Finite Group Databasebeta

← C127×#13311 #44576984

Subgroups — C127×#13311 #44576984

Order 32512.

520 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic, complemented
2C127×#3067C211yesmaximal, characteristic
3C127×#3059C211yesmaximal, characteristic, complemented
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C127×#2145C211yesmaximal, characteristic, complemented
6C127×#2117C211yesmaximal, characteristic, complemented
7C127×#1389C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C22×Q16×C127C2211yescharacteristic
11C2×#131×C127C2211yescharacteristic
12#536×C127—21no—
13#510×C127—22no—
14#510×C127—22no—
15C2×Q32×C127—21no—
16C2×SD32×C127—21no—
17C2×M32×C127C2211yescharacteristic
18C2×M32×C127C2211yescharacteristic
19#473×C127—21no—
20#472×C127—21no—
21#471×C127—22no—
22#470×C127—22no—
23#467×C127—22no—
24C2×#108×C127C2211yescharacteristic
25#427×C127C2211yescharacteristic
26#419×C127—21no—
27#413×C127—21no—
28#362×C127—22no—
29#360×C127—22no—
30#350×C127—22no—
31C2×#41×C127—21no—
32C2×#41×C127D411yescharacteristic
33C22×Q8×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×C127—21no—
44C2×Q16×C127—21no—
45C2×Q16×C127—21no—
46C2×Q16×C127—21no—
47C2×Q16×C127—21no—
48C2×Q16×C127D411yescharacteristic
49C2×Q16×C127D412yes—
50C2×SD16×C127—21no—
51C2×D8×C127D411yescharacteristic
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
61C4⋊Q8×C127—41no—
62#124×C127—41no—
63#123×C127—42no—
64C22⋊Q8×C127—24no—
65#117×C127—21no—
66Q32×C127—24no—
67SD32×C127—24no—
68M32×C127—21no—
69M32×C127—21no—
70M32×C127—21no—
71M32×C127D412yes—
72C2×C16×C127—21no—
73C2×C16×C127—21no—
74#108×C127—21no—
75#108×C127D412yes—
76#107×C127—21no—
77#106×C127D412yes—
78#103×C127—24no—
79#101×C127—22no—
80#100×C127—22no—
81#41×C127—21no—
82#41×C127—21no—
83#41×C127—21no—
84#41×C127—21no—
85#41×C127—41no—
86#41×C127—41no—
87#41×C127—41no—
88#41×C127—41no—
89C2×Q8×C127—21no—
90C2×Q8×C127—22no—
91C2×Q8×C127—41no—
92C2×Q8×C127—41no—
93C2×Q8×C127—41no—
94C2×Q8×C127—41no—
95C2×Q8×C127—41no—
96C2×Q8×C127D811yescharacteristic
97C2×D4×C127—21no—
98C2×D4×C127—21no—
99C2×D4×C127—41no—
100C2×D4×C127D811yescharacteristic
101C22×C4×C127—21no—
102C22×C4×C127—41no—
103C22×C4×C127—41no—
104C22×C4×C127C2×D411yescharacteristic
105Q16×C127—22no—
106Q16×C127—21no—
107Q16×C127—22no—
108Q16×C127—21no—
109Q16×C127—42no—
110Q16×C127—41no—
111Q16×C127—41no—
112SD16×C127—42no—
113SD16×C127—42no—
114SD16×C127—41no—
115SD16×C127—41no—
116D8×C127—21no—
117D8×C127—21no—
118D8×C127—42no—
119M16×C127—21no—
120M16×C127—22no—
121M16×C127—21no—
122M16×C127—41no—
123M16×C127—41no—
124M16×C127—41no—
125C2×C8×C127—21no—
126C2×C8×C127—41no—
127C2×C8×C127—41no—
128C2×C8×C127—41no—
129C2×C8×C127C2×D411yescharacteristic
130C2×C8×C127C2×D411yescharacteristic
131C2×C8×C127C2×D411yescharacteristic
132C2×C8×C127C2×D411yescharacteristic
133C2×C8×C127C2×D411yescharacteristic
134C2×C8×C127#4111yescharacteristic
135C4⋊C4×C127—22no—
136C4⋊C4×C127—44no—
137C22⋊C4×C127—44no—
138C22⋊C4×C127—41no—
139C42×C127—41no—
