Finite Group Databasebeta

← C127×#13070 #44576743

Subgroups — C127×#13070 #44576743

Order 32512.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3407C211yesmaximal, characteristic, complemented
2C127×#3067C211yesmaximal, characteristic
3C2×#360×C127C211yesmaximal, characteristic, complemented
4C127×#2143C211yesmaximal, characteristic, complemented
5C127×#1815C211yesmaximal, characteristic, complemented
6C127×#1388C211yesmaximal, characteristic, complemented
7C127×#1383C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C2×#131×C127C2211yescharacteristic
11#504×C127—22no—
12#504×C127—22no—
13C2×M32×C127—22no—
14C2×M32×C127C2211yescharacteristic
15C2×M32×C127C2211yescharacteristic
16#473×C127C412yescomplemented
17#472×C127C412yescomplemented
18#471×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#108×C127C2211yescharacteristic
21C2×#106×C127C2211yescharacteristic
22#417×C127—21no—
23#413×C127—21no—
24#360×C127—22no—
25#359×C127—22no—
26#343×C127—21no—
27C2×#41×C127—21no—
28C2×#41×C127D411yescharacteristic
29#137×C127—22no—
30#137×C127—41no—
31AGL(1,ℤ/8)×C127—22no—
32AGL(1,ℤ/8)×C127—41no—
33#135×C127—21no—
34#135×C127—21no—
35#135×C127—21no—
36#135×C127—21no—
37#135×C127—42no—
38C2×Q16×C127C2×C411yescharacteristic
39C2×SD16×C127—21no—
40C2×D8×C127C2×C411yescharacteristic
41#131×C127—21no—
42#131×C127—21no—
43#131×C127C2×C412yes—
44#131×C127D412yes—
45C2×M16×C127—21no—
46C2×M16×C127—21no—
47C2×M16×C127—21no—
48C2×M16×C127D411yescharacteristic
49C22×C8×C127—21no—
50C22×C8×C127C2311yescharacteristic
51C2×C4⋊C4×C127—21no—
52M32×C127—24no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56M32×C127D412yes—
57C2×C16×C127—24no—
58C2×C16×C127—21no—
59C2×C16×C127D412yes—
60#108×C127—21no—
61#108×C127—21no—
62#108×C127—21no—
63#108×C127C2×C412yes—
64#106×C127—21no—
65#106×C127—21no—
66#103×C127—41no—
67#102×C127—41no—
68#101×C127—22no—
69#100×C127—22no—
70#41×C127—21no—
71#41×C127—21no—
72#41×C127—41no—
73#41×C127—41no—
74#41×C127—41no—
75#41×C127—41no—
76#41×C127C22⋊C412yes—
77#41×C127SD1612yes—
78C2×Q8×C127—21no—
79C2×Q8×C127D811yescharacteristic
80C2×D4×C127—21no—
81C2×D4×C127—21no—
82C2×D4×C127—41no—
83C2×D4×C127D811yescharacteristic
84C22×C4×C127—21no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127C2×D411yescharacteristic
88Q16×C127—21no—
89Q16×C127—21no—
90Q16×C127—42no—
91SD16×C127—42no—
92SD16×C127—42no—
93SD16×C127—41no—
94SD16×C127—41no—
95D8×C127—21no—
96D8×C127—21no—
97D8×C127—42no—
98M16×C127—21no—
99M16×C127—22no—
100M16×C127—22no—
101M16×C127—22no—
102M16×C127—41no—
103M16×C127—41no—
104M16×C127—41no—
105M16×C127C22⋊C412yes—
106C2×C8×C127—21no—
107C2×C8×C127—22no—
108C2×C8×C127—22no—
109C2×C8×C127—41no—
110C2×C8×C127—41no—
111C2×C8×C127C22×C411yescharacteristic
112C2×C8×C127C2×D411yescharacteristic
113C2×C8×C127C2×D411yescharacteristic
114C2×C8×C127C2×D411yescharacteristic
115C2×C8×C127#4111yescharacteristic
116C2×C8×C127#4111yescharacteristic
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C16×C127—22no—
120C16×C127—22no—
121C23×C127—21no—
122C23×C127—41no—
123C23×C127#13511yescharacteristic
124Q8×C127—21no—
125Q8×C127—41no—
126Q8×C127—41no—
127Q8×C127#10212yes—
128D4×C127—22no—
129D4×C127—22no—
130D4×C127—21no—
131D4×C127—41no—
132D4×C127—41no—
133D4×C127—81no—
134D4×C127—81no—
135D4×C127#10212yes—
136C2×C4×C127—21no—
137C2×C4×C127—22no—
138C2×C4×C127—22no—
139C2×C4×C127—41no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127—161no—
144C2×C4×C127C2×C22⋊C411yescharacteristic
145C2×C4×C127#12111yescharacteristic
146C2×C4×C127#12111yescharacteristic
147C2×C4×C127C2×D811yescharacteristic
148C2×C4×C127C2×SD1611yescharacteristic
149C2×C4×C127#13511yescharacteristic
150C8×C127—22no—
151C8×C127—42no—
152C8×C127—81no—
153C8×C127C4×D411yescharacteristic
154C8×C127C4×D411yescharacteristic
155C8×C127#12011yescharacteristic
156C8×C127#12311yescharacteristic
157C22×C127—22no—
158C22×C127—41no—
159C22×C127—81no—
160C22×C127—81no—
161C22×C127—161no—
162C22×C127#41611yescharacteristic
163C22×C127#46511yescharacteristic
164C22×C127#46611yescharacteristic
165C4×C127—22no—
166C4×C127—81no—
167C4×C127—161no—
168C4×C127#38611yescharacteristic
169C4×C127C2×#10211yescharacteristic
170C4×C127#46511yescharacteristic
171C4×C127#46611yescharacteristic
172#13070C12711yesmaximal, characteristic, direct product factor, Sylow
173C2×C127—21no—
