Finite Group Databasebeta

← C127×#17149 #44580822

Subgroups — C127×#17149 #44580822

Order 32512.

1790 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#401×C127C211yesmaximal, characteristic, complemented
2C2×#392×C127C211yesmaximal, characteristic
3C127×#1443C211yesmaximal, characteristic, complemented
4C127×#1440C213yesmaximal, complemented
5C127×#1439C213yesmaximal, complemented
6C127×#1438C213yesmaximal, complemented
7C127×#1438C213yesmaximal, complemented
8C23×D4×C127C2213yes—
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2213yes—
11C22×C22⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2213yes—
13C22×C22⋊C4×C127C2213yes—
14C22×C22⋊C4×C127C2213yes—
15#401×C127—24no—
16#392×C127—24no—
17C2×#95×C127C2213yes—
18C2×#95×C127C2213yes—
19C2×#95×C127C2213yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2213yes—
22C2×#95×C127C2211yescharacteristic
23C25×C127C2313yes—
24C22×D4×C127—26no—
25C22×D4×C127—26no—
26C22×D4×C127—26no—
27C22×D4×C127—43no—
28C22×D4×C127—43no—
29C22×D4×C127—43no—
30C22×D4×C127—43no—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2311yescharacteristic
33C23×C4×C127C2313yes—
34C23×C4×C127C2313yes—
35C23×C4×C127C2313yes—
36C23×C4×C127C2311yescharacteristic
37C2×C4⋊C4×C127—43no—
38C2×C22⋊C4×C127—26no—
39C2×C22⋊C4×C127—26no—
40C2×C22⋊C4×C127—26no—
41C2×C22⋊C4×C127—43no—
42C2×C22⋊C4×C127—43no—
43C2×C22⋊C4×C127—43no—
44C2×C22⋊C4×C127—43no—
45C2×C22⋊C4×C127—43no—
46C2×C22⋊C4×C127—43no—
47C2×C22⋊C4×C127—43no—
48C2×C22⋊C4×C127—43no—
49C2×C22⋊C4×C127—43no—
50C2×C22⋊C4×C127—43no—
51C2×C22⋊C4×C127—43no—
52C2×C22⋊C4×C127—43no—
53#95×C127—26no—
54#95×C127—26no—
55#95×C127—43no—
56#95×C127—43no—
57#95×C127—43no—
58#95×C127D414yes—
59C24×C127—23no—
60C24×C127—23no—
61C24×C127—23no—
62C24×C127—23no—
63C24×C127—23no—
64C24×C127—23no—
65C24×C127—23no—
66C24×C127—23no—
67C24×C127—23no—
68C24×C127—23no—
69C24×C127—23no—
70C24×C127—23no—
71C24×C127—23no—
72C24×C127—23no—
73C24×C127#4116yes—
74C24×C127C2411yescharacteristic
75C2×D4×C127—412no—
76C2×D4×C127—412no—
77C2×D4×C127—412no—
78C2×D4×C127—412no—
79C2×D4×C127—412no—
80C2×D4×C127—412no—
81C2×D4×C127—412no—
82C22×C4×C127—23no—
83C22×C4×C127—23no—
84C22×C4×C127—23no—
85C22×C4×C127—23no—
86C22×C4×C127—23no—
87C22×C4×C127—23no—
88C22×C4×C127—23no—
89C22×C4×C127—23no—
90C22×C4×C127—21no—
91C22×C4×C127—23no—
92C22×C4×C127—21no—
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—23no—
100C22×C4×C127—23no—
101C22×C4×C127—23no—
102C22×C4×C127—23no—
103C22×C4×C127—23no—
104C22×C4×C127—23no—
105C22×C4×C127—23no—
106C22×C4×C127—23no—
107C22×C4×C127—23no—
108C22×C4×C127—23no—
109C22×C4×C127—23no—
110C22×C4×C127C2×D416yes—
111C22×C4×C127#4112yes—
112C4⋊C4×C127—44no—
113C22⋊C4×C127—412no—
114C22⋊C4×C127—412no—
115C22⋊C4×C127—412no—
116C22⋊C4×C127—412no—
117C22⋊C4×C127—412no—
118C23×C127—26no—
119C23×C127—26no—
120C23×C127—26no—
121C23×C127—26no—
122C23×C127—26no—
123C23×C127—26no—
124C23×C127—26no—
125C23×C127—43no—
126C23×C127—43no—
127C23×C127—43no—
128C23×C127—43no—
129C23×C127—43no—
130C23×C127—43no—
131C23×C127—43no—
132C23×C127—43no—
133C23×C127—43no—
134C23×C127—43no—
135C23×C127—43no—
136C23×C127—43no—
137C23×C127—43no—
138C23×C127—43no—
139C23×C127—43no—
140C23×C127—43no—
141C23×C127—43no—
142C23×C127—43no—
143C23×C127—43no—
144C23×C127—43no—
145C23×C127—43no—
146C23×C127—43no—
147C23×C127—43no—
148C23×C127—43no—
