Finite Group Databasebeta

← C127×#17008 #44580681

Subgroups — C127×#17008 #44580681

Order 32512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#389×C127C211yesmaximal, characteristic
3C127×#1445C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1442C214yesmaximal
6C127×#1441C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#389×C127—24no—
17#389×C127—24no—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2214yes—
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×C127C2314yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2312yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—24no—
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127—24no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—42no—
46C2×C4⋊C4×C127—42no—
47C2×C4⋊C4×C127—44no—
48C2×C4⋊C4×C127Q814yes—
49C2×C42×C127—42no—
50C2×C42×C127D414yes—
51#95×C127—24no—
52#95×C127—24no—
53#95×C127—28no—
54#95×C127—24no—
55#95×C127—24no—
56#95×C127—44no—
57#95×C127—44no—
58#95×C127—42no—
59#95×C127—44no—
60C24×C127C2411yescharacteristic
61C22×C4×C127—22no—
62C22×C4×C127—22no—
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—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—24no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—24no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
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—24no—
93C22×C4×C127—24no—
94C22×C4×C127C2×D412yes—
95C22×C4×C127C2×D412yes—
96C22×C4×C127C2×D412yes—
97C22×C4×C127C2×Q814yes—
98C22×C4×C127C2×Q812yes—
99C22×C4×C127#4114yes—
100C22×C4×C127#4112yes—
101C22×C4×C127#4114yes—
102C4⋊C4×C127—28no—
103C4⋊C4×C127—28no—
104C4⋊C4×C127—44no—
105C4⋊C4×C127—44no—
106C4⋊C4×C127—48no—
107C4⋊C4×C127—48no—
108C42×C127—44no—
109C23×C127C22×D411yescharacteristic
110C23×C127C22×Q811yescharacteristic
111C23×C127C2×#4111yescharacteristic
112C23×C127C2×#4112yes—
113C23×C127C2×#4112yes—
114C23×C127H(5,𝔽2)12yes—
115C23×C127H(5,𝔽2)12yes—
116C23×C1272−1+412yes—
117C23×C1272−1+412yes—
118C2×C4×C127—22no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—24no—
123C2×C4×C127—24no—
124C2×C4×C127—28no—
125C2×C4×C127—24no—
126C2×C4×C127—24no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—28no—
131C2×C4×C127—24no—
132C2×C4×C127—24no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—44no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—44no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—42no—
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—44no—
154C2×C4×C127—44no—
155C2×C4×C127—48no—
156C2×C4×C127—44no—
157C2×C4×C127C22⋊Q814yes—
158C2×C4×C127#12414yes—
159C22×C127C2×C22⋊Q811yescharacteristic
160C22×C127#52511yescharacteristic
161C22×C127C2×#12411yescharacteristic
162C22×C127#53411yescharacteristic
163C22×C127#53511yescharacteristic
164C22×C127#53611yescharacteristic
165C22×C127#53611yescharacteristic
166C22×C127#53912yes—
167C22×C127#53914yes—
168C22×C127#54114yes—
169C22×C127#54412yes—
170C22×C127#55314yes—
171C22×C127#55412yes—
172C22×C127#55512yes—
173C22×C127#55612yes—
174C22×C127#55712yes—
175C22×C127#56214yes—
176C4×C127—24no—
177C4×C127—24no—
178C4×C127—42no—
179C4×C127—44no—
180C4×C127—44no—
181C4×C127—82no—
182C4×C127—82no—
183C4×C127—84no—
184#17008C12711yesmaximal, characteristic, direct product factor, Sylow
185C2×C127#256311yescharacteristic
186C2×C127#258111yescharacteristic
187C2×C127#259111yescharacteristic
