Finite Group Databasebeta

← C127×#13334 #44577007

Subgroups — C127×#13334 #44577007

Order 32512.

568 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3414C211yesmaximal, characteristic, complemented
2C2×#509×C127C211yesmaximal, characteristic, complemented
3C127×#3155C211yesmaximal, characteristic, complemented
4C127×#2145C211yesmaximal, characteristic, complemented
5C127×#2140C211yesmaximal, characteristic, complemented
6C127×#1976C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C2×#135×C127C2211yescharacteristic
11C22×D8×C127C2211yescharacteristic
12#535×C127—21no—
13#510×C127—21no—
14#510×C127—21no—
15#509×C127—22no—
16#509×C127—21no—
17#509×C127—21no—
18#509×C127—22no—
19#508×C127—22no—
20C2×SD32×C127—21no—
21C2×D16×C127—21no—
22C2×M32×C127C2211yescharacteristic
23C2×M32×C127C2211yescharacteristic
24#496×C127—22no—
25#495×C127—21no—
26#493×C127—21no—
27#427×C127C2211yescharacteristic
28#421×C127—21no—
29#410×C127—21no—
30#405×C127C2211yescharacteristic
31#360×C127—22no—
32#357×C127—22no—
33C2×#41×C127—21no—
34C2×#41×C127—21no—
35C22×D4×C127—21no—
36AGL(1,ℤ/8)×C127—42no—
37AGL(1,ℤ/8)×C127—42no—
38#135×C127—21no—
39#135×C127—21no—
40#135×C127—21no—
41#135×C127—21no—
42#135×C127—21no—
43#135×C127—21no—
44#135×C127—21no—
45#135×C127—21no—
46C2×Q16×C127D411yescharacteristic
47C2×Q16×C127D411yescharacteristic, complemented
48C2×SD16×C127—22no—
49C2×SD16×C127—21no—
50C2×SD16×C127—21no—
51C2×D8×C127—22no—
52C2×D8×C127—21no—
53C2×D8×C127—21no—
54C2×D8×C127—21no—
55C2×D8×C127—21no—
56C2×D8×C127—21no—
57C2×D8×C127D412yes—
58C2×D8×C127D411yescharacteristic
59C2×D8×C127D411yescharacteristic, complemented
60C2×M16×C127D411yescharacteristic
61C22×C8×C127C2311yescharacteristic
62#127×C127—22no—
63#124×C127—22no—
64#121×C127—42no—
65#120×C127—42no—
66#117×C127—21no—
67#117×C127D411yescharacteristic
68Q32×C127—22no—
69SD32×C127—24no—
70SD32×C127—22no—
71SD32×C127—22no—
72D16×C127—24no—
73D16×C127—22no—
74M32×C127—21no—
75M32×C127—21no—
76M32×C127—21no—
77M32×C127D412yescomplemented
78C2×C16×C127—21no—
79C2×C16×C127D412yescomplemented
80#107×C127—21no—
81#106×C127—21no—
82#104×C127—42no—
83#99×C127—42no—
84#97×C127—21no—
85C4×C8×C127—21no—
86C24×C127—41no—
87#41×C127—41no—
88#41×C127—41no—
89#41×C127—41no—
90#41×C127—41no—
91#41×C127—41no—
92#41×C127—41no—
93#41×C127—41no—
94#41×C127—41no—
95C2×Q8×C127—21no—
96C2×Q8×C127—21no—
97C2×D4×C127—22no—
98C2×D4×C127—21no—
99C2×D4×C127—21no—
100C2×D4×C127—44no—
101C2×D4×C127—41no—
102C2×D4×C127—41no—
103C2×D4×C127—41no—
104C2×D4×C127—41no—
105C2×D4×C127—41no—
106C2×D4×C127—41no—
107C2×D4×C127—41no—
108C22×C4×C127—41no—
109C22×C4×C127—41no—
110C22×C4×C127C2×D411yescharacteristic
111Q16×C127—21no—
112Q16×C127—21no—
113Q16×C127—21no—
114Q16×C127—21no—
115SD16×C127—44no—
116SD16×C127—41no—
117SD16×C127—41no—
118SD16×C127—41no—
119SD16×C127—41no—
120D8×C127—21no—
121D8×C127—22no—
122D8×C127—21no—
123D8×C127—21no—
124D8×C127—22no—
125D8×C127—21no—
126D8×C127—44no—
127D8×C127—41no—
128D8×C127—41no—
129M16×C127—21no—
130M16×C127D812yes—
131C2×C8×C127—21no—
132C2×C8×C127C2×D411yescharacteristic
133C2×C8×C127C2×D411yescharacteristic
134C2×C8×C127C2×D411yescharacteristic
135C2×C8×C127C2×D411yescharacteristic
136C2×C8×C127C2×D411yescharacteristic
137C2×C8×C127#4111yescharacteristic
138C4⋊C4×C127—21no—
139C4⋊C4×C127—41no—
