Finite Group Databasebeta

← C127×#9558 #44573231

Subgroups — C127×#9558 #44573231

Order 32512.

446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1954C211yesmaximal, characteristic
2C127×#1939C211yesmaximal, characteristic, complemented
3C4×#102×C127C211yesmaximal, characteristic
4C2×D4⋊C8×C127C211yesmaximal, characteristic
5C2×#322×C127C211yesmaximal, characteristic, complemented
6C127×#1279C211yesmaximal, characteristic, complemented
7C127×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D4×C127C2211yescharacteristic
9C2×C4⋊C8×C127—21no—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×#102×C127C411yescharacteristic
13C2×#102×C127C411yescharacteristic
14C2×C22⋊C8×C127—21no—
15C2×C22⋊C8×C127—21no—
16C2×C4×C8×C127C2211yescharacteristic
17C2×C4×C8×C127C2211yescharacteristic
18C2×C4×C8×C127C2211yescharacteristic
19C4×C4⋊C4×C127C2211yescharacteristic
20#340×C127C411yescharacteristic
21#340×C127C411yescharacteristic
22#336×C127—21no—
23D4⋊C8×C127—22no—
24#322×C127—22no—
25C22×D4×C127C2×C411yescharacteristic
26C23×C4×C127—21no—
27C22×C8×C127—21no—
28C22×C8×C127—21no—
29C22×C8×C127—21no—
30C22×C8×C127C2×C411yescharacteristic
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127D411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C4×D4×C127—21no—
35C4×D4×C127—21no—
36C4×D4×C127—21no—
37C4×D4×C127—21no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C42×C127—21no—
43C2×C42×C127C2311yescharacteristic
44C4⋊C8×C127—21no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127—42no—
49#102×C127—22no—
50#102×C127—22no—
51C22⋊C8×C127—42no—
52C22⋊C8×C127—42no—
53C4×C8×C127—21no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—21no—
57C4×C8×C127—21no—
58C4×C8×C127D412yes—
59#95×C127—21no—
60C24×C127—21no—
61C2×D4×C127—21no—
62C2×D4×C127—21no—
63C2×D4×C127—21no—
64C2×D4×C127—21no—
65C2×D4×C127—21no—
66C2×D4×C127M1612yes—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—41no—
74C22×C4×C127—41no—
75C22×C4×C127—41no—
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127#4111yescharacteristic
79C2×C8×C127—21no—
80C2×C8×C127—21no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—21no—
84C2×C8×C127—21no—
85C2×C8×C127—22no—
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—21no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C2×C8×C127—41no—
94C2×C8×C127—41no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C2×C8×C127D812yes—
99C2×C8×C127SD1612yes—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127M1612yes—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C42×C127—41no—
109C42×C127—41no—
110C42×C127C2×D411yescharacteristic
111C42×C127#4111yescharacteristic
112C42×C127#4111yescharacteristic
113C42×C127#4111yescharacteristic
114C23×C127—22no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127C4×D411yescharacteristic
122D4×C127—22no—
123D4×C127—22no—
124D4×C127—41no—
125D4×C127—41no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—22no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127—81no—
141C2×C4×C127#11711yescharacteristic
142C2×C4×C127C4×D411yescharacteristic
143C2×C4×C127#12111yescharacteristic
144C2×C4×C127#12311yescharacteristic
145C2×C4×C127#12411yescharacteristic
146C2×C4×C127#12611yescharacteristic
147C2×C4×C127C2×M1611yescharacteristic
148C2×C4×C127C2×M1611yescharacteristic
149C2×C4×C127#13111yescharacteristic
150C2×C4×C127#13111yescharacteristic
151C2×C4×C127C2×D811yescharacteristic
152C2×C4×C127C2×SD1611yescharacteristic
153C2×C4×C127#13511yescharacteristic
154C2×C4×C127#13511yescharacteristic
155C8×C127—22no—
156C8×C127—22no—
157C8×C127—42no—
158C8×C127—41no—
159C8×C127—41no—
160C8×C127—81no—
161C8×C127—81no—
162C22×C127—42no—
163C22×C127—42no—
164C22×C127—42no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127#38811yescharacteristic
170C22×C127#43511yescharacteristic
171C22×C127#43511yescharacteristic
172C22×C127C4×D811yescharacteristic
173C22×C127C4×SD1611yescharacteristic
174C22×C127#44411yescharacteristic
175C22×C127#44411yescharacteristic
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—42no—
179C4×C127—81no—
180C4×C127—81no—
181C4×C127#43211yescharacteristic
182C4×C127#43311yescharacteristic
183C4×C127#43511yescharacteristic
184C4×C127#43611yescharacteristic
185C4×C127#46511yescharacteristic
186C4×C127#46611yescharacteristic
187C4×C127#48611yescharacteristic
188C4×C127#48811yescharacteristic
189#9558C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—82no—
191C2×C127#158111yescharacteristic
