Finite Group Databasebeta

← C127×#16695 #44580368

Subgroups — C127×#16695 #44580368

Order 32512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C211yesmaximal, characteristic
2C2×#382×C127C211yesmaximal, characteristic
3C127×#1446C212yesmaximal
4C127×#1445C212yesmaximal
5C127×#1445C212yesmaximal
6C127×#1443C214yesmaximal
7C127×#1442C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C42×C127C2211yescharacteristic
14#391×C127—24no—
15#382×C127—24no—
16C2×#95×C127C2212yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2214yes—
27C22×Q8×C127—22no—
28C22×Q8×C127—24no—
29C22×Q8×C127—24no—
30C22×Q8×C127—42no—
31C23×C4×C127C2312yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2314yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2312yes—
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2311yescharacteristic
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—42no—
45C2×C42×C127—24no—
46C2×C42×C127D414yes—
47#95×C127—24no—
48#95×C127—24no—
49#95×C127—24no—
50#95×C127—24no—
51#95×C127—28no—
52#95×C127—24no—
53#95×C127—24no—
54#95×C127—42no—
55#95×C127—44no—
56#95×C127—44no—
57#95×C127—44no—
58C24×C127C2411yescharacteristic
59C2×Q8×C127—28no—
60C2×Q8×C127—416no—
61C2×Q8×C127—44no—
62C2×Q8×C127—44no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—21no—
72C22×C4×C127—24no—
73C22×C4×C127—22no—
74C22×C4×C127—21no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127C2×D412yes—
97C22×C4×C127C2×D412yes—
98C22×C4×C127C2×D412yes—
99C22×C4×C127#4114yes—
100C22×C4×C127#4114yes—
101C22×C4×C127#4114yes—
102C4⋊C4×C127—44no—
103C4⋊C4×C127—44no—
104C4⋊C4×C127—44no—
105C42×C127—28no—
106C23×C127C22×D411yescharacteristic
107C23×C127C2×#4112yes—
108C23×C127C2×#4112yes—
109C23×C127C2×#4112yes—
110C23×C127H(5,𝔽2)12yes—
111C23×C127H(5,𝔽2)11yescharacteristic
112C23×C1272−1+412yes—
113C23×C1272−1+412yes—
114C23×C1272−1+411yescharacteristic
115Q8×C127—416no—
116C2×C4×C127—22no—
117C2×C4×C127—22no—
118C2×C4×C127—22no—
119C2×C4×C127—22no—
120C2×C4×C127—28no—
121C2×C4×C127—28no—
122C2×C4×C127—22no—
123C2×C4×C127—24no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—28no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—44no—
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—42no—
139C2×C4×C127—42no—
140C2×C4×C127—42no—
141C2×C4×C127—44no—
142C2×C4×C127—48no—
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—44no—
152C2×C4×C127—44no—
153C2×C4×C127#12314yes—
154C2×C4×C127#12414yes—
155C22×C127C2×#12311yescharacteristic
156C22×C127#52511yescharacteristic
157C22×C127C2×#12411yescharacteristic
158C22×C127#53511yescharacteristic
159C22×C127#53611yescharacteristic
160C22×C127#53611yescharacteristic
161C22×C127#53711yescharacteristic
162C22×C127#54112yes—
163C22×C127#54114yes—
164C22×C127#54212yes—
165C22×C127#54214yes—
166C22×C127#55114yes—
167C22×C127#55214yes—
168C22×C127#55612yes—
169C22×C127#55912yes—
170C22×C127#56212yes—
171C22×C127#56312yes—
172C4×C127—24no—
173C4×C127—24no—
174C4×C127—42no—
175C4×C127—44no—
176C4×C127—82no—
177C4×C127—82no—
178C4×C127—82no—
179C4×C127—84no—
180#16695C12711yesmaximal, characteristic, direct product factor, Sylow
181C2×C127#248211yescharacteristic
182C2×C127#250311yescharacteristic
183C2×C127#259211yescharacteristic
184C2×C127#262511yescharacteristic
185C2×C127#263411yescharacteristic
186C2×C127#264011yescharacteristic
187C2×C127#275414yes—
