162no—
127C22×C127—161no—
128C22×C127—161no—
129C22×C127#45911yescharacteristic
130C22×C127#46811yescharacteristic
131C22×C127#47811yescharacteristic
132C4×C127—42no—
133C4×C127—81no—
134C4×C127—81no—
135C4×C127—161no—
136C4×C127#39611yescharacteristic
137C4×C127#46411yescharacteristic
138C4×C127#46611yescharacteristic
139C4×C127#47411yescharacteristic
140#13478C12711yesmaximal, characteristic, direct product factor, Sylow
141C2×C127—21no—
142C2×C127—21no—
143C2×C127—162no—
144C2×C127#206711yescharacteristic
145C2×C127#221211yescharacteristic
146C2×C127#221311yescharacteristic
147#2159C2×C12711yescharacteristic, complemented
148C2×#364C2×C12711yescharacteristic, complemented
149C2×#361C2×C12711yescharacteristic
150#2140C2×C12711yescharacteristic
151#1970C2×C12711yescharacteristic
152#1945C2×C12711yescharacteristic, complemented
153#1387C2×C12711yescharacteristic, complemented
154C127#1347811yescharacteristic, direct product factor, Sylow
155C22×D8C22×C12711yescharacteristic
156C2×M32C22×C12711yescharacteristic
157C2×M32C22×C12711yescharacteristic
158C2×#108C22×C12711yescharacteristic
159#427C22×C12711yescharacteristic
160C2×#107C22×C12711yescharacteristic
161#424—21no—
162C2×#102—21no—
163C2×C4×C8C22×C12711yescharacteristic
164#390—21no—
165#367—21no—
166#366—21no—
167#364—22no—
168#361—22no—
169#357—21no—
170#357—21no—
171#339—21no—
172C22×D4—21no—
173C2×D8—21no—
174C2×D8—21no—
175C2×D8—21no—
176C2×D8—21no—
177C2×D8—21no—
178C2×D8Q8×C12712yes—
179C2×M16—21no—
180C22×C8D4×C12711yescharacteristic
181C22×C8C23×C12711yescharacteristic
182#117—21no—
183C2×C4⋊C4—21no—
184C2×C22⋊C4—42no—
185C2×C42D4×C12711yescharacteristic
186M32—21no—
187M32—21no—
188M32—21no—
189M32D4×C12712yes—
190C2×C16—21no—
191C2×C16—21no—
192#108—21no—
193#108—21no—
194#107—21no—
195#107—21no—
196#107D4×C12711yescharacteristic
197#107D4×C12711yescharacteristic
198#106—21no—
199C4⋊C8—42no—
200#102—42no—
201C4×C8—21no—
202C4×C8—21no—
203C24—41no—
204C2×D4—22no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4C2×D4×C12711yescharacteristic
213D8—22no—
214D8—22no—
215D8—41no—
216D8—41no—
217M16—41no—
218M16—41no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8D8×C12712yes—
223C2×C8C2×D4×C12711yescharacteristic
224C2×C8C2×D4×C12711yescharacteristic
225C2×C8C2×Q8×C12711yescharacteristic
226C2×C8#41×C12711yescharacteristic
227C2×C8#41×C12711yescharacteristic
228C2×C8#41×C12711yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—84no—
235C42—21no—
236C42—21no—
237C42—41no—
238C16—22no—
239C16—41no—
240C23—42no—
241C23—82no—
242C23—82no—
243C23—81no—
244C23—81no—
245C23AGL(1,ℤ/8)×C12711yescharacteristic
246D4—42no—
247D4—42no—
248D4—81no—
249D4—81no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—82no—
256C2×C4—81no—
257C2×C4#121×C12711yescharacteristic
258C2×C4#121×C12711yescharacteristic
259C2×C4C22⋊Q8×C12711yescharacteristic
260C2×C4C2×D8×C12711yescharacteristic
261C2×C4#135×C12711yescharacteristic
262C2×C4#137×C12711yescharacteristic
263C8—22no—
264C8—81no—
265C8#121×C12711yescharacteristic
266C8C22⋊Q8×C12711yescharacteristic
267C8C22⋊Q8×C12711yescharacteristic
268C8#126×C12711yescharacteristic
269C22—21no—
270C22—21no—
271C22—84no—
272C22—82no—
273C22—162no—
274C22—161no—
275C22—161no—
276C22#459×C12711yescharacteristic
277C22#468×C12711yescharacteristic
278C22#478×C12711yescharacteristic
279C4—42no—
280C4—81no—
281C4—81no—
282C4—161no—
283C4#396×C12711yescharacteristic
284C4#464×C12711yescharacteristic
285C4#466×C12711yescharacteristic
286C4#474×C12711yescharacteristic
287C2—21no—
288C2—21no—
289C2—162no—
290C2C127×#206711yescharacteristic
291C2C127×#221211yescharacteristic
292C2C127×#221311yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2159C2semidirect
2. C2×#364×C127C2semidirect
6. C127×#1945C2semidirect
7. C127×#1387C2semidirect
140. #13478C127direct (N × H)
147. #2159C2×C127semidirect
148. C2×#364C2×C127semidirect
152. #1945C2×C127semidirect
153. #1387C2×C127semidirect
154. C127#13478direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21592
C2×#364×C1272
C2×#361×C1272
C127×#21402
C127×#19702
C127×#19452
C127×#13872
#13478127