Finite Group Databasebeta

← C127×#10591 #44574264

Subgroups — C127×#10591 #44574264

Order 32512.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1982C211yesmaximal, characteristic
2C127×#1957C211yesmaximal, characteristic
3C127×#1947C211yesmaximal, characteristic, complemented
4C127×#1939C211yesmaximal, characteristic, complemented
5C2×#335×C127C211yesmaximal, characteristic, complemented
6C2×#331×C127C211yesmaximal, characteristic
7C127×#1296C211yesmaximal, characteristic, complemented
8C2×#127×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×C4⋊C8×C127—21no—
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×#102×C127—21no—
15C2×#102×C127—21no—
16C2×#102×C127—21no—
17C2×#102×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19#384×C127C2211yescharacteristic
20C4×C4⋊C4×C127C2211yescharacteristic
21#340×C127—21no—
22#336×C127—21no—
23#335×C127—22no—
24#331×C127—22no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C22×C8×C127—21no—
29C22×C8×C127—21no—
30C22×C8×C127—21no—
31C22×C8×C127D411yescharacteristic
32C22×C8×C127D411yescharacteristic
33#127×C127—21no—
34#127×C127—21no—
35#127×C127—21no—
36#127×C127Q812yes—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C42×C127—21no—
43C2×C42×C127C2311yescharacteristic
44#107×C127—42no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—42no—
51C4⋊C8×C127D412yes—
52#102×C127—42no—
53#102×C127—42no—
54#102×C127—42no—
55#102×C127—42no—
56C4×C8×C127—21no—
57C4×C8×C127—21no—
58#95×C127—21no—
59C24×C127—41no—
60C2×D4×C127—22no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—41no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—81no—
75C2×D4×C127—81no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—41no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127#4111yescharacteristic
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—41no—
89C2×C8×C127—41no—
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×C127D812yes—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—81no—
105C4⋊C4×C127D812yes—
106C42×C127—41no—
107C42×C127—41no—
108C42×C127C2×D411yescharacteristic
109C42×C127C2×Q811yescharacteristic
110C42×C127#4111yescharacteristic
111C42×C127#4111yescharacteristic
112C23×C127—42no—
113C23×C127—81no—
114C23×C127—81no—
115C23×C127—81no—
116C23×C127—81no—
117C23×C127—81no—
118C23×C127—81no—
119C23×C127#12111yescharacteristic
120D4×C127—42no—
121D4×C127—42no—
122D4×C127—42no—
123D4×C127—42no—
124D4×C127—82no—
125D4×C127—82no—
126D4×C127—81no—
127D4×C127—81no—
128D4×C127—81no—
129D4×C127—81no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—22no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127—81no—
141C2×C4×C127#12111yescharacteristic
142C2×C4×C127#12111yescharacteristic
143C2×C4×C127C22⋊Q811yescharacteristic
144C2×C4×C127C22⋊Q811yescharacteristic
145C2×C4×C127C22⋊Q811yescharacteristic
146C2×C4×C127#12611yescharacteristic
147C2×C4×C127C2×D811yescharacteristic
148C2×C4×C127C2×D811yescharacteristic
149C2×C4×C127#13511yescharacteristic
150C2×C4×C127#13511yescharacteristic
151C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C127#13711yescharacteristic
154C2×C4×C127#13711yescharacteristic
155C8×C127—22no—
156C8×C127—42no—
157C8×C127—41no—
158C8×C127—81no—
159C8×C127—81no—
160C22×C127—82no—
161C22×C127—82no—
162C22×C127—82no—
163C22×C127—161no—
164C22×C127—161no—
165C22×C127—161no—
166C22×C127—161no—
167C22×C127#39611yescharacteristic
168C22×C127#45911yescharacteristic
169C22×C127#46411yescharacteristic
170C22×C127#46611yescharacteristic
171C22×C127#46811yescharacteristic
172C22×C127#47111yescharacteristic
173C22×C127#47211yescharacteristic
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—42no—
177C4×C127—81no—
178C4×C127—161no—
179C4×C127#45911yescharacteristic
180C4×C127#46411yescharacteristic
181C4×C127#46611yescharacteristic
182C4×C127#46811yescharacteristic
183C4×C127#47411yescharacteristic
184C4×C127#47411yescharacteristic
185C4×C127#47811yescharacteristic
186C4×C127#47811yescharacteristic
187#10591C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—162no—
189C2×C127#166711yescharacteristic
190C2×C127#168211yescharacteristic
