Finite Group Databasebeta

← C127×#13939 #44577612

Subgroups — C127×#13939 #44577612

Order 32512.

1862 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C127C211yesmaximal, characteristic
2C2×#380×C127C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
4C127×#1440C214yesmaximal
5C127×C4⋊#95C212yesmaximal, complemented
6C127×C4⋊#95C212yesmaximal, complemented
7C127×#1434C214yesmaximal, complemented
8C24×C4×C127C2211yescharacteristic
9C2×#117×C127—24no—
10C2×#117×C127—24no—
11C2×#117×C127C418yescomplemented
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C42×C127C2212yes—
19C22×C42×C127C2212yes—
20#380×C127—24no—
21C4×C22⋊C4×C127—24no—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2218yes—
25C2×#95×C127C2218yes—
26C25×C127C2311yescharacteristic
27C23×C4×C127—24no—
28C23×C4×C127—24no—
29C23×C4×C127C2×C414yes—
30C23×C4×C127D414yes—
31C23×C4×C127D414yes—
32C23×C4×C127C2314yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2314yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2311yescharacteristic
38#117×C127—232no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127C2×C414yes—
47C2×C4⋊C4×C127C2×C414yes—
48C2×C22⋊C4×C127—24no—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—28no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—44no—
54C2×C22⋊C4×C127C2×C418yes—
55C2×C42×C127—24no—
56C2×C42×C127—24no—
57C2×C42×C127—24no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127C2×C418yes—
61#95×C127—24no—
62#95×C127—24no—
63#95×C127—216no—
64#95×C127—48no—
65C24×C127—24no—
66C24×C127—22no—
67C24×C127—22no—
68C24×C127—22no—
69C24×C127—22no—
70C24×C127C22×C412yes—
71C24×C127C2×D412yes—
72C24×C127C2×D412yes—
73C24×C127C2411yescharacteristic
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—28no—
77C22×C4×C127—28no—
78C22×C4×C127—216no—
79C22×C4×C127—216no—
80C22×C4×C127—24no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—28no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—28no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—28no—
98C22×C4×C127C22⋊C4116yes—
99C22×C4×C127C22×C414yes—
100C22×C4×C127C22×C414yes—
101C22×C4×C127C22×C412yes—
102C22×C4×C127C22×C412yes—
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127#4118yes—
108C22×C4×C127#4114yes—
109C22×C4×C127#4114yes—
110C4⋊C4×C127—28no—
111C4⋊C4×C127—28no—
112C4⋊C4×C127—48no—
113C22⋊C4×C127—216no—
114C22⋊C4×C127—216no—
115C22⋊C4×C127—48no—
116C42×C127—216no—
117C42×C127—48no—
118C23×C127—22no—
119C23×C127—22no—
120C23×C127—24no—
121C23×C127—24no—
122C23×C127—24no—
123C23×C127—24no—
124C23×C127—24no—
125C23×C127—24no—
126C23×C127—22no—
127C23×C127—22no—
128C23×C127—24no—
129C23×C127—44no—
130C23×C127—44no—
131C23×C127—44no—
132C23×C127—44no—
133C23×C127C2×C22⋊C414yes—
134C23×C127C23×C411yescharacteristic
135C23×C127C22×D411yescharacteristic
136C23×C127C22×D411yescharacteristic
137C23×C127C2×#4112yes—
138C23×C127C2×#4112yes—
139C23×C127C2×#4114yes—
140C23×C127H(5,𝔽2)12yes—
141C23×C1272−1+412yes—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—24no—
145C2×C4×C127—24no—
