Finite Group Databasebeta

← C2×C127×#1819 #44584359

Subgroups — C2×C127×#1819 #44584359

Order 32512.

3118 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#379×C127C212yesmaximal
3C127×#1819C218yesmaximal, direct product factor
4C2×#342×C127C214yesmaximal, complemented
5C26×C127C2211yescharacteristic
6C24×C4×C127C412yescomplemented
7C22×C22⋊C4×C127—24no—
8C22×C22⋊C4×C127—24no—
9C22×C22⋊C4×C127—24no—
10C22×C22⋊C4×C127C414yescomplemented
11C22×C22⋊C4×C127C412yescomplemented
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2214yes—
15#379×C127—24no—
16#379×C127C2218yes—
17#342×C127C22116yescomplemented
18C25×C127—28no—
19C25×C127—48no—
20C25×C127C2×C411yescharacteristic
21C25×C127C2×C411yescharacteristic
22C25×C127C2×C412yes—
23C25×C127D414yes—
24C25×C127D414yes—
25C25×C127C2312yes—
26C25×C127C2311yescharacteristic
27C23×C4×C127—24no—
28C23×C4×C127—22no—
29C23×C4×C127—22no—
30C23×C4×C127—24no—
31C23×C4×C127—48no—
32C23×C4×C127C2×C414yes—
33C23×C4×C127C2×C418yescomplemented
34C2×C22⋊C4×C127—216no—
35C2×C22⋊C4×C127—24no—
36C2×C22⋊C4×C127—24no—
37C2×C22⋊C4×C127—24no—
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127—216no—
40C2×C22⋊C4×C127—216no—
41C2×C22⋊C4×C127—216no—
42C2×C22⋊C4×C127—24no—
43C2×C22⋊C4×C127—416no—
44C2×C22⋊C4×C127C2×C414yes—
45C2×C22⋊C4×C127C2×C418yescomplemented
46C2×C22⋊C4×C127C2318yes—
47C2×C22⋊C4×C127C2314yes—
48C24×C127—28no—
49C24×C127—24no—
50C24×C127—216no—
51C24×C127—28no—
52C24×C127—24no—
53C24×C127—216no—
54C24×C127—216no—
55C24×C127—28no—
56C24×C127—48no—
57C24×C127—44no—
58C24×C127—48no—
59C24×C127—416no—
60C24×C127—44no—
61C24×C127—48no—
62C24×C127—464no—
63C24×C127C22⋊C412yes—
64C24×C127C22⋊C412yes—
65C24×C127C22⋊C418yes—
66C24×C127C22⋊C412yes—
67C24×C127C22⋊C412yes—
68C24×C127C22×C412yes—
69C24×C127C22×C411yescharacteristic
70C24×C127C22×C412yes—
71C24×C127C22×C411yescharacteristic
72C24×C127C2×D418yes—
73C24×C127C2×D412yes—
74C24×C127C2×D412yes—
75C24×C127#4118yes—
76C24×C127C2411yescharacteristic
77C22×C4×C127—24no—
78C22×C4×C127—28no—
79C22×C4×C127—28no—
80C22×C4×C127—24no—
81C22×C4×C127—28no—
82C22×C4×C127—416no—
83C22×C4×C127—48no—
84C22×C4×C127—48no—
85C22×C4×C127—48no—
86C22×C4×C127—416no—
87C22×C4×C127—416no—
88C22×C4×C127—48no—
89C22×C4×C127C22×C418yes—
90C22⋊C4×C127—28no—
91C22⋊C4×C127—216no—
92C22⋊C4×C127—28no—
93C22⋊C4×C127—216no—
94C22⋊C4×C127—432no—
95C22⋊C4×C127—48no—
96C23×C127—232no—
97C23×C127—24no—
98C23×C127—24no—
99C23×C127—24no—
100C23×C127—28no—
101C23×C127—24no—
102C23×C127—28no—
103C23×C127—24no—
104C23×C127—28no—
105C23×C127—24no—
106C23×C127—216no—
107C23×C127—216no—
108C23×C127—24no—
109C23×C127—24no—
110C23×C127—216no—
111C23×C127—216no—
112C23×C127—28no—
113C23×C127—48no—
114C23×C127—44no—
115C23×C127—42no—
116C23×C127—44no—
117C23×C127—44no—
118C23×C127—48no—
119C23×C127—416no—
120C23×C127—42no—
121C23×C127—464no—
122C23×C127—432no—
123C23×C127—464no—
124C23×C127—432no—
125C23×C127—416no—
126C23×C127#9918yes—