188C2×C127#262711yescharacteristic
189C2×C127#263311yescharacteristic
190C2×C127#264211yescharacteristic
191C2×C127#278314yes—
192C2×C127#280214yes—
193C2×C127#281611yescharacteristic
194C2×#389C2×C12711yescharacteristic
195C2×#389C2×C12711yescharacteristic
196#1445C2×C12712yes—
197#1442C2×C12712yes—
198#1442C2×C12714yes—
199#1441C2×C12712yes—
200#1441C2×C12712yes—
201#1434C2×C12711yescharacteristic
202C127#1700811yescharacteristic, direct product factor, Sylow
203C22×C4⋊C4C22×C12711yescharacteristic
204C22×C4⋊C4C22×C12712yes—
205C22×C4⋊C4C22×C12711yescharacteristic
206C22×C4⋊C4C22×C12711yescharacteristic
207C22×C4⋊C4C22×C12711yescharacteristic
208C22×C4⋊C4C22×C12712yes—
209C22×C42C22×C12711yescharacteristic
210#389—24no—
211#389—24no—
212C2×#95C22×C12712yes—
213C2×#95C22×C12712yes—
214C2×#95C22×C12714yes—
215C2×#95C22×C12712yes—
216C2×#95C22×C12712yes—
217C2×#95C22×C12712yes—
218C2×#95C22×C12714yes—
219C2×#95C22×C12714yes—
220C2×#95C22×C12714yes—
221C23×C4C23×C12712yes—
222C23×C4C23×C12712yes—
223C23×C4C23×C12714yes—
224C23×C4C23×C12711yescharacteristic
225C23×C4C23×C12712yes—
226C23×C4C23×C12712yes—
227C23×C4C23×C12711yescharacteristic
228C23×C4C23×C12711yescharacteristic
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4Q8×C12714yes—
243C2×C42—42no—
244C2×C42D4×C12714yes—
245#95—24no—
246#95—24no—
247#95—28no—
248#95—24no—
249#95—24no—
250#95—44no—
251#95—44no—
252#95—42no—
253#95—44no—
254C24C24×C12711yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4C2×D4×C12712yes—
289C22×C4C2×D4×C12712yes—
290C22×C4C2×D4×C12712yes—
291C22×C4C2×Q8×C12714yes—
292C22×C4C2×Q8×C12712yes—
293C22×C4#41×C12714yes—
294C22×C4#41×C12712yes—
295C22×C4#41×C12714yes—
296C4⋊C4—28no—
297C4⋊C4—28no—
298C4⋊C4—44no—
299C4⋊C4—44no—
300C4⋊C4—48no—
301C4⋊C4—48no—
302C42—44no—
303C23C22×D4×C12711yescharacteristic
304C23C22×Q8×C12711yescharacteristic
305C23C2×#41×C12711yescharacteristic
306C23C2×#41×C12712yes—
307C23C2×#41×C12712yes—
308C23H(5,𝔽2)×C12712yes—
309C23H(5,𝔽2)×C12712yes—
310C232−1+4×C12712yes—
311C232−1+4×C12712yes—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—28no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—28no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—48no—
351C2×C4C22⋊Q8×C12714yes—
352C2×C4#124×C12714yes—
353C22C2×C22⋊Q8×C12711yescharacteristic
354C22#525×C12711yescharacteristic
355C22C2×#124×C12711yescharacteristic
356C22#534×C12711yescharacteristic
357C22#535×C12711yescharacteristic
358C22#536×C12711yescharacteristic
359C22#536×C12711yescharacteristic
360C22#539×C12712yes—
361C22#539×C12714yes—
362C22#541×C12714yes—
363C22#544×C12712yes—
364C22#553×C12714yes—
365C22#554×C12712yes—
366C22#555×C12712yes—
367C22#556×C12712yes—
368C22#557×C12712yes—
369C22#562×C12714yes—
370C4—24no—
371C4—24no—
372C4—44no—
373C4—42no—
374C4—44no—
375C4—82no—
376C4—84no—
377C4—82no—
378C2C127×#256311yescharacteristic
379C2C127×#258111yescharacteristic
380C2C127×#259111yescharacteristic
381C2C127×#262711yescharacteristic
382C2C127×#263311yescharacteristic
383C2C127×#264211yescharacteristic
384C2C127×#278314yes—
385C2C127×#280214yes—
386C2C127×#281611yescharacteristic
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
184. #17008C127direct (N × H)
202. C127#17008direct (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
C127×#14452
C127×#14422
C127×#14412
C127×#14342
#17008127