Finite Group Databasebeta

← C127×#21481 #44585154

Subgroups — C127×#21481 #44585154

Order 32512.

1494 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×H(5,𝔽2)×C127C211yesmaximal, characteristic
2C2×#458×C127C211yesmaximal, characteristic
3C127×#2322C213yesmaximal, complemented
4C127×#1890C213yesmaximal, complemented
5C127×#1867C213yesmaximal, complemented
6C127×#1790C211yesmaximal, characteristic
7C4×#99×C127C213yesmaximal, complemented
8C2×H(5,𝔽2)×C127C2211yescharacteristic
9C2×#123×C127C2213yes—
10#520×C127—23no—
11#518×C127—23no—
12#518×C127C2213yes—
13C4×#41×C127—23no—
14C2×C4×D4×C127—23no—
15C2×C4×D4×C127C2213yes—
16C22×C4⋊C4×C127C2211yescharacteristic, complemented
17#458×C127C418yescomplemented
18C2×#99×C127C2213yes—
19C2×#99×C127C2213yes—
20#389×C127—23no—
21#388×C127—23no—
22#387×C127—23no—
23#386×C127C2213yes—
24#385×C127—23no—
25#385×C127C2213yescomplemented
26#381×C127C2213yescomplemented
27C4×C22⋊C4×C127C2213yescomplemented
28#342×C127C2216yescomplemented
29H(5,𝔽2)×C127—26no—
30H(5,𝔽2)×C127C2×C414yes—
31C2×#41×C127—23no—
32C22×D4×C127—23no—
33C22×D4×C127C2313yes—
34C23×C4×C127—21no—
35C23×C4×C127D413yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2311yescharacteristic
39#123×C127—26no—
40#123×C127C2×C4112yescomplemented
41C4×Q8×C127—21no—
42C4×Q8×C127—23no—
43C4×D4×C127—23no—
44C4×D4×C127—26no—
45C4×D4×C127—23no—
46C4×D4×C127—26no—
47C4×D4×C127—26no—
48C4×D4×C127—26no—
49C4×D4×C127—26no—
50#117×C127—26no—
51#117×C127—23no—
52C2×C4⋊C4×C127—23no—
53C2×C4⋊C4×C127—23no—
54C2×C4⋊C4×C127—23no—
55C2×C4⋊C4×C127—23no—
56C2×C4⋊C4×C127—23no—
57C2×C4⋊C4×C127D413yes—
58C2×C22⋊C4×C127—23no—
59C2×C22⋊C4×C127—23no—
60C2×C22⋊C4×C127—23no—
61C2×C22⋊C4×C127—23no—
62C2×C22⋊C4×C127D413yes—
63C2×C22⋊C4×C127C2313yes—
64C2×C22⋊C4×C127C2313yes—
65C2×C22⋊C4×C127C2313yes—
66C2×C42×C127—23no—
67C2×C42×C127—23no—
68C2×C42×C127D413yes—
69#99×C127—26no—
70#99×C127C2×C4112yescomplemented
71#95×C127—23no—
72#95×C127—23no—
73#95×C127—23no—
74#95×C127—23no—
75#95×C127—23no—
76C24×C127—21no—
77C24×C127C2×D413yes—
78C24×C127C2411yescharacteristic
79#41×C127—212no—
80#41×C127—212no—
81C2×Q8×C127—21no—
82C2×D4×C127—23no—
83C2×D4×C127—212no—
84C2×D4×C127—212no—
85C2×D4×C127—26no—
86C2×D4×C127—26no—
87C2×D4×C127C22×C416yes—
88C2×D4×C127#4116yes—
89C22×C4×C127—23no—
90C22×C4×C127—23no—
91C22×C4×C127—23no—
92C22×C4×C127—23no—
93C22×C4×C127—23no—
94C22×C4×C127—23no—
95C22×C4×C127—23no—
96C22×C4×C127—23no—
97C22×C4×C127—23no—
98C22×C4×C127—23no—
99C22×C4×C127—81no—
100C22×C4×C127—81no—
101C22×C4×C127—83no—
102C22×C4×C127—82no—
103C22×C4×C127C22×C412yescomplemented
104C22×C4×C127C2×D413yes—
105C22×C4×C127C2×D413yes—
106C22×C4×C127C2×D413yes—
107C22×C4×C127C2×D413yes—
108C22×C4×C127C2×D413yes—
109C4⋊C4×C127—23no—
110C4⋊C4×C127—23no—
111C4⋊C4×C127—212no—
112C4⋊C4×C127—26no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—43no—
115C4⋊C4×C127—83no—
116C22⋊C4×C127—26no—
117C22⋊C4×C127—212no—
118C22⋊C4×C127—26no—
119C22⋊C4×C127—23no—
120C22⋊C4×C127—26no—
121C22⋊C4×C127—26no—
122C22⋊C4×C127—83no—
123C22⋊C4×C127C22×C416yescomplemented
124C42×C127—26no—
125C42×C127—23no—
126C42×C127—23no—
127C42×C127—83no—
128C23×C127—24no—
129C23×C127—23no—
130C23×C127—23no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—43no—
