Finite Group Databasebeta

← C127×#7633 #44571306

Subgroups — C127×#7633 #44571306

Order 32512.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C127C211yesmaximal, characteristic
2C127×#1749C211yesmaximal, characteristic, complemented
3C127×#1728C211yesmaximal, characteristic, complemented
4C127×#1271C212yesmaximal, complemented
5C127×#1270C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×#121×C127C411yescharacteristic
8C2×C4×D4×C127—21no—
9C2×C4×D4×C127C411yescharacteristic
10C22×C42×C127C2211yescharacteristic
11C2×C22⋊C8×C127—21no—
12C2×#97×C127—21no—
13#390×C127C2211yescharacteristic
14#389×C127C2211yescharacteristic
15#388×C127—21no—
16#386×C127—21no—
17#380×C127C411yescharacteristic
18C4×C4⋊C4×C127C411yescharacteristic
19C4×C22⋊C4×C127—21no—
20#336×C127—21no—
21#336×C127C2212yes—
22#336×C127C2212yes—
23C22×D4×C127—21no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127—21no—
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C23×C4×C127D411yescharacteristic
29C2×M16×C127—24no—
30C2×M16×C127—42no—
31C2×M16×C127—42no—
32C22×C8×C127—22no—
33C22×C8×C127—22no—
34#121×C127—22no—
35#121×C127—22no—
36C4×D4×C127—42no—
37C4×D4×C127—44no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C42×C127—21no—
48C2×C42×C127—42no—
49C2×C42×C127C2×C411yescharacteristic
50C2×C42×C127D411yescharacteristic
51C2×C42×C127D411yescharacteristic
52C2×C42×C127C2311yescharacteristic
53C22⋊C8×C127—24no—
54#97×C127—42no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58C24×C127—21no—
59C24×C127C22⋊C411yescharacteristic
60C2×D4×C127—24no—
61C2×D4×C127—21no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127M1612yescomplemented
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—22no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—22no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22×C411yescharacteristic
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90M16×C127—48no—
91C2×C8×C127—24no—
92C2×C8×C127—24no—
93C2×C8×C127—42no—
94C2×C8×C127—42no—
95C2×C8×C127—42no—
96C2×C8×C127—42no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—42no—
101C4⋊C4×C127M1612yescomplemented
102C22⋊C4×C127—24no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—42no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—42no—
107C22⋊C4×C127—41no—
108C42×C127—22no—
109C42×C127—22no—
110C42×C127—41no—
111C42×C127—41no—
112C42×C127—42no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—21no—
118C23×C127—21no—
119C23×C127—22no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127#10412yes—
127C23×C127C2×C22⋊C411yescharacteristic
128D4×C127—42no—
129D4×C127—42no—
130D4×C127—48no—
131C2×C4×C127—24no—
132C2×C4×C127—24no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—22no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—44no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—84no—
159C2×C4×C127#9912yes—
160C2×C4×C127#10412yes—
161C2×C4×C127C2×M1611yescharacteristic
162C2×C4×C127C2×M1611yescharacteristic
163C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C127AGL(1,ℤ/8)12yes—
165C2×C4×C127#13711yescharacteristic
166C8×C127—44no—
167C8×C127—44no—
168C22×C127—22no—
169C22×C127—22no—
170C22×C127—22no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—42no—
176C22×C127—42no—
177C22×C127—42no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127—81no—
181C22×C127—81no—
182C22×C127#40711yescharacteristic
183C22×C127C2×#9911yescharacteristic
184C22×C127#41311yescharacteristic
185C22×C127#41711yescharacteristic
186C22×C127#41811yescharacteristic
187C22×C127C2×#10411yescharacteristic
188C22×C127C2×#10411yescharacteristic
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—22no—
193C4×C127—21no—
194C4×C127—22no—
195C4×C127—22no—
196C4×C127—41no—
197C4×C127—42no—
198C4×C127—81no—
199C4×C127—81no—
200#7633C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—42no—
202C2×C127—82no—
203C2×C127#146511yescharacteristic
204C2×C127#148911yescharacteristic
205C2×C127#149011yescharacteristic