140C16×C127—22no—
141C16×C127—41no—
142C23×C127—21no—
143C23×C127—41no—
144C23×C127AGL(1,ℤ/8)11yescharacteristic
145Q8×C127—21no—
146Q8×C127—21no—
147Q8×C127—41no—
148Q8×C127—42no—
149Q8×C127—41no—
150Q8×C127—42no—
151Q8×C127—81no—
152Q8×C127—81no—
153D4×C127—21no—
154D4×C127—21no—
155D4×C127—41no—
156D4×C127—41no—
157D4×C127—41no—
158D4×C127—41no—
159D4×C127—81no—
160D4×C127—81no—
161C2×C4×C127—21no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—41no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127—81no—
171C2×C4×C127#12011yescharacteristic
172C2×C4×C127#12011yescharacteristic
173C2×C4×C127#12111yescharacteristic
174C2×C4×C127C2×D811yescharacteristic
175C2×C4×C127#13511yescharacteristic
176C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
177C8×C127—41no—
178C8×C127—42no—
179C8×C127#12011yescharacteristic
180C8×C127#12111yescharacteristic
181C8×C127#12111yescharacteristic
182C8×C127#12711yescharacteristic
183C22×C127—41no—
184C22×C127—42no—
185C22×C127—41no—
186C22×C127—81no—
187C22×C127—161no—
188C22×C127#44711yescharacteristic
189C22×C127#44911yescharacteristic
190C22×C127#46911yescharacteristic
191C4×C127—41no—
192C4×C127—82no—
193C4×C127—81no—
194C4×C127—82no—
195C4×C127#39211yescharacteristic
196C4×C127#44711yescharacteristic
197C4×C127#44911yescharacteristic
198C4×C127#46611yescharacteristic
199#13311C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127—21no—
201C2×C127—21no—
202C2×C127—21no—
203C2×C127—81no—
204C2×C127—161no—
205C2×C127#199911yescharacteristic
206C2×#510C2×C12711yescharacteristic, complemented
207#3067C2×C12711yescharacteristic
208#3059C2×C12711yescharacteristic, complemented
209C2×#362C2×C12711yescharacteristic, complemented
210#2145C2×C12711yescharacteristic, complemented
211#2117C2×C12711yescharacteristic, complemented
212#1389C2×C12711yescharacteristic, complemented
213C127#1331111yescharacteristic, direct product factor, Sylow
214#575—21no—
215C2×#135C22×C12711yescharacteristic
216C22×Q16C22×C12711yescharacteristic
217C2×#131C22×C12711yescharacteristic
218#536—21no—
219#510—22no—
220#510—22no—
221C2×Q32—21no—
222C2×SD32—21no—
223C2×M32C22×C12711yescharacteristic
224C2×M32C22×C12711yescharacteristic
225#473—21no—
226#472—21no—
227#471—22no—
228#470—22no—
229#467—22no—
230C2×#108C22×C12711yescharacteristic
231#427C22×C12711yescharacteristic
232#419—21no—
233#413—21no—
234#362—22no—
235#360—22no—
236#350—22no—
237C2×#41—21no—
238C2×#41D4×C12711yescharacteristic
239C22×Q8—21no—
240#137—22no—
241#137—41no—
242AGL(1,ℤ/8)—22no—
243AGL(1,ℤ/8)—41no—
244#135—21no—
245#135—21no—
246#135—21no—
247#135—21no—
248#135—42no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16D4×C12712yes—
255C2×Q16D4×C12711yescharacteristic
256C2×SD16—21no—
257C2×D8D4×C12711yescharacteristic
258#131—21no—
259#131—21no—
260#131—21no—
261#131—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16D4×C12711yescharacteristic
265C22×C8—21no—
266C22×C8C23×C12711yescharacteristic
267C4⋊Q8—41no—
268#124—41no—
269#123—42no—
