Finite Group Databasebeta

← C2×C127×#1821 #44584365

Subgroups — C2×C127×#1821 #44584365

Order 32512.

1734 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C127C211yesmaximal, characteristic
2C2×#407×C127C212yesmaximal
3C127×#1821C218yesmaximal, direct product factor
4C2×#343×C127C214yesmaximal, complemented
5C24×C4×C127C412yes—
6C24×C4×C127C2211yescharacteristic
7C22×M16×C127C2214yes—
8C22×C4⋊C4×C127—22no—
9C22×C4⋊C4×C127—22no—
10C22×C4⋊C4×C127—24no—
11C22×C4⋊C4×C127C414yes—
12C22×C4⋊C4×C127C412yes—
13C22×C4⋊C4×C127C2214yes—
14C22×C4⋊C4×C127C2212yes—
15#407×C127—24no—
16#407×C127C2218yes—
17C2×C22⋊C8×C127—22no—
18C2×C22⋊C8×C127—22no—
19#343×C127C22116yescomplemented
20C25×C127C2×C411yescharacteristic
21C23×C4×C127—28no—
22C23×C4×C127—24no—
23C23×C4×C127—22no—
24C23×C4×C127—22no—
25C23×C4×C127—48no—
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127C2×C412yes—
28C23×C4×C127C2×C418yes—
29C23×C4×C127C2×C414yes—
30C23×C4×C127D412yes—
31C23×C4×C127D412yes—
32C23×C4×C127D414yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2311yescharacteristic
35C2×M16×C127—24no—
36C2×M16×C127—216no—
37C2×M16×C127C2318yes—
38C22×C8×C127—24no—
39C2×C4⋊C4×C127—24no—
40C2×C4⋊C4×C127—28no—
41C2×C4⋊C4×C127—28no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—28no—
44C2×C4⋊C4×C127—28no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127C2×C418yes—
48C2×C4⋊C4×C127C2×C414yes—
49C2×C4⋊C4×C127C2314yes—
50C22⋊C8×C127—28no—
51C22⋊C8×C127—28no—
52C24×C127—24no—
53C24×C127—24no—
54C24×C127—24no—
55C24×C127C22⋊C412yes—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127C22×C412yes—
59C24×C127C22×C411yescharacteristic
60C22×C4×C127—24no—
61C22×C4×C127—28no—
62C22×C4×C127—28no—
63C22×C4×C127—28no—
64C22×C4×C127—216no—
65C22×C4×C127—28no—
66C22×C4×C127—24no—
67C22×C4×C127—28no—
68C22×C4×C127—28no—
69C22×C4×C127—24no—
70C22×C4×C127—416no—
71C22×C4×C127—48no—
72C22×C4×C127—48no—
73C22×C4×C127—416no—
74C22×C4×C127—48no—
75C22×C4×C127C22⋊C412yes—
76C22×C4×C127C22⋊C414yes—
77C22×C4×C127C22⋊C414yes—
78C22×C4×C127C22⋊C412yes—
79C22×C4×C127C22×C412yes—
80C22×C4×C127C22×C418yes—
81C22×C4×C127C22×C411yescharacteristic
82C22×C4×C127C2×D414yes—
83C22×C4×C127C2×D414yes—
84C22×C4×C127C2×D412yes—
85C22×C4×C127C2×D412yes—
86C22×C4×C127#4118yes—
87C22×C4×C127C2411yescharacteristic
88M16×C127—216no—
89M16×C127—48no—
90C2×C8×C127—28no—
91C2×C8×C127—48no—
92C4⋊C4×C127—216no—
93C4⋊C4×C127—28no—
94C4⋊C4×C127—28no—
95C23×C127—232no—
96C23×C127—24no—
97C23×C127—24no—
98C23×C127—22no—
99C23×C127—22no—
100C23×C127—24no—
101C23×C127—22no—
102C23×C127—24no—
103C23×C127—22no—
104C23×C127—24no—
105C23×C127—22no—
106C23×C127—24no—
107C23×C127—22no—
108C23×C127#10014yes—
109C23×C127#10114yes—
