Finite Group Databasebeta

← C127×#8569 #44572242

Subgroups — C127×#8569 #44572242

Order 32512.

548 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2293C211yesmaximal, characteristic
2C127×#1831C211yesmaximal, characteristic, complemented
3C4×C4⋊C8×C127C211yesmaximal, characteristic, complemented
4C2×D4⋊C8×C127C212yesmaximal
5C127×#1279C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C2×#117×C127—21no—
8C2×C4⋊C8×C127—21no—
9C2×C4⋊C8×C127C2212yes—
10C2×C4×C8×C127C2212yes—
11#390×C127C411yescharacteristic
12#390×C127C411yescharacteristic
13#389×C127C411yescharacteristic
14#389×C127C411yescharacteristic
15#388×C127—21no—
16#388×C127—21no—
17C4×C4⋊C4×C127C2211yescharacteristic
18C4×C22⋊C4×C127—21no—
19C43×C127C2211yescharacteristic
20#336×C127—21no—
21#336×C127—21no—
22#336×C127—21no—
23D4⋊C8×C127—24no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127—21no—
26C22×C8×C127—22no—
27C22×C8×C127—22no—
28C4×D4×C127—21no—
29C4×D4×C127—21no—
30C4×D4×C127D412yes—
31C4×D4×C127Q812yes—
32#117×C127—44no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C42×C127—21no—
44C2×C42×C127C2×C411yescharacteristic
45C2×C42×C127C2×C411yescharacteristic
46C2×C42×C127D411yescharacteristic
47C2×C42×C127D411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C2×C42×C127D411yescharacteristic
50C2×C42×C127C2311yescharacteristic
51C4⋊C8×C127—24no—
52C4⋊C8×C127—22no—
53C4⋊C8×C127—22no—
54C4×C8×C127—22no—
55C4×C8×C127—22no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59C24×C127—21no—
60C2×D4×C127—21no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127C4⋊C412yes—
64C22×C4×C127—21no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C2×C8×C127—24no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—42no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—22no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127C4⋊C412yes—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—42no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—42no—
96C42×C127—22no—
97C42×C127—22no—
98C42×C127—22no—
99C42×C127—22no—
100C42×C127—22no—
101C42×C127—41no—
102C42×C127—42no—
103C42×C127C2×D411yescharacteristic
104C42×C127C2×Q811yescharacteristic
105C42×C127#4111yescharacteristic
106C42×C127#4111yescharacteristic
107C23×C127—22no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127C2×C22⋊C411yescharacteristic
115D4×C127—24no—
116D4×C127—42no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—22no—
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—21no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—44no—
134C2×C4×C127—44no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127#10412yes—
142C2×C4×C127C2×C4⋊C411yescharacteristic
143C2×C4×C127#11711yescharacteristic
144C2×C4×C127#12111yescharacteristic
145C2×C4×C127#12111yescharacteristic
146C2×C4×C127C22⋊Q811yescharacteristic
147C2×C4×C127C22⋊Q811yescharacteristic
148C2×C4×C127#13112yes—
149C2×C4×C127#13112yes—
150C2×C4×C127#13512yes—
151C2×C4×C127AGL(1,ℤ/8)12yes—
152C8×C127—44no—
153C8×C127—82no—
154C22×C127—42no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127—81no—
160C22×C127—81no—
161C22×C127#38011yescharacteristic
162C22×C127#40811yescharacteristic
163C22×C127#40811yescharacteristic
164C22×C127#41611yescharacteristic
165C22×C127#41811yescharacteristic
166C22×C127C2×#10411yescharacteristic
167C22×C127#42111yescharacteristic
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—22no—
171C4×C127—42no—
172C4×C127—41no—
173C4×C127—41no—
174C4×C127—41no—
175C4×C127—81no—
176C4×C127—81no—
177C4×C127#42412yes—
178C4×C127#43312yes—
179C4×C127#46312yes—
180C4×C127#47812yes—
181#8569C12711yesmaximal, characteristic, direct product factor, Sylow
182C2×C127—82no—
183C2×C127#148211yescharacteristic
184C2×C127#148411yescharacteristic
185C2×C127#149411yescharacteristic
186C2×C127#149611yescharacteristic
187C2×C127#179811yescharacteristic
188C2×C127#180411yescharacteristic
