Finite Group Databasebeta

← C127×#13031 #44576704

Subgroups — C127×#13031 #44576704

Order 32512.

456 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C127×#2957C211yesmaximal, characteristic
3C127×#2148C211yesmaximal, characteristic
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C127×#1979C211yesmaximal, characteristic, complemented
6C127×#1388C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10#568×C127—21no—
11#510×C127—22no—
12#510×C127C414yescomplemented
13C2×Q32×C127—21no—
14C2×SD32×C127—21no—
15C2×M32×C127C2211yescharacteristic
16C2×M32×C127C2211yescharacteristic
17#444×C127—22no—
18#443×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#108×C127C2211yescharacteristic
21#421×C127—21no—
22#419×C127—21no—
23C2×#101×C127—21no—
24#405×C127C2211yescharacteristic
25#362×C127—21no—
26#362×C127—22no—
27#361×C127—21no—
28C2×#41×C127—21no—
29C22×Q8×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127C2×C412yes—
33#135×C127D412yes—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127C2×C412yes—
40C2×Q16×C127D411yescharacteristic
41C2×SD16×C127—21no—
42C2×D8×C127D411yescharacteristic
43#131×C127—24no—
44#131×C127—42no—
45C2×M16×C127—21no—
46C2×M16×C127—21no—
47C2×M16×C127—42no—
48C2×M16×C127D411yescharacteristic
49C22×C8×C127C2311yescharacteristic
50#117×C127D411yescharacteristic
51Q32×C127—24no—
52SD32×C127—24no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56M32×C127C2×C412yes—
57C2×C16×C127—21no—
58C2×C16×C127—21no—
59#108×C127—21no—
60#108×C127—21no—
61#108×C127—21no—
62#108×C127D412yes—
63#104×C127—24no—
64#103×C127—42no—
65#101×C127—42no—
66#97×C127—21no—
67C4×C8×C127—21no—
68#41×C127—22no—
69#41×C127—22no—
70#41×C127—41no—
71#41×C127—41no—
72C2×Q8×C127—22no—
73C2×Q8×C127—21no—
74C2×Q8×C127—41no—
75C2×Q8×C127—41no—
76C2×Q8×C127—41no—
77C2×Q8×C127—41no—
78C2×Q8×C127—41no—
79C2×D4×C127—21no—
80C2×D4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127C2×D411yescharacteristic
84Q16×C127—22no—
85Q16×C127—22no—
86Q16×C127—21no—
87Q16×C127—41no—
88Q16×C127—41no—
89Q16×C127C22⋊C412yes—
90SD16×C127—22no—
91SD16×C127—22no—
92D8×C127—21no—
93D8×C127C22⋊C412yes—
94M16×C127—21no—
95M16×C127—22no—
96M16×C127—44no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127—41no—
100M16×C127D812yes—
101C2×C8×C127—21no—
102C2×C8×C127—44no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127C22×C411yescharacteristic
106C2×C8×C127C2×D411yescharacteristic
107C2×C8×C127C2×D411yescharacteristic
108C2×C8×C127C2×D411yescharacteristic
109C2×C8×C127#4111yescharacteristic
110C2×C8×C127#4111yescharacteristic
111C4⋊C4×C127—21no—
112C22⋊C4×C127—21no—
113C42×C127—21no—
114C16×C127—22no—
115C16×C127—41no—
116C23×C127—41no—
117C23×C127#13511yescharacteristic
118Q8×C127—22no—
119Q8×C127—41no—
120Q8×C127—42no—
121Q8×C127—42no—
122Q8×C127—81no—
123Q8×C127—81no—
124D4×C127—22no—
125D4×C127—42no—
126D4×C127—42no—
127D4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—41no—
133C2×C4×C127—81no—
134C2×C4×C127—81no—
135C2×C4×C127C4×D411yescharacteristic
136C2×C4×C127#12011yescharacteristic
137C2×C4×C127#12111yescharacteristic
138C2×C4×C127C2×D811yescharacteristic
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
141C8×C127—22no—
142C8×C127—42no—
143C8×C127—81no—
144C8×C127C2×C22⋊C411yescharacteristic
145C8×C127C4×D411yescharacteristic
146C8×C127#12111yescharacteristic
147C8×C127#12311yescharacteristic
148C22×C127—41no—
149C22×C127—42no—
150C22×C127—161no—
151C22×C127C4×D811yescharacteristic
152C22×C127#44911yescharacteristic
153C22×C127#46311yescharacteristic
154C4×C127—42no—
155C4×C127—81no—
156C4×C127—82no—
157C4×C127#38611yescharacteristic
158C4×C127#44211yescharacteristic
159C4×C127#44711yescharacteristic
160C4×C127#45911yescharacteristic
161#13031C12711yesmaximal, characteristic, direct product factor, Sylow
162C2×C127—21no—
163C2×C127—21no—
164C2×C127—21no—
165C2×C127—82no—
166C2×C127#187911yescharacteristic
167C2×#510C2×C12711yescharacteristic
