Finite Group Databasebeta

← C127×#13310 #44576983

Subgroups — C127×#13310 #44576983

Order 32512.

552 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic, complemented
2C127×#3067C211yesmaximal, characteristic, complemented
3C127×#3058C211yesmaximal, characteristic, complemented
4C2×#361×C127C211yesmaximal, characteristic, complemented
5C127×#2145C211yesmaximal, characteristic, complemented
6C127×#2117C211yesmaximal, characteristic, complemented
7C127×#1389C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C22×D8×C127C2211yescharacteristic
11C2×#131×C127C2211yescharacteristic
12#535×C127—21no—
13#509×C127—22no—
14#509×C127—22no—
15C2×SD32×C127—21no—
16C2×D16×C127—21no—
17C2×M32×C127C2211yescharacteristic
18C2×M32×C127C2211yescharacteristic
19#473×C127—21no—
20#472×C127—21no—
21#471×C127—22no—
22#469×C127—22no—
23#466×C127—22no—
24C2×#108×C127C2211yescharacteristic
25#427×C127C2211yescharacteristic
26#418×C127—21no—
27#413×C127—21no—
28#361×C127—22no—
29#360×C127—22no—
30#350×C127—22no—
31C2×#41×C127—21no—
32C2×#41×C127D411yescharacteristic
33C22×D4×C127—21no—
34#137×C127—22no—
35#137×C127—41no—
36AGL(1,ℤ/8)×C127—22no—
37AGL(1,ℤ/8)×C127—41no—
38#135×C127—21no—
39#135×C127—21no—
40#135×C127—21no—
41#135×C127—21no—
42#135×C127—42no—
43C2×Q16×C127D411yescharacteristic, complemented
44C2×SD16×C127—21no—
45C2×D8×C127—21no—
46C2×D8×C127—21no—
47C2×D8×C127—21no—
48C2×D8×C127—21no—
49C2×D8×C127—21no—
50C2×D8×C127D412yes—
51C2×D8×C127D411yescharacteristic, complemented
52#131×C127—21no—
53#131×C127—21no—
54#131×C127—21no—
55#131×C127—21no—
56C2×M16×C127—21no—
57C2×M16×C127—21no—
58C2×M16×C127D411yescharacteristic
59C22×C8×C127—21no—
60C22×C8×C127C2311yescharacteristic
61#127×C127—41no—
62#124×C127—41no—
63#121×C127—24no—
64#120×C127—42no—
65#117×C127—21no—
66SD32×C127—24no—
67D16×C127—24no—
68M32×C127—21no—
69M32×C127—21no—
70M32×C127—21no—
71M32×C127D412yescomplemented
72C2×C16×C127—21no—
73C2×C16×C127—21no—
74#108×C127—21no—
75#108×C127D412yescomplemented
76#107×C127—21no—
77#106×C127D412yes—
78#102×C127—24no—
79#101×C127—22no—
80#100×C127—22no—
81C24×C127—41no—
82#41×C127—21no—
83#41×C127—21no—
84#41×C127—21no—
85#41×C127—21no—
86#41×C127—41no—
87#41×C127—41no—
88#41×C127—41no—
89#41×C127—41no—
90C2×Q8×C127—21no—
91C2×Q8×C127D811yescharacteristic
92C2×D4×C127—21no—
93C2×D4×C127—21no—
94C2×D4×C127—22no—
95C2×D4×C127—41no—
96C2×D4×C127—44no—
97C2×D4×C127—41no—
98C2×D4×C127—41no—
99C2×D4×C127—41no—
100C2×D4×C127—41no—
101C2×D4×C127—41no—
102C2×D4×C127D811yescharacteristic
103C22×C4×C127—21no—
104C22×C4×C127—41no—
105C22×C4×C127C2×D411yescharacteristic
106Q16×C127—21no—
107Q16×C127—21no—
108Q16×C127—42no—
109SD16×C127—42no—
110SD16×C127—42no—
111SD16×C127—41no—
112SD16×C127—41no—
113D8×C127—21no—
114D8×C127—22no—
115D8×C127—22no—
116D8×C127—21no—
117D8×C127—42no—
118D8×C127—41no—
119D8×C127—41no—
120M16×C127—21no—
121M16×C127—22no—
122M16×C127—21no—
123M16×C127—41no—
124M16×C127—41no—
125M16×C127—41no—
126C2×C8×C127—21no—
127C2×C8×C127—41no—
128C2×C8×C127—41no—
129C2×C8×C127—41no—
130C2×C8×C127C2×D411yescharacteristic
131C2×C8×C127C2×D411yescharacteristic
132C2×C8×C127C2×D411yescharacteristic
133C2×C8×C127C2×D411yescharacteristic
134C2×C8×C127C2×D411yescharacteristic
135C2×C8×C127#4111yescharacteristic
136C4⋊C4×C127—22no—