191C2×C127#168511yescharacteristic
192C2×C127#169811yescharacteristic
193C2×C127#206311yescharacteristic
194C2×C127#206711yescharacteristic
195C2×C127#206711yescharacteristic
196#1982C2×C12711yescharacteristic
197#1957C2×C12711yescharacteristic
198#1947C2×C12711yescharacteristic, complemented
199#1939C2×C12711yescharacteristic, complemented
200C2×#335C2×C12711yescharacteristic, complemented
201C2×#331C2×C12711yescharacteristic
202#1296C2×C12711yescharacteristic, complemented
203C127#1059111yescharacteristic, direct product factor, Sylow
204C2×#127C22×C12711yescharacteristic
205C2×#107—21no—
206C2×C4⋊C8—21no—
207C2×C4⋊C8C22×C12711yescharacteristic
208C2×C4⋊C8C22×C12711yescharacteristic
209C2×C4⋊C8C22×C12711yescharacteristic
210C2×#102—21no—
211C2×#102—21no—
212C2×#102—21no—
213C2×#102—21no—
214C2×C4×C8C22×C12711yescharacteristic
215#384C22×C12711yescharacteristic
216C4×C4⋊C4C22×C12711yescharacteristic
217#340—21no—
218#336—21no—
219#335—22no—
220#331—22no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8D4×C12711yescharacteristic
228C22×C8D4×C12711yescharacteristic
229#127—21no—
230#127—21no—
231#127—21no—
232#127Q8×C12712yes—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C12711yescharacteristic
237C2×C4⋊C4D4×C12711yescharacteristic
238C2×C42—21no—
239C2×C42C23×C12711yescharacteristic
240#107—42no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—42no—
247C4⋊C8D4×C12712yes—
248#102—42no—
249#102—42no—
250#102—42no—
251#102—42no—
252C4×C8—21no—
253C4×C8—21no—
254#95—21no—
255C24—41no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—81no—
271C2×D4—81no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4C2×D4×C12711yescharacteristic
276C22×C4C2×D4×C12711yescharacteristic
277C22×C4#41×C12711yescharacteristic
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8D8×C12712yes—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4D8×C12712yes—
302C42—41no—
303C42—41no—
304C42C2×D4×C12711yescharacteristic
305C42C2×Q8×C12711yescharacteristic
306C42#41×C12711yescharacteristic
307C42#41×C12711yescharacteristic
308C23—42no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23#121×C12711yescharacteristic
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#121×C12711yescharacteristic
338C2×C4#121×C12711yescharacteristic
339C2×C4C22⋊Q8×C12711yescharacteristic
340C2×C4C22⋊Q8×C12711yescharacteristic
341C2×C4C22⋊Q8×C12711yescharacteristic
342C2×C4#126×C12711yescharacteristic
343C2×C4C2×D8×C12711yescharacteristic
344C2×C4C2×D8×C12711yescharacteristic
345C2×C4#135×C12711yescharacteristic
346C2×C4#135×C12711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
348C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
349C2×C4#137×C12711yescharacteristic
350C2×C4#137×C12711yescharacteristic
351C8—22no—
352C8—42no—
353C8—41no—
354C8—81no—
355C8—81no—
356C22—82no—
357C22—82no—
358C22—82no—
359C22—161no—
360C22—161no—
361C22—161no—
362C22—161no—
363C22#396×C12711yescharacteristic
364C22#459×C12711yescharacteristic
365C22#464×C12711yescharacteristic
366C22#466×C12711yescharacteristic
367C22#468×C12711yescharacteristic
368C22#471×C12711yescharacteristic
369C22#472×C12711yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#459×C12711yescharacteristic
376C4#464×C12711yescharacteristic
377C4#466×C12711yescharacteristic
378C4#468×C12711yescharacteristic
379C4#474×C12711yescharacteristic
380C4#474×C12711yescharacteristic
381C4#478×C12711yescharacteristic
382C4#478×C12711yescharacteristic
383C2—162no—
384C2C127×#166711yescharacteristic
385C2C127×#168211yescharacteristic
386C2C127×#168511yescharacteristic
387C2C127×#169811yescharacteristic
388C2C127×#206311yescharacteristic
389C2C127×#206711yescharacteristic
390C2C127×#206711yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1947C2semidirect
4. C127×#1939C2semidirect
5. C2×#335×C127C2semidirect
7. C127×#1296C2semidirect
187. #10591C127direct (N × H)
198. #1947C2×C127semidirect
199. #1939C2×C127semidirect
200. C2×#335C2×C127semidirect
202. #1296C2×C127semidirect
203. C127#10591direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19822
C127×#19572
C127×#19472
C127×#19392
C2×#335×C1272
C2×#331×C1272
C127×#12962
#10591127