Finite Group Databasebeta

← C127×#13335 #44577008

Subgroups — C127×#13335 #44577008

Order 32512.

536 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
1C127×#3414C211yesmaximal, characteristic
2C2×#510×C127C211yesmaximal, characteristic, complemented
3C127×#3156C211yesmaximal, characteristic, complemented
4C127×#2145C211yesmaximal, characteristic, complemented
5C127×#2141C211yesmaximal, characteristic, complemented
6C127×#1976C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C2×#135×C127C2211yescharacteristic
11C22×Q16×C127C2211yescharacteristic
12#536×C127—21no—
13#510×C127—22no—
14#510×C127—21no—
15#510×C127—21no—
16#510×C127—22no—
17#509×C127—21no—
18#509×C127—21no—
19#508×C127—22no—
20C2×Q32×C127—21no—
21C2×SD32×C127—21no—
22C2×M32×C127C2211yescharacteristic
23C2×M32×C127C2211yescharacteristic
24#497×C127—22no—
25#495×C127—21no—
26#494×C127—21no—
27#427×C127C2211yescharacteristic
28#421×C127—21no—
29#410×C127—21no—
30#405×C127C2211yescharacteristic
31#360×C127—22no—
32#358×C127—22no—
33C2×#41×C127—21no—
34C2×#41×C127—21no—
35C22×Q8×C127—21no—
36#137×C127—42no—
37#137×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×C127—22no—
47C2×Q16×C127—21no—
48C2×Q16×C127—21no—
49C2×Q16×C127—21no—
50C2×Q16×C127—21no—
51C2×Q16×C127—21no—
52C2×Q16×C127D412yes—
53C2×Q16×C127D411yescharacteristic
54C2×Q16×C127D411yescharacteristic
55C2×SD16×C127—22no—
56C2×SD16×C127—21no—
57C2×SD16×C127—21no—
58C2×D8×C127D411yescharacteristic
59C2×D8×C127D411yescharacteristic
60C2×M16×C127D411yescharacteristic
61C22×C8×C127C2311yescharacteristic
62C4⋊Q8×C127—22no—
63#124×C127—22no—
64#123×C127—42no—
65C22⋊Q8×C127—42no—
66#117×C127—21no—
67#117×C127D411yescharacteristic
68Q32×C127—24no—
69Q32×C127—22no—
70SD32×C127—24no—
71SD32×C127—22no—
72SD32×C127—22no—
73D16×C127—22no—
74M32×C127—21no—
75M32×C127—21no—
76M32×C127—21no—
77M32×C127D412yes—
78C2×C16×C127—21no—
79C2×C16×C127D412yes—
80#107×C127—21no—
81#106×C127—21no—
82#104×C127—42no—
83#99×C127—42no—
84#97×C127—21no—
85C4×C8×C127—21no—
86#41×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—
94C2×Q8×C127—22no—
95C2×Q8×C127—21no—
96C2×Q8×C127—21no—
97C2×Q8×C127—41no—
98C2×Q8×C127—41no—
99C2×Q8×C127—41no—
100C2×Q8×C127—41no—
101C2×Q8×C127—41no—
102C2×D4×C127—21no—
103C2×D4×C127—21no—
104C2×D4×C127—41no—
105C2×D4×C127—41no—
106C22×C4×C127—41no—
107C22×C4×C127—41no—
108C22×C4×C127—41no—
109C22×C4×C127C2×D411yescharacteristic
110Q16×C127—22no—
111Q16×C127—21no—
112Q16×C127—21no—
113Q16×C127—21no—
114Q16×C127—22no—
115Q16×C127—21no—
116Q16×C127—44no—
117Q16×C127—41no—
118Q16×C127—41no—
119SD16×C127—44no—
120SD16×C127—41no—
121SD16×C127—41no—
122SD16×C127—41no—
123SD16×C127—41no—
124D8×C127—21no—
125D8×C127—21no—
126D8×C127—21no—
127D8×C127—21no—
128M16×C127—21no—
129M16×C127D812yes—
130C2×C8×C127—21no—
131C2×C8×C127C2×D411yescharacteristic
132C2×C8×C127C2×D411yescharacteristic
133C2×C8×C127C2×D411yescharacteristic
134C2×C8×C127C2×D411yescharacteristic
135C2×C8×C127C2×D411yescharacteristic
136C2×C8×C127#4111yescharacteristic
137C4⋊C4×C127—21no—