146C2×C4×C127—232no—
147C2×C4×C127—24no—
148C2×C4×C127—24no—
149C2×C4×C127—28no—
150C2×C4×C127—28no—
151C2×C4×C127—28no—
152C2×C4×C127—28no—
153C2×C4×C127—28no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127—44no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—44no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—48no—
167C2×C4×C127—48no—
168C2×C4×C127C2×C22⋊C414yes—
169C2×C4×C127C2×C22⋊C414yes—
170C2×C4×C127#11714yes—
171C2×C4×C127#11714yes—
172C2×C4×C127#12318yes—
173C2×C4×C127#12318yes—
174C22×C127—24no—
175C22×C127—24no—
176C22×C127—24no—
177C22×C127—44no—
178C22×C127—44no—
179C22×C127—48no—
180C22×C127—44no—
181C22×C127—44no—
182C22×C127C22×C22⋊C411yescharacteristic
183C22×C127C2×#11711yescharacteristic
184C22×C127C2×#11711yescharacteristic
185C22×C127C4×#4112yes—
186C22×C127#52012yes—
187C22×C127C2×#12312yes—
188C22×C127C2×#12312yes—
189C22×C127#52512yes—
190C22×C127#53212yes—
191C22×C127#53511yescharacteristic
192C22×C127#53611yescharacteristic
193C22×C127#53712yes—
194C22×C127#55214yes—
195C22×C127#55314yes—
196C22×C127#55514yes—
197C22×C127#55614yes—
198C4×C127—24no—
199C4×C127—44no—
200C4×C127—48no—
201C4×C127—44no—
202C4×C127—84no—
203C4×C127#38118yes—
204#13939C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—44no—
206C2×C127C2×#38111yescharacteristic
207C2×C127#229711yescharacteristic
208C2×C127#231111yescharacteristic
209C2×C127#234612yes—
210C2×C127#234712yes—
211C2×C127#248514yes—
212C2×C127#249912yes—
213C2×C127#250012yes—
214C22×#117C2×C12711yescharacteristic
215C2×#380C2×C12711yescharacteristic
216C2×C4×C22⋊C4C2×C12711yescharacteristic
217#1440C2×C12714yes—
218C4⋊#95C2×C12712yescomplemented
219C4⋊#95C2×C12712yescomplemented
220#1434C2×C12714yescomplemented
221C127#1393911yescharacteristic, direct product factor, Sylow
222C24×C4C22×C12711yescharacteristic
223C2×#117—24no—
224C2×#117—24no—
225C2×#117C4×C12718yescomplemented
226C22×C4⋊C4C22×C12712yes—
227C22×C4⋊C4C22×C12711yescharacteristic
228C22×C4⋊C4C22×C12711yescharacteristic
229C22×C22⋊C4C22×C12712yes—
230C22×C22⋊C4C22×C12712yes—
231C22×C22⋊C4C22×C12712yes—
232C22×C42C22×C12712yes—
233C22×C42C22×C12712yes—
234#380—24no—
235C4×C22⋊C4—24no—
236C2×#95C22×C12712yes—
237C2×#95C22×C12712yes—
238C2×#95C22×C12718yes—
239C2×#95C22×C12718yes—
240C25C23×C12711yescharacteristic
241C23×C4—24no—
242C23×C4—24no—
243C23×C4C2×C4×C12714yes—
244C23×C4D4×C12714yes—
245C23×C4D4×C12714yes—
246C23×C4C23×C12714yes—
247C23×C4C23×C12712yes—
248C23×C4C23×C12712yes—
249C23×C4C23×C12714yes—
250C23×C4C23×C12711yescharacteristic
251C23×C4C23×C12711yescharacteristic
252#117—232no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4C2×C4×C12714yes—
261C2×C4⋊C4C2×C4×C12714yes—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—28no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—44no—
268C2×C22⋊C4C2×C4×C12718yes—
269C2×C42—24no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—24no—
273C2×C42—24no—
274C2×C42C2×C4×C12718yes—
275#95—24no—
276#95—24no—
277#95—216no—
278#95—48no—
279C24—24no—
280C24—22no—
