Finite Group Databasebeta

← C2×C127×#1341 #44575359

Subgroups — C2×C127×#1341 #44575359

Order 32512.

480 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C127C211yesmaximal, characteristic
2C2×#349×C127C211yesmaximal, characteristic, complemented
3C2×#338×C127C211yesmaximal, characteristic, complemented
4C127×#1341C214yesmaximal, direct product factor
5C22×D8×C127C411yescharacteristic
6C22×M16×C127—21no—
7C22×M16×C127C2211yescharacteristic
8C2×#121×C127—21no—
9C2×M32×C127—21no—
10#469×C127—21no—
11#469×C127—21no—
12#469×C127C412yes—
13#469×C127C2212yes—
14C2×#106×C127C411yescharacteristic
15C2×#102×C127—21no—
16#349×C127—21no—
17#349×C127C2212yescomplemented
18#338×C127—21no—
19#338×C127C2212yescomplemented
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127D411yescharacteristic
23C2×D8×C127—21no—
24C2×D8×C127—41no—
25C2×D8×C127—41no—
26C2×D8×C127C2×C412yes—
27C2×M16×C127—22no—
28C2×M16×C127—22no—
29C2×M16×C127—41no—
30C2×M16×C127—41no—
31C2×M16×C127—41no—
32C2×M16×C127—41no—
33C2×M16×C127—41no—
34C2×M16×C127—41no—
35C2×M16×C127C2×C411yescharacteristic
36C2×M16×C127D411yescharacteristic
37C2×M16×C127D411yescharacteristic
38C2×M16×C127C2311yescharacteristic
39C22×C8×C127—22no—
40C22×C8×C127C2×C411yescharacteristic
41C22×C8×C127D411yescharacteristic
42#121×C127—22no—
43#121×C127—22no—
44#121×C127—41no—
45#121×C127—41no—
46C2×C4⋊C4×C127—21no—
47C2×C22⋊C4×C127—41no—
48M32×C127—22no—
49M32×C127—41no—
50C2×C16×C127—41no—
51#106×C127—21no—
52#106×C127C2×C412yes—
53#102×C127—22no—
54#102×C127—22no—
55C24×C127—41no—
56C24×C127SD1611yescharacteristic
57C2×D4×C127—22no—
58C2×D4×C127—42no—
59C2×D4×C127—42no—
60C2×D4×C127—41no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—84no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127D811yescharacteristic
74C22×C4×C127D811yescharacteristic
75C22×C4×C127SD1611yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77D8×C127—42no—
78D8×C127—42no—
79M16×C127—41no—
80M16×C127—41no—
81M16×C127—41no—
82M16×C127—41no—
83M16×C127—42no—
84M16×C127—42no—
85M16×C127—42no—
86M16×C127—42no—
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—21no—
90C2×C8×C127—21no—
91C2×C8×C127—24no—
92C2×C8×C127—42no—
93C2×C8×C127—42no—
94C2×C8×C127C22⋊C411yescharacteristic
95C2×C8×C127C22⋊C411yescharacteristic
96C2×C8×C127C22×C411yescharacteristic
97C2×C8×C127C2×D411yescharacteristic
98C4⋊C4×C127—22no—
99C4⋊C4×C127—41no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—42no—
102C16×C127—42no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—42no—
106C23×C127—42no—
107C23×C127—82no—
108C23×C127—82no—
109C23×C127—81no—
110C23×C127—81no—
111C23×C127#10211yescharacteristic
112C23×C127#10211yescharacteristic
113C23×C127C2×SD1611yescharacteristic
114D4×C127—42no—
115D4×C127—42no—
116D4×C127—84no—
117D4×C127—84no—
118D4×C127—81no—
119D4×C127—81no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—42no—
131C2×C4×C127—82no—
132C2×C4×C127#9911yescharacteristic
133C2×C4×C127#9911yescharacteristic
134C2×C4×C127#10211yescharacteristic
135C2×C4×C127#10211yescharacteristic
136C2×C4×C127#10411yescharacteristic
137C2×C4×C127#10411yescharacteristic
138C2×C4×C127C2×C22⋊C411yescharacteristic
139C2×C4×C127C2×D811yescharacteristic
140C8×C127—21no—
141C8×C127—21no—
142C8×C127—21no—
143C8×C127—21no—
144C8×C127—44no—
145C22×C127—22no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—42no—
151C22×C127—81no—
152C22×C127—82no—
153C22×C127—82no—
154C22×C127—82no—
155C22×C127—162no—
156C22×C127—162no—
157C22×C127#32711yescharacteristic
158C22×C127#32711yescharacteristic
159C22×C127C2×#10211yescharacteristic
160C4×C127—21no—
161C4×C127—21no—
162C4×C127—82no—
163C4×C127#32711yescharacteristic
164C4×C127#32711yescharacteristic
165C4×C127C2×#9911yescharacteristic
166C4×C127C2×#10411yescharacteristic
167C2×#1341C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—21no—
169C2×C127—21no—
170C2×C127—41no—
171C2×C127—41no—
172C2×C127—162no—
