Finite Group Databasebeta

← C127×#16694 #44580367

Subgroups — C127×#16694 #44580367

Order 32512.

1210 conjugacy classes of subgroups.

The subgroup lattice has 386 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×#1444C212yesmaximal
5C127×#1444C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C214yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2214yes—
14C22×C42×C127C2211yescharacteristic
15#391×C127—24no—
16#382×C127—24no—
17C2×#95×C127C2212yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
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×C127C2311yescharacteristic
35C23×C4×C127C2314yes—
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—42no—
43C2×C4⋊C4×C127—42no—
44C2×C4⋊C4×C127—42no—
45C2×C4⋊C4×C127—44no—
46C2×C4⋊C4×C127—44no—
47C2×C4⋊C4×C127—44no—
48C2×C42×C127—24no—
49C2×C42×C127D414yes—
50#95×C127—24no—
51#95×C127—24no—
52#95×C127—24no—
53#95×C127—24no—
54#95×C127—24no—
55#95×C127—28no—
56#95×C127—42no—
57#95×C127—44no—
58#95×C127—44no—
59#95×C127Q818yescomplemented
60C24×C127C2411yescharacteristic
61C2×Q8×C127—28no—
62C2×Q8×C127—416no—
63C2×Q8×C127—44no—
64C2×Q8×C127—44no—
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—24no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—24no—
75C22×C4×C127—21no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—22no—
81C22×C4×C127—21no—
82C22×C4×C127—24no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
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—22no—
93C22×C4×C127—22no—
94C22×C4×C127—24no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127C2×D412yes—
98C22×C4×C127C2×D412yes—
99C22×C4×C127C2×D412yes—
100C22×C4×C127C2×Q818yes—
101C22×C4×C127C2×Q814yes—
102C22×C4×C127#4114yes—
103C22×C4×C127#4114yes—
104C4⋊C4×C127—44no—
105C4⋊C4×C127—44no—
106C4⋊C4×C127—44no—
107C4⋊C4×C127—416no—
108C42×C127—28no—
109C23×C127C22×D411yescharacteristic
110C23×C127C22×Q812yes—
111C23×C127C2×#4112yes—
112C23×C127C2×#4112yes—
113C23×C127H(5,𝔽2)12yes—
114C23×C127H(5,𝔽2)12yes—
115C23×C127H(5,𝔽2)11yescharacteristic
116C23×C1272−1+412yes—
117C23×C1272−1+411yescharacteristic
118Q8×C127—416no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—22no—
123C2×C4×C127—28no—
124C2×C4×C127—28no—
125C2×C4×C127—22no—
126C2×C4×C127—24no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—28no—
130C2×C4×C127—28no—
131C2×C4×C127—28no—
132C2×C4×C127—28no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—44no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—48no—
152C2×C4×C127—44no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127#12314yes—
157C2×C4×C127C4⋊Q814yes—
158C22×C127C2×#12311yescharacteristic
159C22×C127#52511yescharacteristic
160C22×C127C2×C4⋊Q811yescharacteristic
161C22×C127#53511yescharacteristic
162C22×C127#53511yescharacteristic
163C22×C127#53611yescharacteristic
164C22×C127#53711yescharacteristic
165C22×C127#54112yes—
166C22×C127#54212yes—
167C22×C127#54214yes—
168C22×C127#54414yes—
169C22×C127#55114yes—
170C22×C127#55412yes—
171C22×C127#55414yes—
172C22×C127#55712yes—
173C22×C127H(3,𝔽4)12yes—
174C22×C127#56212yes—
175C4×C127—24no—
176C4×C127—24no—
177C4×C127—42no—
178C4×C127—44no—
179C4×C127—48no—
180C4×C127—82no—
181C4×C127—82no—
182C4×C127—82no—
183#16694C12711yesmaximal, characteristic, direct product factor, Sylow
184C2×C127#248211yescharacteristic
185C2×C127#250211yescharacteristic
186C2×C127#258411yescharacteristic
187C2×C127#262511yescharacteristic
188C2×C127#263211yescharacteristic
189C2×C127#266011yescharacteristic