138C4⋊C4×C127—44no—
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—41no—
148C23×C127—41no—
149C23×C127C2×D811yescharacteristic
150Q8×C127—41no—
151Q8×C127—41no—
152Q8×C127—42no—
153Q8×C127—42no—
154Q8×C127—41no—
155Q8×C127—41no—
156Q8×C127—81no—
157Q8×C127—81no—
158D4×C127—41no—
159D4×C127—41no—
160D4×C127—41no—
161D4×C127—41no—
162D4×C127—81no—
163D4×C127—81no—
164D4×C127—81no—
165D4×C127—81no—
166C2×C4×C127—22no—
167C2×C4×C127—42no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—81no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127—81no—
174C2×C4×C127—81no—
175C2×C4×C127—81no—
176C2×C4×C127—81no—
177C2×C4×C127#12011yescharacteristic
178C2×C4×C127#12111yescharacteristic
179C2×C4×C127#12711yescharacteristic
180C2×C4×C127C2×D811yescharacteristic
181C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
183C8×C127—22no—
184C8×C127#12011yescharacteristic
185C8×C127#12011yescharacteristic
186C8×C127#12111yescharacteristic
187C8×C127#12111yescharacteristic
188C22×C127—41no—
189C22×C127—82no—
190C22×C127—81no—
191C22×C127—81no—
192C22×C127—161no—
193C22×C127#44711yescharacteristic
194C22×C127#45911yescharacteristic
195C22×C127#49311yescharacteristic
196C4×C127—42no—
197C4×C127—81no—
198C4×C127—81no—
199C4×C127—82no—
200C4×C127—161no—
201C4×C127#39211yescharacteristic
202C4×C127#44711yescharacteristic
203C4×C127#45911yescharacteristic
204C4×C127#49611yescharacteristic
205#13335C12711yesmaximal, characteristic, direct product factor, Sylow
206C2×C127—21no—
207C2×C127—21no—
208C2×C127—21no—
209C2×C127—161no—
210C2×C127—161no—
211C2×C127#201111yescharacteristic
212#3414C2×C12711yescharacteristic
213C2×#510C2×C12711yescharacteristic, complemented
214#3156C2×C12711yescharacteristic, complemented
215#2145C2×C12711yescharacteristic, complemented
216#2141C2×C12711yescharacteristic, complemented
217#1976C2×C12711yescharacteristic, complemented
218#1378C2×C12711yescharacteristic, complemented
219C127#1333511yescharacteristic, direct product factor, Sylow
220C2×#137—21no—
221C2×#135C22×C12711yescharacteristic
222C2×#135C22×C12711yescharacteristic
223C22×Q16C22×C12711yescharacteristic
224#536—21no—
225#510—22no—
226#510—21no—
227#510—21no—
228#510—22no—
229#509—21no—
230#509—21no—
231#508—22no—
232C2×Q32—21no—
233C2×SD32—21no—
234C2×M32C22×C12711yescharacteristic
235C2×M32C22×C12711yescharacteristic
236#497—22no—
237#495—21no—
238#494—21no—
239#427C22×C12711yescharacteristic
240#421—21no—
241#410—21no—
242#405C22×C12711yescharacteristic
243#360—22no—
244#358—22no—
245C2×#41—21no—
246C2×#41—21no—
247C22×Q8—21no—
248#137—42no—
249#137—42no—
250#135—21no—
251#135—21no—
252#135—21no—
253#135—21no—
254#135—21no—
255#135—21no—
256#135—21no—
257#135—21no—
258C2×Q16—22no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—21no—
263C2×Q16—21no—
264C2×Q16D4×C12712yes—
265C2×Q16D4×C12711yescharacteristic
266C2×Q16D4×C12711yescharacteristic
267C2×SD16—22no—
268C2×SD16—21no—
269C2×SD16—21no—
270C2×D8D4×C12711yescharacteristic
271C2×D8D4×C12711yescharacteristic
