Finite Group Databasebeta

← C127×#9830 #44573503

Subgroups — C127×#9830 #44573503

Order 32512.

578 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C127C211yesmaximal, characteristic
2C127×#1990C211yesmaximal, characteristic, complemented
3C127×#1957C211yesmaximal, characteristic
4C127×#1957C211yesmaximal, characteristic
5C127×#1956C211yesmaximal, characteristic, complemented
6C127×#1845C211yesmaximal, characteristic, complemented
7C2×#322×C127C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×#127×C127C2211yescharacteristic
10#486×C127—22no—
11#486×C127C414yescomplemented
12C2×#107×C127—22no—
13C2×#103×C127—22no—
14C2×#102×C127—22no—
15C2×#102×C127—22no—
16C2×#102×C127—22no—
17C2×C4×C8×C127C2211yescharacteristic
18C2×C4×C8×C127C2211yescharacteristic
19C2×C4×C8×C127C2211yescharacteristic
20#384×C127C2211yescharacteristic
21#384×C127C2211yescharacteristic
22#340×C127—22no—
23#322×C127—22no—
24C22×Q8×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C22×C8×C127D412yes—
29C22×C8×C127D412yes—
30C22×C8×C127D412yes—
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127C2×C412yes—
35#127×C127—21no—
36#127×C127—21no—
37#127×C127—21no—
38#127×C127C2×C412yes—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C42×C127C2311yescharacteristic
48#107×C127—44no—
49#103×C127—44no—
50#102×C127—28no—
51#102×C127—44no—
52#102×C127—44no—
53C4×C8×C127—21no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—21no—
57C4×C8×C127C2×C412yes—
58C4×C8×C127D412yes—
59C24×C127—41no—
60C2×Q8×C127—22no—
61C2×Q8×C127—41no—
62C2×Q8×C127—42no—
63C2×Q8×C127—42no—
64C2×D4×C127—22no—
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127—42no—
73C2×D4×C127—42no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82C2×C8×C127—22no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—22no—
86C2×C8×C127—22no—
87C2×C8×C127—22no—
88C2×C8×C127—22no—
89C2×C8×C127C22⋊C414yes—
90C2×C8×C127D814yes—
91C4⋊C4×C127—22no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—42no—
96C4⋊C4×C127—42no—
97C4⋊C4×C127—42no—
98C4⋊C4×C127—42no—
99C4⋊C4×C127—42no—
100C4⋊C4×C127—42no—
101C42×C127C22×C411yescharacteristic
102C42×C127C2×D411yescharacteristic
103C42×C127#4111yescharacteristic
104C42×C127#4111yescharacteristic
105C23×C127—42no—
106C23×C127—81no—
107C23×C127—81no—
108C23×C127—81no—
109C23×C127—81no—
110C23×C127—81no—
111C23×C127—81no—
112C23×C127#12711yescharacteristic
113Q8×C127—44no—
114Q8×C127—82no—
115D4×C127—44no—
116D4×C127—44no—
117D4×C127—44no—
118D4×C127—82no—
119D4×C127—82no—
120D4×C127—82no—
121C2×C4×C127—42no—
122C2×C4×C127—81no—
123C2×C4×C127—81no—
124C2×C4×C127—81no—
125C2×C4×C127—81no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127C2×C22⋊C411yescharacteristic
131C2×C4×C127C4×D411yescharacteristic
132C2×C4×C127C4×D411yescharacteristic
133C2×C4×C127#12111yescharacteristic
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127#12411yescharacteristic
136C2×C4×C127C2×D812yes—
137C2×C4×C127#13512yes—
138C2×C4×C127AGL(1,ℤ/8)12yes—
139C2×C4×C127AGL(1,ℤ/8)12yes—
140C2×C4×C127#13712yes—
141C2×C4×C127#13712yes—
142C8×C127—24no—
143C8×C127—24no—
144C8×C127—42no—
145C22×C127—82no—
146C22×C127—82no—
147C22×C127—82no—
148C22×C127—161no—
149C22×C127—161no—
150C22×C127—161no—
151C22×C127—161no—
152C22×C127#39011yescharacteristic
153C22×C127#49311yescharacteristic
154C22×C127#49511yescharacteristic
155C22×C127#49611yescharacteristic
156C22×C127#49611yescharacteristic
157C22×C127#49711yescharacteristic
158C22×C127#49711yescharacteristic
159C4×C127—82no—
160C4×C127—161no—
161C4×C127—161no—
162C4×C127#41712yes—
163C4×C127C4×D812yes—
164C4×C127#44012yes—
165C4×C127#46612yes—
166C4×C127#46812yes—
167C4×C127#48912yes—
168#9830C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—162no—
170C2×C127#171911yescharacteristic
171C2×C127#172011yescharacteristic
172C2×C127#172111yescharacteristic
173C2×C127#172211yescharacteristic
