Finite Group Databasebeta

← C127×#8298 #44571971

Subgroups — C127×#8298 #44571971

Order 32512.

2574 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C127×#1779C212yesmaximal, complemented
3C2×#323×C127C214yesmaximal, complemented
4C26×C127C411yescharacteristic
5C24×C4×C127C411yescharacteristic
6C24×C4×C127C2211yescharacteristic
7C22×C22⋊C4×C127—24no—
8C22×C22⋊C4×C127—28no—
9C22×C22⋊C4×C127C412yes—
10C22×C22⋊C4×C127C2212yes—
11C2×C22⋊C8×C127—24no—
12C2×C22⋊C8×C127C2214yescomplemented
13#323×C127—28no—
14C25×C127—24no—
15C25×C127—22no—
16C25×C127—24no—
17C25×C127—22no—
18C25×C127—44no—
19C25×C127—44no—
20C25×C127C814yescomplemented
21C25×C127C2×C411yescharacteristic
22C25×C127C2×C412yes—
23C23×C4×C127—22no—
24C23×C4×C127—24no—
25C23×C4×C127—24no—
26C23×C4×C127—44no—
27C23×C4×C127—44no—
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127C2×C412yes—
30C23×C4×C127D414yes—
31C23×C4×C127C2311yescharacteristic
32C22×C8×C127—24no—
33C2×C22⋊C4×C127—232no—
34C2×C22⋊C4×C127—24no—
35C2×C22⋊C4×C127—24no—
36C2×C22⋊C4×C127—24no—
37C2×C22⋊C4×C127—24no—
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127D418yes—
40C22⋊C8×C127—28no—
41C22⋊C8×C127—48no—
42C24×C127—24no—
43C24×C127—24no—
44C24×C127—22no—
45C24×C127—22no—
46C24×C127—28no—
47C24×C127—28no—
48C24×C127—216no—
49C24×C127—28no—
50C24×C127—216no—
51C24×C127—22no—
52C24×C127—22no—
53C24×C127—22no—
54C24×C127—22no—
55C24×C127—416no—
56C24×C127—44no—
57C24×C127—44no—
58C24×C127—416no—
59C24×C127—416no—
60C24×C127—432no—
61C24×C127—416no—
62C24×C127—44no—
63C24×C127—44no—
64C24×C127—44no—
65C24×C127—44no—
66C24×C127C22⋊C412yes—
67C24×C127C22⋊C414yes—
68C24×C127C2×C812yes—
69C24×C127C2×C814yes—
70C24×C127M1612yes—
71C24×C127M1614yes—
72C24×C127C22×C411yescharacteristic
73C22×C4×C127—28no—
74C22×C4×C127—28no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—28no—
79C22×C4×C127—42no—
80C22×C4×C127—44no—
81C22×C4×C127—42no—
82C22×C4×C127—416no—
83C22×C4×C127—416no—
84C22×C4×C127—44no—
85C22×C4×C127—44no—
86C22×C4×C127—44no—
87C22×C4×C127C22⋊C412yes—
88C22×C4×C127C22⋊C414yes—
89C22×C4×C127C2×D412yes—
90C22×C4×C127C2×D414yes—
91C2×C8×C127—48no—
92C2×C8×C127—44no—
93C22⋊C4×C127—216no—
94C22⋊C4×C127—216no—
95C23×C127—28no—
96C23×C127—28no—
97C23×C127—216no—
98C23×C127—28no—
99C23×C127—28no—
100C23×C127—22no—
101C23×C127—24no—
102C23×C127—22no—
103C23×C127—24no—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—22no—
107C23×C127—22no—
108C23×C127—232no—
109C23×C127—24no—
110C23×C127—24no—
111C23×C127—24no—
112C23×C127—24no—
113C23×C127—24no—
114C23×C127—24no—
115C23×C127—44no—
116C23×C127—44no—
117C23×C127—48no—
118C23×C127—48no—
119C23×C127—464no—
120C23×C127—464no—
121C23×C127—416no—
122C23×C127—48no—
123C23×C127—416no—
124C23×C127—416no—
125C23×C127—48no—
126C23×C127—416no—
127C23×C127—44no—
128C23×C127—416no—
129C23×C127—44no—
130C23×C127—416no—
131C23×C127—44no—