149C23×C127—43no—
150C23×C127—43no—
151C23×C127—43no—
152C23×C127—43no—
153C23×C127C22×D411yescharacteristic
154C23×C127C2×#4113yes—
155C23×C127C2×#4111yescharacteristic
156C23×C127H(5,𝔽2)13yes—
157C23×C127H(5,𝔽2)13yes—
158C23×C127H(5,𝔽2)13yes—
159C23×C127H(5,𝔽2)11yescharacteristic
160D4×C127—448no—
161C2×C4×C127—26no—
162C2×C4×C127—26no—
163C2×C4×C127—26no—
164C2×C4×C127—26no—
165C2×C4×C127—43no—
166C2×C4×C127—43no—
167C2×C4×C127—43no—
168C2×C4×C127—41no—
169C2×C4×C127—43no—
170C2×C4×C127—43no—
171C2×C4×C127—43no—
172C2×C4×C127—43no—
173C2×C4×C127—43no—
174C2×C4×C127—43no—
175C2×C4×C127—43no—
176C2×C4×C127—43no—
177C2×C4×C127—43no—
178C2×C4×C127—43no—
179C2×C4×C127—43no—
180C2×C4×C127—43no—
181C2×C4×C127—43no—
182C2×C4×C127—43no—
183C2×C4×C127—43no—
184C2×C4×C127—43no—
185C2×C4×C127—43no—
186C2×C4×C127—41no—
187C2×C4×C127—41no—
188C2×C4×C127—43no—
189C2×C4×C127—43no—
190C2×C4×C127—43no—
191C22×C127—46no—
192C22×C127—46no—
193C22×C127—46no—
194C22×C127—46no—
195C22×C127—46no—
196C22×C127—46no—
197C22×C127—46no—
198C22×C127—83no—
199C22×C127—83no—
200C22×C127—83no—
201C22×C127—83no—
202C22×C127—83no—
203C22×C127—83no—
204C22×C127—83no—
205C22×C127—83no—
206C22×C127#53513yes—
207C22×C127#53813yes—
208C22×C127#53813yes—
209C22×C127#53813yes—
210C22×C127#53813yes—
211C22×C127#54613yes—
212C22×C127#55011yescharacteristic
213C22×C127#55113yes—
214C22×C127#55313yes—
215C22×C127#56011yescharacteristic
216C22×C127#56013yes—
217C22×C127#56013yes—
218C22×C127#56013yes—
219C4×C127—42no—
220C4×C127—46no—
221C4×C127—81no—
222C4×C127—81no—
223C4×C127—83no—
224C4×C127—83no—
225#17149C12711yesmaximal, characteristic, direct product factor, Sylow
226C2×C127—86no—
227C2×C127#268513yes—
228C2×C127#271413yes—
229C2×C127#276011yescharacteristic
230C2×C127#277813yes—
231C2×C127#281811yescharacteristic
232C2×C127#282511yescharacteristic
233C2×C127#282513yes—
234C2×#401C2×C12711yescharacteristic, complemented
235C2×#392C2×C12711yescharacteristic
236#1443C2×C12711yescharacteristic, complemented
237#1440C2×C12713yescomplemented
238#1439C2×C12713yescomplemented
239#1438C2×C12713yescomplemented
240#1438C2×C12713yescomplemented
241C127#1714911yescharacteristic, direct product factor, Sylow
242C23×D4C22×C12713yes—
243C22×C4⋊C4C22×C12711yescharacteristic
244C22×C22⋊C4C22×C12713yes—
245C22×C22⋊C4C22×C12713yes—
246C22×C22⋊C4C22×C12713yes—
247C22×C22⋊C4C22×C12713yes—
248C22×C22⋊C4C22×C12713yes—
249#401—24no—
250#392—24no—
251C2×#95C22×C12713yes—
252C2×#95C22×C12713yes—
253C2×#95C22×C12713yes—
254C2×#95C22×C12713yes—
255C2×#95C22×C12713yes—
256C2×#95C22×C12711yescharacteristic
257C25C23×C12713yes—
258C22×D4—26no—
259C22×D4—26no—
260C22×D4—26no—
261C22×D4—43no—
262C22×D4—43no—
263C22×D4—43no—
264C22×D4—43no—
265C23×C4C23×C12711yescharacteristic
266C23×C4C23×C12711yescharacteristic
267C23×C4C23×C12713yes—
268C23×C4C23×C12713yes—
269C23×C4C23×C12713yes—
270C23×C4C23×C12711yescharacteristic
271C2×C4⋊C4—43no—
272C2×C22⋊C4—26no—
273C2×C22⋊C4—26no—
274C2×C22⋊C4—26no—
275C2×C22⋊C4—43no—
276C2×C22⋊C4—43no—
277C2×C22⋊C4—43no—
278C2×C22⋊C4—43no—
279C2×C22⋊C4—43no—
280C2×C22⋊C4—43no—
281C2×C22⋊C4—43no—
282C2×C22⋊C4—43no—
283C2×C22⋊C4—43no—
284C2×C22⋊C4—43no—
285C2×C22⋊C4—43no—
286C2×C22⋊C4—43no—
287#95—26no—
288#95—26no—
289#95—43no—
290#95—43no—
291#95—43no—
292#95D4×C12714yes—
293C24—23no—
294C24—23no—
295C24—23no—
296C24—23no—
297C24—23no—
