Finite Group Databasebeta

← C127×#13446 #44577119

Subgroups — C127×#13446 #44577119

Order 32512.

396 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C2×#364×C127C211yesmaximal, characteristic, complemented
3C2×#362×C127C211yesmaximal, characteristic, complemented
4C127×#2139C211yesmaximal, characteristic
5C127×#1974C211yesmaximal, characteristic
6C127×#1969C211yesmaximal, characteristic, complemented
7C127×#1387C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10#510×C127—22no—
11#510×C127—22no—
12C2×Q32×C127—21no—
13C2×SD32×C127—21no—
14C2×M32×C127C2211yescharacteristic
15C2×M32×C127C2211yescharacteristic
16C2×#108×C127C2211yescharacteristic
17C2×#107×C127C2211yescharacteristic
18C2×#104×C127—21no—
19C2×#103×C127—21no—
20#408×C127—21no—
21C2×C4×C8×C127C2211yescharacteristic
22#391×C127—21no—
23#364×C127—22no—
24#362×C127—22no—
25#358×C127—21no—
26#357×C127—21no—
27C2×#41×C127—21no—
28C22×Q8×C127—21no—
29#135×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127—21no—
33C2×Q16×C127—21no—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127D411yescharacteristic
39C2×Q16×C127D412yes—
40C2×SD16×C127—21no—
41C2×D8×C127D411yescharacteristic
42C2×M16×C127—21no—
43C22×C8×C127D411yescharacteristic
44C22×C8×C127C2311yescharacteristic
45C2×C4⋊C4×C127—21no—
46C2×C42×C127D411yescharacteristic
47Q32×C127—24no—
48SD32×C127—24no—
49M32×C127—21no—
50M32×C127—21no—
51M32×C127—21no—
52M32×C127D412yes—
53C2×C16×C127—21no—
54C2×C16×C127—21no—
55#108×C127—21no—
56#108×C127—21no—
57#107×C127—21no—
58#107×C127—21no—
59#104×C127—42no—
60#103×C127—42no—
61C22⋊C8×C127—42no—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64#95×C127—42no—
65#41×C127—41no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69C2×Q8×C127—21no—
70C2×Q8×C127—22no—
71C2×Q8×C127—41no—
72C2×Q8×C127—41no—
73C2×Q8×C127—41no—
74C2×Q8×C127—41no—
75C2×Q8×C127—41no—
76C2×D4×C127—21no—
77C2×D4×C127—41no—
78C22×C4×C127—21no—
79C22×C4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127C2×D411yescharacteristic
83Q16×C127—22no—
84Q16×C127—21no—
85Q16×C127—22no—
86Q16×C127—21no—
87Q16×C127—41no—
88Q16×C127—41no—
89SD16×C127—41no—
90SD16×C127—41no—
91D8×C127—21no—
92D8×C127—21no—
93M16×C127—41no—
94M16×C127—41no—
95C2×C8×C127—21no—
96C2×C8×C127—21no—
97C2×C8×C127—41no—
98C2×C8×C127D812yes—
99C2×C8×C127C2×D411yescharacteristic
100C2×C8×C127C2×D411yescharacteristic
101C2×C8×C127C2×D411yescharacteristic
102C2×C8×C127#4111yescharacteristic
103C2×C8×C127#4111yescharacteristic
104C2×C8×C127#4111yescharacteristic
105C4⋊C4×C127—41no—
106C4⋊C4×C127—41no—
107C42×C127—21no—
108C42×C127—21no—
109C16×C127—22no—
110C16×C127—41no—
111C23×C127—41no—
112C23×C127AGL(1,ℤ/8)11yescharacteristic
113Q8×C127—41no—
114Q8×C127—42no—
115Q8×C127—42no—
116Q8×C127—41no—
117Q8×C127—81no—
118Q8×C127—81no—
119D4×C127—41no—
120D4×C127—41no—
121D4×C127—81no—
122D4×C127—81no—
123C2×C4×C127—22no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—42no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127—81no—
131C2×C4×C127—81no—
132C2×C4×C127—82no—
133C2×C4×C127—81no—
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127#12111yescharacteristic
136C2×C4×C127#12111yescharacteristic
137C2×C4×C127C2×D811yescharacteristic
138C2×C4×C127#13511yescharacteristic
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C8×C127—22no—
141C8×C127—81no—
142C8×C127#12011yescharacteristic
143C8×C127#12311yescharacteristic
144C8×C127#12311yescharacteristic
145C8×C127#12411yescharacteristic
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—81no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127#45911yescharacteristic
152C22×C127#46311yescharacteristic
153C22×C127#46911yescharacteristic
154C4×C127—42no—
155C4×C127—81no—
156C4×C127—82no—
157C4×C127—161no—
158C4×C127#39411yescharacteristic
159C4×C127#45911yescharacteristic
160C4×C127#46311yescharacteristic