174C2×C127#195911yescharacteristic
175C2×C127#197011yescharacteristic
176C2×C127#197311yescharacteristic
177C2×#486C2×C12711yescharacteristic
178#1990C2×C12711yescharacteristic, complemented
179#1957C2×C12711yescharacteristic
180#1957C2×C12711yescharacteristic
181#1956C2×C12711yescharacteristic, complemented
182#1845C2×C12711yescharacteristic, complemented
183C2×#322C2×C12711yescharacteristic, complemented
184C127#983011yescharacteristic, direct product factor, Sylow
185C2×C4⋊Q8C22×C12711yescharacteristic
186C2×#127C22×C12711yescharacteristic
187#486—22no—
188#486C4×C12714yescomplemented
189C2×#107—22no—
190C2×#103—22no—
191C2×#102—22no—
192C2×#102—22no—
193C2×#102—22no—
194C2×C4×C8C22×C12711yescharacteristic
195C2×C4×C8C22×C12711yescharacteristic
196C2×C4×C8C22×C12711yescharacteristic
197#384C22×C12711yescharacteristic
198#384C22×C12711yescharacteristic
199#340—22no—
200#322—22no—
201C22×Q8—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×C8D4×C12712yes—
206C22×C8D4×C12712yes—
207C22×C8D4×C12712yes—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C2×C4×C12712yes—
212#127—21no—
213#127—21no—
214#127—21no—
215#127C2×C4×C12712yes—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C42C23×C12711yescharacteristic
225#107—44no—
226#103—44no—
227#102—28no—
228#102—44no—
229#102—44no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8C2×C4×C12712yes—
235C4×C8D4×C12712yes—
236C24—41no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C2×D4×C12711yescharacteristic
257C22×C4C2×D4×C12711yescharacteristic
258C22×C4C2×D4×C12711yescharacteristic
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8C22⋊C4×C12714yes—
267C2×C8D8×C12714yes—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C42C22×C4×C12711yescharacteristic
279C42C2×D4×C12711yescharacteristic
280C42#41×C12711yescharacteristic
281C42#41×C12711yescharacteristic
282C23—42no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23#127×C12711yescharacteristic
290Q8—44no—
291Q8—82no—
292D4—44no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—82no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×C22⋊C4×C12711yescharacteristic
308C2×C4C4×D4×C12711yescharacteristic
309C2×C4C4×D4×C12711yescharacteristic
310C2×C4#121×C12711yescharacteristic
311C2×C4#121×C12711yescharacteristic
312C2×C4#124×C12711yescharacteristic
313C2×C4C2×D8×C12712yes—
314C2×C4#135×C12712yes—
315C2×C4AGL(1,ℤ/8)×C12712yes—
316C2×C4AGL(1,ℤ/8)×C12712yes—
317C2×C4#137×C12712yes—
318C2×C4#137×C12712yes—
319C8—24no—
320C8—24no—
321C8—42no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22—161no—
326C22—161no—
327C22—161no—
328C22—161no—
329C22#390×C12711yescharacteristic
330C22#493×C12711yescharacteristic
331C22#495×C12711yescharacteristic
332C22#496×C12711yescharacteristic
333C22#496×C12711yescharacteristic
334C22#497×C12711yescharacteristic
335C22#497×C12711yescharacteristic
336C4—82no—
337C4—161no—
338C4—161no—
339C4#417×C12712yes—
340C4C4×D8×C12712yes—
341C4#440×C12712yes—
342C4#466×C12712yes—
343C4#468×C12712yes—
344C4#489×C12712yes—
345C2—162no—
346C2C127×#171911yescharacteristic
347C2C127×#172011yescharacteristic
348C2C127×#172111yescharacteristic
349C2C127×#172211yescharacteristic
350C2C127×#195911yescharacteristic
351C2C127×#197011yescharacteristic
352C2C127×#197311yescharacteristic
subgroupG/H
center, socleC23×C127#127
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
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
2. C127×#1990C2semidirect
5. C127×#1956C2semidirect
6. C127×#1845C2semidirect
7. C2×#322×C127C2semidirect
11. #486×C127C4semidirect
168. #9830C127direct (N × H)
178. #1990C2×C127semidirect
181. #1956C2×C127semidirect
182. #1845C2×C127semidirect
183. C2×#322C2×C127semidirect
184. C127#9830direct (N × H)
188. #486C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C1272
C127×#19902
C127×#19572
C127×#19562
C127×#18452
C2×#322×C1272
#9830127