189C2×C127#180611yescharacteristic
190#2293C2×C12711yescharacteristic
191#1831C2×C12711yescharacteristic, complemented
192C4×C4⋊C8C2×C12711yescharacteristic, complemented
193C2×D4⋊C8C2×C12712yes—
194#1279C2×C12712yescomplemented
195C127#856911yescharacteristic, direct product factor, Sylow
196C2×C4×D4C22×C12711yescharacteristic
197C2×#117—21no—
198C2×C4⋊C8—21no—
199C2×C4⋊C8C22×C12712yes—
200C2×C4×C8C22×C12712yes—
201#390C4×C12711yescharacteristic
202#390C4×C12711yescharacteristic
203#389C4×C12711yescharacteristic
204#389C4×C12711yescharacteristic
205#388—21no—
206#388—21no—
207C4×C4⋊C4C22×C12711yescharacteristic
208C4×C22⋊C4—21no—
209C43C22×C12711yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213D4⋊C8—24no—
214C22×D4C2×C4×C12711yescharacteristic
215C23×C4—21no—
216C22×C8—22no—
217C22×C8—22no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4D4×C12712yes—
221C4×D4Q8×C12712yes—
222#117—44no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×C4×C12711yescharacteristic
226C2×C4⋊C4C2×C4×C12711yescharacteristic
227C2×C4⋊C4C2×C4×C12711yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—21no—
234C2×C42C2×C4×C12711yescharacteristic
235C2×C42C2×C4×C12711yescharacteristic
236C2×C42D4×C12711yescharacteristic
237C2×C42D4×C12711yescharacteristic
238C2×C42D4×C12711yescharacteristic
239C2×C42D4×C12711yescharacteristic
240C2×C42C23×C12711yescharacteristic
241C4⋊C8—24no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4×C8—22no—
245C4×C8—22no—
246#95—21no—
247#95—21no—
248#95—21no—
249C24—21no—
250C2×D4—21no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4C4⋊C4×C12712yes—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4C22⋊C4×C12711yescharacteristic
262C22×C4C22⋊C4×C12711yescharacteristic
263C22×C4C22⋊C4×C12711yescharacteristic
264C22×C4C22⋊C4×C12711yescharacteristic
265C22×C4C22×C4×C12711yescharacteristic
266C22×C4C2×D4×C12711yescharacteristic
267C22×C4C2×D4×C12711yescharacteristic
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4C4⋊C4×C12712yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—42no—
293C42C2×D4×C12711yescharacteristic
294C42C2×Q8×C12711yescharacteristic
295C42#41×C12711yescharacteristic
296C42#41×C12711yescharacteristic
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C2×C22⋊C4×C12711yescharacteristic
305D4—24no—
306D4—42no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4#104×C12712yes—
332C2×C4C2×C4⋊C4×C12711yescharacteristic
333C2×C4#117×C12711yescharacteristic
334C2×C4#121×C12711yescharacteristic
335C2×C4#121×C12711yescharacteristic
336C2×C4C22⋊Q8×C12711yescharacteristic
337C2×C4C22⋊Q8×C12711yescharacteristic
338C2×C4#131×C12712yes—
339C2×C4#131×C12712yes—
340C2×C4#135×C12712yes—
341C2×C4AGL(1,ℤ/8)×C12712yes—
342C8—44no—
343C8—82no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22#380×C12711yescharacteristic
352C22#408×C12711yescharacteristic
353C22#408×C12711yescharacteristic
354C22#416×C12711yescharacteristic
355C22#418×C12711yescharacteristic
356C22C2×#104×C12711yescharacteristic
357C22#421×C12711yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4#424×C12712yes—
368C4#433×C12712yes—
369C4#463×C12712yes—
370C4#478×C12712yes—
371C2—82no—
372C2C127×#148211yescharacteristic
373C2C127×#148411yescharacteristic
374C2C127×#149411yescharacteristic
375C2C127×#149611yescharacteristic
376C2C127×#179811yescharacteristic
377C2C127×#180411yescharacteristic
378C2C127×#180611yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC23×C127C2×C22⋊C4
prime radicalC22×D4×C127C2×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
2. C127×#1831C2semidirect
3. C4×C4⋊C8×C127C2semidirect
5. C127×#1279C2semidirect
181. #8569C127direct (N × H)
191. #1831C2×C127semidirect
192. C4×C4⋊C8C2×C127semidirect
194. #1279C2×C127semidirect
195. C127#8569direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22932
C127×#18312
C4×C4⋊C8×C1272
C2×D4⋊C8×C1272
C127×#12792
#8569127