Finite Group Databasebeta

← C127×#12336 #44576009

Subgroups — C127×#12336 #44576009

Order 32512.

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3403C211yesmaximal, characteristic, complemented
2C127×#2250C211yesmaximal, characteristic, complemented
3C127×#2206C211yesmaximal, characteristic, complemented
4C127×#1688C211yesmaximal, characteristic, complemented
5C127×#1360C211yesmaximal, characteristic, complemented
6C127×#1338C211yesmaximal, characteristic, complemented
7C127×#1333C211yesmaximal, characteristic, complemented
8#559×C127—21no—
9C2×SD32×C127—21no—
10C2×D16×C127—21no—
11C2×D16×C127—21no—
12#496×C127—21no—
13#495×C127C2211yescharacteristic
14#493×C127C2211yescharacteristic
15#464×C127—21no—
16#463×C127—21no—
17#460×C127—21no—
18#459×C127—21no—
19#446×C127C2211yescharacteristic
20#440×C127—21no—
21C4×D8×C127C2211yescharacteristic
22C4⋊C16×C127C2211yescharacteristic
23#357×C127—21no—
24#346×C127C2211yescharacteristic
25#334×C127C2211yescharacteristic
26#331×C127—21no—
27C2×Q16×C127D411yescharacteristic
28C2×SD16×C127—21no—
29C2×SD16×C127—21no—
30C2×SD16×C127—41no—
31C2×D8×C127—21no—
32C2×D8×C127—21no—
33C2×D8×C127—21no—
34C2×D8×C127D411yescharacteristic
35C2×D8×C127D411yescharacteristic
36#127×C127—21no—
37#127×C127—21no—
38#124×C127—21no—
39#124×C127—21no—
40#124×C127—41no—
41#123×C127—41no—
42#123×C127—41no—
43C4×Q8×C127—21no—
44C4×Q8×C127D411yescharacteristic
45C4×D4×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—41no—
48SD32×C127—42no—
49D16×C127—42no—
50D16×C127—42no—
51C2×C16×C127—21no—
52C2×C16×C127—21no—
53#107×C127D411yescharacteristic
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127D411yescharacteristic
57#103×C127—21no—
58#102×C127—21no—
59#102×C127—21no—
60#102×C127—41no—
61#97×C127—21no—
62C4×C8×C127C2311yescharacteristic
63C2×Q8×C127—21no—
64C2×Q8×C127D811yescharacteristic
65C2×D4×C127—21no—
66C2×D4×C127—21no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—41no—
71C2×D4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—41no—
74Q16×C127—41no—
75SD16×C127—41no—
76SD16×C127—41no—
77SD16×C127—81no—
78SD16×C127—82no—
79D8×C127—21no—
80D8×C127—21no—
81D8×C127—41no—
82D8×C127—41no—
83D8×C127—41no—
84D8×C127—41no—
85D8×C127—41no—
86D8×C127—81no—
87C2×C8×C127—21no—
88C2×C8×C127—41no—
89C2×C8×C127C2×D411yescharacteristic
90C2×C8×C127C2×D411yescharacteristic
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127D811yescharacteristic
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C42×C127—21no—
102C42×C127—41no—
103C42×C127C2×D411yescharacteristic
104C16×C127—22no—
105C16×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—81no—
109Q8×C127—41no—
110Q8×C127—41no—
111Q8×C127—41no—
112D4×C127—41no—
113D4×C127—41no—
114D4×C127—41no—
115D4×C127—41no—
116D4×C127—81no—
117D4×C127—81no—
118D4×C127—82no—
119D4×C127—81no—
120D4×C127—81no—
121D4×C127—161no—
122D4×C127—161no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—161no—
128C2×C4×C127—161no—
129C2×C4×C127#12011yescharacteristic
130C2×C4×C127C2×D811yescharacteristic
131C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
132C8×C127—21no—
133C8×C127—41no—
134C8×C127—81no—
135C8×C127#13511yescharacteristic
136C8×C127AGL(1,ℤ/8)11yescharacteristic
137C22×C127—81no—
138C22×C127—81no—
139C22×C127—81no—
140C22×C127—81no—
141C22×C127—81no—
142C22×C127—81no—
143C22×C127—161no—
144C22×C127—161no—
145C22×C127—161no—
146C22×C127#44711yescharacteristic
147C4×C127—21no—
148C4×C127—21no—
149C4×C127—41no—
150C4×C127—41no—
151C4×C127—81no—
152C4×C127—81no—
153C4×C127#44911yescharacteristic
154C4×C127#45311yescharacteristic
155#12336C12711yesmaximal, characteristic, direct product factor, Sylow
156C2×C127—161no—
157C2×C127—161no—
158C2×C127—321no—
159C2×C127#162111yescharacteristic
