Finite Group Databasebeta

← C127×#12319 #44575992

Subgroups — C127×#12319 #44575992

Order 32512.

390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3283C211yesmaximal, characteristic, complemented
2C127×#2248C211yesmaximal, characteristic, complemented
3C127×#2206C211yesmaximal, characteristic, complemented
4C127×#1667C211yesmaximal, characteristic, complemented
5C127×#1362C211yesmaximal, characteristic, complemented
6C127×#1331C211yesmaximal, characteristic, complemented
7C127×D4⋊C16C211yesmaximal, characteristic, complemented
8C2×#135×C127—21no—
9#547×C127—21no—
10C2×SD32×C127—22no—
11C2×D16×C127—21no—
12#494×C127C2211yescharacteristic
13#493×C127C2211yescharacteristic
14#467×C127—21no—
15#461×C127—21no—
16#459×C127—21no—
17#452×C127—22no—
18C4×D8×C127C2211yescharacteristic
19C8×D4×C127C2211yescharacteristic
20C4⋊C16×C127C2211yescharacteristic
21#357×C127—21no—
22C4×C16×C127C2211yescharacteristic
23#335×C127C2211yescharacteristic
24#331×C127—21no—
25C2×#41×C127—22no—
26#135×C127—42no—
27#135×C127—42no—
28C2×Q16×C127—21no—
29C2×Q16×C127D412yes—
30C2×SD16×C127—22no—
31C2×D8×C127—21no—
32C2×D8×C127—21no—
33C2×D8×C127—41no—
34C2×D8×C127D411yescharacteristic
35C22×C8×C127—21no—
36C4⋊Q8×C127—21no—
37#127×C127—21no—
38#123×C127—42no—
39C22⋊Q8×C127—22no—
40#121×C127—41no—
41C4×D4×C127—21no—
42C4×D4×C127D411yescharacteristic
43C2×C4⋊C4×C127—41no—
44SD32×C127—44no—
45D16×C127—42no—
46C2×C16×C127—21no—
47C2×C16×C127—21no—
48#107×C127D411yescharacteristic
49C4⋊C8×C127—21no—
50C4⋊C8×C127D411yescharacteristic
51#103×C127—22no—
52#102×C127—21no—
53#102×C127—41no—
54C22⋊C8×C127—21no—
55C4×C8×C127C2311yescharacteristic
56#41×C127—44no—
57#41×C127—82no—
58C2×Q8×C127—22no—
59C2×D4×C127—21no—
60C2×D4×C127—42no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127D811yescharacteristic
65C22×C4×C127—21no—
66C22×C4×C127—42no—
67C22×C4×C127—41no—
68Q16×C127—42no—
69Q16×C127—41no—
70Q16×C127—41no—
71SD16×C127—44no—
72D8×C127—21no—
73D8×C127—42no—
74D8×C127—41no—
75D8×C127—41no—
76D8×C127—82no—
77D8×C127D812yescomplemented
78C2×C8×C127—21no—
79C2×C8×C127—41no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C2×C8×C127C2×D411yescharacteristic
83C2×C8×C127C2×D411yescharacteristic
84C4⋊C4×C127—21no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127D811yescharacteristic
89C22⋊C4×C127—21no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—41no—
92C42×C127C2×D411yescharacteristic
93C16×C127—22no—
94C16×C127—41no—
95C23×C127—21no—
96C23×C127—41no—
97C23×C127—81no—
98Q8×C127—42no—
99Q8×C127—42no—
100D4×C127—22no—
101D4×C127—21no—
102D4×C127—21no—
103D4×C127—41no—
104D4×C127—84no—
105D4×C127—81no—
106D4×C127—81no—
107D4×C127—81no—
108D4×C127—81no—
109D4×C127—161no—
110C2×C4×C127—21no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—42no—
115C2×C4×C127—84no—
116C2×C4×C127—81no—
117C2×C4×C127—81no—
118C2×C4×C127#12011yescharacteristic
119C2×C4×C127C2×D811yescharacteristic
120C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
121C8×C127—21no—
122C8×C127—41no—
123C8×C127—81no—
124C8×C127C2×D811yescharacteristic
125C8×C127AGL(1,ℤ/8)11yescharacteristic
126C22×C127—41no—
127C22×C127—42no—
128C22×C127—41no—
129C22×C127—41no—
130C22×C127—81no—
131C22×C127—81no—
132C22×C127—161no—
133C22×C127—161no—
134C22×C127—161no—
135C22×C127#44711yescharacteristic
136C4×C127—21no—
137C4×C127—41no—
138C4×C127—82no—
139C4×C127—81no—
140C4×C127#44711yescharacteristic
141C4×C127#45311yescharacteristic
142C4×C127#50811yescharacteristic
143C4×C127#50911yescharacteristic
144#12319C12711yesmaximal, characteristic, direct product factor, Sylow
145C2×C127—81no—
146C2×C127—82no—
147C2×C127—321no—
148C2×C127#161911yescharacteristic
149C2×C127#218611yescharacteristic
