Finite Group Databasebeta

← C127×#8568 #44572241

Subgroups — C127×#8568 #44572241

Order 32512.

492 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2295C211yesmaximal, characteristic
2C127×#1842C211yesmaximal, characteristic
3C4×C4⋊C8×C127C211yesmaximal, characteristic
4C2×Q8⋊C8×C127C212yesmaximal
5C127×#1279C212yesmaximal
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4⋊C8×C127—21no—
8C2×C4⋊C8×C127—21no—
9C2×C4⋊C8×C127—21no—
10C2×C4⋊C8×C127C2212yes—
11C2×C4×C8×C127C2212yes—
12#391×C127C411yescharacteristic
13#391×C127C411yescharacteristic
14#389×C127C411yescharacteristic
15#389×C127C411yescharacteristic
16#387×C127—21no—
17#387×C127—21no—
18C4×C4⋊C4×C127—21no—
19C4×C4⋊C4×C127C2211yescharacteristic
20#376×C127—21no—
21C43×C127C2211yescharacteristic
22#336×C127—21no—
23Q8⋊C8×C127—24no—
24C22×Q8×C127C2×C411yescharacteristic
25C22×C8×C127—22no—
26C22×C8×C127—22no—
27C4×Q8×C127—21no—
28C4×Q8×C127—21no—
29C4×Q8×C127D412yes—
30C4×Q8×C127Q812yes—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C42×C127—21no—
38C2×C42×C127—21no—
39C2×C42×C127C2×C411yescharacteristic
40C2×C42×C127C2×C411yescharacteristic
41C2×C42×C127D411yescharacteristic
42C2×C42×C127D411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C2×C42×C127C2311yescharacteristic
46C4⋊C8×C127—24no—
47C4⋊C8×C127—22no—
48C4⋊C8×C127—22no—
49C4⋊C8×C127—42no—
50C4⋊C8×C127—42no—
51C4×C8×C127—22no—
52C4×C8×C127—22no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—22no—
62C2×Q8×C127—22no—
63C2×Q8×C127C4⋊C412yes—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22×C411yescharacteristic
73C22×C4×C127C2×D411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C2×C8×C127—24no—
76C2×C8×C127—42no—
77C2×C8×C127—42no—
78C2×C8×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127C4⋊C412yes—
89C42×C127—22no—
90C42×C127—22no—
91C42×C127—22no—
92C42×C127—22no—
93C42×C127—22no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—41no—
97C42×C127—41no—
98C42×C127—41no—
99C42×C127SD1612yes—
100C42×C127Q1612yes—
101C42×C127C2×D411yescharacteristic
102C42×C127C2×Q811yescharacteristic
103C42×C127#4111yescharacteristic
104C42×C127#4111yescharacteristic
105C23×C127C2×C22⋊C411yescharacteristic
106Q8×C127—24no—
107Q8×C127—42no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—22no—
117C2×C4×C127—22no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127#10312yes—
132C2×C4×C127#10312yes—
133C2×C4×C127#10412yes—
134C2×C4×C127C2×C4⋊C411yescharacteristic
135C2×C4×C127#11711yescharacteristic
136C2×C4×C127#12111yescharacteristic
137C2×C4×C127#12111yescharacteristic
138C2×C4×C127C22⋊Q811yescharacteristic
139C2×C4×C127C22⋊Q811yescharacteristic
140C2×C4×C127#13112yes—
141C2×C4×C127#13112yes—
142C2×C4×C127C2×SD1611yescharacteristic
143C2×C4×C127C2×Q1611yescharacteristic
144C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C127#13711yescharacteristic
146C8×C127—44no—
147C8×C127—82no—
148C22×C127#38011yescharacteristic
149C22×C127#40811yescharacteristic
150C22×C127#40811yescharacteristic
151C22×C127C2×#10311yescharacteristic
152C22×C127#41711yescharacteristic
153C22×C127C2×#10411yescharacteristic
154C22×C127#42111yescharacteristic
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—22no—
158C4×C127—22no—
159C4×C127—22no—
160C4×C127—42no—
161C4×C127—42no—
162C4×C127—41no—
163C4×C127—81no—
164C4×C127—81no—
165C4×C127#42412yes—
166C4×C127#43312yes—
167C4×C127#46011yescharacteristic
168C4×C127#46211yescharacteristic
169C4×C127#47511yescharacteristic
170C4×C127#47711yescharacteristic
171#8568C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127#148111yescharacteristic
173C2×C127#148311yescharacteristic
174C2×C127#149311yescharacteristic
175C2×C127#149511yescharacteristic
176C2×C127#179811yescharacteristic
177C2×C127#180311yescharacteristic
178C2×C127#180611yescharacteristic
179#2295C2×C12711yescharacteristic
180#1842C2×C12711yescharacteristic