137C22⋊C4×C127—44no—
138C22⋊C4×C127—41no—
139C42×C127—41no—
140C16×C127—22no—
141C16×C127—41no—
142C23×C127—21no—
143C23×C127—42no—
144C23×C127—41no—
145C23×C127—81no—
146C23×C127—81no—
147C23×C127—162no—
148C23×C127AGL(1,ℤ/8)11yescharacteristic
149Q8×C127—21no—
150Q8×C127—21no—
151Q8×C127—41no—
152Q8×C127—41no—
153D4×C127—21no—
154D4×C127—21no—
155D4×C127—41no—
156D4×C127—41no—
157D4×C127—42no—
158D4×C127—41no—
159D4×C127—41no—
160D4×C127—42no—
161D4×C127—81no—
162D4×C127—81no—
163D4×C127—81no—
164D4×C127—81no—
165D4×C127—164no—
166C2×C4×C127—21no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—42no—
170C2×C4×C127—41no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127#12011yescharacteristic
174C2×C4×C127#12011yescharacteristic
175C2×C4×C127#12111yescharacteristic
176C2×C4×C127C2×D811yescharacteristic
177C2×C4×C127#13511yescharacteristic
178C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
179C8×C127—41no—
180C8×C127—42no—
181C8×C127#12011yescharacteristic
182C8×C127#12111yescharacteristic
183C8×C127#12111yescharacteristic
184C8×C127#12711yescharacteristic
185C22×C127—41no—
186C22×C127—42no—
187C22×C127—41no—
188C22×C127—84no—
189C22×C127—81no—
190C22×C127—82no—
191C22×C127—161no—
192C22×C127—162no—
193C22×C127—162no—
194C22×C127#44711yescharacteristic
195C22×C127#44911yescharacteristic
196C22×C127#46911yescharacteristic
197C4×C127—41no—
198C4×C127—82no—
199C4×C127—81no—
200C4×C127#39211yescharacteristic
201C4×C127#44711yescharacteristic
202C4×C127#44911yescharacteristic
203C4×C127#46611yescharacteristic
204#13310C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—21no—
206C2×C127—21no—
207C2×C127—21no—
208C2×C127—81no—
209C2×C127—162no—
210C2×C127—161no—
211C2×C127#199911yescharacteristic
212C2×#509C2×C12711yescharacteristic, complemented
213#3067C2×C12711yescharacteristic, complemented
214#3058C2×C12711yescharacteristic, complemented
215C2×#361C2×C12711yescharacteristic, complemented
216#2145C2×C12711yescharacteristic, complemented
217#2117C2×C12711yescharacteristic, complemented
218#1389C2×C12711yescharacteristic, complemented
219C127#1331011yescharacteristic, direct product factor, Sylow
220#575—21no—
221C2×#135C22×C12711yescharacteristic
222C22×D8C22×C12711yescharacteristic
223C2×#131C22×C12711yescharacteristic
224#535—21no—
225#509—22no—
226#509—22no—
227C2×SD32—21no—
228C2×D16—21no—
229C2×M32C22×C12711yescharacteristic
230C2×M32C22×C12711yescharacteristic
231#473—21no—
232#472—21no—
233#471—22no—
234#469—22no—
235#466—22no—
236C2×#108C22×C12711yescharacteristic
237#427C22×C12711yescharacteristic
238#418—21no—
239#413—21no—
240#361—22no—
241#360—22no—
242#350—22no—
243C2×#41—21no—
244C2×#41D4×C12711yescharacteristic
245C22×D4—21no—
246#137—22no—
247#137—41no—
248AGL(1,ℤ/8)—22no—
249AGL(1,ℤ/8)—41no—
250#135—21no—
251#135—21no—
252#135—21no—
253#135—21no—
254#135—42no—
255C2×Q16D4×C12711yescharacteristic, complemented
256C2×SD16—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8D4×C12712yes—
263C2×D8D4×C12711yescharacteristic, complemented
264#131—21no—
265#131—21no—
266#131—21no—
267#131—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16D4×C12711yescharacteristic
271C22×C8—21no—
272C22×C8C23×C12711yescharacteristic
273#127—41no—
274#124—41no—
275#121—24no—
276#120—42no—
277#117—21no—
278SD32—24no—
