Finite Group Databasebeta

← C127×#9660 #44573333

Subgroups — C127×#9660 #44573333

Order 32512.

538 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C127C211yesmaximal, characteristic
2C127×#1984C211yesmaximal, characteristic, complemented
3C127×#1954C211yesmaximal, characteristic
4C2×#335×C127C211yesmaximal, characteristic, complemented
5C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C211yesmaximal, characteristic
7C2×#322×C127C211yesmaximal, characteristic, complemented
8C22×SD16×C127C411yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11C4×SD16×C127—22no—
12C4×SD16×C127—22no—
13C2×#106×C127C411yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×#103×C127C411yescharacteristic
17C2×#102×C127C411yescharacteristic
18C2×C22⋊C8×C127—22no—
19C2×C4×C8×C127C2211yescharacteristic
20C2×C4×C8×C127C2211yescharacteristic
21C2×C4×C8×C127C2211yescharacteristic
22#336×C127—22no—
23#335×C127—22no—
24Q8⋊C8×C127—22no—
25D4⋊C8×C127—22no—
26#322×C127—22no—
27C22×Q8×C127C2×C411yescharacteristic
28C22×D4×C127C2×C411yescharacteristic
29C23×C4×C127—21no—
30C2×SD16×C127—22no—
31C2×SD16×C127—22no—
32C2×SD16×C127C814yescomplemented
33C22×C8×C127—21no—
34C22×C8×C127—21no—
35C22×C8×C127—21no—
36C22×C8×C127C2×C411yescharacteristic
37C22×C8×C127C2×C411yescharacteristic
38C22×C8×C127D412yes—
39C4×Q8×C127—21no—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127—21no—
43C4×D4×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C4×D4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127C2×C411yescharacteristic
49C2×C4⋊C4×C127C2×C411yescharacteristic
50C2×C22⋊C4×C127—21no—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53#106×C127—22no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58#103×C127—22no—
59#102×C127—22no—
60C22⋊C8×C127—44no—
61C4×C8×C127—21no—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64C4×C8×C127D412yes—
65C4×C8×C127D412yes—
66C4×C8×C127D412yes—
67C24×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—21no—
70C2×Q8×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×Q8×C127C2×C812yes—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—21no—
79C2×D4×C127C2×C812yes—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—42no—
86C22×C4×C127—42no—
87C22×C4×C127C22×C411yescharacteristic
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127#4111yescharacteristic
90SD16×C127—28no—
91C2×C8×C127—21no—
92C2×C8×C127—21no—
93C2×C8×C127—22no—
94C2×C8×C127—22no—
95C2×C8×C127—22no—
96C2×C8×C127—22no—
97C2×C8×C127—42no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—42no—
101C2×C8×C127—42no—
102C2×C8×C127C22⋊C412yes—
103C2×C8×C127C22⋊C412yes—
104C2×C8×C127C2×C812yes—
105C2×C8×C127M1612yes—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C42×C127—41no—
115C42×C127—41no—
116C42×C127C2×D411yescharacteristic
117C42×C127C2×D411yescharacteristic
118C42×C127C2×D411yescharacteristic
119C42×C127#4111yescharacteristic
120C23×C127—22no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—42no—
124C23×C127—42no—
125C23×C127C4×D411yescharacteristic
126Q8×C127—22no—
127Q8×C127—22no—
128Q8×C127—41no—
129Q8×C127—41no—
130D4×C127—22no—
131D4×C127—22no—
132D4×C127—41no—
133D4×C127—41no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—82no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127C2×C22⋊C411yescharacteristic
146C2×C4×C127C4×D411yescharacteristic
147C2×C4×C127#12111yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127#12411yescharacteristic
150C2×C4×C127#12711yescharacteristic
151C2×C4×C127C22×C811yescharacteristic
152C2×C4×C127C2×M1611yescharacteristic
153C2×C4×C127#13111yescharacteristic
154C2×C4×C127#13111yescharacteristic
155C2×C4×C127AGL(1,ℤ/8)12yes—
156C2×C4×C127#13712yes—
157C8×C127—22no—
158C8×C127—42no—
159C8×C127—42no—
160C8×C127—81no—
161C8×C127—81no—
162C8×C127C22⋊C814yescomplemented
163C22×C127—44no—
164C22×C127—42no—
165C22×C127—82no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127#39011yescharacteristic
169C22×C127C8×D411yescharacteristic
170C22×C127#43611yescharacteristic
171C22×C127#44012yes—
172C22×C127#44412yes—
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—42no—
176C4×C127—81no—
177C4×C127—81no—
178C4×C127C2×C22⋊C811yescharacteristic
179C4×C127#40811yescharacteristic
180C4×C127C8×D411yescharacteristic
181C4×C127#43611yescharacteristic
182C4×C127#46812yes—
183C4×C127#49611yescharacteristic
184C4×C127#49711yescharacteristic
185#9660C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—82no—
187C2×C127SD16⋊C812yes—
188C2×C127#159212yes—
