Finite Group Databasebeta

← C127×#9784 #44573457

Subgroups — C127×#9784 #44573457

Order 32512.

510 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C127C211yesmaximal, characteristic
2C127×#1996C212yesmaximal
3C127×#1807C211yesmaximal, characteristic
4C127×#1752C211yesmaximal, characteristic
5C127×#1520C212yesmaximal
6C22×Q16×C127C411yescharacteristic, complemented
7C23×C8×C127C2211yescharacteristic
8C2×C22⋊Q8×C127C2212yes—
9#467×C127—21no—
10#467×C127—21no—
11#467×C127—21no—
12#467×C127—21no—
13C2×#107×C127C411yescharacteristic, complemented
14C2×#106×C127—21no—
15C2×#103×C127C412yescomplemented
16C2×C22⋊C8×C127C2211yescharacteristic
17C2×#97×C127—21no—
18#380×C127C2212yes—
19C4×C22⋊C4×C127C2211yescharacteristic
20#342×C127—24no—
21#340×C127—21no—
22#336×C127—21no—
23#328×C127—24no—
24C22×Q8×C127C2×C412yes—
25C23×C4×C127C2311yescharacteristic
26C2×Q16×C127—21no—
27C2×Q16×C127—21no—
28C2×Q16×C127—42no—
29C22×C8×C127—21no—
30C22×C8×C127—42no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22⋊Q8×C127—22no—
38C22⋊Q8×C127—22no—
39C22⋊Q8×C127—22no—
40C22⋊Q8×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127C2×C412yes—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127D412yes—
47C2×C42×C127—21no—
48#107×C127—21no—
49#107×C127—21no—
50#106×C127—42no—
51#103×C127—22no—
52#103×C127—22no—
53C22⋊C8×C127—21no—
54C22⋊C8×C127D412yes—
55#97×C127—42no—
56#95×C127—21no—
57#95×C127—22no—
58C24×C127C2×D411yescharacteristic
59C2×Q8×C127—22no—
60C2×Q8×C127—22no—
61C2×Q8×C127—42no—
62C2×Q8×C127—42no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—42no—
69C22×C4×C127C22×C411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73C22×C4×C127#4111yescharacteristic
74C22×C4×C127#4111yescharacteristic
75Q16×C127—42no—
76Q16×C127—42no—
77C2×C8×C127—22no—
78C2×C8×C127—22no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—41no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127C22⋊C411yescharacteristic
87C2×C8×C127C22⋊C411yescharacteristic
88C2×C8×C127C22⋊C411yescharacteristic
89C2×C8×C127C22⋊C411yescharacteristic
90C4⋊C4×C127—22no—
91C4⋊C4×C127—22no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127—42no—
96C22⋊C4×C127—24no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—42no—
99C22⋊C4×C127—44no—
100C42×C127—41no—
101C42×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127C4×D411yescharacteristic
105C23×C127#12111yescharacteristic
106C23×C127#12711yescharacteristic
107C23×C127#13714yes—
108Q8×C127—42no—
109Q8×C127—42no—
110Q8×C127—82no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—82no—
126C2×C4×C127—82no—
127C2×C4×C127—82no—
128C2×C4×C127—82no—
129C2×C4×C127—82no—
130C2×C4×C127C2×C22⋊C411yescharacteristic
131C2×C4×C127C4×D411yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12411yescharacteristic
134C8×C127—21no—
135C8×C127—21no—
136C8×C127—21no—
137C8×C127—42no—
138C8×C127#9912yes—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—44no—
146C22×C127#39011yescharacteristic
147C22×C127#44112yes—
148C22×C127#47012yes—
149C22×C127#49712yes—
150C4×C127—21no—
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—82no—
154C4×C127—82no—
155C4×C127—82no—
156C4×C127—162no—
157C4×C127C2×#9911yescharacteristic
158C4×C127#41011yescharacteristic
159#9784C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—22no—
161C2×C127—22no—
162C2×C127—22no—
163C2×C127#196411yescharacteristic
164C2×C127#197111yescharacteristic
165C2×C127#197611yescharacteristic