174C2×C127—21no—
175C2×C127—21no—
176C2×C127—42no—
177C2×C127—161no—
178C2×C127#189311yescharacteristic
179#3407C2×C12711yescharacteristic, complemented
180#3067C2×C12711yescharacteristic
181C2×#360C2×C12711yescharacteristic, complemented
182#2143C2×C12711yescharacteristic, complemented
183#1815C2×C12711yescharacteristic, complemented
184#1388C2×C12711yescharacteristic, complemented
185#1383C2×C12711yescharacteristic, complemented
186C127#1307011yescharacteristic, direct product factor, Sylow
187#575—21no—
188C2×#135C22×C12711yescharacteristic
189C2×#131C22×C12711yescharacteristic
190#504—22no—
191#504—22no—
192C2×M32—22no—
193C2×M32C22×C12711yescharacteristic
194C2×M32C22×C12711yescharacteristic
195#473C4×C12712yescomplemented
196#472C4×C12712yescomplemented
197#471—22no—
198C2×#108C22×C12711yescharacteristic
199C2×#108C22×C12711yescharacteristic
200C2×#106C22×C12711yescharacteristic
201#417—21no—
202#413—21no—
203#360—22no—
204#359—22no—
205#343—21no—
206C2×#41—21no—
207C2×#41D4×C12711yescharacteristic
208#137—22no—
209#137—41no—
210AGL(1,ℤ/8)—22no—
211AGL(1,ℤ/8)—41no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—42no—
217C2×Q16C2×C4×C12711yescharacteristic
218C2×SD16—21no—
219C2×D8C2×C4×C12711yescharacteristic
220#131—21no—
221#131—21no—
222#131C2×C4×C12712yes—
223#131D4×C12712yes—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16D4×C12711yescharacteristic
228C22×C8—21no—
229C22×C8C23×C12711yescharacteristic
230C2×C4⋊C4—21no—
231M32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32D4×C12712yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16D4×C12712yes—
239#108—21no—
240#108—21no—
241#108—21no—
242#108C2×C4×C12712yes—
243#106—21no—
244#106—21no—
245#103—41no—
246#102—41no—
247#101—22no—
248#100—22no—
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41C22⋊C4×C12712yes—
256#41SD16×C12712yes—
257C2×Q8—21no—
258C2×Q8D8×C12711yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4D8×C12711yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C12711yescharacteristic
267Q16—21no—
268Q16—21no—
269Q16—42no—
270SD16—42no—
271SD16—42no—
272SD16—41no—
273SD16—41no—
274D8—21no—
275D8—21no—
276D8—42no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16C22⋊C4×C12712yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8C22×C4×C12711yescharacteristic
291C2×C8C2×D4×C12711yescharacteristic
292C2×C8C2×D4×C12711yescharacteristic
293C2×C8C2×D4×C12711yescharacteristic
294C2×C8#41×C12711yescharacteristic
295C2×C8#41×C12711yescharacteristic
296C4⋊C4—41no—
297C4⋊C4—41no—
298C16—22no—
299C16—22no—
300C23—21no—
301C23—41no—
302C23#135×C12711yescharacteristic
303Q8—21no—
304Q8—41no—
305Q8—41no—
306Q8#102×C12712yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—81no—
313D4—81no—
314D4#102×C12712yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—161no—
323C2×C4C2×C22⋊C4×C12711yescharacteristic
324C2×C4#121×C12711yescharacteristic
325C2×C4#121×C12711yescharacteristic
326C2×C4C2×D8×C12711yescharacteristic
327C2×C4C2×SD16×C12711yescharacteristic
328C2×C4#135×C12711yescharacteristic
329C8—22no—
330C8—42no—
331C8—81no—
332C8C4×D4×C12711yescharacteristic
333C8C4×D4×C12711yescharacteristic
334C8#120×C12711yescharacteristic
335C8#123×C12711yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22—161no—
341C22#416×C12711yescharacteristic
342C22#465×C12711yescharacteristic
343C22#466×C12711yescharacteristic
344C4—22no—
345C4—81no—
346C4—161no—
347C4#386×C12711yescharacteristic
348C4C2×#102×C12711yescharacteristic
349C4#465×C12711yescharacteristic
350C4#466×C12711yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2C127×#189311yescharacteristic
subgroupG/H
center, socleC2×C127#1893
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3407C2semidirect
3. C2×#360×C127C2semidirect
4. C127×#2143C2semidirect
5. C127×#1815C2semidirect
6. C127×#1388C2semidirect
7. C127×#1383C2semidirect
16. #473×C127C4semidirect
17. #472×C127C4semidirect
172. #13070C127direct (N × H)
179. #3407C2×C127semidirect
181. C2×#360C2×C127semidirect
182. #2143C2×C127semidirect
183. #1815C2×C127semidirect
184. #1388C2×C127semidirect
185. #1383C2×C127semidirect
186. C127#13070direct (N × H)
195. #473C4×C127semidirect
196. #472C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34072
C127×#30672
C2×#360×C1272
C127×#21432
C127×#18152
C127×#13882
C127×#13832
#13070127