134C23×C127—43no—
135C23×C127—81no—
136C23×C127—81no—
137C23×C127C4×D416yes—
138C23×C127C23×C411yescharacteristic
139C23×C127C22×D413yes—
140C23×C127C2×#4113yes—
141Q8×C127—24no—
142D4×C127—212no—
143D4×C127—212no—
144D4×C127—212no—
145C2×C4×C127—212no—
146C2×C4×C127—23no—
147C2×C4×C127—23no—
148C2×C4×C127—26no—
149C2×C4×C127—26no—
150C2×C4×C127—23no—
151C2×C4×C127—23no—
152C2×C4×C127—43no—
153C2×C4×C127—43no—
154C2×C4×C127—46no—
155C2×C4×C127—43no—
156C2×C4×C127—43no—
157C2×C4×C127—41no—
158C2×C4×C127—43no—
159C2×C4×C127—43no—
160C2×C4×C127—43no—
161C2×C4×C127—43no—
162C2×C4×C127—43no—
163C2×C4×C127—43no—
164C2×C4×C127—43no—
165C2×C4×C127—41no—
166C2×C4×C127—43no—
167C2×C4×C127—83no—
168C2×C4×C127—83no—
169C2×C4×C127—83no—
170C2×C4×C127C4×D416yes—
171C2×C4×C127#12011yescharacteristic
172C2×C4×C127#12013yes—
173C22×C127—23no—
174C22×C127—23no—
175C22×C127—26no—
176C22×C127—41no—
177C22×C127—43no—
178C22×C127—46no—
179C22×C127—43no—
180C22×C127—43no—
181C22×C127—83no—
182C22×C127—84no—
183C22×C127C2×C4×D413yes—
184C22×C127C2×#12011yescharacteristic
185C22×C127#52513yes—
186C4×C127—21no—
187C4×C127—23no—
188C4×C127—26no—
189C4×C127—46no—
190C4×C127—43no—
191C4×C127—43no—
192C4×C127—42no—
193C4×C127—83no—
194C4×C127—81no—
195#21481C12711yesmaximal, characteristic, direct product factor, Sylow
196C2×C127—23no—
197C2×C127—23no—
198C2×C127—46no—
199C2×C127C4×#12011yescharacteristic
200C2×C127#302611yescharacteristic
201C2×C127#302811yescharacteristic
202C4×H(5,𝔽2)C2×C12711yescharacteristic
203C2×#458C2×C12711yescharacteristic
204#2322C2×C12713yescomplemented
205#1890C2×C12713yescomplemented
206#1867C2×C12713yescomplemented
207#1790C2×C12711yescharacteristic
208C4×#99C2×C12713yescomplemented
209C127#2148111yescharacteristic, direct product factor, Sylow
210C2×H(5,𝔽2)C22×C12711yescharacteristic
211C2×#123C22×C12713yes—
212#520—23no—
213#518—23no—
214#518C22×C12713yes—
215C4×#41—23no—
216C2×C4×D4—23no—
217C2×C4×D4C22×C12713yes—
218C22×C4⋊C4C22×C12711yescharacteristic, complemented
219#458C4×C12718yescomplemented
220C2×#99C22×C12713yes—
221C2×#99C22×C12713yes—
222#389—23no—
223#388—23no—
224#387—23no—
225#386C22×C12713yes—
226#385—23no—
227#385C22×C12713yescomplemented
228#381C22×C12713yescomplemented
229C4×C22⋊C4C22×C12713yescomplemented
230#342C22×C12716yescomplemented
231H(5,𝔽2)—26no—
232H(5,𝔽2)C2×C4×C12714yes—
233C2×#41—23no—
234C22×D4—23no—
235C22×D4C23×C12713yes—
236C23×C4—21no—
237C23×C4D4×C12713yes—
238C23×C4C23×C12711yescharacteristic
239C23×C4C23×C12711yescharacteristic
240C23×C4C23×C12711yescharacteristic
241#123—26no—
242#123C2×C4×C127112yescomplemented
243C4×Q8—21no—
244C4×Q8—23no—
245C4×D4—23no—
246C4×D4—26no—
247C4×D4—23no—
248C4×D4—26no—
249C4×D4—26no—
250C4×D4—26no—
251C4×D4—26no—
252#117—26no—
253#117—23no—
254C2×C4⋊C4—23no—
255C2×C4⋊C4—23no—
256C2×C4⋊C4—23no—
257C2×C4⋊C4—23no—
258C2×C4⋊C4—23no—
259C2×C4⋊C4D4×C12713yes—
260C2×C22⋊C4—23no—
261C2×C22⋊C4—23no—
262C2×C22⋊C4—23no—
263C2×C22⋊C4—23no—
264C2×C22⋊C4D4×C12713yes—
265C2×C22⋊C4C23×C12713yes—
266C2×C22⋊C4C23×C12713yes—
267C2×C22⋊C4C23×C12713yes—
268C2×C42—23no—
269C2×C42—23no—
270C2×C42D4×C12713yes—
271#99—26no—
272#99C2×C4×C127112yescomplemented
273#95—23no—
274#95—23no—
275#95—23no—
276#95—23no—
277#95—23no—
