Finite Group Databasebeta

← C2×C127×#1691 #44582807

Subgroups — C2×C127×#1691 #44582807

Order 32512.

726 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×#498×C127C211yesmaximal, characteristic, complemented
2C2×#476×C127C211yesmaximal, characteristic
3C2×#461×C127C211yesmaximal, characteristic
4C2×#436×C127C211yesmaximal, characteristic
5C127×#1691C218yesmaximal, direct product factor
6C2×#335×C127C211yesmaximal, characteristic, complemented
7C2×#333×C127C211yesmaximal, characteristic, complemented
8C2×#332×C127C211yesmaximal, characteristic, complemented
9C22×SD16×C127—21no—
10C22×M16×C127—21no—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4⋊Q8×C127C2211yescharacteristic
13C2×C4×D4×C127C2211yescharacteristic
14#498×C127—22no—
15#498×C127C2214yescomplemented
16#476×C127—22no—
17#476×C127C2214yes—
18#461×C127—22no—
19#461×C127C2214yes—
20#436×C127—22no—
21#436×C127C2214yes—
22C2×#106×C127—21no—
23C2×#106×C127—21no—
24C2×#106×C127—21no—
25C2×C4⋊C8×C127C2211yescharacteristic
26C2×C4⋊C8×C127C2211yescharacteristic
27C2×C4⋊C8×C127C2211yescharacteristic
28C2×#103×C127—21no—
29C2×#102×C127—21no—
30C2×C22⋊C8×C127—21no—
31C2×C4×C8×C127C2211yescharacteristic
32#335×C127C2214yescomplemented
33#333×C127C2214yescomplemented
34#332×C127C2214yescomplemented
35C22×Q8×C127—21no—
36C22×Q8×C127—21no—
37C22×D4×C127D411yescharacteristic
38C23×C4×C127—21no—
39C2×SD16×C127—24no—
40C2×SD16×C127—44no—
41C2×M16×C127—24no—
42C2×M16×C127—44no—
43C22×C8×C127—21no—
44C22×C8×C127—21no—
45C22×C8×C127—21no—
46C22×C8×C127D411yescharacteristic
47C22×C8×C127D411yescharacteristic
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127C2312yes—
55C4⋊Q8×C127C2312yes—
56C4×D4×C127—21no—
57C4×D4×C127—21no—
58C4×D4×C127D412yes—
59C4×D4×C127C2312yes—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127D411yescharacteristic
65C2×C22⋊C4×C127—21no—
66C2×C42×C127C2311yescharacteristic
67#106×C127—24no—
68#106×C127—24no—
69#106×C127—24no—
70C4⋊C8×C127—21no—
71C4⋊C8×C127—21no—
72C4⋊C8×C127—21no—
73C4⋊C8×C127C2312yes—
74C4⋊C8×C127C2312yes—
75C4⋊C8×C127C2312yes—
76#103×C127—24no—
77#102×C127—24no—
78C22⋊C8×C127—24no—
79C4×C8×C127D412yes—
80C4×C8×C127C2312yes—
81C24×C127—21no—
82C2×Q8×C127—22no—
83C2×Q8×C127—22no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127—42no—
87C2×Q8×C127—42no—
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—42no—
97C22×C4×C127—42no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127#4111yescharacteristic
103SD16×C127—48no—
104M16×C127—48no—
105C2×C8×C127—22no—
106C2×C8×C127—22no—
107C2×C8×C127—22no—
108C2×C8×C127—22no—
109C2×C8×C127—42no—
110C2×C8×C127—42no—
111C2×C8×C127—42no—
112C2×C8×C127SD1614yescomplemented
113C2×C8×C127C2×D412yes—
114C2×C8×C127C2×D412yes—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—22no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—22no—
120C4⋊C4×C127—41no—
121C4⋊C4×C127—41no—
122C4⋊C4×C127—41no—
123C4⋊C4×C127—41no—
124C4⋊C4×C127C2×D412yes—
125C22⋊C4×C127—22no—
126C22⋊C4×C127—22no—
127C42×C127C2×D411yescharacteristic
128C42×C127C2×D411yescharacteristic
129C42×C127#4111yescharacteristic
130C42×C127C2411yescharacteristic
131C23×C127—22no—