166C2×#467C2×C12711yescharacteristic
167#1996C2×C12712yes—
168#1807C2×C12711yescharacteristic
169#1752C2×C12711yescharacteristic
170#1520C2×C12712yes—
171C127#978411yescharacteristic, direct product factor, Sylow
172C22×Q16C4×C12711yescharacteristic, complemented
173C23×C8C22×C12711yescharacteristic
174C2×C22⋊Q8C22×C12712yes—
175#467—21no—
176#467—21no—
177#467—21no—
178#467—21no—
179C2×#107C4×C12711yescharacteristic, complemented
180C2×#106—21no—
181C2×#103C4×C12712yescomplemented
182C2×C22⋊C8C22×C12711yescharacteristic
183C2×#97—21no—
184#380C22×C12712yes—
185C4×C22⋊C4C22×C12711yescharacteristic
186#342—24no—
187#340—21no—
188#336—21no—
189#328—24no—
190C22×Q8C2×C4×C12712yes—
191C23×C4C23×C12711yescharacteristic
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—42no—
195C22×C8—21no—
196C22×C8—42no—
197C22×C8C2×C4×C12711yescharacteristic
198C22×C8C2×C4×C12711yescharacteristic
199C22×C8D4×C12711yescharacteristic
200C22×C8D4×C12711yescharacteristic
201C22×C8D4×C12711yescharacteristic
202C22×C8D4×C12711yescharacteristic
203C22⋊Q8—22no—
204C22⋊Q8—22no—
205C22⋊Q8—22no—
206C22⋊Q8—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4C2×C4×C12712yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4D4×C12712yes—
213C2×C42—21no—
214#107—21no—
215#107—21no—
216#106—42no—
217#103—22no—
218#103—22no—
219C22⋊C8—21no—
220C22⋊C8D4×C12712yes—
221#97—42no—
222#95—21no—
223#95—22no—
224C24C2×D4×C12711yescharacteristic
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—42no—
228C2×Q8—42no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4C22×C4×C12711yescharacteristic
236C22×C4C2×D4×C12711yescharacteristic
237C22×C4C2×D4×C12711yescharacteristic
238C22×C4C2×D4×C12711yescharacteristic
239C22×C4#41×C12711yescharacteristic
240C22×C4#41×C12711yescharacteristic
241Q16—42no—
242Q16—42no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8C22⋊C4×C12711yescharacteristic
253C2×C8C22⋊C4×C12711yescharacteristic
254C2×C8C22⋊C4×C12711yescharacteristic
255C2×C8C22⋊C4×C12711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C22⋊C4—24no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—44no—
266C42—41no—
267C42—41no—
268C23—41no—
269C23—41no—
270C23C4×D4×C12711yescharacteristic
271C23#121×C12711yescharacteristic
272C23#127×C12711yescharacteristic
273C23#137×C12714yes—
274Q8—42no—
275Q8—42no—
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4C2×C22⋊C4×C12711yescharacteristic
297C2×C4C4×D4×C12711yescharacteristic
298C2×C4#121×C12711yescharacteristic
299C2×C4#124×C12711yescharacteristic
300C8—21no—
301C8—21no—
302C8—21no—
303C8—42no—
304C8#99×C12712yes—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—44no—
312C22#390×C12711yescharacteristic
313C22#441×C12712yes—
314C22#470×C12712yes—
315C22#497×C12712yes—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—82no—
320C4—82no—
321C4—82no—
322C4—162no—
323C4C2×#99×C12711yescharacteristic
324C4#410×C12711yescharacteristic
325C2—22no—
326C2—22no—
327C2—22no—
328C2C127×#196411yescharacteristic
329C2C127×#197111yescharacteristic
330C2C127×#197611yescharacteristic
subgroupG/H
center, socleC22×C127#390
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×Q16×C127C4semidirect
13. C2×#107×C127C4semidirect
15. C2×#103×C127C4semidirect
159. #9784C127direct (N × H)
171. C127#9784direct (N × H)
172. C22×Q16C4×C127semidirect
179. C2×#107C4×C127semidirect
181. C2×#103C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1272
C127×#19962
C127×#18072
C127×#17522
C127×#15202
#9784127