281C24—22no—
282C24—22no—
283C24—22no—
284C24C22×C4×C12712yes—
285C24C2×D4×C12712yes—
286C24C2×D4×C12712yes—
287C24C24×C12711yescharacteristic
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—28no—
291C22×C4—28no—
292C22×C4—216no—
293C22×C4—216no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—28no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—28no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—28no—
312C22×C4C22⋊C4×C127116yes—
313C22×C4C22×C4×C12714yes—
314C22×C4C22×C4×C12714yes—
315C22×C4C22×C4×C12712yes—
316C22×C4C22×C4×C12712yes—
317C22×C4C2×D4×C12712yes—
318C22×C4C2×D4×C12712yes—
319C22×C4C2×D4×C12712yes—
320C22×C4C2×D4×C12712yes—
321C22×C4#41×C12718yes—
322C22×C4#41×C12714yes—
323C22×C4#41×C12714yes—
324C4⋊C4—28no—
325C4⋊C4—28no—
326C4⋊C4—48no—
327C22⋊C4—216no—
328C22⋊C4—216no—
329C22⋊C4—48no—
330C42—216no—
331C42—48no—
332C23—22no—
333C23—22no—
334C23—24no—
335C23—24no—
336C23—24no—
337C23—24no—
338C23—24no—
339C23—24no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—44no—
344C23—44no—
345C23—44no—
346C23—44no—
347C23C2×C22⋊C4×C12714yes—
348C23C23×C4×C12711yescharacteristic
349C23C22×D4×C12711yescharacteristic
350C23C22×D4×C12711yescharacteristic
351C23C2×#41×C12712yes—
352C23C2×#41×C12712yes—
353C23C2×#41×C12714yes—
354C23H(5,𝔽2)×C12712yes—
355C232−1+4×C12712yes—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—232no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—28no—
364C2×C4—28no—
365C2×C4—28no—
366C2×C4—28no—
367C2×C4—28no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—48no—
381C2×C4—48no—
382C2×C4C2×C22⋊C4×C12714yes—
383C2×C4C2×C22⋊C4×C12714yes—
384C2×C4#117×C12714yes—
385C2×C4#117×C12714yes—
386C2×C4#123×C12718yes—
387C2×C4#123×C12718yes—
388C22—24no—
389C22—24no—
390C22—24no—
391C22—44no—
392C22—44no—
393C22—48no—
394C22—44no—
395C22—44no—
396C22C22×C22⋊C4×C12711yescharacteristic
397C22C2×#117×C12711yescharacteristic
398C22C2×#117×C12711yescharacteristic
399C22C4×#41×C12712yes—
400C22#520×C12712yes—
401C22C2×#123×C12712yes—
402C22C2×#123×C12712yes—
403C22#525×C12712yes—
404C22#532×C12712yes—
405C22#535×C12711yescharacteristic
406C22#536×C12711yescharacteristic
407C22#537×C12712yes—
408C22#552×C12714yes—
409C22#553×C12714yes—
410C22#555×C12714yes—
411C22#556×C12714yes—
412C4—24no—
413C4—48no—
414C4—44no—
415C4—44no—
416C4—84no—
417C4#381×C12718yes—
418C2—44no—
419C2C2×#381×C12711yescharacteristic
420C2C127×#229711yescharacteristic
421C2C127×#231111yescharacteristic
422C2C127×#234612yes—
423C2C127×#234712yes—
424C2C127×#248514yes—
425C2C127×#249912yes—
426C2C127×#250012yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C127×C4⋊#95C2semidirect
6. C127×C4⋊#95C2semidirect
7. C127×#1434C2semidirect
11. C2×#117×C127C4semidirect
204. #13939C127direct (N × H)
218. C4⋊#95C2×C127semidirect
219. C4⋊#95C2×C127semidirect
220. #1434C2×C127semidirect
221. C127#13939direct (N × H)
225. C2×#117C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C1272
C2×#380×C1272
C2×C4×C22⋊C4×C1272
C127×#14402
C127×C4⋊#952
C127×#14342
#13939127