Finite Group Databasebeta

← C127×#13320 #44576993

Subgroups — C127×#13320 #44576993

Order 32512.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C127C211yesmaximal, characteristic, complemented
2C2×#472×C127C211yesmaximal, characteristic
3C127×#3059C211yesmaximal, characteristic, complemented
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C127×#2140C211yesmaximal, characteristic, complemented
6C2×#350×C127C211yesmaximal, characteristic, complemented
7C127×#1382C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9C22×Q16×C127C2211yescharacteristic
10C22×D8×C127C2211yescharacteristic
11C2×#131×C127C2211yescharacteristic
12#536×C127—21no—
13C2×SD32×C127—22no—
14C2×SD32×C127—22no—
15C2×SD32×C127—22no—
16C2×M32×C127C2211yescharacteristic
17C22×C16×C127C2211yescharacteristic
18#472×C127—22no—
19#472×C127—22no—
20#470×C127—22no—
21#467×C127—22no—
22C2×#108×C127C2211yescharacteristic
23#427×C127C2211yescharacteristic
24#419×C127—21no—
25C2×#100×C127—21no—
26#362×C127—22no—
27#357×C127—22no—
28#350×C127—22no—
29C2×#41×C127D411yescharacteristic
30C22×Q8×C127—21no—
31C22×D4×C127—21no—
32AGL(1,ℤ/8)×C127—24no—
33AGL(1,ℤ/8)×C127—42no—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127D412yes—
40C2×SD16×C127—41no—
41C2×D8×C127—21no—
42C2×D8×C127—21no—
43C2×D8×C127—21no—
44C2×D8×C127—21no—
45C2×D8×C127—21no—
46C2×D8×C127—41no—
47C2×D8×C127D412yes—
48#131×C127—21no—
49#131×C127—21no—
50#131×C127—21no—
51#131×C127—21no—
52C2×M16×C127—21no—
53C2×M16×C127—21no—
54C2×M16×C127D411yescharacteristic
55C22×C8×C127—21no—
56C22×C8×C127C2311yescharacteristic
57C4⋊Q8×C127—41no—
58#124×C127—41no—
59#123×C127—42no—
60C22⋊Q8×C127—24no—
61#117×C127—21no—
62SD32×C127—28no—
63M32×C127—21no—
64M32×C127—21no—
65C2×C16×C127—21no—
66C2×C16×C127—21no—
67C2×C16×C127—21no—
68C2×C16×C127D412yes—
69#108×C127—21no—
70#108×C127D412yes—
71#107×C127D412yes—
72#106×C127—21no—
73#103×C127—24no—
74#100×C127—24no—
75C24×C127—41no—
76#41×C127—21no—
77#41×C127—21no—
78#41×C127—21no—
79#41×C127—21no—
80C2×Q8×C127—22no—
81C2×Q8×C127—41no—
82C2×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127D811yescharacteristic
87C2×D4×C127—21no—
88C2×D4×C127—22no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127D811yescharacteristic
95C22×C4×C127—21no—
96C22×C4×C127—41no—
97C22×C4×C127C2×D411yescharacteristic
98Q16×C127—22no—
99Q16×C127—22no—
100Q16×C127—41no—
101Q16×C127—41no—
102SD16×C127—44no—
103D8×C127—22no—
104D8×C127—22no—
105D8×C127—44no—
106D8×C127—41no—
107D8×C127—41no—
108M16×C127—21no—
109M16×C127—22no—
110M16×C127—21no—
111M16×C127—41no—
112M16×C127—41no—
113M16×C127—41no—
114C2×C8×C127—21no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127C2×D411yescharacteristic
119C2×C8×C127C2×D411yescharacteristic
120C2×C8×C127C2×D411yescharacteristic
121C2×C8×C127C2×D411yescharacteristic
122C2×C8×C127C2×D411yescharacteristic
123C2×C8×C127#4111yescharacteristic
124C4⋊C4×C127—22no—
125C4⋊C4×C127—44no—
126C22⋊C4×C127—44no—
127C22⋊C4×C127—41no—
128C42×C127—41no—
129C16×C127—22no—
130C16×C127—41no—
131C23×C127—21no—
132C23×C127—42no—
133C23×C127—81no—
134C23×C127—81no—
135C23×C127—162no—
136C23×C127AGL(1,ℤ/8)11yescharacteristic
137Q8×C127—21no—
138Q8×C127—21no—
139Q8×C127—42no—
140Q8×C127—42no—
141Q8×C127—81no—
142Q8×C127—81no—
143D4×C127—21no—
144D4×C127—21no—
145D4×C127—41no—
146D4×C127—41no—
147D4×C127—42no—
148D4×C127—42no—
149D4×C127—81no—
150D4×C127—81no—
151C2×C4×C127—21no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—42no—
155C2×C4×C127—42no—
156C2×C4×C127—81no—
157C2×C4×C127—81no—
158C2×C4×C127#12011yescharacteristic
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127C2×D811yescharacteristic
162C2×C4×C127#13511yescharacteristic
163C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
164C8×C127—41no—
165C8×C127—42no—
166C8×C127#12011yescharacteristic
167C8×C127#12111yescharacteristic
168C8×C127#12111yescharacteristic
169C8×C127#12711yescharacteristic
170C22×C127—22no—
171C22×C127—42no—
172C22×C127—41no—
173C22×C127—82no—
174C22×C127—162no—
175C22×C127—162no—
176C22×C127—162no—
177C22×C127#44711yescharacteristic
178C22×C127#44911yescharacteristic
179C22×C127#46911yescharacteristic
180C4×C127—41no—
181C4×C127—82no—
182C4×C127—82no—
183C4×C127#39211yescharacteristic
184C4×C127#44711yescharacteristic
185C4×C127#44911yescharacteristic
186C4×C127#46611yescharacteristic
187#13320C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—21no—
189C2×C127—21no—