272C2×M16D4×C12711yescharacteristic
273C22×C8C23×C12711yescharacteristic
274C4⋊Q8—22no—
275#124—22no—
276#123—42no—
277C22⋊Q8—42no—
278#117—21no—
279#117D4×C12711yescharacteristic
280Q32—24no—
281Q32—22no—
282SD32—24no—
283SD32—22no—
284SD32—22no—
285D16—22no—
286M32—21no—
287M32—21no—
288M32—21no—
289M32D4×C12712yes—
290C2×C16—21no—
291C2×C16D4×C12712yes—
292#107—21no—
293#106—21no—
294#104—42no—
295#99—42no—
296#97—21no—
297C4×C8—21no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—41no—
306C2×Q8—22no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4C2×D4×C12711yescharacteristic
322Q16—22no—
323Q16—21no—
324Q16—21no—
325Q16—21no—
326Q16—22no—
327Q16—21no—
328Q16—44no—
329Q16—41no—
330Q16—41no—
331SD16—44no—
332SD16—41no—
333SD16—41no—
334SD16—41no—
335SD16—41no—
336D8—21no—
337D8—21no—
338D8—21no—
339D8—21no—
340M16—21no—
341M16D8×C12712yes—
342C2×C8—21no—
343C2×C8C2×D4×C12711yescharacteristic
344C2×C8C2×D4×C12711yescharacteristic
345C2×C8C2×D4×C12711yescharacteristic
346C2×C8C2×D4×C12711yescharacteristic
347C2×C8C2×D4×C12711yescharacteristic
348C2×C8#41×C12711yescharacteristic
349C4⋊C4—21no—
350C4⋊C4—44no—
351C4⋊C4—41no—
352C22⋊C4—44no—
353C22⋊C4—41no—
354C22⋊C4D8×C12712yes—
355C42—21no—
356C42—41no—
357C16—22no—
358C16—22no—
359C23—41no—
360C23—41no—
361C23C2×D8×C12711yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—42no—
365Q8—42no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369Q8—81no—
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4#120×C12711yescharacteristic
390C2×C4#121×C12711yescharacteristic
391C2×C4#127×C12711yescharacteristic
392C2×C4C2×D8×C12711yescharacteristic
393C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
394C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
395C8—22no—
396C8#120×C12711yescharacteristic
397C8#120×C12711yescharacteristic
398C8#121×C12711yescharacteristic
399C8#121×C12711yescharacteristic
400C22—41no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22—161no—
405C22#447×C12711yescharacteristic
406C22#459×C12711yescharacteristic
407C22#493×C12711yescharacteristic
408C4—42no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—161no—
413C4#392×C12711yescharacteristic
414C4#447×C12711yescharacteristic
415C4#459×C12711yescharacteristic
416C4#496×C12711yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—161no—
421C2—161no—
422C2C127×#201111yescharacteristic
subgroupG/H
center, socleC2×C127#2011
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3414C2
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
2. C2×#510×C127C2semidirect
3. C127×#3156C2semidirect
4. C127×#2145C2semidirect
5. C127×#2141C2semidirect
6. C127×#1976C2semidirect
7. C127×#1378C2semidirect
205. #13335C127direct (N × H)
213. C2×#510C2×C127semidirect
214. #3156C2×C127semidirect
215. #2145C2×C127semidirect
216. #2141C2×C127semidirect
217. #1976C2×C127semidirect
218. #1378C2×C127semidirect
219. C127#13335direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34142
C2×#510×C1272
C127×#31562
C127×#21452
C127×#21412
C127×#19762
C127×#13782
#13335127