Finite Group Databasebeta

← C127×#13443 #44577116

Subgroups — C127×#13443 #44577116

Order 32512.

378 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C127×#2153C211yesmaximal, characteristic, complemented
3C127×#2148C211yesmaximal, characteristic
4C127×#2141C211yesmaximal, characteristic, complemented
5C127×#1979C211yesmaximal, characteristic, complemented
6C127×#1976C211yesmaximal, characteristic
7C127×#1389C211yesmaximal, 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
17#427×C127C2211yescharacteristic
18#421×C127—21no—
19#419×C127—21no—
20C2×#101×C127—21no—
21#410×C127—21no—
22#405×C127C2211yescharacteristic
23#364×C127—22no—
24#362×C127—21no—
25#361×C127—21no—
26#358×C127—22no—
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—
43C2×M16×C127D411yescharacteristic
44C22×C8×C127C2311yescharacteristic
45#117×C127—21no—
46#117×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#106×C127—21no—
59#104×C127—42no—
60#103×C127—42no—
61#101×C127—42no—
62#99×C127—42no—
63#97×C127—21no—
64C4×C8×C127—21no—
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—41no—
79C22×C4×C127—41no—
80C22×C4×C127C2×D411yescharacteristic
81Q16×C127—22no—
82Q16×C127—21no—
83Q16×C127—22no—
84Q16×C127—21no—
85Q16×C127—41no—
86Q16×C127—41no—
87SD16×C127—41no—
88SD16×C127—41no—
89D8×C127—21no—
90D8×C127—21no—
91M16×C127—21no—
92M16×C127—41no—
93M16×C127—41no—
94M16×C127D812yes—
95C2×C8×C127—21no—
96C2×C8×C127—41no—
97C2×C8×C127C2×D411yescharacteristic
98C2×C8×C127C2×D411yescharacteristic
99C2×C8×C127C2×D411yescharacteristic
100C2×C8×C127#4111yescharacteristic
101C2×C8×C127#4111yescharacteristic
102C2×C8×C127#4111yescharacteristic
103C4⋊C4×C127—21no—
104C4⋊C4×C127—41no—
105C22⋊C4×C127—21no—
106C22⋊C4×C127—41no—
107C42×C127—21no—
108C42×C127—41no—
109C16×C127—22no—
110C16×C127—41no—
111C23×C127—41no—
112C23×C127AGL(1,ℤ/8)11yescharacteristic
113Q8×C127—41no—
114Q8×C127—42no—
115Q8×C127—41no—
116Q8×C127—42no—
117Q8×C127—81no—
118Q8×C127—81no—
119D4×C127—41no—
120D4×C127—41no—
121D4×C127—81no—
122D4×C127—81no—
123C2×C4×C127—42no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127—81no—
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12111yescharacteristic
134C2×C4×C127C2×D811yescharacteristic
135C2×C4×C127#13511yescharacteristic
136C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
137C8×C127—22no—
138C8×C127—81no—
139C8×C127#12011yescharacteristic
140C8×C127#12311yescharacteristic
141C8×C127#12311yescharacteristic
142C8×C127#12411yescharacteristic
143C22×C127—41no—
144C22×C127—81no—
145C22×C127—161no—
146C22×C127#45911yescharacteristic
147C22×C127#46311yescharacteristic
148C22×C127#46911yescharacteristic
149C4×C127—81no—
150C4×C127—81no—
151C4×C127—82no—
152C4×C127—161no—
153C4×C127#39411yescharacteristic
154C4×C127#45911yescharacteristic
155C4×C127#46311yescharacteristic
156C4×C127#46611yescharacteristic
157#13443C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—21no—
161C2×C127—161no—
162C2×C127#205411yescharacteristic
163C2×#510C2×C12711yescharacteristic
164#2153C2×C12711yescharacteristic, complemented
165#2148C2×C12711yescharacteristic
166#2141C2×C12711yescharacteristic, complemented
167#1979C2×C12711yescharacteristic, complemented
168#1976C2×C12711yescharacteristic
169#1389C2×C12711yescharacteristic, complemented