160C2×C127#219011yescharacteristic
161C2×C127#219211yescharacteristic
162#3403C2×C12711yescharacteristic, complemented
163#2250C2×C12711yescharacteristic, complemented
164#2206C2×C12711yescharacteristic, complemented
165#1688C2×C12711yescharacteristic, complemented
166#1360C2×C12711yescharacteristic, complemented
167#1338C2×C12711yescharacteristic, complemented
168#1333C2×C12711yescharacteristic, complemented
169C127#1233611yescharacteristic, direct product factor, Sylow
170#559—21no—
171C2×SD32—21no—
172C2×D16—21no—
173C2×D16—21no—
174#496—21no—
175#495C22×C12711yescharacteristic
176#493C22×C12711yescharacteristic
177#464—21no—
178#463—21no—
179#460—21no—
180#459—21no—
181#446C22×C12711yescharacteristic
182#440—21no—
183C4×D8C22×C12711yescharacteristic
184C4⋊C16C22×C12711yescharacteristic
185#357—21no—
186#346C22×C12711yescharacteristic
187#334C22×C12711yescharacteristic
188#331—21no—
189C2×Q16D4×C12711yescharacteristic
190C2×SD16—21no—
191C2×SD16—21no—
192C2×SD16—41no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8D4×C12711yescharacteristic
197C2×D8D4×C12711yescharacteristic
198#127—21no—
199#127—21no—
200#124—21no—
201#124—21no—
202#124—41no—
203#123—41no—
204#123—41no—
205C4×Q8—21no—
206C4×Q8D4×C12711yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—41no—
210SD32—42no—
211D16—42no—
212D16—42no—
213C2×C16—21no—
214C2×C16—21no—
215#107D4×C12711yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8D4×C12711yescharacteristic
219#103—21no—
220#102—21no—
221#102—21no—
222#102—41no—
223#97—21no—
224C4×C8C23×C12711yescharacteristic
225C2×Q8—21no—
226C2×Q8D8×C12711yescharacteristic
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—41no—
236Q16—41no—
237SD16—41no—
238SD16—41no—
239SD16—81no—
240SD16—82no—
241D8—21no—
242D8—21no—
243D8—41no—
244D8—41no—
245D8—41no—
246D8—41no—
247D8—41no—
248D8—81no—
249C2×C8—21no—
250C2×C8—41no—
251C2×C8C2×D4×C12711yescharacteristic
252C2×C8C2×D4×C12711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4D8×C12711yescharacteristic
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C42—21no—
264C42—41no—
265C42C2×D4×C12711yescharacteristic
266C16—22no—
267C16—41no—
268C23—41no—
269C23—41no—
270C23—81no—
271Q8—41no—
272Q8—41no—
273Q8—41no—
274D4—41no—
275D4—41no—
276D4—41no—
277D4—41no—
278D4—81no—
279D4—81no—
280D4—82no—
281D4—81no—
282D4—81no—
283D4—161no—
284D4—161no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—161no—
290C2×C4—161no—
291C2×C4#120×C12711yescharacteristic
292C2×C4C2×D8×C12711yescharacteristic
293C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
294C8—21no—
295C8—41no—
296C8—81no—
297C8#135×C12711yescharacteristic
298C8AGL(1,ℤ/8)×C12711yescharacteristic
299C22—81no—
300C22—81no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—161no—
306C22—161no—
307C22—161no—
308C22#447×C12711yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4#449×C12711yescharacteristic
316C4#453×C12711yescharacteristic
317C2—161no—
318C2—161no—
319C2—321no—
320C2C127×#162111yescharacteristic
321C2C127×#219011yescharacteristic
322C2C127×#219211yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ #446×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3403C2semidirect
2. C127×#2250C2semidirect
3. C127×#2206C2semidirect
4. C127×#1688C2semidirect
5. C127×#1360C2semidirect
6. C127×#1338C2semidirect
7. C127×#1333C2semidirect
155. #12336C127direct (N × H)
162. #3403C2×C127semidirect
163. #2250C2×C127semidirect
164. #2206C2×C127semidirect
165. #1688C2×C127semidirect
166. #1360C2×C127semidirect
167. #1338C2×C127semidirect
168. #1333C2×C127semidirect
169. C127#12336direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34032
C127×#22502
C127×#22062
C127×#16882
C127×#13602
C127×#13382
C127×#13332
#12336127