188C2×C127#276214yes—
189C2×C127#282011yescharacteristic
190C2×#391C2×C12711yescharacteristic
191C2×#382C2×C12711yescharacteristic
192#1446C2×C12712yes—
193#1445C2×C12712yes—
194#1445C2×C12712yes—
195#1443C2×C12714yes—
196#1442C2×C12712yes—
197#1434C2×C12711yescharacteristic
198C127#1669511yescharacteristic, direct product factor, Sylow
199C23×Q8C22×C12711yescharacteristic
200C22×C4⋊C4C22×C12711yescharacteristic
201C22×C4⋊C4C22×C12711yescharacteristic
202C22×C4⋊C4C22×C12711yescharacteristic
203C22×C42C22×C12711yescharacteristic
204#391—24no—
205#382—24no—
206C2×#95C22×C12712yes—
207C2×#95C22×C12712yes—
208C2×#95C22×C12712yes—
209C2×#95C22×C12712yes—
210C2×#95C22×C12712yes—
211C2×#95C22×C12714yes—
212C2×#95C22×C12712yes—
213C2×#95C22×C12712yes—
214C2×#95C22×C12714yes—
215C2×#95C22×C12714yes—
216C2×#95C22×C12714yes—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—42no—
221C23×C4C23×C12712yes—
222C23×C4C23×C12712yes—
223C23×C4C23×C12712yes—
224C23×C4C23×C12714yes—
225C23×C4C23×C12711yescharacteristic
226C23×C4C23×C12712yes—
227C23×C4C23×C12711yescharacteristic
228C23×C4C23×C12711yescharacteristic
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—42no—
235C2×C42—24no—
236C2×C42D4×C12714yes—
237#95—24no—
238#95—24no—
239#95—24no—
240#95—24no—
241#95—28no—
242#95—24no—
243#95—24no—
244#95—42no—
245#95—44no—
246#95—44no—
247#95—44no—
248C24C24×C12711yescharacteristic
249C2×Q8—28no—
250C2×Q8—416no—
251C2×Q8—44no—
252C2×Q8—44no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—21no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4C2×D4×C12712yes—
287C22×C4C2×D4×C12712yes—
288C22×C4C2×D4×C12712yes—
289C22×C4#41×C12714yes—
290C22×C4#41×C12714yes—
291C22×C4#41×C12714yes—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4—44no—
295C42—28no—
296C23C22×D4×C12711yescharacteristic
297C23C2×#41×C12712yes—
298C23C2×#41×C12712yes—
299C23C2×#41×C12712yes—
300C23H(5,𝔽2)×C12712yes—
301C23H(5,𝔽2)×C12711yescharacteristic
302C232−1+4×C12712yes—
303C232−1+4×C12712yes—
304C232−1+4×C12711yescharacteristic
305Q8—416no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—28no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—48no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4#123×C12714yes—
344C2×C4#124×C12714yes—
345C22C2×#123×C12711yescharacteristic
346C22#525×C12711yescharacteristic
347C22C2×#124×C12711yescharacteristic
348C22#535×C12711yescharacteristic
349C22#536×C12711yescharacteristic
350C22#536×C12711yescharacteristic
351C22#537×C12711yescharacteristic
352C22#541×C12712yes—
353C22#541×C12714yes—
354C22#542×C12712yes—
355C22#542×C12714yes—
356C22#551×C12714yes—
357C22#552×C12714yes—
358C22#556×C12712yes—
359C22#559×C12712yes—
360C22#562×C12712yes—
361C22#563×C12712yes—
362C4—24no—
363C4—24no—
364C4—42no—
365C4—44no—
366C4—82no—
367C4—82no—
368C4—84no—
369C4—82no—
370C2C127×#248211yescharacteristic
371C2C127×#250311yescharacteristic
372C2C127×#259211yescharacteristic
373C2C127×#262511yescharacteristic
374C2C127×#263411yescharacteristic
375C2C127×#264011yescharacteristic
376C2C127×#275414yes—
377C2C127×#276214yes—
378C2C127×#282011yescharacteristic
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
180. #16695C127direct (N × H)
198. C127#16695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C2×#382×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14422
C127×#14342
#16695127