Finite Group Databasebeta

← C127×#16634 #44580307

Subgroups — C127×#16634 #44580307

Order 32512.

1338 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C127C211yesmaximal, characteristic
2C2×#400×C127C212yesmaximal
3C2×#389×C127C211yesmaximal, characteristic
4C127×#1442C214yesmaximal
5C127×#1441C212yesmaximal
6C127×#1441C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C2×#125×C127—28no—
10C2×#125×C127—24no—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#400×C127—28no—
20#389×C127—24no—
21C2×#95×C127C2212yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2214yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2214yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37#125×C127—232no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—24no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127D418yes—
55C2×C42×C127—24no—
56C2×C42×C127D414yes—
57#95×C127—24no—
58#95×C127—24no—
59#95×C127—28no—
60#95×C127—28no—
61#95×C127—28no—
62#95×C127—24no—
63#95×C127—44no—
64#95×C127—42no—
65C24×C127C2411yescharacteristic
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—22no—
75C22×C4×C127—22no—
76C22×C4×C127—24no—
77C22×C4×C127—22no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—21no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—21no—
88C22×C4×C127—24no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—22no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127C2×D412yes—
103C22×C4×C127C2×D414yes—
104C22×C4×C127C2×D414yes—
105C22×C4×C127C2×D414yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×D412yes—
108C22×C4×C127#4114yes—
109C22×C4×C127#4114yes—
110C4⋊C4×C127—28no—
111C4⋊C4×C127—28no—
112C4⋊C4×C127—28no—
113C4⋊C4×C127—216no—
114C4⋊C4×C127—216no—
115C4⋊C4×C127—44no—
116C4⋊C4×C127—48no—
117C42×C127—28no—
118C23×C127C22×D411yescharacteristic
119C23×C127C22×D412yes—
120C23×C127C2×#4112yes—
121C23×C127C2×#4112yes—
122C23×C127H(5,𝔽2)11yescharacteristic
123C23×C1272−1+412yes—
124C23×C1272−1+411yescharacteristic
125C23×C1272−1+412yes—
126C23×C1272−1+412yes—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—22no—
131C2×C4×C127—28no—
132C2×C4×C127—28no—
133C2×C4×C127—22no—
134C2×C4×C127—24no—
135C2×C4×C127—24no—
136C2×C4×C127—24no—
137C2×C4×C127—22no—
138C2×C4×C127—24no—
139C2×C4×C127—22no—
140C2×C4×C127—24no—
141C2×C4×C127—28no—
142C2×C4×C127—24no—
143C2×C4×C127—24no—
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—42no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
154C2×C4×C127—44no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127#12014yes—
170C2×C4×C127#12414yes—
171C22×C127C2×#12011yescharacteristic
172C22×C127#52511yescharacteristic
173C22×C127C2×#12411yescharacteristic
174C22×C127#53611yescharacteristic
175C22×C127#53611yescharacteristic
176C22×C127#53611yescharacteristic
177C22×C127#53612yes—
178C22×C127#53711yescharacteristic
179C22×C127#53712yes—
180C22×C127#54114yes—
181C22×C127#54114yes—
182C22×C127#54714yes—
183C22×C127#54814yes—
184C22×C127#55212yes—
185C22×C127#55312yes—
186C22×C127#56312yes—
187C22×C127#56412yes—
188C4×C127—24no—
189C4×C127—24no—
190C4×C127—44no—
191C4×C127—42no—
192C4×C127—44no—
193C4×C127—44no—
194C4×C127—82no—
195C4×C127—84no—
196#16634C12711yesmaximal, characteristic, direct product factor, Sylow
197C2×C127#240611yescharacteristic
198C2×C127#243611yescharacteristic
199C2×C127#256211yescharacteristic
200C2×C127#261611yescharacteristic