127C23×C127C2×C22⋊C414yes—
128C23×C127C2×C22⋊C412yes—
129C23×C127C2×C22⋊C411yescharacteristic
130C23×C127C2×C22⋊C414yes—
131C23×C127C2×C22⋊C411yescharacteristic
132C23×C127#11714yes—
133C23×C127#11714yes—
134C23×C127#12318yes—
135C23×C127#12318yes—
136C23×C127C23×C411yescharacteristic
137C23×C127C22×D412yes—
138C23×C127C2×#4114yes—
139C2×C4×C127—28no—
140C2×C4×C127—48no—
141C2×C4×C127—416no—
142C2×C4×C127—416no—
143C2×C4×C127—48no—
144C2×C4×C127—48no—
145C2×C4×C127—416no—
146C2×C4×C127—48no—
147C2×C4×C127—816no—
148C22×C127—216no—
149C22×C127—216no—
150C22×C127—216no—
151C22×C127—216no—
152C22×C127—28no—
153C22×C127—22no—
154C22×C127—24no—
155C22×C127—22no—
156C22×C127—24no—
157C22×C127—24no—
158C22×C127—24no—
159C22×C127—28no—
160C22×C127—24no—
161C22×C127—44no—
162C22×C127—48no—
163C22×C127—44no—
164C22×C127—432no—
165C22×C127—432no—
166C22×C127—48no—
167C22×C127—48no—
168C22×C127—48no—
169C22×C127#38112yes—
170C22×C127#38114yes—
171C22×C127#38112yes—
172C22×C127C2×#9918yes—
173C22×C127C2×#9914yes—
174C22×C127C22×C22⋊C411yescharacteristic
175C22×C127C2×#11712yes—
176C22×C127C2×#12314yes—
177C4×C127—48no—
178C4×C127—88no—
179C2×#1819C12711yesmaximal, characteristic, direct product factor, Sylow
180C2×C127—24no—
181C2×C127—22no—
182C2×C127—22no—
183C2×C127—28no—
184C2×C127—24no—
185C2×C127—44no—
186C2×C127#181914yesdirect product factor
187C2×C127C2×#38111yescharacteristic
188C2×C127C22×#9912yes—
189C23×C22⋊C4C2×C12711yescharacteristic
190C2×#379C2×C12712yes—
191#1819C2×C12718yesdirect product factor
192C2×#342C2×C12714yescomplemented
193C127C2×#181911yescharacteristic, direct product factor, Sylow
194C26C22×C12711yescharacteristic
195C24×C4C4×C12712yescomplemented
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4C4×C12714yescomplemented
200C22×C22⋊C4C4×C12712yescomplemented
201C22×C22⋊C4C22×C12714yes—
202C22×C22⋊C4C22×C12712yes—
203C22×C22⋊C4C22×C12714yes—
204#379—24no—
205#379C22×C12718yes—
206#342C22×C127116yescomplemented
207C25—28no—
208C25—48no—
209C25C2×C4×C12711yescharacteristic
210C25C2×C4×C12711yescharacteristic
211C25C2×C4×C12712yes—
212C25D4×C12714yes—
213C25D4×C12714yes—
214C25C23×C12712yes—
215C25C23×C12711yescharacteristic
216C23×C4—24no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—48no—
221C23×C4C2×C4×C12714yes—
222C23×C4C2×C4×C12718yescomplemented
223C2×C22⋊C4—216no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—216no—
229C2×C22⋊C4—216no—
230C2×C22⋊C4—216no—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—416no—
233C2×C22⋊C4C2×C4×C12714yes—
234C2×C22⋊C4C2×C4×C12718yescomplemented
235C2×C22⋊C4C23×C12718yes—
236C2×C22⋊C4C23×C12714yes—
237C24—28no—
238C24—24no—
239C24—216no—
240C24—28no—
241C24—24no—
242C24—216no—
243C24—216no—
244C24—28no—
245C24—48no—
246C24—44no—
247C24—48no—
248C24—416no—
249C24—44no—
250C24—48no—
251C24—464no—
252C24C22⋊C4×C12712yes—
253C24C22⋊C4×C12712yes—
254C24C22⋊C4×C12718yes—
255C24C22⋊C4×C12712yes—
256C24C22⋊C4×C12712yes—
