Finite Group Databasebeta

← C127×#13071 #44576744

Subgroups — C127×#13071 #44576744

Order 32512.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#504×C127C211yesmaximal, characteristic, complemented
2C127×#3067C211yesmaximal, characteristic
3C127×#2145C211yesmaximal, characteristic, complemented
4C2×#359×C127C211yesmaximal, characteristic, complemented
5C127×#1814C211yesmaximal, characteristic, complemented
6C127×#1388C211yesmaximal, characteristic, complemented
7C127×#1382C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C2×#131×C127C2211yescharacteristic
11#504×C127—22no—
12#504×C127—22no—
13C2×M32×C127—21no—
14C2×M32×C127C2211yescharacteristic
15C22×C16×C127—21no—
16C22×C16×C127C2211yescharacteristic
17#473×C127C412yescomplemented
18#472×C127C412yescomplemented
19#471×C127—22no—
20C2×#108×C127C2211yescharacteristic
21C2×#108×C127C2211yescharacteristic
22#427×C127C2211yescharacteristic
23#421×C127—21no—
24#413×C127—21no—
25#360×C127—22no—
26#359×C127—21no—
27#359×C127—21no—
28#344×C127—21no—
29C2×#41×C127—21no—
30C2×#41×C127D411yescharacteristic
31#137×C127—22no—
32#137×C127—41no—
33AGL(1,ℤ/8)×C127—22no—
34AGL(1,ℤ/8)×C127—41no—
35#135×C127—21no—
36#135×C127—21no—
37#135×C127—21no—
38#135×C127—21no—
39#135×C127—42no—
40C2×Q16×C127C2×C411yescharacteristic
41C2×SD16×C127—21no—
42C2×D8×C127C2×C411yescharacteristic
43#131×C127—21no—
44#131×C127—21no—
45#131×C127C2×C412yes—
46#131×C127D412yes—
47C2×M16×C127—21no—
48C2×M16×C127—21no—
49C2×M16×C127—21no—
50C2×M16×C127D411yescharacteristic
51C22×C8×C127—21no—
52C22×C8×C127C2311yescharacteristic
53#117×C127—21no—
54M32×C127—24no—
55M32×C127—21no—
56M32×C127D412yes—
57C2×C16×C127—24no—
58C2×C16×C127—21no—
59C2×C16×C127—21no—
60C2×C16×C127—21no—
61C2×C16×C127D411yescharacteristic
62C2×C16×C127D411yescharacteristic
63#108×C127—21no—
64#108×C127—21no—
65#108×C127—21no—
66#108×C127C2×C412yes—
67#107×C127—21no—
68#106×C127—21no—
69#104×C127—42no—
70#101×C127—22no—
71#100×C127—22no—
72#41×C127—21no—
73#41×C127—21no—
74#41×C127—41no—
75#41×C127—41no—
76#41×C127—41no—
77#41×C127—41no—
78#41×C127C22⋊C412yes—
79#41×C127D812yes—
80C2×Q8×C127—21no—
81C2×Q8×C127SD1611yescharacteristic
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—41no—
85C2×D4×C127SD1611yescharacteristic
86C22×C4×C127—21no—
87C22×C4×C127—41no—
88C22×C4×C127C2×D411yescharacteristic
89Q16×C127—21no—
90Q16×C127—21no—
91Q16×C127—42no—
92SD16×C127—42no—
93SD16×C127—42no—
94SD16×C127—41no—
95SD16×C127—41no—
96D8×C127—21no—
97D8×C127—21no—
98D8×C127—42no—
99M16×C127—21no—
100M16×C127—22no—
101M16×C127—22no—
102M16×C127—22no—
103M16×C127—41no—
104M16×C127—41no—
105M16×C127—41no—
106M16×C127C22⋊C412yes—
107C2×C8×C127—21no—
108C2×C8×C127—22no—
109C2×C8×C127—22no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127C22×C411yescharacteristic
113C2×C8×C127C2×D411yescharacteristic
114C2×C8×C127C2×D411yescharacteristic
115C2×C8×C127C2×D411yescharacteristic
116C2×C8×C127#4111yescharacteristic
117C2×C8×C127#4111yescharacteristic
118C4⋊C4×C127—41no—
119C22⋊C4×C127—41no—
120C42×C127—41no—
121C16×C127—21no—
122C16×C127—22no—
123C16×C127—21no—
124C23×C127—21no—
125C23×C127—41no—
126C23×C127#13511yescharacteristic
127Q8×C127—21no—
128Q8×C127—41no—
129Q8×C127—41no—
130Q8×C127#10212yes—
131D4×C127—22no—
132D4×C127—22no—
133D4×C127—21no—
134D4×C127—41no—
135D4×C127—41no—
136D4×C127—81no—
137D4×C127—81no—
138D4×C127#10212yes—
139C2×C4×C127—21no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—41no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127—81no—
146C2×C4×C127C2×C22⋊C411yescharacteristic
147C2×C4×C127#12111yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127C2×D811yescharacteristic
150C2×C4×C127C2×SD1611yescharacteristic
151C2×C4×C127#13511yescharacteristic
152C8×C127—22no—
153C8×C127—42no—
154C8×C127—81no—
155C8×C127C4×D411yescharacteristic
156C8×C127C4×D411yescharacteristic
157C8×C127#12011yescharacteristic
158C8×C127#12311yescharacteristic
159C22×C127—22no—
160C22×C127—41no—
161C22×C127—42no—
162C22×C127—81no—
163C22×C127—161no—
164C22×C127#41611yescharacteristic
165C22×C127#46511yescharacteristic
166C22×C127#46611yescharacteristic
167C4×C127—22no—
168C4×C127—81no—
169C4×C127—161no—
170C4×C127#38611yescharacteristic
171C4×C127C2×#10211yescharacteristic
172C4×C127#46511yescharacteristic
173C4×C127#46611yescharacteristic
174#13071C12711yesmaximal, characteristic, direct product factor, Sylow
175C2×C127—21no—
176C2×C127—21no—
177C2×C127—21no—
178C2×C127—42no—
179C2×C127—161no—