278C24—21no—
279C24C2×D4×C12713yes—
280C24C24×C12711yescharacteristic
281#41—212no—
282#41—212no—
283C2×Q8—21no—
284C2×D4—23no—
285C2×D4—212no—
286C2×D4—212no—
287C2×D4—26no—
288C2×D4—26no—
289C2×D4C22×C4×C12716yes—
290C2×D4#41×C12716yes—
291C22×C4—23no—
292C22×C4—23no—
293C22×C4—23no—
294C22×C4—23no—
295C22×C4—23no—
296C22×C4—23no—
297C22×C4—23no—
298C22×C4—23no—
299C22×C4—23no—
300C22×C4—23no—
301C22×C4—81no—
302C22×C4—81no—
303C22×C4—83no—
304C22×C4—82no—
305C22×C4C22×C4×C12712yescomplemented
306C22×C4C2×D4×C12713yes—
307C22×C4C2×D4×C12713yes—
308C22×C4C2×D4×C12713yes—
309C22×C4C2×D4×C12713yes—
310C22×C4C2×D4×C12713yes—
311C4⋊C4—23no—
312C4⋊C4—23no—
313C4⋊C4—212no—
314C4⋊C4—26no—
315C4⋊C4—41no—
316C4⋊C4—43no—
317C4⋊C4—83no—
318C22⋊C4—26no—
319C22⋊C4—212no—
320C22⋊C4—26no—
321C22⋊C4—23no—
322C22⋊C4—26no—
323C22⋊C4—26no—
324C22⋊C4—83no—
325C22⋊C4C22×C4×C12716yescomplemented
326C42—26no—
327C42—23no—
328C42—23no—
329C42—83no—
330C23—24no—
331C23—23no—
332C23—23no—
333C23—41no—
334C23—41no—
335C23—43no—
336C23—43no—
337C23—81no—
338C23—81no—
339C23C4×D4×C12716yes—
340C23C23×C4×C12711yescharacteristic
341C23C22×D4×C12713yes—
342C23C2×#41×C12713yes—
343Q8—24no—
344D4—212no—
345D4—212no—
346D4—212no—
347C2×C4—212no—
348C2×C4—23no—
349C2×C4—23no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—23no—
353C2×C4—23no—
354C2×C4—43no—
355C2×C4—43no—
356C2×C4—46no—
357C2×C4—43no—
358C2×C4—43no—
359C2×C4—41no—
360C2×C4—43no—
361C2×C4—43no—
362C2×C4—43no—
363C2×C4—43no—
364C2×C4—43no—
365C2×C4—43no—
366C2×C4—43no—
367C2×C4—41no—
368C2×C4—43no—
369C2×C4—83no—
370C2×C4—83no—
371C2×C4—83no—
372C2×C4C4×D4×C12716yes—
373C2×C4#120×C12711yescharacteristic
374C2×C4#120×C12713yes—
375C22—23no—
376C22—23no—
377C22—26no—
378C22—41no—
379C22—43no—
380C22—46no—
381C22—43no—
382C22—43no—
383C22—83no—
384C22—84no—
385C22C2×C4×D4×C12713yes—
386C22C2×#120×C12711yescharacteristic
387C22#525×C12713yes—
388C4—21no—
389C4—23no—
390C4—26no—
391C4—46no—
392C4—43no—
393C4—43no—
394C4—42no—
395C4—83no—
396C4—81no—
397C2—23no—
398C2—23no—
399C2—46no—
400C2C4×#120×C12711yescharacteristic
401C2C127×#302611yescharacteristic
402C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×H(5,𝔽2)×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2322C2semidirect
4. C127×#1890C2semidirect
5. C127×#1867C2semidirect
7. C4×#99×C127C2semidirect
16. C22×C4⋊C4×C127C22semidirect
17. #458×C127C4semidirect
25. #385×C127C22semidirect
26. #381×C127C22semidirect
27. C4×C22⋊C4×C127C22semidirect
28. #342×C127C22semidirect
40. #123×C127C2×C4semidirect
70. #99×C127C2×C4semidirect
103. C22×C4×C127C22×C4semidirect
123. C22⋊C4×C127C22×C4semidirect
195. #21481C127direct (N × H)
204. #2322C2×C127semidirect
205. #1890C2×C127semidirect
206. #1867C2×C127semidirect
208. C4×#99C2×C127semidirect
209. C127#21481direct (N × H)
218. C22×C4⋊C4C22×C127semidirect
219. #458C4×C127semidirect
227. #385C22×C127semidirect
228. #381C22×C127semidirect
229. C4×C22⋊C4C22×C127semidirect
230. #342C22×C127semidirect
242. #123C2×C4×C127semidirect
272. #99C2×C4×C127semidirect
305. C22×C4C22×C4×C127semidirect
325. C22⋊C4C22×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C4×H(5,𝔽2)×C1272
C2×#458×C1272
C127×#23222
C127×#18902
C127×#18672
C127×#17902
C4×#99×C1272
#21481127