132C23×C127—42no—
133C23×C127—42no—
134C23×C127—42no—
135C23×C127#12111yescharacteristic
136Q8×C127—42no—
137Q8×C127—42no—
138Q8×C127—82no—
139Q8×C127—82no—
140Q8×C127—82no—
141D4×C127—22no—
142D4×C127—22no—
143D4×C127—42no—
144C2×C4×C127—22no—
145C2×C4×C127—22no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—44no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—82no—
153C2×C4×C127—82no—
154C2×C4×C127#12111yescharacteristic
155C2×C4×C127#12111yescharacteristic
156C2×C4×C127#12111yescharacteristic
157C2×C4×C127C2×SD1612yes—
158C2×C4×C127AGL(1,ℤ/8)12yes—
159C2×C4×C127#13712yes—
160C2×C4×C127#13712yes—
161C2×C4×C127C22×D411yescharacteristic
162C2×C4×C127C22×D411yescharacteristic
163C2×C4×C127C2×#4111yescharacteristic
164C8×C127—22no—
165C8×C127—42no—
166C8×C127—42no—
167C8×C127—42no—
168C8×C127C2×SD1614yescomplemented
169C22×C127—42no—
170C22×C127—42no—
171C22×C127—42no—
172C22×C127—84no—
173C22×C127#46112yes—
174C22×C127#46812yes—
175C22×C127#47112yes—
176C22×C127C2×#12111yescharacteristic
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—42no—
180C4×C127—82no—
181C4×C127—82no—
182C4×C127#46112yes—
183C4×C127#46812yes—
184C4×C127C22×SD1611yescharacteristic
185C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C127C2×#13711yescharacteristic
187C4×C127C2×#13711yescharacteristic
188C2×#1691C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127—82no—
190C2×C127#169114yesdirect product factor
191C2×C127C2×#46111yescharacteristic
192C2×C127C2×#46811yescharacteristic
193C2×C127C2×#47111yescharacteristic
194C2×#498C2×C12711yescharacteristic, complemented
195C2×#476C2×C12711yescharacteristic
196C2×#461C2×C12711yescharacteristic
197C2×#436C2×C12711yescharacteristic
198#1691C2×C12718yesdirect product factor
199C2×#335C2×C12711yescharacteristic, complemented
200C2×#333C2×C12711yescharacteristic, complemented
201C2×#332C2×C12711yescharacteristic, complemented
202C127C2×#169111yescharacteristic, direct product factor, Sylow
203C22×SD16—21no—
204C22×M16—21no—
205C2×C4⋊Q8C22×C12711yescharacteristic
206C2×C4⋊Q8C22×C12711yescharacteristic
207C2×C4×D4C22×C12711yescharacteristic
208#498—22no—
209#498C22×C12714yescomplemented
210#476—22no—
211#476C22×C12714yes—
212#461—22no—
213#461C22×C12714yes—
214#436—22no—
215#436C22×C12714yes—
216C2×#106—21no—
217C2×#106—21no—
218C2×#106—21no—
219C2×C4⋊C8C22×C12711yescharacteristic
220C2×C4⋊C8C22×C12711yescharacteristic
221C2×C4⋊C8C22×C12711yescharacteristic
222C2×#103—21no—
223C2×#102—21no—
224C2×C22⋊C8—21no—
225C2×C4×C8C22×C12711yescharacteristic
226#335C22×C12714yescomplemented
227#333C22×C12714yescomplemented
228#332C22×C12714yescomplemented
229C22×Q8—21no—
230C22×Q8—21no—
231C22×D4D4×C12711yescharacteristic
232C23×C4—21no—
233C2×SD16—24no—
234C2×SD16—44no—
235C2×M16—24no—
236C2×M16—44no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8D4×C12711yescharacteristic
241C22×C8D4×C12711yescharacteristic
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C23×C12712yes—
249C4⋊Q8C23×C12712yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4D4×C12712yes—
253C4×D4C23×C12712yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C12711yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C12711yescharacteristic
