Finite Group Databasebeta

← C2×C127×#1782 #44584256

Subgroups — C2×C127×#1782 #44584256

Order 32512.

4062 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
1C23×#41×C127C211yesmaximal, characteristic
2C22×#99×C127C214yesmaximal, complemented
3C2×#381×C127C212yesmaximal, complemented
4C127×#1782C218yesmaximal, direct product factor
5C22×#41×C127—216no—
6C22×#41×C127—24no—
7C22×#41×C127—24no—
8C22×#41×C127C414yescomplemented
9C22×#41×C127C2214yes—
10C23×Q8×C127C411yescharacteristic, complemented
11C23×D4×C127C411yescharacteristic, complemented
12C23×D4×C127C2212yes—
13C24×C4×C127C412yescomplemented
14C24×C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2214yes—
16C2×#99×C127—216no—
17C2×#99×C127C22116yescomplemented
18#381×C127—24no—
19#381×C127C2218yescomplemented
20C2×#95×C127—24no—
21C25×C127C2×C412yes—
22C25×C127C2311yescharacteristic
23C2×#41×C127—264no—
24C2×#41×C127—264no—
25C2×#41×C127—232no—
26C2×#41×C127—232no—
27C2×#41×C127—216no—
28C2×#41×C127—216no—
29C22×Q8×C127—28no—
30C22×Q8×C127—22no—
31C22×Q8×C127—22no—
32C22×Q8×C127C2×C414yescomplemented
33C22×D4×C127—28no—
34C22×D4×C127—28no—
35C22×D4×C127—24no—
36C22×D4×C127—24no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C414yes—
40C22×D4×C127C2×C414yescomplemented
41C22×D4×C127D4116yes—
42C22×D4×C127C2314yes—
43C23×C4×C127—28no—
44C23×C4×C127—28no—
45C23×C4×C127—28no—
46C23×C4×C127—24no—
47C23×C4×C127—24no—
48C23×C4×C127—24no—
49C23×C4×C127C2×C411yescharacteristic
50C23×C4×C127C2×C412yes—
51C23×C4×C127C2×C411yescharacteristic
52C23×C4×C127C2×C412yes—
53C23×C4×C127C2×C418yescomplemented
54C23×C4×C127D414yes—
55C23×C4×C127D414yes—
56C23×C4×C127C2312yes—
57C2×C22⋊C4×C127—216no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127C2318yes—
60#99×C127—232no—
61#95×C127—216no—
62C24×C127—24no—
63C24×C127—22no—
64C24×C127—22no—
65C24×C127—44no—
66C24×C127—48no—
67C24×C127C22⋊C418yes—
68C24×C127C22×C411yescharacteristic
69C24×C127C22×C414yes—
70C24×C127C22×C411yescharacteristic
71C24×C127C2×D412yes—
72C24×C127C2×D418yes—
73C24×C127C2×D412yes—
74C24×C127C2411yescharacteristic
75#41×C127—2128no—
76#41×C127—2128no—
77C2×Q8×C127—216no—
78C2×Q8×C127—216no—
79C2×Q8×C127—216no—
80C2×Q8×C127—28no—
81C2×D4×C127—216no—
82C2×D4×C127—216no—
83C2×D4×C127—28no—
84C2×D4×C127—28no—
85C2×D4×C127—216no—
86C2×D4×C127—232no—
87C2×D4×C127—232no—
88C2×D4×C127—28no—
89C2×D4×C127—28no—
90C2×D4×C127—28no—
91C2×D4×C127C22⋊C4116yes—
92C2×D4×C127C2×D4116yes—
93C22×C4×C127—232no—
94C22×C4×C127—232no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—22no—
99C22×C4×C127—28no—
100C22×C4×C127—216no—
101C22×C4×C127—22no—
102C22×C4×C127—216no—
103C22×C4×C127—216no—
104C22×C4×C127—28no—
105C22×C4×C127—216no—
106C22×C4×C127—216no—
107C22×C4×C127—28no—
108C22×C4×C127—416no—
109C22×C4×C127—48no—
110C22×C4×C127C22⋊C412yes—
111C22×C4×C127C22⋊C418yes—
112C22×C4×C127C22⋊C412yes—
113C22×C4×C127C22⋊C418yes—
114C22×C4×C127C22⋊C412yes—
115C22×C4×C127C22⋊C412yes—
116C22×C4×C127C22×C412yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C414yes—
119C22×C4×C127C2×D418yes—
120C22⋊C4×C127—216no—
121C22⋊C4×C127—48no—
122C23×C127—28no—
123C23×C127—24no—
124C23×C127—24no—
125C23×C127—24no—
126C23×C127—28no—
127C23×C127—28no—
128C23×C127—42no—
129C23×C127—44no—
130C23×C127—416no—
131C23×C127—42no—
132C23×C127—416no—
133C23×C127—48no—
134C23×C127—48no—
135C23×C127—416no—
136C23×C127—48no—
137C23×C127C2×C22⋊C414yes—