110C23×C127C2×C22⋊C411yescharacteristic
111C23×C127C2×C22⋊C412yes—
112C23×C127C2×C22⋊C412yes—
113C23×C127C2×C22⋊C411yescharacteristic
114C23×C127#11714yes—
115C23×C127C23×C411yescharacteristic
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—24no—
119C2×C4×C127—28no—
120C2×C4×C127—28no—
121C2×C4×C127—28no—
122C2×C4×C127—28no—
123C2×C4×C127—28no—
124C2×C4×C127—48no—
125C2×C4×C127—416no—
126C2×C4×C127—416no—
127C2×C4×C127—48no—
128C2×C4×C127—48no—
129C2×C4×C127C2×C22⋊C414yes—
130C2×C4×C127C2×C22⋊C412yes—
131C2×C4×C127#11714yes—
132C2×C4×C127#12318yes—
133C2×C4×C127#12318yes—
134C2×C4×C127C22×D412yes—
135C2×C4×C127C2×#4114yes—
136C8×C127—48no—
137C22×C127—216no—
138C22×C127—216no—
139C22×C127—28no—
140C22×C127—28no—
141C22×C127—28no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—22no—
147C22×C127—21no—
148C22×C127—22no—
149C22×C127—22no—
150C22×C127#38112yes—
151C22×C127#38112yes—
152C22×C127C2×#10014yes—
153C22×C127C2×#10012yes—
154C22×C127C2×#10114yes—
155C22×C127C2×#10112yes—
156C22×C127C22×C22⋊C411yescharacteristic
157C22×C127C2×#11712yes—
158C4×C127—24no—
159C4×C127—48no—
160C4×C127#38114yes—
161C4×C127C2×#12314yes—
162C2×#1821C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127—22no—
164C2×C127—22no—
165C2×C127—24no—
166C2×C127—24no—
167C2×C127#182114yesdirect product factor
168C2×C127C2×#38111yescharacteristic
169C2×C127C22×#10011yescharacteristic
170C2×C127C22×#10111yescharacteristic
171C23×C4⋊C4C2×C12711yescharacteristic
172C2×#407C2×C12712yes—
173#1821C2×C12718yesdirect product factor
174C2×#343C2×C12714yescomplemented
175C127C2×#182111yescharacteristic, direct product factor, Sylow
176C24×C4C4×C12712yes—
177C24×C4C22×C12711yescharacteristic
178C22×M16C22×C12714yes—
179C22×C4⋊C4—22no—
180C22×C4⋊C4—22no—
181C22×C4⋊C4—24no—
182C22×C4⋊C4C4×C12712yes—
183C22×C4⋊C4C4×C12714yes—
184C22×C4⋊C4C22×C12714yes—
185C22×C4⋊C4C22×C12712yes—
186#407—24no—
187#407C22×C12718yes—
188C2×C22⋊C8—22no—
189C2×C22⋊C8—22no—
190#343C22×C127116yescomplemented
191C25C2×C4×C12711yescharacteristic
192C23×C4—28no—
193C23×C4—24no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—48no—
197C23×C4C2×C4×C12711yescharacteristic
198C23×C4C2×C4×C12712yes—
199C23×C4C2×C4×C12718yes—
200C23×C4C2×C4×C12714yes—
201C23×C4D4×C12712yes—
202C23×C4D4×C12712yes—
203C23×C4D4×C12714yes—
204C23×C4C23×C12712yes—
205C23×C4C23×C12711yescharacteristic
206C2×M16—24no—
207C2×M16—216no—
208C2×M16C23×C12718yes—
209C22×C8—24no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—28no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4C2×C4×C12718yes—
219C2×C4⋊C4C2×C4×C12714yes—
220C2×C4⋊C4C23×C12714yes—
221C22⋊C8—28no—
222C22⋊C8—28no—
223C24—24no—
224C24—24no—
225C24—24no—
226C24C22⋊C4×C12712yes—
227C24C22⋊C4×C12711yescharacteristic