168#2957C2×C12711yescharacteristic
169#2148C2×C12711yescharacteristic
170C2×#362C2×C12711yescharacteristic, complemented
171#1979C2×C12711yescharacteristic, complemented
172#1388C2×C12711yescharacteristic, complemented
173#1378C2×C12711yescharacteristic, complemented
174C127#1303111yescharacteristic, direct product factor, Sylow
175C2×#135C22×C12711yescharacteristic
176C22×Q16C22×C12711yescharacteristic
177#568—21no—
178#510—22no—
179#510C4×C12714yescomplemented
180C2×Q32—21no—
181C2×SD32—21no—
182C2×M32C22×C12711yescharacteristic
183C2×M32C22×C12711yescharacteristic
184#444—22no—
185#443—22no—
186C2×#108C22×C12711yescharacteristic
187C2×#108C22×C12711yescharacteristic
188#421—21no—
189#419—21no—
190C2×#101—21no—
191#405C22×C12711yescharacteristic
192#362—21no—
193#362—22no—
194#361—21no—
195C2×#41—21no—
196C22×Q8—21no—
197#135—21no—
198#135—21no—
199#135C2×C4×C12712yes—
200#135D4×C12712yes—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16C2×C4×C12712yes—
207C2×Q16D4×C12711yescharacteristic
208C2×SD16—21no—
209C2×D8D4×C12711yescharacteristic
210#131—24no—
211#131—42no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—42no—
215C2×M16D4×C12711yescharacteristic
216C22×C8C23×C12711yescharacteristic
217#117D4×C12711yescharacteristic
218Q32—24no—
219SD32—24no—
220M32—21no—
221M32—21no—
222M32—21no—
223M32C2×C4×C12712yes—
224C2×C16—21no—
225C2×C16—21no—
226#108—21no—
227#108—21no—
228#108—21no—
229#108D4×C12712yes—
230#104—24no—
231#103—42no—
232#101—42no—
233#97—21no—
234C4×C8—21no—
235#41—22no—
236#41—22no—
237#41—41no—
238#41—41no—
239C2×Q8—22no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C2×D4×C12711yescharacteristic
251Q16—22no—
252Q16—22no—
253Q16—21no—
254Q16—41no—
255Q16—41no—
256Q16C22⋊C4×C12712yes—
257SD16—22no—
258SD16—22no—
259D8—21no—
260D8C22⋊C4×C12712yes—
261M16—21no—
262M16—22no—
263M16—44no—
264M16—41no—
265M16—41no—
266M16—41no—
267M16D8×C12712yes—
268C2×C8—21no—
269C2×C8—44no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8C22×C4×C12711yescharacteristic
273C2×C8C2×D4×C12711yescharacteristic
274C2×C8C2×D4×C12711yescharacteristic
275C2×C8C2×D4×C12711yescharacteristic
276C2×C8#41×C12711yescharacteristic
277C2×C8#41×C12711yescharacteristic
278C4⋊C4—21no—
279C22⋊C4—21no—
280C42—21no—
281C16—22no—
282C16—41no—
283C23—41no—
284C23#135×C12711yescharacteristic
285Q8—22no—
286Q8—41no—
287Q8—42no—
288Q8—42no—
289Q8—81no—
290Q8—81no—
291D4—22no—
292D4—42no—
293D4—42no—
294D4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4C4×D4×C12711yescharacteristic
303C2×C4#120×C12711yescharacteristic
304C2×C4#121×C12711yescharacteristic
305C2×C4C2×D8×C12711yescharacteristic
306C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
307C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
308C8—22no—
309C8—42no—
310C8—81no—
311C8C2×C22⋊C4×C12711yescharacteristic
312C8C4×D4×C12711yescharacteristic
313C8#121×C12711yescharacteristic
314C8#123×C12711yescharacteristic
315C22—41no—
316C22—42no—
317C22—161no—
318C22C4×D8×C12711yescharacteristic
319C22#449×C12711yescharacteristic
320C22#463×C12711yescharacteristic
321C4—42no—
322C4—81no—
323C4—82no—
324C4#386×C12711yescharacteristic
325C4#442×C12711yescharacteristic
326C4#447×C12711yescharacteristic
327C4#459×C12711yescharacteristic
328C2—21no—
329C2—21no—
330C2—21no—
331C2—82no—
332C2C127×#187911yescharacteristic
subgroupG/H
center, socleC2×C127#1879
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C2×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
4. C2×#362×C127C2semidirect
5. C127×#1979C2semidirect
6. C127×#1388C2semidirect
7. C127×#1378C2semidirect
12. #510×C127C4semidirect
161. #13031C127direct (N × H)
170. C2×#362C2×C127semidirect
171. #1979C2×C127semidirect
172. #1388C2×C127semidirect
173. #1378C2×C127semidirect
174. C127#13031direct (N × H)
179. #510C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C127×#29572
C127×#21482
C2×#362×C1272
C127×#19792
C127×#13882
C127×#13782
#13031127