138C23×C127C2×C22⋊C411yescharacteristic
139C23×C127C2×C22⋊C412yes—
140C23×C127C2×C22⋊C418yes—
141C23×C127C2×C22⋊C414yes—
142C23×C127C2×C22⋊C411yescharacteristic
143C23×C127#12018yes—
144C23×C127#12018yes—
145C23×C127C23×C411yescharacteristic
146C23×C127C22×D412yes—
147C23×C127C22×D414yes—
148Q8×C127—232no—
149D4×C127—232no—
150D4×C127—232no—
151D4×C127—232no—
152C2×C4×C127—264no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—24no—
156C2×C4×C127—24no—
157C2×C4×C127—216no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—28no—
161C2×C4×C127—24no—
162C2×C4×C127—28no—
163C2×C4×C127—24no—
164C2×C4×C127—216no—
165C2×C4×C127—416no—
166C2×C4×C127—48no—
167C2×C4×C127—816no—
168C2×C4×C127C2×C22⋊C414yes—
169C2×C4×C127C2×C22⋊C418yes—
170C2×C4×C127C2×C22⋊C414yes—
171C22×C127—24no—
172C22×C127—22no—
173C22×C127—22no—
174C22×C127—24no—
175C22×C127—216no—
176C22×C127—28no—
177C22×C127—28no—
178C22×C127—44no—
179C22×C127—48no—
180C22×C127—44no—
181C22×C127—48no—
182C22×C127—48no—
183C22×C127—416no—
184C22×C127—48no—
185C22×C127—416no—
186C22×C127#37912yes—
187C22×C127#37914yes—
188C22×C127#37912yes—
189C22×C127#41014yes—
190C22×C127C22×C22⋊C412yes—
191C22×C127C22×C22⋊C411yescharacteristic
192C22×C127C2×#12014yes—
193C4×C127—24no—
194C4×C127—28no—
195C4×C127—24no—
196C4×C127—88no—
197C2×#1782C12711yesmaximal, characteristic, direct product factor, Sylow
198C2×C127—24no—
199C2×C127—22no—
200C2×C127—22no—
201C2×C127—24no—
202C2×C127—48no—
203C2×C127#178214yesdirect product factor
204C2×C127C2×#37911yescharacteristic
205C2×C127C2×#41012yes—
206C23×#41C2×C12711yescharacteristic
207C22×#99C2×C12714yescomplemented
208C2×#381C2×C12712yescomplemented
209#1782C2×C12718yesdirect product factor
210C127C2×#178211yescharacteristic, direct product factor, Sylow
211C22×#41—216no—
212C22×#41—24no—
213C22×#41—24no—
214C22×#41C4×C12714yescomplemented
215C22×#41C22×C12714yes—
216C23×Q8C4×C12711yescharacteristic, complemented
217C23×D4C4×C12711yescharacteristic, complemented
218C23×D4C22×C12712yes—
219C24×C4C4×C12712yescomplemented
220C24×C4C22×C12711yescharacteristic
221C22×C22⋊C4C22×C12714yes—
222C2×#99—216no—
223C2×#99C22×C127116yescomplemented
224#381—24no—
225#381C22×C12718yescomplemented
226C2×#95—24no—
227C25C2×C4×C12712yes—
228C25C23×C12711yescharacteristic
229C2×#41—264no—
230C2×#41—264no—
231C2×#41—232no—
232C2×#41—232no—
233C2×#41—216no—
234C2×#41—216no—
235C22×Q8—28no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8C2×C4×C12714yescomplemented
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—28no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4C2×C4×C12714yes—
246C22×D4C2×C4×C12714yescomplemented
247C22×D4D4×C127116yes—
248C22×D4C23×C12714yes—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—28no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4C2×C4×C12711yescharacteristic
256C23×C4C2×C4×C12712yes—
257C23×C4C2×C4×C12711yescharacteristic
258C23×C4C2×C4×C12712yes—
259C23×C4C2×C4×C12718yescomplemented
260C23×C4D4×C12714yes—
261C23×C4D4×C12714yes—
262C23×C4C23×C12712yes—
263C2×C22⋊C4—216no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4C23×C12718yes—
266#99—232no—
267#95—216no—
268C24—24no—
269C24—22no—
270C24—22no—
271C24—44no—
272C24—48no—
273C24C22⋊C4×C12718yes—
274C24C22×C4×C12711yescharacteristic
275C24C22×C4×C12714yes—
276C24C22×C4×C12711yescharacteristic
277C24C2×D4×C12712yes—
278C24C2×D4×C12718yes—
279C24C2×D4×C12712yes—