228C24C22⋊C4×C12711yescharacteristic
229C24C22×C4×C12712yes—
230C24C22×C4×C12711yescharacteristic
231C22×C4—24no—
232C22×C4—28no—
233C22×C4—28no—
234C22×C4—28no—
235C22×C4—216no—
236C22×C4—28no—
237C22×C4—24no—
238C22×C4—28no—
239C22×C4—28no—
240C22×C4—24no—
241C22×C4—416no—
242C22×C4—48no—
243C22×C4—48no—
244C22×C4—416no—
245C22×C4—48no—
246C22×C4C22⋊C4×C12712yes—
247C22×C4C22⋊C4×C12712yes—
248C22×C4C22⋊C4×C12714yes—
249C22×C4C22⋊C4×C12714yes—
250C22×C4C22×C4×C12712yes—
251C22×C4C22×C4×C12718yes—
252C22×C4C22×C4×C12711yescharacteristic
253C22×C4C2×D4×C12714yes—
254C22×C4C2×D4×C12714yes—
255C22×C4C2×D4×C12712yes—
256C22×C4C2×D4×C12712yes—
257C22×C4#41×C12718yes—
258C22×C4C24×C12711yescharacteristic
259M16—216no—
260M16—48no—
261C2×C8—28no—
262C2×C8—48no—
263C4⋊C4—216no—
264C4⋊C4—28no—
265C4⋊C4—28no—
266C23—232no—
267C23—24no—
268C23—24no—
269C23—22no—
270C23—22no—
271C23—24no—
272C23—22no—
273C23—24no—
274C23—22no—
275C23—24no—
276C23—22no—
277C23—24no—
278C23—22no—
279C23#100×C12714yes—
280C23#101×C12714yes—
281C23C2×C22⋊C4×C12711yescharacteristic
282C23C2×C22⋊C4×C12712yes—
283C23C2×C22⋊C4×C12712yes—
284C23C2×C22⋊C4×C12711yescharacteristic
285C23#117×C12714yes—
286C23C23×C4×C12711yescharacteristic
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—28no—
295C2×C4—48no—
296C2×C4—416no—
297C2×C4—416no—
298C2×C4—48no—
299C2×C4—48no—
300C2×C4C2×C22⋊C4×C12714yes—
301C2×C4C2×C22⋊C4×C12712yes—
302C2×C4#117×C12714yes—
303C2×C4#123×C12718yes—
304C2×C4#123×C12718yes—
305C2×C4C22×D4×C12712yes—
306C2×C4C2×#41×C12714yes—
307C8—48no—
308C22—216no—
309C22—216no—
310C22—28no—
311C22—28no—
312C22—28no—
313C22—21no—
314C22—22no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—21no—
319C22—22no—
320C22—22no—
321C22#381×C12712yes—
322C22#381×C12712yes—
323C22C2×#100×C12714yes—
324C22C2×#100×C12712yes—
325C22C2×#101×C12714yes—
326C22C2×#101×C12712yes—
327C22C22×C22⋊C4×C12711yescharacteristic
328C22C2×#117×C12712yes—
329C4—24no—
330C4—48no—
331C4#381×C12714yes—
332C4C2×#123×C12714yes—
333C2—22no—
334C2—22no—
335C2—24no—
336C2—24no—
337C2C127×#182114yesdirect product factor
338C2C2×#381×C12711yescharacteristic
339C2C22×#100×C12711yescharacteristic
340C2C22×#101×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC25×C127C2×C4
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
3. C127×#1821C2direct (N × H)
4. C2×#343×C127C2semidirect
19. #343×C127C22semidirect
162. C2×#1821C127direct (N × H)
167. C2×C127#1821direct (N × H)
173. #1821C2×C127direct (N × H)
174. C2×#343C2×C127semidirect
175. C127C2×#1821direct (N × H)
190. #343C22×C127semidirect
337. C2C127×#1821direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C1272
C2×#407×C1272
C127×#18212
C2×#343×C1272
C2×#1821127