Finite Group Databasebeta

← C127×#13449 #44577122

Subgroups — C127×#13449 #44577122

Order 32512.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C127C211yesmaximal, characteristic
2C2×C4⋊C16×C127C211yesmaximal, characteristic, complemented
3C2×#358×C127C211yesmaximal, characteristic, complemented
4C2×#357×C127C211yesmaximal, characteristic
5C127×#1970C211yesmaximal, characteristic
6C127×#1969C211yesmaximal, characteristic, complemented
7C127×#1380C211yesmaximal, characteristic, complemented
8C22×Q16×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10C2×SD32×C127—22no—
11C2×SD32×C127—22no—
12C2×SD32×C127—22no—
13C22×C16×C127C2211yescharacteristic
14C22×C16×C127C2211yescharacteristic
15C2×#107×C127C2211yescharacteristic
16C2×#107×C127C2211yescharacteristic
17C2×#103×C127—21no—
18C2×#102×C127—21no—
19C2×C4×C8×C127C2211yescharacteristic
20#391×C127—21no—
21#390×C127—21no—
22C4⋊C16×C127—22no—
23#358×C127—22no—
24#357×C127—22no—
25C22×Q8×C127—21no—
26C22×D4×C127—21no—
27C2×Q16×C127—21no—
28C2×Q16×C127—21no—
29C2×Q16×C127—21no—
30C2×Q16×C127—21no—
31C2×Q16×C127—21no—
32C2×Q16×C127D412yes—
33C2×D8×C127—21no—
34C2×D8×C127—21no—
35C2×D8×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×D8×C127D412yes—
39C22×C8×C127D411yescharacteristic
40C22×C8×C127C2311yescharacteristic
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C22⋊C4×C127—41no—
44C2×C22⋊C4×C127—41no—
45C2×C42×C127D411yescharacteristic
46SD32×C127—28no—
47C2×C16×C127—21no—
48C2×C16×C127—21no—
49C2×C16×C127—21no—
50C2×C16×C127—21no—
51C2×C16×C127—21no—
52C2×C16×C127D412yes—
53#107×C127—21no—
54#107×C127—21no—
55#107×C127—21no—
56#107×C127—21no—
57#103×C127—42no—
58#102×C127—42no—
59C4×C8×C127—21no—
60C4×C8×C127—21no—
61#95×C127—41no—
62#95×C127—41no—
63C24×C127—41no—
64C2×Q8×C127—22no—
65C2×Q8×C127—41no—
66C2×Q8×C127—41no—
67C2×Q8×C127—41no—
68C2×Q8×C127—41no—
69C2×Q8×C127—41no—
70C2×D4×C127—22no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127D811yescharacteristic
80C22×C4×C127D811yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82Q16×C127—22no—
83Q16×C127—22no—
84Q16×C127—41no—
85Q16×C127—41no—
86D8×C127—22no—
87D8×C127—22no—
88D8×C127—41no—
89D8×C127—41no—
90C2×C8×C127—21no—
91C2×C8×C127—21no—
92C2×C8×C127—21no—
93C2×C8×C127C2×D411yescharacteristic
94C2×C8×C127C2×D411yescharacteristic
95C2×C8×C127C2×D411yescharacteristic
96C2×C8×C127#4111yescharacteristic
97C2×C8×C127#4111yescharacteristic
98C2×C8×C127#4111yescharacteristic
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C22⋊C4×C127—82no—
104C22⋊C4×C127—82no—
105C42×C127—21no—
106C42×C127—21no—
107C16×C127—22no—
108C16×C127—41no—
109C23×C127—42no—
110C23×C127—81no—
111C23×C127—81no—
112C23×C127—81no—
113C23×C127—81no—
114C23×C127—81no—
115C23×C127—81no—
116C23×C127C2×D811yescharacteristic
117Q8×C127—42no—
118Q8×C127—42no—
119Q8×C127—81no—
120Q8×C127—81no—
121D4×C127—42no—
122D4×C127—42no—
123D4×C127—81no—
124D4×C127—81no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—42no—
131C2×C4×C127—81no—
132C2×C4×C127—81no—
133C2×C4×C127—81no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127SD3212yescomplemented
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#12111yescharacteristic
142C2×C4×C127#12111yescharacteristic
143C2×C4×C127#13511yescharacteristic
144C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
146C8×C127—41no—
147C8×C127#12011yescharacteristic
148C8×C127#12311yescharacteristic
149C8×C127#12311yescharacteristic
150C8×C127#12411yescharacteristic
151C22×C127—82no—
152C22×C127—82no—
153C22×C127—82no—
154C22×C127—161no—
155C22×C127—161no—
156C22×C127—161no—
157C22×C127—161no—
158C22×C127#45911yescharacteristic
159C22×C127#45911yescharacteristic
160C22×C127#46611yescharacteristic
161C22×C127C2×SD3211yescharacteristic
162C22×C127#50811yescharacteristic
163C22×C127#50911yescharacteristic
164C22×C127#51011yescharacteristic
165C4×C127—22no—
166C4×C127—41no—
167C4×C127—82no—
168C4×C127—161no—
169C4×C127—161no—
170C4×C127#39411yescharacteristic
171C4×C127#46311yescharacteristic
172C4×C127#46311yescharacteristic
173C4×C127#46911yescharacteristic