206C2×C127#150411yescharacteristic
207C2×C127#150711yescharacteristic
208C2×C127#152411yescharacteristic
209C2×C127#155711yescharacteristic
210C4×#121C2×C12711yescharacteristic
211#1749C2×C12711yescharacteristic, complemented
212#1728C2×C12711yescharacteristic, complemented
213#1271C2×C12712yescomplemented
214#1270C2×C12712yescomplemented
215C127#763311yescharacteristic, direct product factor, Sylow
216C22×M16—21no—
217C2×#121C4×C12711yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4C4×C12711yescharacteristic
220C22×C42C22×C12711yescharacteristic
221C2×C22⋊C8—21no—
222C2×#97—21no—
223#390C22×C12711yescharacteristic
224#389C22×C12711yescharacteristic
225#388—21no—
226#386—21no—
227#380C4×C12711yescharacteristic
228C4×C4⋊C4C4×C12711yescharacteristic
229C4×C22⋊C4—21no—
230#336—21no—
231#336C22×C12712yes—
232#336C22×C12712yes—
233C22×D4—21no—
234C22×D4C2×C4×C12711yescharacteristic
235C23×C4—21no—
236C23×C4C2×C4×C12711yescharacteristic
237C23×C4D4×C12711yescharacteristic
238C23×C4D4×C12711yescharacteristic
239C2×M16—24no—
240C2×M16—42no—
241C2×M16—42no—
242C22×C8—22no—
243C22×C8—22no—
244#121—22no—
245#121—22no—
246C4×D4—42no—
247C4×D4—44no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C2×C4×C12711yescharacteristic
250C2×C4⋊C4C2×C4×C12711yescharacteristic
251C2×C4⋊C4C2×C4×C12711yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C42—21no—
258C2×C42—42no—
259C2×C42C2×C4×C12711yescharacteristic
260C2×C42D4×C12711yescharacteristic
261C2×C42D4×C12711yescharacteristic
262C2×C42C23×C12711yescharacteristic
263C22⋊C8—24no—
264#97—42no—
265#95—21no—
266#95—21no—
267#95—21no—
268C24—21no—
269C24C22⋊C4×C12711yescharacteristic
270C2×D4—24no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4M16×C12712yescomplemented
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4C22⋊C4×C12711yescharacteristic
295C22×C4C22⋊C4×C12711yescharacteristic
296C22×C4C22⋊C4×C12711yescharacteristic
297C22×C4C22×C4×C12711yescharacteristic
298C22×C4C2×D4×C12711yescharacteristic
299C22×C4C2×D4×C12711yescharacteristic
300M16—48no—
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4M16×C12712yescomplemented
312C22⋊C4—24no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C42—42no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#104×C12712yes—
337C23C2×C22⋊C4×C12711yescharacteristic
338D4—42no—
339D4—42no—
340D4—48no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—84no—
369C2×C4#99×C12712yes—
370C2×C4#104×C12712yes—
371C2×C4C2×M16×C12711yescharacteristic
372C2×C4C2×M16×C12711yescharacteristic
373C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
374C2×C4AGL(1,ℤ/8)×C12712yes—
375C2×C4#137×C12711yescharacteristic
376C8—44no—
377C8—44no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#407×C12711yescharacteristic
393C22C2×#99×C12711yescharacteristic
394C22#413×C12711yescharacteristic
395C22#417×C12711yescharacteristic
396C22#418×C12711yescharacteristic
397C22C2×#104×C12711yescharacteristic
398C22C2×#104×C12711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—21no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—42no—
408C4—81no—
409C4—81no—
410C2—42no—
411C2—82no—
412C2C127×#146511yescharacteristic
413C2C127×#148911yescharacteristic
414C2C127×#149011yescharacteristic
415C2C127×#150411yescharacteristic
416C2C127×#150711yescharacteristic
417C2C127×#152411yescharacteristic
418C2C127×#155711yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#121×C127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1749C2semidirect
3. C127×#1728C2semidirect
4. C127×#1271C2semidirect
5. C127×#1270C2semidirect
66. C2×D4×C127M16semidirect
101. C4⋊C4×C127M16semidirect
200. #7633C127direct (N × H)
211. #1749C2×C127semidirect
212. #1728C2×C127semidirect
213. #1271C2×C127semidirect
214. #1270C2×C127semidirect
215. C127#7633direct (N × H)
276. C2×D4M16×C127semidirect
311. C4⋊C4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1272
C127×#17492
C127×#17282
C127×#12712
C127×#12702
#7633127