Finite Group Databasebeta

← C127×#19423 #44583096

Subgroups — C127×#19423 #44583096

Order 32512.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3209C211yesmaximal, characteristic, complemented
2C127×#3077C211yesmaximal, characteristic
3C2×#474×C127C211yesmaximal, characteristic
4C127×#2975C211yesmaximal, characteristic
5C127×#1703C214yesmaximal, complemented
6C127×#1689C214yesmaximal, complemented
7C127×#1570C211yesmaximal, characteristic, complemented
8C127×#1549C211yesmaximal, characteristic, complemented
9C127×#1542C211yesmaximal, characteristic, complemented
10#533×C127C2211yescharacteristic
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4×D4×C127C2211yescharacteristic
13#494×C127C2212yescomplemented
14#487×C127C2212yescomplemented
15#478×C127—22no—
16#476×C127C2212yes—
17#474×C127—22no—
18#474×C127C2212yes—
19#474×C127C2214yes—
20#462×C127—22no—
21#451×C127—22no—
22#436×C127—22no—
23#436×C127C2214yes—
24#431×C127C2211yescharacteristic
25#431×C127C2211yescharacteristic
26#428×C127—21no—
27C2×#107×C127—21no—
28#423×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30#418×C127—21no—
31C2×#102×C127—21no—
32#407×C127—22no—
33#334×C127C2214yescomplemented
34#333×C127C2212yescomplemented
35#332×C127C2214yescomplemented
36#332×C127C2212yescomplemented
37C22×Q8×C127—21no—
38C22×D4×C127D411yescharacteristic
39C23×C4×C127—21no—
40C2×Q16×C127—24no—
41C2×M16×C127—21no—
42C2×M16×C127—24no—
43C22×C8×C127—21no—
44C4⋊Q8×C127—21no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127C2312yes—
48C4⋊Q8×C127C2311yescharacteristic
49C4⋊Q8×C127C2311yescharacteristic
50#125×C127—21no—
51C22⋊Q8×C127—21no—
52C22⋊Q8×C127—21no—
53C4×Q8×C127—21no—
54C4×Q8×C127—21no—
55C4×D4×C127—21no—
56C4×D4×C127—21no—
57C4×D4×C127D412yes—
58C4×D4×C127C2312yes—
59#117×C127—21no—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127D411yescharacteristic
63C2×C22⋊C4×C127—21no—
64C2×C42×C127C2311yescharacteristic
65#107×C127—24no—
66#107×C127—22no—
67#106×C127—22no—
68C4⋊C8×C127—21no—
69C4⋊C8×C127—21no—
70C4⋊C8×C127D412yes—
71C4⋊C8×C127C2312yes—
72C4⋊C8×C127C2312yes—
73C4⋊C8×C127C2312yes—
74#103×C127—24no—
75#102×C127—24no—
76#102×C127—22no—
77#102×C127—22no—
78C22⋊C8×C127—21no—
79C22⋊C8×C127—24no—
80C22⋊C8×C127D412yes—
81C4×C8×C127—21no—
82C4×C8×C127C2312yes—
83C24×C127—21no—
84C2×Q8×C127—22no—
85C2×Q8×C127—21no—
86C2×Q8×C127—21no—
87C2×Q8×C127—41no—
88C2×Q8×C127—82no—
89C2×D4×C127—21no—
90C2×D4×C127—22no—
91C2×D4×C127—22no—
92C2×D4×C127C2×D412yes—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—41no—
97C22×C4×C127—82no—
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×D411yescharacteristic
100C22×C4×C127#4111yescharacteristic
101Q16×C127—84no—
102M16×C127—42no—
103M16×C127—84no—
104C2×C8×C127—22no—
105C2×C8×C127—22no—
106C2×C8×C127—22no—
107C2×C8×C127—42no—
108C2×C8×C127C2×D414yes—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—22no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—22no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127C2×D412yes—
121C22⋊C4×C127—22no—
122C22⋊C4×C127—22no—
123C22⋊C4×C127—41no—
124C42×C127—41no—
125C42×C127C2×D411yescharacteristic
126C42×C127C2×D411yescharacteristic
127C42×C127#4111yescharacteristic
128C42×C127C2411yescharacteristic
129C23×C127—22no—
130C23×C127—42no—
131C23×C127—81no—
132C23×C127—81no—
133C23×C127#12111yescharacteristic
134Q8×C127—42no—
135Q8×C127—44no—
136Q8×C127—81no—
137Q8×C127—82no—
138D4×C127—22no—
139D4×C127—22no—
140D4×C127—42no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—41no—
144C2×C4×C127—44no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—42no—
148C2×C4×C127—82no—
149C2×C4×C127—81no—
150C2×C4×C127—82no—
151C2×C4×C127#12111yescharacteristic
152C2×C4×C127#12111yescharacteristic
153C2×C4×C127#12111yescharacteristic
154C2×C4×C127#13712yes—
155C2×C4×C127#13712yes—
156C2×C4×C127C22×D411yescharacteristic
157C2×C4×C127C22×D411yescharacteristic
158C2×C4×C127C2×#4111yescharacteristic
159C8×C127—24no—
160C8×C127—42no—
161C8×C127—42no—
162C8×C127—42no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—42no—
166C22×C127—42no—
167C22×C127—42no—
168C22×C127—84no—
169C22×C127#47012yes—
170C22×C127C2×#12111yescharacteristic
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—42no—
175C4×C127—82no—
176C4×C127—81no—
177C4×C127—81no—
178C4×C127#47012yes—
179C4×C127C2×#13711yescharacteristic
180C4×C127C2×#13711yescharacteristic
181C4×C127#57612yes—
182#19423C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—22no—