170C127#1344311yescharacteristic, direct product factor, Sylow
171C2×#135C22×C12711yescharacteristic
172C22×Q16C22×C12711yescharacteristic
173#510—22no—
174#510—22no—
175C2×Q32—21no—
176C2×SD32—21no—
177C2×M32C22×C12711yescharacteristic
178C2×M32C22×C12711yescharacteristic
179C2×#108C22×C12711yescharacteristic
180#427C22×C12711yescharacteristic
181#421—21no—
182#419—21no—
183C2×#101—21no—
184#410—21no—
185#405C22×C12711yescharacteristic
186#364—22no—
187#362—21no—
188#361—21no—
189#358—22no—
190C2×#41—21no—
191C22×Q8—21no—
192#135—21no—
193#135—21no—
194#135—21no—
195#135—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16D4×C12712yes—
202C2×Q16D4×C12711yescharacteristic
203C2×SD16—21no—
204C2×D8D4×C12711yescharacteristic
205C2×M16—21no—
206C2×M16D4×C12711yescharacteristic
207C22×C8C23×C12711yescharacteristic
208#117—21no—
209#117D4×C12711yescharacteristic
210Q32—24no—
211SD32—24no—
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C12712yes—
216C2×C16—21no—
217C2×C16—21no—
218#108—21no—
219#108—21no—
220#107—21no—
221#106—21no—
222#104—42no—
223#103—42no—
224#101—42no—
225#99—42no—
226#97—21no—
227C4×C8—21no—
228#41—41no—
229#41—41no—
230#41—41no—
231#41—41no—
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C12711yescharacteristic
244Q16—22no—
245Q16—21no—
246Q16—22no—
247Q16—21no—
248Q16—41no—
249Q16—41no—
250SD16—41no—
251SD16—41no—
252D8—21no—
253D8—21no—
254M16—21no—
255M16—41no—
256M16—41no—
257M16D8×C12712yes—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8C2×D4×C12711yescharacteristic
261C2×C8C2×D4×C12711yescharacteristic
262C2×C8C2×D4×C12711yescharacteristic
263C2×C8#41×C12711yescharacteristic
264C2×C8#41×C12711yescharacteristic
265C2×C8#41×C12711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—41no—
268C22⋊C4—21no—
269C22⋊C4—41no—
270C42—21no—
271C42—41no—
272C16—22no—
273C16—41no—
274C23—41no—
275C23AGL(1,ℤ/8)×C12711yescharacteristic
276Q8—41no—
277Q8—42no—
278Q8—41no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#121×C12711yescharacteristic
295C2×C4#121×C12711yescharacteristic
296C2×C4#121×C12711yescharacteristic
297C2×C4C2×D8×C12711yescharacteristic
298C2×C4#135×C12711yescharacteristic
299C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
300C8—22no—
301C8—81no—
302C8#120×C12711yescharacteristic
303C8#123×C12711yescharacteristic
304C8#123×C12711yescharacteristic
305C8#124×C12711yescharacteristic
306C22—41no—
307C22—81no—
308C22—161no—
309C22#459×C12711yescharacteristic
310C22#463×C12711yescharacteristic
311C22#469×C12711yescharacteristic
312C4—81no—
313C4—81no—
314C4—82no—
315C4—161no—
316C4#394×C12711yescharacteristic
317C4#459×C12711yescharacteristic
318C4#463×C12711yescharacteristic
319C4#466×C12711yescharacteristic
320C2—21no—
321C2—21no—
322C2—21no—
323C2—161no—
324C2C127×#205411yescharacteristic
subgroupG/H
center, socleC2×C127#2054
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2153C2semidirect
4. C127×#2141C2semidirect
5. C127×#1979C2semidirect
7. C127×#1389C2semidirect
157. #13443C127direct (N × H)
164. #2153C2×C127semidirect
166. #2141C2×C127semidirect
167. #1979C2×C127semidirect
169. #1389C2×C127semidirect
170. C127#13443direct (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
C127×#21532
C127×#21482
C127×#21412
C127×#19792
C127×#19762
C127×#13892
#13443127