Finite Group Databasebeta

← C127×#8570 #44572243

Subgroups — C127×#8570 #44572243

Order 32512.

472 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2295C211yesmaximal, characteristic
2C127×#1831C211yesmaximal, characteristic
3C4×C4⋊C8×C127C211yesmaximal, characteristic
4C2×Q8⋊C8×C127C212yesmaximal
5C127×#1279C212yesmaximal
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4⋊C8×C127—21no—
8C2×C4⋊C8×C127C2212yes—
9C2×C4×C8×C127C2212yes—
10#391×C127C411yescharacteristic
11#391×C127C411yescharacteristic
12#389×C127C411yescharacteristic
13#389×C127C411yescharacteristic
14#387×C127—21no—
15#387×C127—21no—
16C4×C4⋊C4×C127—21no—
17C4×C4⋊C4×C127C2211yescharacteristic
18#376×C127—21no—
19C43×C127C2211yescharacteristic
20#336×C127—21no—
21#336×C127—21no—
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—22no—
50C4×C8×C127—22no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—22no—
60C2×Q8×C127—22no—
61C2×Q8×C127C4⋊C412yes—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22×C411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73C2×C8×C127—24no—
74C2×C8×C127—42no—
75C2×C8×C127—42no—
76C2×C8×C127—42no—
77C2×C8×C127—42no—
78C2×C8×C127—42no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127C4⋊C412yes—
87C42×C127—22no—
88C42×C127—22no—
89C42×C127—22no—
90C42×C127—22no—
91C42×C127—22no—
92C42×C127—22no—
93C42×C127—22no—
94C42×C127—41no—
95C42×C127—42no—
96C42×C127C2×D411yescharacteristic
97C42×C127C2×Q811yescharacteristic
98C42×C127#4111yescharacteristic
99C42×C127#4111yescharacteristic
100C23×C127C2×C22⋊C411yescharacteristic
101Q8×C127—24no—
102Q8×C127—42no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
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—21no—
117C2×C4×C127—21no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
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#10412yes—
129C2×C4×C127C2×C4⋊C411yescharacteristic
130C2×C4×C127#11711yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127C22⋊Q811yescharacteristic
134C2×C4×C127C22⋊Q811yescharacteristic
135C2×C4×C127#13112yes—
136C2×C4×C127#13112yes—
137C2×C4×C127#13512yes—
138C2×C4×C127#13712yes—
139C8×C127—44no—
140C8×C127—82no—
141C22×C127#38011yescharacteristic
142C22×C127#40811yescharacteristic
143C22×C127#40811yescharacteristic
144C22×C127#41611yescharacteristic
145C22×C127#41911yescharacteristic
146C22×C127C2×#10411yescharacteristic
147C22×C127#42111yescharacteristic
148C4×C127—21no—
149C4×C127—21no—
150C4×C127—22no—
151C4×C127—42no—
152C4×C127—42no—
153C4×C127—41no—
154C4×C127—41no—
155C4×C127—41no—
156C4×C127—81no—
157C4×C127—81no—
158C4×C127#42412yes—
159C4×C127#43312yes—
160C4×C127#46412yes—
161C4×C127#47912yes—
162#8570C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127#148211yescharacteristic
164C2×C127#148511yescharacteristic
165C2×C127#149411yescharacteristic
166C2×C127#149711yescharacteristic
167C2×C127#179811yescharacteristic
168C2×C127#180511yescharacteristic
169C2×C127#180611yescharacteristic
170#2295C2×C12711yescharacteristic
171#1831C2×C12711yescharacteristic
172C4×C4⋊C8C2×C12711yescharacteristic
173C2×Q8⋊C8C2×C12712yes—
174#1279C2×C12712yes—
175C127#857011yescharacteristic, direct product factor, Sylow
176C2×C4×Q8C22×C12711yescharacteristic
177C2×C4⋊C8—21no—
178C2×C4⋊C8C22×C12712yes—
179C2×C4×C8C22×C12712yes—
180#391C4×C12711yescharacteristic
181#391C4×C12711yescharacteristic
182#389C4×C12711yescharacteristic
183#389C4×C12711yescharacteristic
184#387—21no—
185#387—21no—
186C4×C4⋊C4—21no—
187C4×C4⋊C4C22×C12711yescharacteristic
188#376—21no—
189C43C22×C12711yescharacteristic
190#336—21no—
191#336—21no—
192#336—21no—
193Q8⋊C8—24no—
194C22×Q8C2×C4×C12711yescharacteristic
195C22×C8—22no—
196C22×C8—22no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8D4×C12712yes—
200C4×Q8Q8×C12712yes—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C12711yescharacteristic
205C2×C4⋊C4C2×C4×C12711yescharacteristic
206C2×C4⋊C4C2×C4×C12711yescharacteristic
207C2×C42—21no—
208C2×C42—21no—
209C2×C42C2×C4×C12711yescharacteristic
210C2×C42C2×C4×C12711yescharacteristic
211C2×C42D4×C12711yescharacteristic
212C2×C42D4×C12711yescharacteristic
213C2×C42D4×C12711yescharacteristic
214C2×C42D4×C12711yescharacteristic
215C2×C42C23×C12711yescharacteristic
216C4⋊C8—24no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4×C8—22no—
220C4×C8—22no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228C2×Q8—21no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8C4⋊C4×C12712yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4C22⋊C4×C12711yescharacteristic
240C22×C4C22×C4×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242C22×C4C2×D4×C12711yescharacteristic
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4C4⋊C4×C12712yes—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—42no—
266C42C2×D4×C12711yescharacteristic
267C42C2×Q8×C12711yescharacteristic
268C42#41×C12711yescharacteristic
269C42#41×C12711yescharacteristic
270C23C2×C22⋊C4×C12711yescharacteristic
271Q8—24no—
272Q8—42no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#104×C12712yes—
299C2×C4C2×C4⋊C4×C12711yescharacteristic
300C2×C4#117×C12711yescharacteristic
301C2×C4#121×C12711yescharacteristic
302C2×C4#121×C12711yescharacteristic
303C2×C4C22⋊Q8×C12711yescharacteristic
304C2×C4C22⋊Q8×C12711yescharacteristic
305C2×C4#131×C12712yes—
306C2×C4#131×C12712yes—
307C2×C4#135×C12712yes—
308C2×C4#137×C12712yes—
309C8—44no—
310C8—82no—
311C22#380×C12711yescharacteristic
312C22#408×C12711yescharacteristic
313C22#408×C12711yescharacteristic
314C22#416×C12711yescharacteristic
315C22#419×C12711yescharacteristic
316C22C2×#104×C12711yescharacteristic
317C22#421×C12711yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4#424×C12712yes—
329C4#433×C12712yes—
330C4#464×C12712yes—
331C4#479×C12712yes—
332C2C127×#148211yescharacteristic
333C2C127×#148511yescharacteristic
334C2C127×#149411yescharacteristic
335C2C127×#149711yescharacteristic
336C2C127×#179811yescharacteristic
337C2C127×#180511yescharacteristic
338C2C127×#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
162. #8570C127direct (N × H)
175. C127#8570direct (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×#18312
C4×C4⋊C8×C1272
C2×Q8⋊C8×C1272
C127×#12792
#8570127