140C22⋊C4×C127—44no—
141C22⋊C4×C127—41no—
142C22⋊C4×C127D812yes—
143C42×C127—21no—
144C42×C127—41no—
145C16×C127—22no—
146C16×C127—22no—
147C23×C127—42no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—81no—
151C23×C127—81no—
152C23×C127—162no—
153C23×C127C2×D811yescharacteristic
154Q8×C127—41no—
155Q8×C127—41no—
156Q8×C127—41no—
157Q8×C127—41no—
158D4×C127—42no—
159D4×C127—41no—
160D4×C127—41no—
161D4×C127—41no—
162D4×C127—42no—
163D4×C127—41no—
164D4×C127—81no—
165D4×C127—81no—
166D4×C127—81no—
167D4×C127—81no—
168D4×C127—81no—
169D4×C127—81no—
170D4×C127—164no—
171C2×C4×C127—22no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—81no—
175C2×C4×C127—81no—
176C2×C4×C127—81no—
177C2×C4×C127—81no—
178C2×C4×C127—81no—
179C2×C4×C127#12011yescharacteristic
180C2×C4×C127#12111yescharacteristic
181C2×C4×C127#12711yescharacteristic
182C2×C4×C127C2×D811yescharacteristic
183C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
185C8×C127—22no—
186C8×C127#12011yescharacteristic
187C8×C127#12011yescharacteristic
188C8×C127#12111yescharacteristic
189C8×C127#12111yescharacteristic
190C22×C127—41no—
191C22×C127—82no—
192C22×C127—84no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—82no—
196C22×C127—161no—
197C22×C127—162no—
198C22×C127—162no—
199C22×C127#44711yescharacteristic
200C22×C127#45911yescharacteristic
201C22×C127#49311yescharacteristic
202C4×C127—42no—
203C4×C127—81no—
204C4×C127—81no—
205C4×C127—161no—
206C4×C127#39211yescharacteristic
207C4×C127#44711yescharacteristic
208C4×C127#45911yescharacteristic
209C4×C127#49611yescharacteristic
210#13334C12711yesmaximal, characteristic, direct product factor, Sylow
211C2×C127—21no—
212C2×C127—21no—
213C2×C127—21no—
214C2×C127—161no—
215C2×C127—162no—
216C2×C127—161no—
217C2×C127#201111yescharacteristic
218#3414C2×C12711yescharacteristic, complemented
219C2×#509C2×C12711yescharacteristic, complemented
220#3155C2×C12711yescharacteristic, complemented
221#2145C2×C12711yescharacteristic, complemented
222#2140C2×C12711yescharacteristic, complemented
223#1976C2×C12711yescharacteristic, complemented
224#1378C2×C12711yescharacteristic, complemented
225C127#1333411yescharacteristic, direct product factor, Sylow
226C2×AGL(1,ℤ/8)—21no—
227C2×#135C22×C12711yescharacteristic
228C2×#135C22×C12711yescharacteristic
229C22×D8C22×C12711yescharacteristic
230#535—21no—
231#510—21no—
232#510—21no—
233#509—22no—
234#509—21no—
235#509—21no—
236#509—22no—
237#508—22no—
238C2×SD32—21no—
239C2×D16—21no—
240C2×M32C22×C12711yescharacteristic
241C2×M32C22×C12711yescharacteristic
242#496—22no—
243#495—21no—
244#493—21no—
245#427C22×C12711yescharacteristic
246#421—21no—
247#410—21no—
248#405C22×C12711yescharacteristic
249#360—22no—
250#357—22no—
251C2×#41—21no—
252C2×#41—21no—
253C22×D4—21no—
254AGL(1,ℤ/8)—42no—
255AGL(1,ℤ/8)—42no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—21no—
264C2×Q16D4×C12711yescharacteristic
265C2×Q16D4×C12711yescharacteristic, complemented
266C2×SD16—22no—
267C2×SD16—21no—
268C2×SD16—21no—
269C2×D8—22no—
270C2×D8—21no—
271C2×D8—21no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8D4×C12712yes—
276C2×D8D4×C12711yescharacteristic
277C2×D8D4×C12711yescharacteristic, complemented
278C2×M16D4×C12711yescharacteristic
279C22×C8C23×C12711yescharacteristic
280#127—22no—
281#124—22no—
282#121—42no—
283#120—42no—