201C2×C127#263411yescharacteristic
202C2×C127#264211yescharacteristic
203C2×C127#271914yes—
204C2×C127#272514yes—
205C2×C127#282211yescharacteristic
206C22×#125C2×C12711yescharacteristic
207C2×#400C2×C12712yes—
208C2×#389C2×C12711yescharacteristic
209#1442C2×C12714yes—
210#1441C2×C12712yes—
211#1441C2×C12712yes—
212#1441C2×C12712yes—
213#1434C2×C12711yescharacteristic
214C127#1663411yescharacteristic, direct product factor, Sylow
215C2×#125—28no—
216C2×#125—24no—
217C22×C4⋊C4C22×C12711yescharacteristic
218C22×C4⋊C4C22×C12711yescharacteristic
219C22×C4⋊C4C22×C12711yescharacteristic
220C22×C4⋊C4C22×C12712yes—
221C22×C4⋊C4C22×C12711yescharacteristic
222C22×C4⋊C4C22×C12712yes—
223C22×C4⋊C4C22×C12712yes—
224C22×C42C22×C12711yescharacteristic
225#400—28no—
226#389—24no—
227C2×#95C22×C12712yes—
228C2×#95C22×C12714yes—
229C2×#95C22×C12714yes—
230C2×#95C22×C12712yes—
231C2×#95C22×C12714yes—
232C2×#95C22×C12712yes—
233C2×#95C22×C12712yes—
234C2×#95C22×C12714yes—
235C23×C4C23×C12712yes—
236C23×C4C23×C12714yes—
237C23×C4C23×C12712yes—
238C23×C4C23×C12712yes—
239C23×C4C23×C12711yescharacteristic
240C23×C4C23×C12712yes—
241C23×C4C23×C12711yescharacteristic
242C23×C4C23×C12711yescharacteristic
243#125—232no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4D4×C12718yes—
261C2×C42—24no—
262C2×C42D4×C12714yes—
263#95—24no—
264#95—24no—
265#95—28no—
266#95—28no—
267#95—28no—
268#95—24no—
269#95—44no—
270#95—42no—
271C24C24×C12711yescharacteristic
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4C2×D4×C12712yes—
309C22×C4C2×D4×C12714yes—
310C22×C4C2×D4×C12714yes—
311C22×C4C2×D4×C12714yes—
312C22×C4C2×D4×C12712yes—
313C22×C4C2×D4×C12712yes—
314C22×C4#41×C12714yes—
315C22×C4#41×C12714yes—
316C4⋊C4—28no—
317C4⋊C4—28no—
318C4⋊C4—28no—
319C4⋊C4—216no—
320C4⋊C4—216no—
321C4⋊C4—44no—
322C4⋊C4—48no—
323C42—28no—
324C23C22×D4×C12711yescharacteristic
325C23C22×D4×C12712yes—
326C23C2×#41×C12712yes—
327C23C2×#41×C12712yes—
328C23H(5,𝔽2)×C12711yescharacteristic
329C232−1+4×C12712yes—
330C232−1+4×C12711yescharacteristic
331C232−1+4×C12712yes—
332C232−1+4×C12712yes—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—28no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—28no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4#120×C12714yes—
376C2×C4#124×C12714yes—
377C22C2×#120×C12711yescharacteristic
378C22#525×C12711yescharacteristic
379C22C2×#124×C12711yescharacteristic
380C22#536×C12711yescharacteristic
381C22#536×C12712yes—
382C22#536×C12711yescharacteristic
383C22#536×C12711yescharacteristic
384C22#537×C12712yes—
385C22#537×C12711yescharacteristic
386C22#541×C12714yes—
387C22#541×C12714yes—
388C22#547×C12714yes—
389C22#548×C12714yes—
390C22#552×C12712yes—
391C22#553×C12712yes—
392C22#563×C12712yes—
393C22#564×C12712yes—
394C4—24no—
395C4—24no—
396C4—42no—
397C4—44no—
398C4—44no—
399C4—44no—
400C4—82no—
401C4—84no—
402C2C127×#240611yescharacteristic
403C2C127×#243611yescharacteristic
404C2C127×#256211yescharacteristic
405C2C127×#261611yescharacteristic
406C2C127×#263411yescharacteristic
407C2C127×#264211yescharacteristic
408C2C127×#271914yes—
409C2C127×#272514yes—
410C2C127×#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
196. #16634C127direct (N × H)
214. C127#16634direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C1272
C2×#400×C1272
C2×#389×C1272
C127×#14422
C127×#14412
C127×#14342
#16634127