174#13449C12711yesmaximal, characteristic, direct product factor, Sylow
175C2×C127—162no—
176C2×C127#205411yescharacteristic
177C2×C127#220711yescharacteristic
178C2×C127#220811yescharacteristic
179C2×C127#221011yescharacteristic
180C2×C127#221111yescharacteristic
181C2×C127#221711yescharacteristic
182C2×C127#222011yescharacteristic
183C22×SD32C2×C12711yescharacteristic
184C2×C4⋊C16C2×C12711yescharacteristic, complemented
185C2×#358C2×C12711yescharacteristic, complemented
186C2×#357C2×C12711yescharacteristic
187#1970C2×C12711yescharacteristic
188#1969C2×C12711yescharacteristic, complemented
189#1380C2×C12711yescharacteristic, complemented
190C127#1344911yescharacteristic, direct product factor, Sylow
191C22×Q16C22×C12711yescharacteristic
192C22×D8C22×C12711yescharacteristic
193C2×SD32—22no—
194C2×SD32—22no—
195C2×SD32—22no—
196C22×C16C22×C12711yescharacteristic
197C22×C16C22×C12711yescharacteristic
198C2×#107C22×C12711yescharacteristic
199C2×#107C22×C12711yescharacteristic
200C2×#103—21no—
201C2×#102—21no—
202C2×C4×C8C22×C12711yescharacteristic
203#391—21no—
204#390—21no—
205C4⋊C16—22no—
206#358—22no—
207#357—22no—
208C22×Q8—21no—
209C22×D4—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16D4×C12712yes—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8D4×C12712yes—
222C22×C8D4×C12711yescharacteristic
223C22×C8C23×C12711yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4—41no—
228C2×C42D4×C12711yescharacteristic
229SD32—28no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16D4×C12712yes—
236#107—21no—
237#107—21no—
238#107—21no—
239#107—21no—
240#103—42no—
241#102—42no—
242C4×C8—21no—
243C4×C8—21no—
244#95—41no—
245#95—41no—
246C24—41no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4D8×C12711yescharacteristic
263C22×C4D8×C12711yescharacteristic
264C22×C4C2×D4×C12711yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8C2×D4×C12711yescharacteristic
277C2×C8C2×D4×C12711yescharacteristic
278C2×C8C2×D4×C12711yescharacteristic
279C2×C8#41×C12711yescharacteristic
280C2×C8#41×C12711yescharacteristic
281C2×C8#41×C12711yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—82no—
287C22⋊C4—82no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23—81no—
299C23C2×D8×C12711yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—81no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4SD32×C12712yescomplemented
323C2×C4#121×C12711yescharacteristic
324C2×C4#121×C12711yescharacteristic
325C2×C4#121×C12711yescharacteristic
326C2×C4#135×C12711yescharacteristic
327C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
328C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
329C8—41no—
330C8#120×C12711yescharacteristic
331C8#123×C12711yescharacteristic
332C8#123×C12711yescharacteristic
333C8#124×C12711yescharacteristic
334C22—82no—
335C22—82no—
336C22—82no—
337C22—161no—
338C22—161no—
339C22—161no—
340C22—161no—
341C22#459×C12711yescharacteristic
342C22#459×C12711yescharacteristic
343C22#466×C12711yescharacteristic
344C22C2×SD32×C12711yescharacteristic
345C22#508×C12711yescharacteristic
346C22#509×C12711yescharacteristic
347C22#510×C12711yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—161no—
353C4#394×C12711yescharacteristic
354C4#463×C12711yescharacteristic
355C4#463×C12711yescharacteristic
356C4#469×C12711yescharacteristic
357C2—162no—
358C2C127×#205411yescharacteristic
359C2C127×#220711yescharacteristic
360C2C127×#220811yescharacteristic
361C2C127×#221011yescharacteristic
362C2C127×#221111yescharacteristic
363C2C127×#221711yescharacteristic
364C2C127×#222011yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C16×C127C2semidirect
3. C2×#358×C127C2semidirect
6. C127×#1969C2semidirect
7. C127×#1380C2semidirect
139. C2×C4×C127SD32semidirect
174. #13449C127direct (N × H)
184. C2×C4⋊C16C2×C127semidirect
185. C2×#358C2×C127semidirect
188. #1969C2×C127semidirect
189. #1380C2×C127semidirect
190. C127#13449direct (N × H)
322. C2×C4SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C22×SD32×C1272
C2×C4⋊C16×C1272
C2×#358×C1272
C2×#357×C1272
C127×#19702
C127×#19692
C127×#13802
#13449127