190C2×C127—81no—
191C2×C127—162no—
192C2×C127#199911yescharacteristic
193C2×C127#219312yes—
194C22×SD32C2×C12711yescharacteristic, complemented
195C2×#472C2×C12711yescharacteristic
196#3059C2×C12711yescharacteristic, complemented
197C2×#362C2×C12711yescharacteristic, complemented
198#2140C2×C12711yescharacteristic, complemented
199C2×#350C2×C12711yescharacteristic, complemented
200#1382C2×C12711yescharacteristic, complemented
201C127#1332011yescharacteristic, direct product factor, Sylow
202C2×AGL(1,ℤ/8)—21no—
203C22×Q16C22×C12711yescharacteristic
204C22×D8C22×C12711yescharacteristic
205C2×#131C22×C12711yescharacteristic
206#536—21no—
207C2×SD32—22no—
208C2×SD32—22no—
209C2×SD32—22no—
210C2×M32C22×C12711yescharacteristic
211C22×C16C22×C12711yescharacteristic
212#472—22no—
213#472—22no—
214#470—22no—
215#467—22no—
216C2×#108C22×C12711yescharacteristic
217#427C22×C12711yescharacteristic
218#419—21no—
219C2×#100—21no—
220#362—22no—
221#357—22no—
222#350—22no—
223C2×#41D4×C12711yescharacteristic
224C22×Q8—21no—
225C22×D4—21no—
226AGL(1,ℤ/8)—24no—
227AGL(1,ℤ/8)—42no—
228C2×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16D4×C12712yes—
234C2×SD16—41no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—41no—
241C2×D8D4×C12712yes—
242#131—21no—
243#131—21no—
244#131—21no—
245#131—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16D4×C12711yescharacteristic
249C22×C8—21no—
250C22×C8C23×C12711yescharacteristic
251C4⋊Q8—41no—
252#124—41no—
253#123—42no—
254C22⋊Q8—24no—
255#117—21no—
256SD32—28no—
257M32—21no—
258M32—21no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16D4×C12712yes—
263#108—21no—
264#108D4×C12712yes—
265#107D4×C12712yes—
266#106—21no—
267#103—24no—
268#100—24no—
269C24—41no—
270#41—21no—
271#41—21no—
272#41—21no—
273#41—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8D8×C12711yescharacteristic
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4D8×C12711yescharacteristic
289C22×C4—21no—
290C22×C4—41no—
291C22×C4C2×D4×C12711yescharacteristic
292Q16—22no—
293Q16—22no—
294Q16—41no—
295Q16—41no—
296SD16—44no—
297D8—22no—
298D8—22no—
299D8—44no—
300D8—41no—
301D8—41no—
302M16—21no—
303M16—22no—
304M16—21no—
305M16—41no—
306M16—41no—
307M16—41no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8C2×D4×C12711yescharacteristic
313C2×C8C2×D4×C12711yescharacteristic
314C2×C8C2×D4×C12711yescharacteristic
315C2×C8C2×D4×C12711yescharacteristic
316C2×C8C2×D4×C12711yescharacteristic
317C2×C8#41×C12711yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—44no—
320C22⋊C4—44no—
321C22⋊C4—41no—
322C42—41no—
323C16—22no—
324C16—41no—
325C23—21no—
326C23—42no—
327C23—81no—
328C23—81no—
329C23—162no—
330C23AGL(1,ℤ/8)×C12711yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336Q8—81no—
337D4—21no—
338D4—21no—
339D4—41no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—81no—
344D4—81no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4#120×C12711yescharacteristic
353C2×C4#120×C12711yescharacteristic
354C2×C4#121×C12711yescharacteristic
355C2×C4C2×D8×C12711yescharacteristic
356C2×C4#135×C12711yescharacteristic
357C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
358C8—41no—
359C8—42no—
360C8#120×C12711yescharacteristic
361C8#121×C12711yescharacteristic
362C8#121×C12711yescharacteristic
363C8#127×C12711yescharacteristic
364C22—22no—
365C22—42no—
366C22—41no—
367C22—82no—
368C22—162no—
369C22—162no—
370C22—162no—
371C22#447×C12711yescharacteristic
372C22#449×C12711yescharacteristic
373C22#469×C12711yescharacteristic
374C4—41no—
375C4—82no—
376C4—82no—
377C4#392×C12711yescharacteristic
378C4#447×C12711yescharacteristic
379C4#449×C12711yescharacteristic
380C4#466×C12711yescharacteristic
381C2—21no—
382C2—21no—
383C2—81no—
384C2—162no—
385C2C127×#199911yescharacteristic
386C2C127×#219312yes—
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#472×C127C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×SD32×C127C2semidirect
3. C127×#3059C2semidirect
4. C2×#362×C127C2semidirect
5. C127×#2140C2semidirect
6. C2×#350×C127C2semidirect
7. C127×#1382C2semidirect
187. #13320C127direct (N × H)
194. C22×SD32C2×C127semidirect
196. #3059C2×C127semidirect
197. C2×#362C2×C127semidirect
198. #2140C2×C127semidirect
199. C2×#350C2×C127semidirect
200. #1382C2×C127semidirect
201. C127#13320direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD32×C1272
C2×#472×C1272
C127×#30592
C2×#362×C1272
C127×#21402
C2×#350×C1272
C127×#13822
#13320127