261#106—24no—
262#106—24no—
263#106—24no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C23×C12712yes—
268C4⋊C8C23×C12712yes—
269C4⋊C8C23×C12712yes—
270#103—24no—
271#102—24no—
272C22⋊C8—24no—
273C4×C8D4×C12712yes—
274C4×C8C23×C12712yes—
275C24—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—82no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4C2×D4×C12712yes—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C12711yescharacteristic
295C22×C4C2×D4×C12711yescharacteristic
296C22×C4#41×C12711yescharacteristic
297SD16—48no—
298M16—48no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8SD16×C12714yescomplemented
307C2×C8C2×D4×C12712yes—
308C2×C8C2×D4×C12712yes—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4C2×D4×C12712yes—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C42C2×D4×C12711yescharacteristic
322C42C2×D4×C12711yescharacteristic
323C42#41×C12711yescharacteristic
324C42C24×C12711yescharacteristic
325C23—22no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23#121×C12711yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—82no—
335D4—22no—
336D4—22no—
337D4—42no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4#121×C12711yescharacteristic
349C2×C4#121×C12711yescharacteristic
350C2×C4#121×C12711yescharacteristic
351C2×C4C2×SD16×C12712yes—
352C2×C4AGL(1,ℤ/8)×C12712yes—
353C2×C4#137×C12712yes—
354C2×C4#137×C12712yes—
355C2×C4C22×D4×C12711yescharacteristic
356C2×C4C22×D4×C12711yescharacteristic
357C2×C4C2×#41×C12711yescharacteristic
358C8—22no—
359C8—42no—
360C8—42no—
361C8—42no—
362C8C2×SD16×C12714yescomplemented
363C22—42no—
364C22—42no—
365C22—42no—
366C22—84no—
367C22#461×C12712yes—
368C22#468×C12712yes—
369C22#471×C12712yes—
370C22C2×#121×C12711yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4#461×C12712yes—
377C4#468×C12712yes—
378C4C22×SD16×C12711yescharacteristic
379C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
380C4C2×#137×C12711yescharacteristic
381C4C2×#137×C12711yescharacteristic
382C2—82no—
383C2C127×#169114yesdirect product factor
384C2C2×#461×C12711yescharacteristic
385C2C2×#468×C12711yescharacteristic
386C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#498×C127C2semidirect
5. C127×#1691C2direct (N × H)
6. C2×#335×C127C2semidirect
7. C2×#333×C127C2semidirect
8. C2×#332×C127C2semidirect
15. #498×C127C22semidirect
32. #335×C127C22semidirect
33. #333×C127C22semidirect
34. #332×C127C22semidirect
112. C2×C8×C127SD16semidirect
168. C8×C127C2×SD16semidirect
188. C2×#1691C127direct (N × H)
190. C2×C127#1691direct (N × H)
194. C2×#498C2×C127semidirect
198. #1691C2×C127direct (N × H)
199. C2×#335C2×C127semidirect
200. C2×#333C2×C127semidirect
201. C2×#332C2×C127semidirect
202. C127C2×#1691direct (N × H)
209. #498C22×C127semidirect
226. #335C22×C127semidirect
227. #333C22×C127semidirect
228. #332C22×C127semidirect
306. C2×C8SD16×C127semidirect
362. C8C2×SD16×C127semidirect
383. C2C127×#1691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#498×C1272
C2×#476×C1272
C2×#461×C1272
C2×#436×C1272
C127×#16912
C2×#335×C1272
C2×#333×C1272
C2×#332×C1272
C2×#1691127