Finite Group Databasebeta

← C127×#13035 #44576708

Subgroups — C127×#13035 #44576708

Order 32512.

456 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C127×#2957C211yesmaximal, characteristic
3C2×#362×C127C211yesmaximal, characteristic, complemented
4C127×#2143C211yesmaximal, characteristic
5C127×#1979C211yesmaximal, characteristic, complemented
6C127×#1385C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10#568×C127—21no—
11#510×C127—22no—
12#510×C127—22no—
13C2×Q32×C127C412yescomplemented
14C2×SD32×C127C412yescomplemented
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—22no—
26#359×C127—22no—
27C2×#41×C127—21no—
28C22×Q8×C127—21no—
29#135×C127—21no—
30#135×C127—21no—
31#135×C127D412yes—
32#135×C127D412yes—
33C2×Q16×C127—21no—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127C2×C412yes—
39C2×Q16×C127C2×C411yescharacteristic
40C2×SD16×C127—21no—
41C2×D8×C127C2×C411yescharacteristic
42#131×C127—24no—
43#131×C127—42no—
44C2×M16×C127—21no—
45C2×M16×C127—21no—
46C2×M16×C127—42no—
47C2×M16×C127D411yescharacteristic
48C22×C8×C127C2311yescharacteristic
49#117×C127D411yescharacteristic
50Q32×C127—24no—
51SD32×C127—24no—
52M32×C127—21no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56C2×C16×C127—21no—
57C2×C16×C127C2×C412yes—
58#108×C127—21no—
59#108×C127—21no—
60#108×C127—21no—
61#108×C127D412yes—
62#104×C127—24no—
63#103×C127—42no—
64#101×C127—42no—
65#97×C127—21no—
66C4×C8×C127—21no—
67#41×C127—22no—
68#41×C127—22no—
69#41×C127—41no—
70#41×C127—41no—
71C2×Q8×C127—21no—
72C2×Q8×C127—22no—
73C2×Q8×C127—41no—
74C2×Q8×C127—41no—
75C2×Q8×C127—41no—
76C2×Q8×C127—41no—
77C2×Q8×C127—41no—
78C2×D4×C127—21no—
79C2×D4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127C2×D411yescharacteristic
83Q16×C127—22no—
84Q16×C127—21no—
85Q16×C127—22no—
86Q16×C127—41no—
87Q16×C127—41no—
88Q16×C127C22⋊C412yes—
89SD16×C127—22no—
90SD16×C127—22no—
91D8×C127—21no—
92D8×C127C22⋊C412yes—
93M16×C127—21no—
94M16×C127—22no—
95M16×C127—44no—
96M16×C127—41no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127D812yes—
100C2×C8×C127—21no—
101C2×C8×C127—44no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127C22×C411yescharacteristic
105C2×C8×C127C2×D411yescharacteristic
106C2×C8×C127C2×D411yescharacteristic
107C2×C8×C127C2×D411yescharacteristic
108C2×C8×C127#4111yescharacteristic
109C2×C8×C127#4111yescharacteristic
110C4⋊C4×C127—21no—
111C22⋊C4×C127—21no—
112C42×C127—21no—
113C16×C127—22no—
114C16×C127—41no—
115C23×C127—41no—
116C23×C127#13511yescharacteristic
117Q8×C127—22no—
118Q8×C127—41no—
119Q8×C127—42no—
120Q8×C127—42no—
121Q8×C127—81no—
122Q8×C127—81no—
123D4×C127—22no—
124D4×C127—42no—
125D4×C127—42no—
126D4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—41no—
132C2×C4×C127—81no—
133C2×C4×C127—81no—
134C2×C4×C127C4×D411yescharacteristic
135C2×C4×C127#12011yescharacteristic
136C2×C4×C127#12111yescharacteristic
137C2×C4×C127C2×D811yescharacteristic
138C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C8×C127—22no—
141C8×C127—42no—
142C8×C127—81no—
143C8×C127C2×C22⋊C411yescharacteristic
144C8×C127C4×D411yescharacteristic
145C8×C127#12111yescharacteristic
146C8×C127#12311yescharacteristic
147C22×C127—41no—
148C22×C127—42no—
149C22×C127—161no—
150C22×C127C4×D811yescharacteristic
151C22×C127#44911yescharacteristic
152C22×C127#46311yescharacteristic
153C4×C127—42no—
154C4×C127—81no—
155C4×C127—82no—
156C4×C127#38611yescharacteristic
157C4×C127#44211yescharacteristic
158C4×C127#44711yescharacteristic
159C4×C127#45911yescharacteristic
160#13035C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—21no—
162C2×C127—21no—
163C2×C127—21no—
164C2×C127—82no—
165C2×C127#187911yescharacteristic
166C2×#510C2×C12711yescharacteristic
167#2957C2×C12711yescharacteristic
168C2×#362C2×C12711yescharacteristic, complemented
169#2143C2×C12711yescharacteristic