270C22⋊Q8—24no—
271#117—21no—
272Q32—24no—
273SD32—24no—
274M32—21no—
275M32—21no—
276M32—21no—
277M32D4×C12712yes—
278C2×C16—21no—
279C2×C16—21no—
280#108—21no—
281#108D4×C12712yes—
282#107—21no—
283#106D4×C12712yes—
284#103—24no—
285#101—22no—
286#100—22no—
287#41—21no—
288#41—21no—
289#41—21no—
290#41—21no—
291#41—41no—
292#41—41no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—22no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8D8×C12711yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4D8×C12711yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C12711yescharacteristic
311Q16—22no—
312Q16—21no—
313Q16—22no—
314Q16—21no—
315Q16—42no—
316Q16—41no—
317Q16—41no—
318SD16—42no—
319SD16—42no—
320SD16—41no—
321SD16—41no—
322D8—21no—
323D8—21no—
324D8—42no—
325M16—21no—
326M16—22no—
327M16—21no—
328M16—41no—
329M16—41no—
330M16—41no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8C2×D4×C12711yescharacteristic
336C2×C8C2×D4×C12711yescharacteristic
337C2×C8C2×D4×C12711yescharacteristic
338C2×C8C2×D4×C12711yescharacteristic
339C2×C8C2×D4×C12711yescharacteristic
340C2×C8#41×C12711yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—44no—
343C22⋊C4—44no—
344C22⋊C4—41no—
345C42—41no—
346C16—22no—
347C16—41no—
348C23—21no—
349C23—41no—
350C23AGL(1,ℤ/8)×C12711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—41no—
354Q8—42no—
355Q8—41no—
356Q8—42no—
357Q8—81no—
358Q8—81no—
359D4—21no—
360D4—21no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4#120×C12711yescharacteristic
378C2×C4#120×C12711yescharacteristic
379C2×C4#121×C12711yescharacteristic
380C2×C4C2×D8×C12711yescharacteristic
381C2×C4#135×C12711yescharacteristic
382C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
383C8—41no—
384C8—42no—
385C8#120×C12711yescharacteristic
386C8#121×C12711yescharacteristic
387C8#121×C12711yescharacteristic
388C8#127×C12711yescharacteristic
389C22—41no—
390C22—42no—
391C22—41no—
392C22—81no—
393C22—161no—
394C22#447×C12711yescharacteristic
395C22#449×C12711yescharacteristic
396C22#469×C12711yescharacteristic
397C4—41no—
398C4—82no—
399C4—81no—
400C4—82no—
401C4#392×C12711yescharacteristic
402C4#447×C12711yescharacteristic
403C4#449×C12711yescharacteristic
404C4#466×C12711yescharacteristic
405C2—21no—
406C2—21no—
407C2—21no—
408C2—81no—
409C2—161no—
410C2C127×#199911yescharacteristic
subgroupG/H
center, socleC2×C127#1999
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3067C2
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×#510×C127C2semidirect
3. C127×#3059C2semidirect
4. C2×#362×C127C2semidirect
5. C127×#2145C2semidirect
6. C127×#2117C2semidirect
7. C127×#1389C2semidirect
199. #13311C127direct (N × H)
206. C2×#510C2×C127semidirect
208. #3059C2×C127semidirect
209. C2×#362C2×C127semidirect
210. #2145C2×C127semidirect
211. #2117C2×C127semidirect
212. #1389C2×C127semidirect
213. C127#13311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C127×#30672
C127×#30592
C2×#362×C1272
C127×#21452
C127×#21172
C127×#13892
#13311127