284#117—21no—
285#117D4×C12711yescharacteristic
286Q32—22no—
287SD32—24no—
288SD32—22no—
289SD32—22no—
290D16—24no—
291D16—22no—
292M32—21no—
293M32—21no—
294M32—21no—
295M32D4×C12712yescomplemented
296C2×C16—21no—
297C2×C16D4×C12712yescomplemented
298#107—21no—
299#106—21no—
300#104—42no—
301#99—42no—
302#97—21no—
303C4×C8—21no—
304C24—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—41no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—44no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4C2×D4×C12711yescharacteristic
329Q16—21no—
330Q16—21no—
331Q16—21no—
332Q16—21no—
333SD16—44no—
334SD16—41no—
335SD16—41no—
336SD16—41no—
337SD16—41no—
338D8—21no—
339D8—22no—
340D8—21no—
341D8—21no—
342D8—22no—
343D8—21no—
344D8—44no—
345D8—41no—
346D8—41no—
347M16—21no—
348M16D8×C12712yes—
349C2×C8—21no—
350C2×C8C2×D4×C12711yescharacteristic
351C2×C8C2×D4×C12711yescharacteristic
352C2×C8C2×D4×C12711yescharacteristic
353C2×C8C2×D4×C12711yescharacteristic
354C2×C8C2×D4×C12711yescharacteristic
355C2×C8#41×C12711yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—41no—
358C22⋊C4—44no—
359C22⋊C4—41no—
360C22⋊C4D8×C12712yes—
361C42—21no—
362C42—41no—
363C16—22no—
364C16—22no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—81no—
369C23—81no—
370C23—162no—
371C23C2×D8×C12711yescharacteristic
372Q8—41no—
373Q8—41no—
374Q8—41no—
375Q8—41no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—42no—
381D4—41no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—164no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4#120×C12711yescharacteristic
398C2×C4#121×C12711yescharacteristic
399C2×C4#127×C12711yescharacteristic
400C2×C4C2×D8×C12711yescharacteristic
401C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
402C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
403C8—22no—
404C8#120×C12711yescharacteristic
405C8#120×C12711yescharacteristic
406C8#121×C12711yescharacteristic
407C8#121×C12711yescharacteristic
408C22—41no—
409C22—82no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22#447×C12711yescharacteristic
418C22#459×C12711yescharacteristic
419C22#493×C12711yescharacteristic
420C4—42no—
421C4—81no—
422C4—81no—
423C4—161no—
424C4#392×C12711yescharacteristic
425C4#447×C12711yescharacteristic
426C4#459×C12711yescharacteristic
427C4#496×C12711yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—161no—
434C2C127×#201111yescharacteristic
subgroupG/H
center, socleC2×C127#2011
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×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
1. C127×#3414C2semidirect
2. C2×#509×C127C2semidirect
3. C127×#3155C2semidirect
4. C127×#2145C2semidirect
5. C127×#2140C2semidirect
6. C127×#1976C2semidirect
7. C127×#1378C2semidirect
47. C2×Q16×C127D4semidirect
59. C2×D8×C127D4semidirect
77. M32×C127D4semidirect
79. C2×C16×C127D4semidirect
210. #13334C127direct (N × H)
218. #3414C2×C127semidirect
219. C2×#509C2×C127semidirect
220. #3155C2×C127semidirect
221. #2145C2×C127semidirect
222. #2140C2×C127semidirect
223. #1976C2×C127semidirect
224. #1378C2×C127semidirect
225. C127#13334direct (N × H)
265. C2×Q16D4×C127semidirect
277. C2×D8D4×C127semidirect
295. M32D4×C127semidirect
297. C2×C16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34142
C2×#509×C1272
C127×#31552
C127×#21452
C127×#21402
C127×#19762
C127×#13782
#13334127