170#1979C2×C12711yescharacteristic, complemented
171#1385C2×C12711yescharacteristic, complemented
172#1378C2×C12711yescharacteristic, complemented
173C127#1303511yescharacteristic, direct product factor, Sylow
174C2×#135C22×C12711yescharacteristic
175C22×Q16C22×C12711yescharacteristic
176#568—21no—
177#510—22no—
178#510—22no—
179C2×Q32C4×C12712yescomplemented
180C2×SD32C4×C12712yescomplemented
181C2×M32C22×C12711yescharacteristic
182C2×M32C22×C12711yescharacteristic
183#444—22no—
184#443—22no—
185C2×#108C22×C12711yescharacteristic
186C2×#108C22×C12711yescharacteristic
187#421—21no—
188#419—21no—
189C2×#101—21no—
190#405C22×C12711yescharacteristic
191#362—22no—
192#359—22no—
193C2×#41—21no—
194C22×Q8—21no—
195#135—21no—
196#135—21no—
197#135D4×C12712yes—
198#135D4×C12712yes—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16C2×C4×C12712yes—
205C2×Q16C2×C4×C12711yescharacteristic
206C2×SD16—21no—
207C2×D8C2×C4×C12711yescharacteristic
208#131—24no—
209#131—42no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—42no—
213C2×M16D4×C12711yescharacteristic
214C22×C8C23×C12711yescharacteristic
215#117D4×C12711yescharacteristic
216Q32—24no—
217SD32—24no—
218M32—21no—
219M32—21no—
220M32—21no—
221M32—21no—
222C2×C16—21no—
223C2×C16C2×C4×C12712yes—
224#108—21no—
225#108—21no—
226#108—21no—
227#108D4×C12712yes—
228#104—24no—
229#103—42no—
230#101—42no—
231#97—21no—
232C4×C8—21no—
233#41—22no—
234#41—22no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×D4—21no—
245C2×D4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C2×D4×C12711yescharacteristic
249Q16—22no—
250Q16—21no—
251Q16—22no—
252Q16—41no—
253Q16—41no—
254Q16C22⋊C4×C12712yes—
255SD16—22no—
256SD16—22no—
257D8—21no—
258D8C22⋊C4×C12712yes—
259M16—21no—
260M16—22no—
261M16—44no—
262M16—41no—
263M16—41no—
264M16—41no—
265M16D8×C12712yes—
266C2×C8—21no—
267C2×C8—44no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8C22×C4×C12711yescharacteristic
271C2×C8C2×D4×C12711yescharacteristic
272C2×C8C2×D4×C12711yescharacteristic
273C2×C8C2×D4×C12711yescharacteristic
274C2×C8#41×C12711yescharacteristic
275C2×C8#41×C12711yescharacteristic
276C4⋊C4—21no—
277C22⋊C4—21no—
278C42—21no—
279C16—22no—
280C16—41no—
281C23—41no—
282C23#135×C12711yescharacteristic
283Q8—22no—
284Q8—41no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288Q8—81no—
289D4—22no—
290D4—42no—
291D4—42no—
292D4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C4×D4×C12711yescharacteristic
301C2×C4#120×C12711yescharacteristic
302C2×C4#121×C12711yescharacteristic
303C2×C4C2×D8×C12711yescharacteristic
304C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
305C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
306C8—22no—
307C8—42no—
308C8—81no—
309C8C2×C22⋊C4×C12711yescharacteristic
310C8C4×D4×C12711yescharacteristic
311C8#121×C12711yescharacteristic
312C8#123×C12711yescharacteristic
313C22—41no—
314C22—42no—
315C22—161no—
316C22C4×D8×C12711yescharacteristic
317C22#449×C12711yescharacteristic
318C22#463×C12711yescharacteristic
319C4—42no—
320C4—81no—
321C4—82no—
322C4#386×C12711yescharacteristic
323C4#442×C12711yescharacteristic
324C4#447×C12711yescharacteristic
325C4#459×C12711yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—82no—
330C2C127×#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
3. C2×#362×C127C2semidirect
5. C127×#1979C2semidirect
6. C127×#1385C2semidirect
7. C127×#1378C2semidirect
13. C2×Q32×C127C4semidirect
14. C2×SD32×C127C4semidirect
160. #13035C127direct (N × H)
168. C2×#362C2×C127semidirect
170. #1979C2×C127semidirect
171. #1385C2×C127semidirect
172. #1378C2×C127semidirect
173. C127#13035direct (N × H)
179. C2×Q32C4×C127semidirect
180. C2×SD32C4×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
C2×#362×C1272
C127×#21432
C127×#19792
C127×#13852
C127×#13782
#13035127