161C4×C127#46611yescharacteristic
162#13446C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127—21no—
164C2×C127—21no—
165C2×C127—161no—
166C2×C127#205411yescharacteristic
167C2×C127#221211yescharacteristic
168C2×C127#221411yescharacteristic
169C2×#510C2×C12711yescharacteristic
170C2×#364C2×C12711yescharacteristic, complemented
171C2×#362C2×C12711yescharacteristic, complemented
172#2139C2×C12711yescharacteristic
173#1974C2×C12711yescharacteristic
174#1969C2×C12711yescharacteristic, complemented
175#1387C2×C12711yescharacteristic, complemented
176C127#1344611yescharacteristic, direct product factor, Sylow
177C2×#135C22×C12711yescharacteristic
178C22×Q16C22×C12711yescharacteristic
179#510—22no—
180#510—22no—
181C2×Q32—21no—
182C2×SD32—21no—
183C2×M32C22×C12711yescharacteristic
184C2×M32C22×C12711yescharacteristic
185C2×#108C22×C12711yescharacteristic
186C2×#107C22×C12711yescharacteristic
187C2×#104—21no—
188C2×#103—21no—
189#408—21no—
190C2×C4×C8C22×C12711yescharacteristic
191#391—21no—
192#364—22no—
193#362—22no—
194#358—21no—
195#357—21no—
196C2×#41—21no—
197C22×Q8—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201#135—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16D4×C12712yes—
208C2×Q16D4×C12711yescharacteristic
209C2×SD16—21no—
210C2×D8D4×C12711yescharacteristic
211C2×M16—21no—
212C22×C8D4×C12711yescharacteristic
213C22×C8C23×C12711yescharacteristic
214C2×C4⋊C4—21no—
215C2×C42D4×C12711yescharacteristic
216Q32—24no—
217SD32—24no—
218M32—21no—
219M32—21no—
220M32—21no—
221M32D4×C12712yes—
222C2×C16—21no—
223C2×C16—21no—
224#108—21no—
225#108—21no—
226#107—21no—
227#107—21no—
228#104—42no—
229#103—42no—
230C22⋊C8—42no—
231C4×C8—21no—
232C4×C8—21no—
233#95—42no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C12711yescharacteristic
252Q16—22no—
253Q16—21no—
254Q16—22no—
255Q16—21no—
256Q16—41no—
257Q16—41no—
258SD16—41no—
259SD16—41no—
260D8—21no—
261D8—21no—
262M16—41no—
263M16—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8D8×C12712yes—
268C2×C8C2×D4×C12711yescharacteristic
269C2×C8C2×D4×C12711yescharacteristic
270C2×C8C2×D4×C12711yescharacteristic
271C2×C8#41×C12711yescharacteristic
272C2×C8#41×C12711yescharacteristic
273C2×C8#41×C12711yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C42—21no—
277C42—21no—
278C16—22no—
279C16—41no—
280C23—41no—
281C23AGL(1,ℤ/8)×C12711yescharacteristic
282Q8—41no—
283Q8—42no—
284Q8—42no—
285Q8—41no—
286Q8—81no—
287Q8—81no—
288D4—41no—
289D4—41no—
290D4—81no—
291D4—81no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4#121×C12711yescharacteristic
304C2×C4#121×C12711yescharacteristic
305C2×C4#121×C12711yescharacteristic
306C2×C4C2×D8×C12711yescharacteristic
307C2×C4#135×C12711yescharacteristic
308C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
309C8—22no—
310C8—81no—
311C8#120×C12711yescharacteristic
312C8#123×C12711yescharacteristic
313C8#123×C12711yescharacteristic
314C8#124×C12711yescharacteristic
315C22—21no—
316C22—21no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#459×C12711yescharacteristic
321C22#463×C12711yescharacteristic
322C22#469×C12711yescharacteristic
323C4—42no—
324C4—81no—
325C4—82no—
326C4—161no—
327C4#394×C12711yescharacteristic
328C4#459×C12711yescharacteristic
329C4#463×C12711yescharacteristic
330C4#466×C12711yescharacteristic
331C2—21no—
332C2—21no—
333C2—161no—
334C2C127×#205411yescharacteristic
335C2C127×#221211yescharacteristic
336C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#364×C127C2semidirect
3. C2×#362×C127C2semidirect
6. C127×#1969C2semidirect
7. C127×#1387C2semidirect
162. #13446C127direct (N × H)
170. C2×#364C2×C127semidirect
171. C2×#362C2×C127semidirect
174. #1969C2×C127semidirect
175. #1387C2×C127semidirect
176. C127#13446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C2×#364×C1272
C2×#362×C1272
C127×#21392
C127×#19742
C127×#19692
C127×#13872
#13446127