184C2×C127—82no—
185C2×C127#304111yescharacteristic
186C2×C127C2×#47011yescharacteristic
187C2×C127#306911yescharacteristic
188#3209C2×C12711yescharacteristic, complemented
189#3077C2×C12711yescharacteristic
190C2×#474C2×C12711yescharacteristic
191#2975C2×C12711yescharacteristic
192#1703C2×C12714yescomplemented
193#1689C2×C12714yescomplemented
194#1570C2×C12711yescharacteristic, complemented
195#1549C2×C12711yescharacteristic, complemented
196#1542C2×C12711yescharacteristic, complemented
197C127#1942311yescharacteristic, direct product factor, Sylow
198#533C22×C12711yescharacteristic
199C2×C4⋊Q8C22×C12711yescharacteristic
200C2×C4×D4C22×C12711yescharacteristic
201#494C22×C12712yescomplemented
202#487C22×C12712yescomplemented
203#478—22no—
204#476C22×C12712yes—
205#474—22no—
206#474C22×C12712yes—
207#474C22×C12714yes—
208#462—22no—
209#451—22no—
210#436—22no—
211#436C22×C12714yes—
212#431C22×C12711yescharacteristic
213#431C22×C12711yescharacteristic
214#428—21no—
215C2×#107—21no—
216#423C22×C12711yescharacteristic
217C2×C4⋊C8C22×C12711yescharacteristic
218#418—21no—
219C2×#102—21no—
220#407—22no—
221#334C22×C12714yescomplemented
222#333C22×C12712yescomplemented
223#332C22×C12712yescomplemented
224#332C22×C12714yescomplemented
225C22×Q8—21no—
226C22×D4D4×C12711yescharacteristic
227C23×C4—21no—
228C2×Q16—24no—
229C2×M16—21no—
230C2×M16—24no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C23×C12712yes—
236C4⋊Q8C23×C12711yescharacteristic
237C4⋊Q8C23×C12711yescharacteristic
238#125—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4D4×C12712yes—
246C4×D4C23×C12712yes—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C12711yescharacteristic
251C2×C22⋊C4—21no—
252C2×C42C23×C12711yescharacteristic
253#107—24no—
254#107—22no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8D4×C12712yes—
259C4⋊C8C23×C12712yes—
260C4⋊C8C23×C12712yes—
261C4⋊C8C23×C12712yes—
262#103—24no—
263#102—24no—
264#102—22no—
265#102—22no—
266C22⋊C8—21no—
267C22⋊C8—24no—
268C22⋊C8D4×C12712yes—
269C4×C8—21no—
270C4×C8C23×C12712yes—
271C24—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—82no—
277C2×D4—21no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4C2×D4×C12712yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—82no—
286C22×C4C2×D4×C12711yescharacteristic
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4#41×C12711yescharacteristic
289Q16—84no—
290M16—42no—
291M16—84no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8C2×D4×C12714yes—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C2×D4×C12712yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C42—41no—
313C42C2×D4×C12711yescharacteristic
314C42C2×D4×C12711yescharacteristic
315C42#41×C12711yescharacteristic
316C42C24×C12711yescharacteristic
317C23—22no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23#121×C12711yescharacteristic
322Q8—42no—
323Q8—44no—
324Q8—81no—
325Q8—82no—
326D4—22no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4#121×C12711yescharacteristic
340C2×C4#121×C12711yescharacteristic
341C2×C4#121×C12711yescharacteristic
342C2×C4#137×C12712yes—
343C2×C4#137×C12712yes—
344C2×C4C22×D4×C12711yescharacteristic
345C2×C4C22×D4×C12711yescharacteristic
346C2×C4C2×#41×C12711yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—84no—
357C22#470×C12712yes—
358C22C2×#121×C12711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4#470×C12712yes—
367C4C2×#137×C12711yescharacteristic
368C4C2×#137×C12711yescharacteristic
369C4#576×C12712yes—
370C2—22no—
371C2—82no—
372C2C127×#304111yescharacteristic
373C2C2×#470×C12711yescharacteristic
374C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3209C2semidirect
5. C127×#1703C2semidirect
6. C127×#1689C2semidirect
7. C127×#1570C2semidirect
8. C127×#1549C2semidirect
9. C127×#1542C2semidirect
13. #494×C127C22semidirect
14. #487×C127C22semidirect
33. #334×C127C22semidirect
34. #333×C127C22semidirect
35. #332×C127C22semidirect
36. #332×C127C22semidirect
182. #19423C127direct (N × H)
188. #3209C2×C127semidirect
192. #1703C2×C127semidirect
193. #1689C2×C127semidirect
194. #1570C2×C127semidirect
195. #1549C2×C127semidirect
196. #1542C2×C127semidirect
197. C127#19423direct (N × H)
201. #494C22×C127semidirect
202. #487C22×C127semidirect
221. #334C22×C127semidirect
222. #333C22×C127semidirect
223. #332C22×C127semidirect
224. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32092
C127×#30772
C2×#474×C1272
C127×#29752
C127×#17032
C127×#16892
C127×#15702
C127×#15492
C127×#15422
#19423127