257C24C22×C4×C12712yes—
258C24C22×C4×C12711yescharacteristic
259C24C22×C4×C12712yes—
260C24C22×C4×C12711yescharacteristic
261C24C2×D4×C12718yes—
262C24C2×D4×C12712yes—
263C24C2×D4×C12712yes—
264C24#41×C12718yes—
265C24C24×C12711yescharacteristic
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—416no—
272C22×C4—48no—
273C22×C4—48no—
274C22×C4—48no—
275C22×C4—416no—
276C22×C4—416no—
277C22×C4—48no—
278C22×C4C22×C4×C12718yes—
279C22⋊C4—28no—
280C22⋊C4—216no—
281C22⋊C4—28no—
282C22⋊C4—216no—
283C22⋊C4—432no—
284C22⋊C4—48no—
285C23—232no—
286C23—24no—
287C23—24no—
288C23—24no—
289C23—28no—
290C23—24no—
291C23—28no—
292C23—24no—
293C23—28no—
294C23—24no—
295C23—216no—
296C23—216no—
297C23—24no—
298C23—24no—
299C23—216no—
300C23—216no—
301C23—28no—
302C23—48no—
303C23—44no—
304C23—42no—
305C23—44no—
306C23—44no—
307C23—48no—
308C23—416no—
309C23—42no—
310C23—464no—
311C23—432no—
312C23—464no—
313C23—432no—
314C23—416no—
315C23#99×C12718yes—
316C23C2×C22⋊C4×C12714yes—
317C23C2×C22⋊C4×C12712yes—
318C23C2×C22⋊C4×C12711yescharacteristic
319C23C2×C22⋊C4×C12714yes—
320C23C2×C22⋊C4×C12711yescharacteristic
321C23#117×C12714yes—
322C23#117×C12714yes—
323C23#123×C12718yes—
324C23#123×C12718yes—
325C23C23×C4×C12711yescharacteristic
326C23C22×D4×C12712yes—
327C23C2×#41×C12714yes—
328C2×C4—28no—
329C2×C4—48no—
330C2×C4—416no—
331C2×C4—416no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—416no—
335C2×C4—48no—
336C2×C4—816no—
337C22—216no—
338C22—216no—
339C22—216no—
340C22—216no—
341C22—28no—
342C22—22no—
343C22—24no—
344C22—22no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—28no—
349C22—24no—
350C22—44no—
351C22—48no—
352C22—44no—
353C22—432no—
354C22—432no—
355C22—48no—
356C22—48no—
357C22—48no—
358C22#381×C12712yes—
359C22#381×C12714yes—
360C22#381×C12712yes—
361C22C2×#99×C12718yes—
362C22C2×#99×C12714yes—
363C22C22×C22⋊C4×C12711yescharacteristic
364C22C2×#117×C12712yes—
365C22C2×#123×C12714yes—
366C4—48no—
367C4—88no—
368C2—24no—
369C2—22no—
370C2—22no—
371C2—28no—
372C2—24no—
373C2—44no—
374C2C127×#181914yesdirect product factor
375C2C2×#381×C12711yescharacteristic
376C2C22×#99×C12712yes—
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C26×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1819C2direct (N × H)
4. C2×#342×C127C2semidirect
6. C24×C4×C127C4semidirect
10. C22×C22⋊C4×C127C4semidirect
11. C22×C22⋊C4×C127C4semidirect
17. #342×C127C22semidirect
33. C23×C4×C127C2×C4semidirect
45. C2×C22⋊C4×C127C2×C4semidirect
179. C2×#1819C127direct (N × H)
186. C2×C127#1819direct (N × H)
191. #1819C2×C127direct (N × H)
192. C2×#342C2×C127semidirect
193. C127C2×#1819direct (N × H)
195. C24×C4C4×C127semidirect
199. C22×C22⋊C4C4×C127semidirect
200. C22×C22⋊C4C4×C127semidirect
206. #342C22×C127semidirect
222. C23×C4C2×C4×C127semidirect
234. C2×C22⋊C4C2×C4×C127semidirect
374. C2C127×#1819direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#379×C1272
C127×#18192
C2×#342×C1272
C2×#1819127