279D16—24no—
280M32—21no—
281M32—21no—
282M32—21no—
283M32D4×C12712yescomplemented
284C2×C16—21no—
285C2×C16—21no—
286#108—21no—
287#108D4×C12712yescomplemented
288#107—21no—
289#106D4×C12712yes—
290#102—24no—
291#101—22no—
292#100—22no—
293C24—41no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302C2×Q8—21no—
303C2×Q8D8×C12711yescharacteristic
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—44no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4D8×C12711yescharacteristic
315C22×C4—21no—
316C22×C4—41no—
317C22×C4C2×D4×C12711yescharacteristic
318Q16—21no—
319Q16—21no—
320Q16—42no—
321SD16—42no—
322SD16—42no—
323SD16—41no—
324SD16—41no—
325D8—21no—
326D8—22no—
327D8—22no—
328D8—21no—
329D8—42no—
330D8—41no—
331D8—41no—
332M16—21no—
333M16—22no—
334M16—21no—
335M16—41no—
336M16—41no—
337M16—41no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8C2×D4×C12711yescharacteristic
343C2×C8C2×D4×C12711yescharacteristic
344C2×C8C2×D4×C12711yescharacteristic
345C2×C8C2×D4×C12711yescharacteristic
346C2×C8C2×D4×C12711yescharacteristic
347C2×C8#41×C12711yescharacteristic
348C4⋊C4—22no—
349C22⋊C4—44no—
350C22⋊C4—41no—
351C42—41no—
352C16—22no—
353C16—41no—
354C23—21no—
355C23—42no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23—162no—
360C23AGL(1,ℤ/8)×C12711yescharacteristic
361Q8—21no—
362Q8—21no—
363Q8—41no—
364Q8—41no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—164no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4#120×C12711yescharacteristic
386C2×C4#120×C12711yescharacteristic
387C2×C4#121×C12711yescharacteristic
388C2×C4C2×D8×C12711yescharacteristic
389C2×C4#135×C12711yescharacteristic
390C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
391C8—41no—
392C8—42no—
393C8#120×C12711yescharacteristic
394C8#121×C12711yescharacteristic
395C8#121×C12711yescharacteristic
396C8#127×C12711yescharacteristic
397C22—41no—
398C22—42no—
399C22—41no—
400C22—84no—
401C22—81no—
402C22—82no—
403C22—161no—
404C22—162no—
405C22—162no—
406C22#447×C12711yescharacteristic
407C22#449×C12711yescharacteristic
408C22#469×C12711yescharacteristic
409C4—41no—
410C4—82no—
411C4—81no—
412C4#392×C12711yescharacteristic
413C4#447×C12711yescharacteristic
414C4#449×C12711yescharacteristic
415C4#466×C12711yescharacteristic
416C2—21no—
417C2—21no—
418C2—21no—
419C2—81no—
420C2—162no—
421C2—161no—
422C2C127×#199911yescharacteristic
subgroupG/H
center, socleC2×C127#1999
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×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. C2×#509×C127C2semidirect
2. C127×#3067C2semidirect
3. C127×#3058C2semidirect
4. C2×#361×C127C2semidirect
5. C127×#2145C2semidirect
6. C127×#2117C2semidirect
7. C127×#1389C2semidirect
43. C2×Q16×C127D4semidirect
51. C2×D8×C127D4semidirect
71. M32×C127D4semidirect
75. #108×C127D4semidirect
204. #13310C127direct (N × H)
212. C2×#509C2×C127semidirect
213. #3067C2×C127semidirect
214. #3058C2×C127semidirect
215. C2×#361C2×C127semidirect
216. #2145C2×C127semidirect
217. #2117C2×C127semidirect
218. #1389C2×C127semidirect
219. C127#13310direct (N × H)
255. C2×Q16D4×C127semidirect
263. C2×D8D4×C127semidirect
283. M32D4×C127semidirect
287. #108D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C127×#30672
C127×#30582
C2×#361×C1272
C127×#21452
C127×#21172
C127×#13892
#13310127