189C2×C127#195411yescharacteristic
190C2×C127#197311yescharacteristic
191C2×C127#197511yescharacteristic
192C2×C4×SD16C2×C12711yescharacteristic
193#1984C2×C12711yescharacteristic, complemented
194#1954C2×C12711yescharacteristic
195C2×#335C2×C12711yescharacteristic, complemented
196C2×Q8⋊C8C2×C12711yescharacteristic, complemented
197C2×D4⋊C8C2×C12711yescharacteristic
198C2×#322C2×C12711yescharacteristic, complemented
199C127#966011yescharacteristic, direct product factor, Sylow
200C22×SD16C4×C12711yescharacteristic
201C2×C4×Q8C22×C12711yescharacteristic
202C2×C4×D4C22×C12711yescharacteristic
203C4×SD16—22no—
204C4×SD16—22no—
205C2×#106C4×C12711yescharacteristic
206C2×C4⋊C8C22×C12711yescharacteristic
207C2×C4⋊C8C22×C12711yescharacteristic
208C2×#103C4×C12711yescharacteristic
209C2×#102C4×C12711yescharacteristic
210C2×C22⋊C8—22no—
211C2×C4×C8C22×C12711yescharacteristic
212C2×C4×C8C22×C12711yescharacteristic
213C2×C4×C8C22×C12711yescharacteristic
214#336—22no—
215#335—22no—
216Q8⋊C8—22no—
217D4⋊C8—22no—
218#322—22no—
219C22×Q8C2×C4×C12711yescharacteristic
220C22×D4C2×C4×C12711yescharacteristic
221C23×C4—21no—
222C2×SD16—22no—
223C2×SD16—22no—
224C2×SD16C8×C12714yescomplemented
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C2×C4×C12711yescharacteristic
229C22×C8C2×C4×C12711yescharacteristic
230C22×C8D4×C12712yes—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C12711yescharacteristic
241C2×C4⋊C4C2×C4×C12711yescharacteristic
242C2×C22⋊C4—21no—
243C2×C42—21no—
244C2×C42C23×C12711yescharacteristic
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#103—22no—
251#102—22no—
252C22⋊C8—44no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8D4×C12712yes—
257C4×C8D4×C12712yes—
258C4×C8D4×C12712yes—
259C24—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8C2×C8×C12712yes—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4C2×C8×C12712yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C22×C4×C12711yescharacteristic
280C22×C4C2×D4×C12711yescharacteristic
281C22×C4#41×C12711yescharacteristic
282SD16—28no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8C22⋊C4×C12712yes—
295C2×C8C22⋊C4×C12712yes—
296C2×C8C2×C8×C12712yes—
297C2×C8M16×C12712yes—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—41no—
308C42C2×D4×C12711yescharacteristic
309C42C2×D4×C12711yescharacteristic
310C42C2×D4×C12711yescharacteristic
311C42#41×C12711yescharacteristic
312C23—22no—
313C23—41no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23C4×D4×C12711yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322D4—22no—
323D4—22no—
324D4—41no—
325D4—41no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4C2×C22⋊C4×C12711yescharacteristic
338C2×C4C4×D4×C12711yescharacteristic
339C2×C4#121×C12711yescharacteristic
340C2×C4#121×C12711yescharacteristic
341C2×C4#124×C12711yescharacteristic
342C2×C4#127×C12711yescharacteristic
343C2×C4C22×C8×C12711yescharacteristic
344C2×C4C2×M16×C12711yescharacteristic
345C2×C4#131×C12711yescharacteristic
346C2×C4#131×C12711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C12712yes—
348C2×C4#137×C12712yes—
349C8—22no—
350C8—42no—
351C8—42no—
352C8—81no—
353C8—81no—
354C8C22⋊C8×C12714yescomplemented
355C22—44no—
356C22—42no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22#390×C12711yescharacteristic
361C22C8×D4×C12711yescharacteristic
362C22#436×C12711yescharacteristic
363C22#440×C12712yes—
364C22#444×C12712yes—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—81no—
370C4C2×C22⋊C8×C12711yescharacteristic
371C4#408×C12711yescharacteristic
372C4C8×D4×C12711yescharacteristic
373C4#436×C12711yescharacteristic
374C4#468×C12712yes—
375C4#496×C12711yescharacteristic
376C4#497×C12711yescharacteristic
377C2—82no—
378C2C127×SD16⋊C812yes—
379C2C127×#159212yes—
380C2C127×#195411yescharacteristic
381C2C127×#197311yescharacteristic
382C2C127×#197511yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×C42C23×C127
socleC23×C127C4×D4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1984C2semidirect
4. C2×#335×C127C2semidirect
5. C2×Q8⋊C8×C127C2semidirect
7. C2×#322×C127C2semidirect
32. C2×SD16×C127C8semidirect
162. C8×C127C22⋊C8semidirect
185. #9660C127direct (N × H)
193. #1984C2×C127semidirect
195. C2×#335C2×C127semidirect
196. C2×Q8⋊C8C2×C127semidirect
198. C2×#322C2×C127semidirect
199. C127#9660direct (N × H)
224. C2×SD16C8×C127semidirect
354. C8C22⋊C8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1272
C127×#19842
C127×#19542
C2×#335×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#322×C1272
#9660127