Finite Group Databasebeta

← C127×#16961 #44580634

Subgroups — C127×#16961 #44580634

Order 32512.

1058 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#382×C127C211yesmaximal, characteristic
3C127×#1445C212yesmaximal
4C127×#1445C212yesmaximal
5C127×#1445C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C214yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C42×C127C2211yescharacteristic
15#389×C127—24no—
16#382×C127—24no—
17C2×#95×C127C2212yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2214yes—
27C23×C4×C127C2312yes—
28C23×C4×C127C2312yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2312yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—24no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127—24no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—44no—
45C2×C42×C127—24no—
46C2×C42×C127D414yes—
47#95×C127—24no—
48#95×C127—24no—
49#95×C127—24no—
50#95×C127—28no—
51#95×C127—24no—
52#95×C127—24no—
53#95×C127—42no—
54#95×C127—44no—
55#95×C127—44no—
56#95×C127—44no—
57C24×C127C2411yescharacteristic
58C22×C4×C127—22no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—21no—
66C22×C4×C127—24no—
67C22×C4×C127—22no—
68C22×C4×C127—21no—
69C22×C4×C127—24no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127C2×D412yes—
93C22×C4×C127C2×D412yes—
94C22×C4×C127C2×D412yes—
95C22×C4×C127#4114yes—
96C22×C4×C127#4114yes—
97C22×C4×C127#4114yes—
98C4⋊C4×C127—28no—
99C4⋊C4×C127—48no—
100C4⋊C4×C127—44no—
101C4⋊C4×C127—44no—
102C4⋊C4×C127—44no—
103C42×C127—28no—
104C23×C127C22×D411yescharacteristic
105C23×C127C2×#4112yes—
106C23×C127C2×#4112yes—
107C23×C127C2×#4112yes—
108C23×C127H(5,𝔽2)12yes—
109C23×C127H(5,𝔽2)11yescharacteristic
110C23×C1272−1+412yes—
111C23×C1272−1+412yes—
112C23×C1272−1+411yescharacteristic
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—22no—
117C2×C4×C127—28no—
118C2×C4×C127—28no—
119C2×C4×C127—22no—
120C2×C4×C127—24no—
121C2×C4×C127—22no—
122C2×C4×C127—22no—
123C2×C4×C127—28no—
124C2×C4×C127—42no—
125C2×C4×C127—42no—
126C2×C4×C127—44no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—42no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—44no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—44no—
142C2×C4×C127—44no—
143C2×C4×C127—44no—
144C2×C4×C127—44no—
145C2×C4×C127—44no—
146C2×C4×C127—44no—
147C2×C4×C127—44no—
148C2×C4×C127—44no—
149C2×C4×C127—44no—
150C2×C4×C127—44no—
151C2×C4×C127#12314yes—
152C2×C4×C127#12414yes—
153C22×C127C2×#12311yescharacteristic
154C22×C127#52511yescharacteristic
155C22×C127C2×#12411yescharacteristic
156C22×C127#53511yescharacteristic
157C22×C127#53611yescharacteristic
158C22×C127#53611yescharacteristic
159C22×C127#53711yescharacteristic
160C22×C127#53914yes—
161C22×C127#54012yes—
162C22×C127#54212yes—
163C22×C127#54214yes—
164C22×C127#55214yes—
165C22×C127#55214yes—
166C22×C127#55612yes—
167C22×C127#55912yes—
168C22×C127#56312yes—
169C22×C127#56412yes—
170C4×C127—24no—
171C4×C127—24no—
172C4×C127—42no—
173C4×C127—44no—
174C4×C127—82no—
175C4×C127—82no—
176C4×C127—82no—
177C4×C127—84no—
178#16961C12711yesmaximal, characteristic, direct product factor, Sylow
179C2×C127#248411yescharacteristic
180C2×C127#250311yescharacteristic
181C2×C127#259211yescharacteristic