192C2×C127#158111yescharacteristic
193C2×C127#158211yescharacteristic
194C2×C127#158311yescharacteristic
195C2×C127#192411yescharacteristic
196C2×C127#193411yescharacteristic
197C2×C127#193811yescharacteristic
198#1954C2×C12711yescharacteristic
199#1939C2×C12711yescharacteristic, complemented
200C4×#102C2×C12711yescharacteristic
201C2×D4⋊C8C2×C12711yescharacteristic
202C2×#322C2×C12711yescharacteristic, complemented
203#1279C2×C12711yescharacteristic, complemented
204#1277C2×C12711yescharacteristic, complemented
205C127#955811yescharacteristic, direct product factor, Sylow
206C2×C4×D4C22×C12711yescharacteristic
207C2×C4⋊C8—21no—
208C2×C4⋊C8C22×C12711yescharacteristic
209C2×C4⋊C8C22×C12711yescharacteristic
210C2×#102C4×C12711yescharacteristic
211C2×#102C4×C12711yescharacteristic
212C2×C22⋊C8—21no—
213C2×C22⋊C8—21no—
214C2×C4×C8C22×C12711yescharacteristic
215C2×C4×C8C22×C12711yescharacteristic
216C2×C4×C8C22×C12711yescharacteristic
217C4×C4⋊C4C22×C12711yescharacteristic
218#340C4×C12711yescharacteristic
219#340C4×C12711yescharacteristic
220#336—21no—
221D4⋊C8—22no—
222#322—22no—
223C22×D4C2×C4×C12711yescharacteristic
224C23×C4—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C2×C4×C12711yescharacteristic
229C22×C8C2×C4×C12711yescharacteristic
230C22×C8D4×C12711yescharacteristic
231C22×C8D4×C12711yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4C2×C4×C12711yescharacteristic
237C2×C4⋊C4C2×C4×C12711yescharacteristic
238C2×C4⋊C4C2×C4×C12711yescharacteristic
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C12711yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—42no—
247#102—22no—
248#102—22no—
249C22⋊C8—42no—
250C22⋊C8—42no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8D4×C12712yes—
257#95—21no—
258C24—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4M16×C12712yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C22×C4×C12711yescharacteristic
275C22×C4C2×D4×C12711yescharacteristic
276C22×C4#41×C12711yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8D8×C12712yes—
297C2×C8SD16×C12712yes—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4M16×C12712yes—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—41no—
308C42C2×D4×C12711yescharacteristic
309C42#41×C12711yescharacteristic
310C42#41×C12711yescharacteristic
311C42#41×C12711yescharacteristic
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23C4×D4×C12711yescharacteristic
320D4—22no—
321D4—22no—
322D4—41no—
323D4—41no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#117×C12711yescharacteristic
340C2×C4C4×D4×C12711yescharacteristic
341C2×C4#121×C12711yescharacteristic
342C2×C4#123×C12711yescharacteristic
343C2×C4#124×C12711yescharacteristic
344C2×C4#126×C12711yescharacteristic
345C2×C4C2×M16×C12711yescharacteristic
346C2×C4C2×M16×C12711yescharacteristic
347C2×C4#131×C12711yescharacteristic
348C2×C4#131×C12711yescharacteristic
349C2×C4C2×D8×C12711yescharacteristic
350C2×C4C2×SD16×C12711yescharacteristic
351C2×C4#135×C12711yescharacteristic
352C2×C4#135×C12711yescharacteristic
353C8—22no—
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—81no—
359C8—81no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#388×C12711yescharacteristic
368C22#435×C12711yescharacteristic
369C22#435×C12711yescharacteristic
370C22C4×D8×C12711yescharacteristic
371C22C4×SD16×C12711yescharacteristic
372C22#444×C12711yescharacteristic
373C22#444×C12711yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4#432×C12711yescharacteristic
380C4#433×C12711yescharacteristic
381C4#435×C12711yescharacteristic
382C4#436×C12711yescharacteristic
383C4#465×C12711yescharacteristic
384C4#466×C12711yescharacteristic
385C4#486×C12711yescharacteristic
386C4#488×C12711yescharacteristic
387C2—82no—
388C2C127×#158111yescharacteristic
389C2C127×#158111yescharacteristic
390C2C127×#158211yescharacteristic
391C2C127×#158311yescharacteristic
392C2C127×#192411yescharacteristic
393C2C127×#193411yescharacteristic
394C2C127×#193811yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC23×C127C4×D4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1939C2semidirect
5. C2×#322×C127C2semidirect
6. C127×#1279C2semidirect
7. C127×#1277C2semidirect
189. #9558C127direct (N × H)
199. #1939C2×C127semidirect
202. C2×#322C2×C127semidirect
203. #1279C2×C127semidirect
204. #1277C2×C127semidirect
205. C127#9558direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19542
C127×#19392
C4×#102×C1272
C2×D4⋊C8×C1272
C2×#322×C1272
C127×#12792
C127×#12772
#9558127