150C2×C127#219311yescharacteristic
151#3283C2×C12711yescharacteristic, complemented
152#2248C2×C12711yescharacteristic, complemented
153#2206C2×C12711yescharacteristic, complemented
154#1667C2×C12711yescharacteristic, complemented
155#1362C2×C12711yescharacteristic, complemented
156#1331C2×C12711yescharacteristic, complemented
157D4⋊C16C2×C12711yescharacteristic, complemented
158C127#1231911yescharacteristic, direct product factor, Sylow
159C2×#135—21no—
160#547—21no—
161C2×SD32—22no—
162C2×D16—21no—
163#494C22×C12711yescharacteristic
164#493C22×C12711yescharacteristic
165#467—21no—
166#461—21no—
167#459—21no—
168#452—22no—
169C4×D8C22×C12711yescharacteristic
170C8×D4C22×C12711yescharacteristic
171C4⋊C16C22×C12711yescharacteristic
172#357—21no—
173C4×C16C22×C12711yescharacteristic
174#335C22×C12711yescharacteristic
175#331—21no—
176C2×#41—22no—
177#135—42no—
178#135—42no—
179C2×Q16—21no—
180C2×Q16D4×C12712yes—
181C2×SD16—22no—
182C2×D8—21no—
183C2×D8—21no—
184C2×D8—41no—
185C2×D8D4×C12711yescharacteristic
186C22×C8—21no—
187C4⋊Q8—21no—
188#127—21no—
189#123—42no—
190C22⋊Q8—22no—
191#121—41no—
192C4×D4—21no—
193C4×D4D4×C12711yescharacteristic
194C2×C4⋊C4—41no—
195SD32—44no—
196D16—42no—
197C2×C16—21no—
198C2×C16—21no—
199#107D4×C12711yescharacteristic
200C4⋊C8—21no—
201C4⋊C8D4×C12711yescharacteristic
202#103—22no—
203#102—21no—
204#102—41no—
205C22⋊C8—21no—
206C4×C8C23×C12711yescharacteristic
207#41—44no—
208#41—82no—
209C2×Q8—22no—
210C2×D4—21no—
211C2×D4—42no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4D8×C12711yescharacteristic
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—41no—
219Q16—42no—
220Q16—41no—
221Q16—41no—
222SD16—44no—
223D8—21no—
224D8—42no—
225D8—41no—
226D8—41no—
227D8—82no—
228D8D8×C12712yescomplemented
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8C2×D4×C12711yescharacteristic
234C2×C8C2×D4×C12711yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4D8×C12711yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—42no—
242C22⋊C4—41no—
243C42C2×D4×C12711yescharacteristic
244C16—22no—
245C16—41no—
246C23—21no—
247C23—41no—
248C23—81no—
249Q8—42no—
250Q8—42no—
251D4—21no—
252D4—21no—
253D4—22no—
254D4—41no—
255D4—84no—
256D4—81no—
257D4—81no—
258D4—81no—
259D4—81no—
260D4—161no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—84no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4#120×C12711yescharacteristic
270C2×C4C2×D8×C12711yescharacteristic
271C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
272C8—21no—
273C8—41no—
274C8—81no—
275C8C2×D8×C12711yescharacteristic
276C8AGL(1,ℤ/8)×C12711yescharacteristic
277C22—41no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22—161no—
284C22—161no—
285C22—161no—
286C22#447×C12711yescharacteristic
287C4—21no—
288C4—41no—
289C4—82no—
290C4—81no—
291C4#447×C12711yescharacteristic
292C4#453×C12711yescharacteristic
293C4#508×C12711yescharacteristic
294C4#509×C12711yescharacteristic
295C2—81no—
296C2—82no—
297C2—321no—
298C2C127×#161911yescharacteristic
299C2C127×#218611yescharacteristic
300C2C127×#219311yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3283C2semidirect
2. C127×#2248C2semidirect
3. C127×#2206C2semidirect
4. C127×#1667C2semidirect
5. C127×#1362C2semidirect
6. C127×#1331C2semidirect
7. C127×D4⋊C16C2semidirect
77. D8×C127D8semidirect
144. #12319C127direct (N × H)
151. #3283C2×C127semidirect
152. #2248C2×C127semidirect
153. #2206C2×C127semidirect
154. #1667C2×C127semidirect
155. #1362C2×C127semidirect
156. #1331C2×C127semidirect
157. D4⋊C16C2×C127semidirect
158. C127#12319direct (N × H)
228. D8D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32832
C127×#22482
C127×#22062
C127×#16672
C127×#13622
C127×#13312
C127×D4⋊C162
#12319127