181C4×C4⋊C8C2×C12711yescharacteristic
182C2×Q8⋊C8C2×C12712yes—
183#1279C2×C12712yes—
184C127#856811yescharacteristic, direct product factor, Sylow
185C2×C4×Q8C22×C12711yescharacteristic
186C2×C4⋊C8—21no—
187C2×C4⋊C8—21no—
188C2×C4⋊C8—21no—
189C2×C4⋊C8C22×C12712yes—
190C2×C4×C8C22×C12712yes—
191#391C4×C12711yescharacteristic
192#391C4×C12711yescharacteristic
193#389C4×C12711yescharacteristic
194#389C4×C12711yescharacteristic
195#387—21no—
196#387—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4C22×C12711yescharacteristic
199#376—21no—
200C43C22×C12711yescharacteristic
201#336—21no—
202Q8⋊C8—24no—
203C22×Q8C2×C4×C12711yescharacteristic
204C22×C8—22no—
205C22×C8—22no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8D4×C12712yes—
209C4×Q8Q8×C12712yes—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C12711yescharacteristic
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C4⋊C4C2×C4×C12711yescharacteristic
216C2×C42—21no—
217C2×C42—21no—
218C2×C42C2×C4×C12711yescharacteristic
219C2×C42C2×C4×C12711yescharacteristic
220C2×C42D4×C12711yescharacteristic
221C2×C42D4×C12711yescharacteristic
222C2×C42D4×C12711yescharacteristic
223C2×C42D4×C12711yescharacteristic
224C2×C42C23×C12711yescharacteristic
225C4⋊C8—24no—
226C4⋊C8—22no—
227C4⋊C8—22no—
228C4⋊C8—42no—
229C4⋊C8—42no—
230C4×C8—22no—
231C4×C8—22no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8C4⋊C4×C12712yes—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C22⋊C4×C12711yescharacteristic
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4C22⋊C4×C12711yescharacteristic
250C22×C4C22⋊C4×C12711yescharacteristic
251C22×C4C22×C4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C22×C4C2×D4×C12711yescharacteristic
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C4⋊C4—21no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4C4⋊C4×C12712yes—
268C42—22no—
269C42—22no—
270C42—22no—
271C42—22no—
272C42—22no—
273C42—21no—
274C42—21no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42SD16×C12712yes—
279C42Q16×C12712yes—
280C42C2×D4×C12711yescharacteristic
281C42C2×Q8×C12711yescharacteristic
282C42#41×C12711yescharacteristic
283C42#41×C12711yescharacteristic
284C23C2×C22⋊C4×C12711yescharacteristic
285Q8—24no—
286Q8—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4#103×C12712yes—
311C2×C4#103×C12712yes—
312C2×C4#104×C12712yes—
313C2×C4C2×C4⋊C4×C12711yescharacteristic
314C2×C4#117×C12711yescharacteristic
315C2×C4#121×C12711yescharacteristic
316C2×C4#121×C12711yescharacteristic
317C2×C4C22⋊Q8×C12711yescharacteristic
318C2×C4C22⋊Q8×C12711yescharacteristic
319C2×C4#131×C12712yes—
320C2×C4#131×C12712yes—
321C2×C4C2×SD16×C12711yescharacteristic
322C2×C4C2×Q16×C12711yescharacteristic
323C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
324C2×C4#137×C12711yescharacteristic
325C8—44no—
326C8—82no—
327C22#380×C12711yescharacteristic
328C22#408×C12711yescharacteristic
329C22#408×C12711yescharacteristic
330C22C2×#103×C12711yescharacteristic
331C22#417×C12711yescharacteristic
332C22C2×#104×C12711yescharacteristic
333C22#421×C12711yescharacteristic
334C4—21no—
335C4—21no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—42no—
340C4—41no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4#424×C12712yes—
345C4#433×C12712yes—
346C4#460×C12711yescharacteristic
347C4#462×C12711yescharacteristic
348C4#475×C12711yescharacteristic
349C4#477×C12711yescharacteristic
350C2C127×#148111yescharacteristic
351C2C127×#148311yescharacteristic
352C2C127×#149311yescharacteristic
353C2C127×#149511yescharacteristic
354C2C127×#179811yescharacteristic
355C2C127×#180311yescharacteristic
356C2C127×#180611yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socle, prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
171. #8568C127direct (N × H)
184. C127#8568direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22952
C127×#18422
C4×C4⋊C8×C1272
C2×Q8⋊C8×C1272
C127×#12792
#8568127