280C24C24×C12711yescharacteristic
281#41—2128no—
282#41—2128no—
283C2×Q8—216no—
284C2×Q8—216no—
285C2×Q8—216no—
286C2×Q8—28no—
287C2×D4—216no—
288C2×D4—216no—
289C2×D4—28no—
290C2×D4—28no—
291C2×D4—216no—
292C2×D4—232no—
293C2×D4—232no—
294C2×D4—28no—
295C2×D4—28no—
296C2×D4—28no—
297C2×D4C22⋊C4×C127116yes—
298C2×D4C2×D4×C127116yes—
299C22×C4—232no—
300C22×C4—232no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—28no—
307C22×C4—216no—
308C22×C4—216no—
309C22×C4—216no—
310C22×C4—28no—
311C22×C4—216no—
312C22×C4—216no—
313C22×C4—28no—
314C22×C4—416no—
315C22×C4—48no—
316C22×C4C22⋊C4×C12712yes—
317C22×C4C22⋊C4×C12712yes—
318C22×C4C22⋊C4×C12718yes—
319C22×C4C22⋊C4×C12712yes—
320C22×C4C22⋊C4×C12712yes—
321C22×C4C22⋊C4×C12718yes—
322C22×C4C22×C4×C12712yes—
323C22×C4C22×C4×C12712yes—
324C22×C4C22×C4×C12714yes—
325C22×C4C2×D4×C12718yes—
326C22⋊C4—216no—
327C22⋊C4—48no—
328C23—28no—
329C23—24no—
330C23—24no—
331C23—24no—
332C23—28no—
333C23—28no—
334C23—42no—
335C23—44no—
336C23—416no—
337C23—42no—
338C23—416no—
339C23—48no—
340C23—48no—
341C23—416no—
342C23—48no—
343C23C2×C22⋊C4×C12714yes—
344C23C2×C22⋊C4×C12711yescharacteristic
345C23C2×C22⋊C4×C12712yes—
346C23C2×C22⋊C4×C12718yes—
347C23C2×C22⋊C4×C12714yes—
348C23C2×C22⋊C4×C12711yescharacteristic
349C23#120×C12718yes—
350C23#120×C12718yes—
351C23C23×C4×C12711yescharacteristic
352C23C22×D4×C12712yes—
353C23C22×D4×C12714yes—
354Q8—232no—
355D4—232no—
356D4—232no—
357D4—232no—
358C2×C4—264no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—216no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—28no—
367C2×C4—24no—
368C2×C4—28no—
369C2×C4—24no—
370C2×C4—216no—
371C2×C4—416no—
372C2×C4—48no—
373C2×C4—816no—
374C2×C4C2×C22⋊C4×C12714yes—
375C2×C4C2×C22⋊C4×C12718yes—
376C2×C4C2×C22⋊C4×C12714yes—
377C22—24no—
378C22—22no—
379C22—22no—
380C22—24no—
381C22—216no—
382C22—28no—
383C22—28no—
384C22—44no—
385C22—48no—
386C22—44no—
387C22—48no—
388C22—48no—
389C22—416no—
390C22—48no—
391C22—416no—
392C22#379×C12712yes—
393C22#379×C12714yes—
394C22#379×C12712yes—
395C22#410×C12714yes—
396C22C22×C22⋊C4×C12712yes—
397C22C22×C22⋊C4×C12711yescharacteristic
398C22C2×#120×C12714yes—
399C4—24no—
400C4—28no—
401C4—24no—
402C4—88no—
403C2—24no—
404C2—22no—
405C2—22no—
406C2—24no—
407C2—48no—
408C2C127×#178214yesdirect product factor
409C2C2×#379×C12711yescharacteristic
410C2C2×#410×C12712yes—
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×#41×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C127C2semidirect
3. C2×#381×C127C2semidirect
4. C127×#1782C2direct (N × H)
8. C22×#41×C127C4semidirect
10. C23×Q8×C127C4semidirect
11. C23×D4×C127C4semidirect
13. C24×C4×C127C4semidirect
17. C2×#99×C127C22semidirect
19. #381×C127C22semidirect
32. C22×Q8×C127C2×C4semidirect
40. C22×D4×C127C2×C4semidirect
53. C23×C4×C127C2×C4semidirect
197. C2×#1782C127direct (N × H)
203. C2×C127#1782direct (N × H)
207. C22×#99C2×C127semidirect
208. C2×#381C2×C127semidirect
209. #1782C2×C127direct (N × H)
210. C127C2×#1782direct (N × H)
214. C22×#41C4×C127semidirect
216. C23×Q8C4×C127semidirect
217. C23×D4C4×C127semidirect
219. C24×C4C4×C127semidirect
223. C2×#99C22×C127semidirect
225. #381C22×C127semidirect
238. C22×Q8C2×C4×C127semidirect
246. C22×D4C2×C4×C127semidirect
259. C23×C4C2×C4×C127semidirect
408. C2C127×#1782direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#41×C1272
C22×#99×C1272
C2×#381×C1272
C127×#17822
C2×#1782127