132C23×C127—44no—
133C23×C127C22⋊C814yes—
134C23×C127C22⋊C818yescomplemented
135C23×C127#9914yes—
136C23×C127#10014yes—
137C23×C127C2×C22⋊C412yes—
138C23×C127C2×C22⋊C411yescharacteristic
139C23×C127C22×C811yescharacteristic
140C23×C127C2×M1611yescharacteristic
141C23×C127C2×M1612yes—
142C2×C4×C127—24no—
143C2×C4×C127—22no—
144C2×C4×C127—24no—
145C2×C4×C127—24no—
146C2×C4×C127—44no—
147C2×C4×C127—416no—
148C2×C4×C127—44no—
149C2×C4×C127—416no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—44no—
153C2×C4×C127#12014yes—
154C8×C127—84no—
155C22×C127—216no—
156C22×C127—216no—
157C22×C127—24no—
158C22×C127—22no—
159C22×C127—22no—
160C22×C127—24no—
161C22×C127—24no—
162C22×C127—24no—
163C22×C127—24no—
164C22×C127—24no—
165C22×C127—22no—
166C22×C127—24no—
167C22×C127—22no—
168C22×C127—28no—
169C22×C127—48no—
170C22×C127—464no—
171C22×C127—48no—
172C22×C127—48no—
173C22×C127—48no—
174C22×C127—48no—
175C22×C127—48no—
176C22×C127—44no—
177C22×C127—44no—
178C22×C127#32318yescomplemented
179C22×C127#37911yescharacteristic
180C22×C127C2×C22⋊C812yes—
181C22×C127C2×C22⋊C811yescharacteristic
182C22×C127#40712yes—
183C22×C127#40711yescharacteristic
184C22×C127C2×#9912yes—
185C22×C127C2×#10012yes—
186C4×C127—24no—
187C4×C127—42no—
188C4×C127—44no—
189#8298C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—28no—
191C2×C127—22no—
192C2×C127—22no—
193C2×C127—48no—
194C2×C127C2×#32312yes—
195C2×C127#146212yes—
196C2×C127#177911yescharacteristic
197C2×C127#178111yescharacteristic
198C2×C127#178311yescharacteristic
199C23×C22⋊C4C2×C12711yescharacteristic
200#1779C2×C12712yescomplemented
201C2×#323C2×C12714yescomplemented
202C127#829811yescharacteristic, direct product factor, Sylow
203C26C4×C12711yescharacteristic
204C24×C4C4×C12711yescharacteristic
205C24×C4C22×C12711yescharacteristic
206C22×C22⋊C4—24no—
207C22×C22⋊C4—28no—
208C22×C22⋊C4C4×C12712yes—
209C22×C22⋊C4C22×C12712yes—
210C2×C22⋊C8—24no—
211C2×C22⋊C8C22×C12714yescomplemented
212#323—28no—
213C25—24no—
214C25—22no—
215C25—24no—
216C25—22no—
217C25—44no—
218C25—44no—
219C25C8×C12714yescomplemented
220C25C2×C4×C12711yescharacteristic
221C25C2×C4×C12712yes—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—44no—
226C23×C4—44no—
227C23×C4C2×C4×C12711yescharacteristic
228C23×C4C2×C4×C12712yes—
229C23×C4D4×C12714yes—
230C23×C4C23×C12711yescharacteristic
231C22×C8—24no—
232C2×C22⋊C4—232no—
233C2×C22⋊C4—24no—
234C2×C22⋊C4—24no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4D4×C12718yes—
239C22⋊C8—28no—
240C22⋊C8—48no—
241C24—24no—
242C24—24no—
243C24—22no—
244C24—22no—
245C24—28no—
246C24—28no—
247C24—216no—
248C24—28no—
249C24—216no—
250C24—22no—
251C24—22no—
252C24—22no—
253C24—22no—
254C24—416no—
255C24—44no—
256C24—44no—
257C24—416no—
258C24—416no—
259C24—432no—
260C24—416no—
261C24—44no—
262C24—44no—
263C24—44no—
264C24—44no—
265C24C22⋊C4×C12712yes—
266C24C22⋊C4×C12714yes—