190C2×C127#275514yes—
191C2×C127#276314yes—
192C2×C127#281911yescharacteristic
193C2×#391C2×C12711yescharacteristic
194C2×#382C2×C12711yescharacteristic
195#1446C2×C12712yes—
196#1444C2×C12712yes—
197#1444C2×C12712yes—
198#1442C2×C12712yes—
199#1442C2×C12714yes—
200#1434C2×C12711yescharacteristic
201C127#1669411yescharacteristic, direct product factor, Sylow
202C23×Q8C22×C12711yescharacteristic
203C22×C4⋊C4C22×C12711yescharacteristic
204C22×C4⋊C4C22×C12711yescharacteristic
205C22×C4⋊C4C22×C12711yescharacteristic
206C22×C4⋊C4C22×C12714yes—
207C22×C42C22×C12711yescharacteristic
208#391—24no—
209#382—24no—
210C2×#95C22×C12712yes—
211C2×#95C22×C12714yes—
212C2×#95C22×C12712yes—
213C2×#95C22×C12712yes—
214C2×#95C22×C12712yes—
215C2×#95C22×C12712yes—
216C2×#95C22×C12712yes—
217C2×#95C22×C12714yes—
218C2×#95C22×C12714yes—
219C2×#95C22×C12712yes—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—42no—
224C23×C4C23×C12712yes—
225C23×C4C23×C12712yes—
226C23×C4C23×C12712yes—
227C23×C4C23×C12711yescharacteristic
228C23×C4C23×C12714yes—
229C23×C4C23×C12712yes—
230C23×C4C23×C12711yescharacteristic
231C23×C4C23×C12711yescharacteristic
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4—44no—
240C2×C4⋊C4—44no—
241C2×C42—24no—
242C2×C42D4×C12714yes—
243#95—24no—
244#95—24no—
245#95—24no—
246#95—24no—
247#95—24no—
248#95—28no—
249#95—42no—
250#95—44no—
251#95—44no—
252#95Q8×C12718yescomplemented
253C24C24×C12711yescharacteristic
254C2×Q8—28no—
255C2×Q8—416no—
256C2×Q8—44no—
257C2×Q8—44no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—21no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4C2×D4×C12712yes—
291C22×C4C2×D4×C12712yes—
292C22×C4C2×D4×C12712yes—
293C22×C4C2×Q8×C12718yes—
294C22×C4C2×Q8×C12714yes—
295C22×C4#41×C12714yes—
296C22×C4#41×C12714yes—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—44no—
300C4⋊C4—416no—
301C42—28no—
302C23C22×D4×C12711yescharacteristic
303C23C22×Q8×C12712yes—
304C23C2×#41×C12712yes—
305C23C2×#41×C12712yes—
306C23H(5,𝔽2)×C12712yes—
307C23H(5,𝔽2)×C12712yes—
308C23H(5,𝔽2)×C12711yescharacteristic
309C232−1+4×C12712yes—
310C232−1+4×C12711yescharacteristic
311Q8—416no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—28no—
323C2×C4—28no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—48no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4#123×C12714yes—
350C2×C4C4⋊Q8×C12714yes—
351C22C2×#123×C12711yescharacteristic
352C22#525×C12711yescharacteristic
353C22C2×C4⋊Q8×C12711yescharacteristic
354C22#535×C12711yescharacteristic
355C22#535×C12711yescharacteristic
356C22#536×C12711yescharacteristic
357C22#537×C12711yescharacteristic
358C22#541×C12712yes—
359C22#542×C12712yes—
360C22#542×C12714yes—
361C22#544×C12714yes—
362C22#551×C12714yes—
363C22#554×C12712yes—
364C22#554×C12714yes—
365C22#557×C12712yes—
366C22H(3,𝔽4)×C12712yes—
367C22#562×C12712yes—
368C4—24no—
369C4—24no—
370C4—42no—
371C4—44no—
372C4—48no—
373C4—82no—
374C4—82no—
375C4—82no—
376C2C127×#248211yescharacteristic
377C2C127×#250211yescharacteristic
378C2C127×#258411yescharacteristic
379C2C127×#262511yescharacteristic
380C2C127×#263211yescharacteristic
381C2C127×#266011yescharacteristic
382C2C127×#275514yes—
383C2C127×#276314yes—
384C2C127×#281911yescharacteristic
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
59. #95×C127Q8semidirect
183. #16694C127direct (N × H)
201. C127#16694direct (N × H)
252. #95Q8×C127semidirect

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×#14442
C127×#14422
C127×#14342
#16694127