182C2×C127#262411yescharacteristic
183C2×C127#263311yescharacteristic
184C2×C127#264011yescharacteristic
185C2×C127#276714yes—
186C2×C127#277314yes—
187C2×C127#282211yescharacteristic
188C2×#389C2×C12711yescharacteristic
189C2×#382C2×C12711yescharacteristic
190#1445C2×C12712yes—
191#1445C2×C12712yes—
192#1445C2×C12712yes—
193#1442C2×C12712yes—
194#1442C2×C12714yes—
195#1434C2×C12711yescharacteristic
196C127#1696111yescharacteristic, direct product factor, Sylow
197C22×C4⋊C4C22×C12711yescharacteristic
198C22×C4⋊C4C22×C12711yescharacteristic
199C22×C4⋊C4C22×C12711yescharacteristic
200C22×C4⋊C4C22×C12711yescharacteristic
201C22×C4⋊C4C22×C12712yes—
202C22×C42C22×C12711yescharacteristic
203#389—24no—
204#382—24no—
205C2×#95C22×C12712yes—
206C2×#95C22×C12712yes—
207C2×#95C22×C12714yes—
208C2×#95C22×C12712yes—
209C2×#95C22×C12712yes—
210C2×#95C22×C12712yes—
211C2×#95C22×C12712yes—
212C2×#95C22×C12714yes—
213C2×#95C22×C12714yes—
214C2×#95C22×C12714yes—
215C23×C4C23×C12712yes—
216C23×C4C23×C12712yes—
217C23×C4C23×C12712yes—
218C23×C4C23×C12714yes—
219C23×C4C23×C12711yescharacteristic
220C23×C4C23×C12712yes—
221C23×C4C23×C12711yescharacteristic
222C23×C4C23×C12711yescharacteristic
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—44no—
233C2×C42—24no—
234C2×C42D4×C12714yes—
235#95—24no—
236#95—24no—
237#95—24no—
238#95—28no—
239#95—24no—
240#95—24no—
241#95—42no—
242#95—44no—
243#95—44no—
244#95—44no—
245C24C24×C12711yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4C2×D4×C12712yes—
281C22×C4C2×D4×C12712yes—
282C22×C4C2×D4×C12712yes—
283C22×C4#41×C12714yes—
284C22×C4#41×C12714yes—
285C22×C4#41×C12714yes—
286C4⋊C4—28no—
287C4⋊C4—48no—
288C4⋊C4—44no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C42—28no—
292C23C22×D4×C12711yescharacteristic
293C23C2×#41×C12712yes—
294C23C2×#41×C12712yes—
295C23C2×#41×C12712yes—
296C23H(5,𝔽2)×C12712yes—
297C23H(5,𝔽2)×C12711yescharacteristic
298C232−1+4×C12712yes—
299C232−1+4×C12712yes—
300C232−1+4×C12711yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—28no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4#123×C12714yes—
340C2×C4#124×C12714yes—
341C22C2×#123×C12711yescharacteristic
342C22#525×C12711yescharacteristic
343C22C2×#124×C12711yescharacteristic
344C22#535×C12711yescharacteristic
345C22#536×C12711yescharacteristic
346C22#536×C12711yescharacteristic
347C22#537×C12711yescharacteristic
348C22#539×C12714yes—
349C22#540×C12712yes—
350C22#542×C12712yes—
351C22#542×C12714yes—
352C22#552×C12714yes—
353C22#552×C12714yes—
354C22#556×C12712yes—
355C22#559×C12712yes—
356C22#563×C12712yes—
357C22#564×C12712yes—
358C4—24no—
359C4—24no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—82no—
364C4—82no—
365C4—84no—
366C2C127×#248411yescharacteristic
367C2C127×#250311yescharacteristic
368C2C127×#259211yescharacteristic
369C2C127×#262411yescharacteristic
370C2C127×#263311yescharacteristic
371C2C127×#264011yescharacteristic
372C2C127×#276714yes—
373C2C127×#277314yes—
374C2C127×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
178. #16961C127direct (N × H)
196. C127#16961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#382×C1272
C127×#14452
C127×#14422
C127×#14342
#16961127