Finite Group Databasebeta

← C127×#10456 #44574129

Subgroups — C127×#10456 #44574129

Order 32512.

460 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3036C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic, complemented
3C127×#1567C211yesmaximal, characteristic, complemented
4C127×#1547C211yesmaximal, characteristic, complemented
5C127×#1492C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
7C127×#1292C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9#532×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11#463×C127—22no—
12#461×C127—21no—
13#459×C127—21no—
14#423×C127C2211yescharacteristic
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#417×C127—21no—
19C2×#100×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21#343×C127—21no—
22#335×C127—22no—
23#332×C127—21no—
24#331×C127—21no—
25D4⋊C8×C127—21no—
26D4⋊C8×C127—21no—
27D4⋊C8×C127—21no—
28D4⋊C8×C127—21no—
29C2×#41×C127—21no—
30C22×D4×C127D411yescharacteristic
31C23×C4×C127—21no—
32AGL(1,ℤ/8)×C127—42no—
33AGL(1,ℤ/8)×C127—42no—
34C2×SD16×C127—22no—
35C2×D8×C127—22no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—21no—
41C4⋊Q8×C127D411yescharacteristic
42#127×C127D411yescharacteristic
43#124×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—21no—
48C4×D4×C127—21no—
49C4×D4×C127—21no—
50C4×D4×C127—21no—
51C4×D4×C127—21no—
52C2×C4⋊C4×C127D411yescharacteristic
53C2×C22⋊C4×C127—21no—
54C2×C42×C127C2311yescharacteristic
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127—21no—
61C4⋊C8×C127—21no—
62C4⋊C8×C127D412yes—
63#103×C127—22no—
64#102×C127—22no—
65#100×C127—42no—
66C4×C8×C127—21no—
67C4×C8×C127D411yescharacteristic
68C4×C8×C127D411yescharacteristic
69C24×C127—21no—
70#41×C127—41no—
71#41×C127—41no—
72#41×C127—41no—
73#41×C127—41no—
74C2×Q8×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—21no—
79C2×D4×C127—21no—
80C2×D4×C127—21no—
81C2×D4×C127—21no—
82C2×D4×C127—21no—
83C2×D4×C127—41no—
84C2×D4×C127D812yes—
85C22×C4×C127—21no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127—41no—
89C22×C4×C127—81no—
90C22×C4×C127—81no—
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127#4111yescharacteristic
93C22×C4×C127#4111yescharacteristic
94SD16×C127—44no—
95D8×C127—44no—
96M16×C127—41no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102C2×C8×C127—21no—
103C2×C8×C127—22no—
104C2×C8×C127—21no—
105C2×C8×C127—42no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—41no—
109C2×C8×C127—81no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127—41no—
117C22⋊C4×C127—41no—
118C42×C127C2×D411yescharacteristic
119C42×C127C2×D411yescharacteristic
120C42×C127C2×D411yescharacteristic
121C42×C127#4111yescharacteristic
122C23×C127—22no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127—81no—
127C23×C127—81no—
128C23×C127#12311yescharacteristic
129Q8×C127—41no—
130Q8×C127—41no—
131D4×C127—22no—
132D4×C127—22no—
133D4×C127—41no—
134D4×C127—41no—
135D4×C127—41no—
136D4×C127—41no—
137D4×C127—41no—
138D4×C127—41no—
139D4×C127—81no—
140D4×C127—81no—
141D4×C127—81no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—82no—
148C2×C4×C127—81no—
149C2×C4×C127—81no—
150C2×C4×C127—81no—
151C2×C4×C127—81no—
152C2×C4×C127—81no—
153C2×C4×C127#12011yescharacteristic
154C2×C4×C127#12111yescharacteristic
155C2×C4×C127#12111yescharacteristic
156C2×C4×C127#12111yescharacteristic
157C2×C4×C127#12311yescharacteristic
158C2×C4×C127#12411yescharacteristic
159C2×C4×C127C2×D811yescharacteristic
160C2×C4×C127#13511yescharacteristic
161C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C127#13711yescharacteristic
163C8×C127—22no—
164C8×C127—41no—
165C8×C127—42no—
166C8×C127—81no—
167C8×C127—81no—
168C8×C127—81no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—42no—
172C22×C127—82no—
173C22×C127—82no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—81no—
179C22×C127#39411yescharacteristic
180C22×C127#48011yescharacteristic
181C22×C127#48211yescharacteristic
182C4×C127—21no—
183C4×C127—21no—
184C4×C127—21no—
185C4×C127—81no—
186C4×C127—81no—
187C4×C127#44711yescharacteristic
188C4×C127#45211yescharacteristic
189C4×C127#46611yescharacteristic
190C4×C127#46811yescharacteristic
191C4×C127#47111yescharacteristic
192C4×C127#47211yescharacteristic