267C24C2×C8×C12712yes—
268C24C2×C8×C12714yes—
269C24M16×C12712yes—
270C24M16×C12714yes—
271C24C22×C4×C12711yescharacteristic
272C22×C4—28no—
273C22×C4—28no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—28no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—42no—
281C22×C4—416no—
282C22×C4—416no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4C22⋊C4×C12712yes—
287C22×C4C22⋊C4×C12714yes—
288C22×C4C2×D4×C12712yes—
289C22×C4C2×D4×C12714yes—
290C2×C8—48no—
291C2×C8—44no—
292C22⋊C4—216no—
293C22⋊C4—216no—
294C23—28no—
295C23—28no—
296C23—216no—
297C23—28no—
298C23—28no—
299C23—22no—
300C23—24no—
301C23—22no—
302C23—24no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—232no—
308C23—24no—
309C23—24no—
310C23—24no—
311C23—24no—
312C23—24no—
313C23—24no—
314C23—44no—
315C23—44no—
316C23—48no—
317C23—48no—
318C23—464no—
319C23—464no—
320C23—416no—
321C23—48no—
322C23—416no—
323C23—416no—
324C23—48no—
325C23—416no—
326C23—44no—
327C23—416no—
328C23—44no—
329C23—416no—
330C23—44no—
331C23—44no—
332C23C22⋊C8×C12714yes—
333C23C22⋊C8×C12718yescomplemented
334C23#99×C12714yes—
335C23#100×C12714yes—
336C23C2×C22⋊C4×C12712yes—
337C23C2×C22⋊C4×C12711yescharacteristic
338C23C22×C8×C12711yescharacteristic
339C23C2×M16×C12711yescharacteristic
340C23C2×M16×C12712yes—
341C2×C4—24no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—44no—
346C2×C4—416no—
347C2×C4—44no—
348C2×C4—416no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4#120×C12714yes—
353C8—84no—
354C22—216no—
355C22—216no—
356C22—24no—
357C22—22no—
358C22—22no—
359C22—24no—
360C22—24no—
361C22—24no—
362C22—24no—
363C22—24no—
364C22—22no—
365C22—24no—
366C22—22no—
367C22—28no—
368C22—48no—
369C22—464no—
370C22—48no—
371C22—48no—
372C22—48no—
373C22—48no—
374C22—48no—
375C22—44no—
376C22—44no—
377C22#323×C12718yescomplemented
378C22#379×C12711yescharacteristic
379C22C2×C22⋊C8×C12712yes—
380C22C2×C22⋊C8×C12711yescharacteristic
381C22#407×C12712yes—
382C22#407×C12711yescharacteristic
383C22C2×#99×C12712yes—
384C22C2×#100×C12712yes—
385C4—24no—
386C4—42no—
387C4—44no—
388C2—28no—
389C2—22no—
390C2—22no—
391C2—48no—
392C2C2×#323×C12712yes—
393C2C127×#146212yes—
394C2C127×#177911yescharacteristic
395C2C127×#178111yescharacteristic
396C2C127×#178311yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C22×C8×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC26×C127C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1779C2semidirect
3. C2×#323×C127C2semidirect
12. C2×C22⋊C8×C127C22semidirect
20. C25×C127C8semidirect
134. C23×C127C22⋊C8semidirect
178. C22×C127#323semidirect
189. #8298C127direct (N × H)
200. #1779C2×C127semidirect
201. C2×#323C2×C127semidirect
202. C127#8298direct (N × H)
211. C2×C22⋊C8C22×C127semidirect
219. C25C8×C127semidirect
333. C23C22⋊C8×C127semidirect
377. C22#323×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C127×#17792
C2×#323×C1272
#8298127