180C2×C127#189311yescharacteristic
181C2×#504C2×C12711yescharacteristic, complemented
182#3067C2×C12711yescharacteristic
183#2145C2×C12711yescharacteristic, complemented
184C2×#359C2×C12711yescharacteristic, complemented
185#1814C2×C12711yescharacteristic, complemented
186#1388C2×C12711yescharacteristic, complemented
187#1382C2×C12711yescharacteristic, complemented
188C127#1307111yescharacteristic, direct product factor, Sylow
189#575—21no—
190C2×#135C22×C12711yescharacteristic
191C2×#131C22×C12711yescharacteristic
192#504—22no—
193#504—22no—
194C2×M32—21no—
195C2×M32C22×C12711yescharacteristic
196C22×C16—21no—
197C22×C16C22×C12711yescharacteristic
198#473C4×C12712yescomplemented
199#472C4×C12712yescomplemented
200#471—22no—
201C2×#108C22×C12711yescharacteristic
202C2×#108C22×C12711yescharacteristic
203#427C22×C12711yescharacteristic
204#421—21no—
205#413—21no—
206#360—22no—
207#359—21no—
208#359—21no—
209#344—21no—
210C2×#41—21no—
211C2×#41D4×C12711yescharacteristic
212#137—22no—
213#137—41no—
214AGL(1,ℤ/8)—22no—
215AGL(1,ℤ/8)—41no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135—42no—
221C2×Q16C2×C4×C12711yescharacteristic
222C2×SD16—21no—
223C2×D8C2×C4×C12711yescharacteristic
224#131—21no—
225#131—21no—
226#131C2×C4×C12712yes—
227#131D4×C12712yes—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16D4×C12711yescharacteristic
232C22×C8—21no—
233C22×C8C23×C12711yescharacteristic
234#117—21no—
235M32—24no—
236M32—21no—
237M32D4×C12712yes—
238C2×C16—24no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16D4×C12711yescharacteristic
243C2×C16D4×C12711yescharacteristic
244#108—21no—
245#108—21no—
246#108—21no—
247#108C2×C4×C12712yes—
248#107—21no—
249#106—21no—
250#104—42no—
251#101—22no—
252#100—22no—
253#41—21no—
254#41—21no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41C22⋊C4×C12712yes—
260#41D8×C12712yes—
261C2×Q8—21no—
262C2×Q8SD16×C12711yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4SD16×C12711yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×D4×C12711yescharacteristic
270Q16—21no—
271Q16—21no—
272Q16—42no—
273SD16—42no—
274SD16—42no—
275SD16—41no—
276SD16—41no—
277D8—21no—
278D8—21no—
279D8—42no—
280M16—21no—
281M16—22no—
282M16—22no—
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16C22⋊C4×C12712yes—
288C2×C8—21no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8C22×C4×C12711yescharacteristic
294C2×C8C2×D4×C12711yescharacteristic
295C2×C8C2×D4×C12711yescharacteristic
296C2×C8C2×D4×C12711yescharacteristic
297C2×C8#41×C12711yescharacteristic
298C2×C8#41×C12711yescharacteristic
299C4⋊C4—41no—
300C22⋊C4—41no—
301C42—41no—
302C16—21no—
303C16—22no—
304C16—21no—
305C23—21no—
306C23—41no—
307C23#135×C12711yescharacteristic
308Q8—21no—
309Q8—41no—
310Q8—41no—
311Q8#102×C12712yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4#102×C12712yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C2×C22⋊C4×C12711yescharacteristic
328C2×C4#121×C12711yescharacteristic
329C2×C4#121×C12711yescharacteristic
330C2×C4C2×D8×C12711yescharacteristic
331C2×C4C2×SD16×C12711yescharacteristic
332C2×C4#135×C12711yescharacteristic
333C8—22no—
334C8—42no—
335C8—81no—
336C8C4×D4×C12711yescharacteristic
337C8C4×D4×C12711yescharacteristic
338C8#120×C12711yescharacteristic
339C8#123×C12711yescharacteristic
340C22—22no—
341C22—41no—
342C22—42no—
343C22—81no—
344C22—161no—
345C22#416×C12711yescharacteristic
346C22#465×C12711yescharacteristic
347C22#466×C12711yescharacteristic
348C4—22no—
349C4—81no—
350C4—161no—
351C4#386×C12711yescharacteristic
352C4C2×#102×C12711yescharacteristic
353C4#465×C12711yescharacteristic
354C4#466×C12711yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—161no—
360C2C127×#189311yescharacteristic
subgroupG/H
centerC4×C127#466
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC2×C127#1893
prime radicalC127×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#504×C127C2semidirect
3. C127×#2145C2semidirect
4. C2×#359×C127C2semidirect
5. C127×#1814C2semidirect
6. C127×#1388C2semidirect
7. C127×#1382C2semidirect
17. #473×C127C4semidirect
18. #472×C127C4semidirect
174. #13071C127direct (N × H)
181. C2×#504C2×C127semidirect
183. #2145C2×C127semidirect
184. C2×#359C2×C127semidirect
185. #1814C2×C127semidirect
186. #1388C2×C127semidirect
187. #1382C2×C127semidirect
188. C127#13071direct (N × H)
198. #473C4×C127semidirect
199. #472C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#504×C1272
C127×#30672
C127×#21452
C2×#359×C1272
C127×#18142
C127×#13882
C127×#13822
#13071127