173C2×C127#134112yesdirect product factor
174C2×C127C2×#32711yescharacteristic
175C2×#469C2×C12711yescharacteristic
176C2×#349C2×C12711yescharacteristic, complemented
177C2×#338C2×C12711yescharacteristic, complemented
178#1341C2×C12714yesdirect product factor
179C127C2×#134111yescharacteristic, direct product factor, Sylow
180C22×D8C4×C12711yescharacteristic
181C22×M16—21no—
182C22×M16C22×C12711yescharacteristic
183C2×#121—21no—
184C2×M32—21no—
185#469—21no—
186#469—21no—
187#469C4×C12712yes—
188#469C22×C12712yes—
189C2×#106C4×C12711yescharacteristic
190C2×#102—21no—
191#349—21no—
192#349C22×C12712yescomplemented
193#338—21no—
194#338C22×C12712yescomplemented
195C22×D4—21no—
196C22×D4—41no—
197C23×C4D4×C12711yescharacteristic
198C2×D8—21no—
199C2×D8—41no—
200C2×D8—41no—
201C2×D8C2×C4×C12712yes—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—41no—
205C2×M16—41no—
206C2×M16—41no—
207C2×M16—41no—
208C2×M16—41no—
209C2×M16—41no—
210C2×M16C2×C4×C12711yescharacteristic
211C2×M16D4×C12711yescharacteristic
212C2×M16D4×C12711yescharacteristic
213C2×M16C23×C12711yescharacteristic
214C22×C8—22no—
215C22×C8C2×C4×C12711yescharacteristic
216C22×C8D4×C12711yescharacteristic
217#121—22no—
218#121—22no—
219#121—41no—
220#121—41no—
221C2×C4⋊C4—21no—
222C2×C22⋊C4—41no—
223M32—22no—
224M32—41no—
225C2×C16—41no—
226#106—21no—
227#106C2×C4×C12712yes—
228#102—22no—
229#102—22no—
230C24—41no—
231C24SD16×C12711yescharacteristic
232C2×D4—22no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—84no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22⋊C4×C12711yescharacteristic
248C22×C4D8×C12711yescharacteristic
249C22×C4D8×C12711yescharacteristic
250C22×C4SD16×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252D8—42no—
253D8—42no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258M16—42no—
259M16—42no—
260M16—42no—
261M16—42no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8C22⋊C4×C12711yescharacteristic
270C2×C8C22⋊C4×C12711yescharacteristic
271C2×C8C22×C4×C12711yescharacteristic
272C2×C8C2×D4×C12711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C16—42no—
278C23—21no—
279C23—21no—
280C23—42no—
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23#102×C12711yescharacteristic
287C23#102×C12711yescharacteristic
288C23C2×SD16×C12711yescharacteristic
289D4—42no—
290D4—42no—
291D4—84no—
292D4—84no—
293D4—81no—
294D4—81no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4#99×C12711yescharacteristic
308C2×C4#99×C12711yescharacteristic
309C2×C4#102×C12711yescharacteristic
310C2×C4#102×C12711yescharacteristic
311C2×C4#104×C12711yescharacteristic
312C2×C4#104×C12711yescharacteristic
313C2×C4C2×C22⋊C4×C12711yescharacteristic
314C2×C4C2×D8×C12711yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8—21no—
319C8—44no—
320C22—22no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—81no—
327C22—82no—
328C22—82no—
329C22—82no—
330C22—162no—
331C22—162no—
332C22#327×C12711yescharacteristic
333C22#327×C12711yescharacteristic
334C22C2×#102×C12711yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4#327×C12711yescharacteristic
339C4#327×C12711yescharacteristic
340C4C2×#99×C12711yescharacteristic
341C4C2×#104×C12711yescharacteristic
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2—162no—
347C2C127×#134112yesdirect product factor
348C2C2×#327×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC2×#469×C127C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#349×C127C2semidirect
3. C2×#338×C127C2semidirect
4. C127×#1341C2direct (N × H)
17. #349×C127C22semidirect
19. #338×C127C22semidirect
167. C2×#1341C127direct (N × H)
173. C2×C127#1341direct (N × H)
176. C2×#349C2×C127semidirect
177. C2×#338C2×C127semidirect
178. #1341C2×C127direct (N × H)
179. C127C2×#1341direct (N × H)
192. #349C22×C127semidirect
194. #338C22×C127semidirect
347. C2C127×#1341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#469×C1272
C2×#349×C1272
C2×#338×C1272
C127×#13412
C2×#1341127