298C24—23no—
299C24—23no—
300C24—23no—
301C24—23no—
302C24—23no—
303C24—23no—
304C24—23no—
305C24—23no—
306C24—23no—
307C24#41×C12716yes—
308C24C24×C12711yescharacteristic
309C2×D4—412no—
310C2×D4—412no—
311C2×D4—412no—
312C2×D4—412no—
313C2×D4—412no—
314C2×D4—412no—
315C2×D4—412no—
316C22×C4—23no—
317C22×C4—23no—
318C22×C4—23no—
319C22×C4—23no—
320C22×C4—23no—
321C22×C4—23no—
322C22×C4—23no—
323C22×C4—23no—
324C22×C4—21no—
325C22×C4—23no—
326C22×C4—21no—
327C22×C4—23no—
328C22×C4—23no—
329C22×C4—23no—
330C22×C4—23no—
331C22×C4—23no—
332C22×C4—23no—
333C22×C4—23no—
334C22×C4—23no—
335C22×C4—23no—
336C22×C4—23no—
337C22×C4—23no—
338C22×C4—23no—
339C22×C4—23no—
340C22×C4—23no—
341C22×C4—23no—
342C22×C4—23no—
343C22×C4—23no—
344C22×C4C2×D4×C12716yes—
345C22×C4#41×C12712yes—
346C4⋊C4—44no—
347C22⋊C4—412no—
348C22⋊C4—412no—
349C22⋊C4—412no—
350C22⋊C4—412no—
351C22⋊C4—412no—
352C23—26no—
353C23—26no—
354C23—26no—
355C23—26no—
356C23—26no—
357C23—26no—
358C23—26no—
359C23—43no—
360C23—43no—
361C23—43no—
362C23—43no—
363C23—43no—
364C23—43no—
365C23—43no—
366C23—43no—
367C23—43no—
368C23—43no—
369C23—43no—
370C23—43no—
371C23—43no—
372C23—43no—
373C23—43no—
374C23—43no—
375C23—43no—
376C23—43no—
377C23—43no—
378C23—43no—
379C23—43no—
380C23—43no—
381C23—43no—
382C23—43no—
383C23—43no—
384C23—43no—
385C23—43no—
386C23—43no—
387C23C22×D4×C12711yescharacteristic
388C23C2×#41×C12713yes—
389C23C2×#41×C12711yescharacteristic
390C23H(5,𝔽2)×C12713yes—
391C23H(5,𝔽2)×C12713yes—
392C23H(5,𝔽2)×C12713yes—
393C23H(5,𝔽2)×C12711yescharacteristic
394D4—448no—
395C2×C4—26no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—43no—
400C2×C4—43no—
401C2×C4—43no—
402C2×C4—41no—
403C2×C4—43no—
404C2×C4—43no—
405C2×C4—43no—
406C2×C4—43no—
407C2×C4—43no—
408C2×C4—43no—
409C2×C4—43no—
410C2×C4—43no—
411C2×C4—43no—
412C2×C4—43no—
413C2×C4—43no—
414C2×C4—43no—
415C2×C4—43no—
416C2×C4—43no—
417C2×C4—43no—
418C2×C4—43no—
419C2×C4—43no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—43no—
423C2×C4—43no—
424C2×C4—43no—
425C22—46no—
426C22—46no—
427C22—46no—
428C22—46no—
429C22—46no—
430C22—46no—
431C22—46no—
432C22—83no—
433C22—83no—
434C22—83no—
435C22—83no—
436C22—83no—
437C22—83no—
438C22—83no—
439C22—83no—
440C22#535×C12713yes—
441C22#538×C12713yes—
442C22#538×C12713yes—
443C22#538×C12713yes—
444C22#538×C12713yes—
445C22#546×C12713yes—
446C22#550×C12711yescharacteristic
447C22#551×C12713yes—
448C22#553×C12713yes—
449C22#560×C12713yes—
450C22#560×C12713yes—
451C22#560×C12711yescharacteristic
452C22#560×C12713yes—
453C4—42no—
454C4—46no—
455C4—83no—
456C4—83no—
457C4—81no—
458C4—81no—
459C2—86no—
460C2C127×#268513yes—
461C2C127×#271413yes—
462C2C127×#276011yescharacteristic
463C2C127×#277813yes—
464C2C127×#281811yescharacteristic
465C2C127×#282511yescharacteristic
466C2C127×#282513yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#401×C127C2semidirect
3. C127×#1443C2semidirect
4. C127×#1440C2semidirect
5. C127×#1439C2semidirect
6. C127×#1438C2semidirect
7. C127×#1438C2semidirect
225. #17149C127direct (N × H)
234. C2×#401C2×C127semidirect
236. #1443C2×C127semidirect
237. #1440C2×C127semidirect
238. #1439C2×C127semidirect
239. #1438C2×C127semidirect
240. #1438C2×C127semidirect
241. C127#17149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#401×C1272
C2×#392×C1272
C127×#14432
C127×#14402
C127×#14392
C127×#14382
#17149127