Finite Group Databasebeta

← C127×#10471 #44574144

Subgroups — C127×#10471 #44574144

Order 32512.

366 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3078C211yesmaximal, characteristic
2C127×#1805C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic
4C127×#1542C211yesmaximal, characteristic
5C127×#1518C211yesmaximal, characteristic
6C127×#1461C211yesmaximal, characteristic
7C127×#1286C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#479×C127—22no—
11#477×C127—21no—
12#475×C127—21no—
13#431×C127C2211yescharacteristic
14#431×C127C2211yescharacteristic
15#428×C127—21no—
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#419×C127—21no—
19C2×#103×C127—21no—
20#382×C127C2211yescharacteristic
21#340×C127—21no—
22#335×C127—22no—
23#333×C127—21no—
24#332×C127—21no—
25#328×C127—22no—
26#324×C127—22no—
27C22×Q8×C127D411yescharacteristic
28C2×M16×C127—21no—
29C22×C8×C127—21no—
30C4⋊Q8×C127D411yescharacteristic
31C4⋊Q8×C127D411yescharacteristic
32#125×C127—21no—
33C22⋊Q8×C127—21no—
34C22⋊Q8×C127—21no—
35C4×Q8×C127—21no—
36C4×Q8×C127—21no—
37C4×Q8×C127—21no—
38C4×Q8×C127—21no—
39C4×Q8×C127—21no—
40C4×Q8×C127—21no—
41#117×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C42×C127—21no—
46C2×C42×C127C2311yescharacteristic
47#107×C127—22no—
48#106×C127—22no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127D412yes—
55#103×C127—22no—
56#103×C127—22no—
57#103×C127—42no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127D412yes—
60C4×C8×C127—21no—
61C4×C8×C127—21no—
62#95×C127—21no—
63#95×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—21no—
70C2×Q8×C127—21no—
71C2×Q8×C127Q1612yes—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—41no—
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127#4111yescharacteristic
78M16×C127—41no—
79M16×C127—41no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—21no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C42×C127—41no—
100C42×C127—41no—
101C42×C127—41no—
102C42×C127C2×D411yescharacteristic
103C42×C127C2×D411yescharacteristic
104C42×C127#4111yescharacteristic
105C42×C127#4111yescharacteristic
106C23×C127#12111yescharacteristic
107Q8×C127—22no—
108Q8×C127—22no—
109Q8×C127—41no—
110Q8×C127—41no—
111Q8×C127—81no—
112Q8×C127—81no—
113C2×C4×C127—22no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—81no—
122C2×C4×C127—81no—
123C2×C4×C127—81no—
124C2×C4×C127—81no—
125C2×C4×C127#12011yescharacteristic
126C2×C4×C127#12111yescharacteristic
127C2×C4×C127#12111yescharacteristic
128C2×C4×C127#12311yescharacteristic
129C2×C4×C127#12311yescharacteristic
130C2×C4×C127#12411yescharacteristic
131C2×C4×C127C2×Q1611yescharacteristic
132C2×C4×C127#13511yescharacteristic
133C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C127#13711yescharacteristic
135C8×C127—42no—
136C8×C127—42no—
137C8×C127—81no—
138C8×C127—81no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127#39411yescharacteristic
142C22×C127#46711yescharacteristic
143C22×C127#46811yescharacteristic
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—21no—
147C4×C127—21no—
148C4×C127—42no—
149C4×C127—81no—
150C4×C127—81no—
151C4×C127—81no—
152C4×C127—161no—
153C4×C127#44911yescharacteristic
154C4×C127#45111yescharacteristic
155C4×C127#48411yescharacteristic
156C4×C127#48511yescharacteristic
157#10471C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127#203611yescharacteristic
161C2×C127#204911yescharacteristic
162C2×C127#205311yescharacteristic
163#3078C2×C12711yescharacteristic
164#1805C2×C12711yescharacteristic
165#1571C2×C12711yescharacteristic
166#1542C2×C12711yescharacteristic
167#1518C2×C12711yescharacteristic
168#1461C2×C12711yescharacteristic
169#1286C2×C12711yescharacteristic
170C127#1047111yescharacteristic, direct product factor, Sylow
171#533C22×C12711yescharacteristic
172C2×C4×Q8C22×C12711yescharacteristic
173#479—22no—
174#477—21no—
175#475—21no—
176#431C22×C12711yescharacteristic
177#431C22×C12711yescharacteristic
178#428—21no—
179#423C22×C12711yescharacteristic
180C2×C4⋊C8C22×C12711yescharacteristic
181#419—21no—
182C2×#103—21no—
183#382C22×C12711yescharacteristic
184#340—21no—
185#335—22no—
186#333—21no—
187#332—21no—
188#328—22no—
189#324—22no—
190C22×Q8D4×C12711yescharacteristic
191C2×M16—21no—
192C22×C8—21no—
193C4⋊Q8D4×C12711yescharacteristic
194C4⋊Q8D4×C12711yescharacteristic
195#125—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4D4×C12711yescharacteristic
208C2×C42—21no—
209C2×C42C23×C12711yescharacteristic
210#107—22no—
211#106—22no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8D4×C12712yes—
218#103—22no—
219#103—22no—
220#103—42no—
221C22⋊C8—21no—
222C22⋊C8D4×C12712yes—
223C4×C8—21no—
224C4×C8—21no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8Q16×C12712yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4C2×D4×C12711yescharacteristic
239C22×C4C2×D4×C12711yescharacteristic
240C22×C4#41×C12711yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C22⋊C4—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42C2×D4×C12711yescharacteristic
266C42C2×D4×C12711yescharacteristic
267C42#41×C12711yescharacteristic
268C42#41×C12711yescharacteristic
269C23#121×C12711yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—81no—
275Q8—81no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4#120×C12711yescharacteristic
289C2×C4#121×C12711yescharacteristic
290C2×C4#121×C12711yescharacteristic
291C2×C4#123×C12711yescharacteristic
292C2×C4#123×C12711yescharacteristic
293C2×C4#124×C12711yescharacteristic
294C2×C4C2×Q16×C12711yescharacteristic
295C2×C4#135×C12711yescharacteristic
296C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
297C2×C4#137×C12711yescharacteristic
298C8—42no—
299C8—42no—
300C8—81no—
301C8—81no—
302C22—21no—
303C22—21no—
304C22#394×C12711yescharacteristic
305C22#467×C12711yescharacteristic
306C22#468×C12711yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—161no—
316C4#449×C12711yescharacteristic
317C4#451×C12711yescharacteristic
318C4#484×C12711yescharacteristic
319C4#485×C12711yescharacteristic
320C2—21no—
321C2—21no—
322C2C127×#203611yescharacteristic
323C2C127×#204911yescharacteristic
324C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
157. #10471C127direct (N × H)
170. C127#10471direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30782
C127×#18052
C127×#15712
C127×#15422
C127×#15182
C127×#14612
C127×#12862
#10471127