193#10456C12711yesmaximal, characteristic, direct product factor, Sylow
194C2×C127—21no—
195C2×C127—21no—
196C2×C127—82no—
197C2×C127—161no—
198C2×C127#203311yescharacteristic
199C2×C127#205011yescharacteristic
200C2×C127#205111yescharacteristic
201#3036C2×C12711yescharacteristic
202#1800C2×C12711yescharacteristic, complemented
203#1567C2×C12711yescharacteristic, complemented
204#1547C2×C12711yescharacteristic, complemented
205#1492C2×C12711yescharacteristic, complemented
206C2×D4⋊C8C2×C12711yescharacteristic, complemented
207#1292C2×C12711yescharacteristic, complemented
208C127#1045611yescharacteristic, direct product factor, Sylow
209C2×AGL(1,ℤ/8)—21no—
210#532C22×C12711yescharacteristic
211C2×C4×D4C22×C12711yescharacteristic
212#463—22no—
213#461—21no—
214#459—21no—
215#423C22×C12711yescharacteristic
216#423C22×C12711yescharacteristic
217#423C22×C12711yescharacteristic
218C2×C4⋊C8C22×C12711yescharacteristic
219#417—21no—
220C2×#100—21no—
221C2×C4×C8C22×C12711yescharacteristic
222#343—21no—
223#335—22no—
224#332—21no—
225#331—21no—
226D4⋊C8—21no—
227D4⋊C8—21no—
228D4⋊C8—21no—
229D4⋊C8—21no—
230C2×#41—21no—
231C22×D4D4×C12711yescharacteristic
232C23×C4—21no—
233AGL(1,ℤ/8)—42no—
234AGL(1,ℤ/8)—42no—
235C2×SD16—22no—
236C2×D8—22no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C22×C8—21no—
241C22×C8—21no—
242C4⋊Q8D4×C12711yescharacteristic
243#127D4×C12711yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C2×C4⋊C4D4×C12711yescharacteristic
254C2×C22⋊C4—21no—
255C2×C42C23×C12711yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8D4×C12712yes—
264#103—22no—
265#102—22no—
266#100—42no—
267C4×C8—21no—
268C4×C8D4×C12711yescharacteristic
269C4×C8D4×C12711yescharacteristic
270C24—21no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4D8×C12712yes—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4C2×D4×C12711yescharacteristic
293C22×C4#41×C12711yescharacteristic
294C22×C4#41×C12711yescharacteristic
295SD16—44no—
296D8—44no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—41no—
301M16—41no—
302M16—41no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—42no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—81no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×D4×C12711yescharacteristic
320C42C2×D4×C12711yescharacteristic
321C42C2×D4×C12711yescharacteristic
322C42#41×C12711yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—81no—
328C23—81no—
329C23#123×C12711yescharacteristic
330Q8—41no—
331Q8—41no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4#120×C12711yescharacteristic
355C2×C4#121×C12711yescharacteristic
356C2×C4#121×C12711yescharacteristic
357C2×C4#121×C12711yescharacteristic
358C2×C4#123×C12711yescharacteristic
359C2×C4#124×C12711yescharacteristic
360C2×C4C2×D8×C12711yescharacteristic
361C2×C4#135×C12711yescharacteristic
362C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
363C2×C4#137×C12711yescharacteristic
364C8—22no—
365C8—41no—
366C8—42no—
367C8—81no—
368C8—81no—
369C8—81no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—82no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22#394×C12711yescharacteristic
381C22#480×C12711yescharacteristic
382C22#482×C12711yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—81no—
388C4#447×C12711yescharacteristic
389C4#452×C12711yescharacteristic
390C4#466×C12711yescharacteristic
391C4#468×C12711yescharacteristic
392C4#471×C12711yescharacteristic
393C4#472×C12711yescharacteristic
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2C127×#203311yescharacteristic
399C2C127×#205011yescharacteristic
400C2C127×#205111yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3036C2
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
2. C127×#1800C2semidirect
3. C127×#1567C2semidirect
4. C127×#1547C2semidirect
5. C127×#1492C2semidirect
6. C2×D4⋊C8×C127C2semidirect
7. C127×#1292C2semidirect
193. #10456C127direct (N × H)
202. #1800C2×C127semidirect
203. #1567C2×C127semidirect
204. #1547C2×C127semidirect
205. #1492C2×C127semidirect
206. C2×D4⋊C8C2×C127semidirect
207. #1292C2×C127semidirect
208. C127#10456direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30362
C127×#18002
C127×#15672
C127×#15472
C127×#14922
C2×D4⋊C8×C1272
C127×#12922
#10456127