Finite Group Databasebeta

← C127×#13442 #44577115

Subgroups — C127×#13442 #44577115

Order 32512.

398 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic
2C127×#2153C211yesmaximal, characteristic, complemented
3C127×#2148C211yesmaximal, characteristic, complemented
4C127×#2140C211yesmaximal, characteristic, complemented
5C127×#1978C211yesmaximal, characteristic, complemented
6C127×#1976C211yesmaximal, characteristic, complemented
7C127×#1389C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10#509×C127—22no—
11#509×C127—22no—
12C2×SD32×C127—21no—
13C2×D16×C127—21no—
14C2×M32×C127C2211yescharacteristic
15C2×M32×C127C2211yescharacteristic
16C2×#108×C127C2211yescharacteristic
17#427×C127C2211yescharacteristic
18#421×C127—21no—
19#418×C127—21no—
20C2×#100×C127—21no—
21#410×C127—21no—
22#405×C127C2211yescharacteristic
23#364×C127—22no—
24#362×C127—21no—
25#361×C127—21no—
26#357×C127—22no—
27C2×#41×C127—21no—
28C22×D4×C127—21no—
29#135×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127—21no—
33C2×Q16×C127D411yescharacteristic
34C2×SD16×C127—21no—
35C2×D8×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×D8×C127—21no—
39C2×D8×C127—21no—
40C2×D8×C127D411yescharacteristic
41C2×D8×C127D412yes—
42C2×M16×C127—21no—
43C2×M16×C127D411yescharacteristic
44C22×C8×C127C2311yescharacteristic
45#117×C127—21no—
46#117×C127D411yescharacteristic
47SD32×C127—24no—
48D16×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#102×C127—42no—
61#100×C127—42no—
62#99×C127—42no—
63#97×C127—21no—
64C4×C8×C127—21no—
65C24×C127—41no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70C2×Q8×C127—21no—
71C2×D4×C127—22no—
72C2×D4×C127—21no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127C2×D411yescharacteristic
81Q16×C127—21no—
82Q16×C127—21no—
83SD16×C127—41no—
84SD16×C127—41no—
85D8×C127—21no—
86D8×C127—22no—
87D8×C127—22no—
88D8×C127—21no—
89D8×C127—41no—
90D8×C127—41no—
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—42no—
112C23×C127—41no—
113C23×C127—81no—
114C23×C127—81no—
115C23×C127—162no—
116C23×C127AGL(1,ℤ/8)11yescharacteristic
117Q8×C127—41no—
118Q8×C127—41no—
119D4×C127—42no—
120D4×C127—41no—
121D4×C127—41no—
122D4×C127—42no—
123D4×C127—81no—
124D4×C127—81no—
125D4×C127—81no—
126D4×C127—81no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—81no—
130C2×C4×C127—81no—
131C2×C4×C127—81no—
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12111yescharacteristic
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127C2×D811yescharacteristic
136C2×C4×C127#13511yescharacteristic
137C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
138C8×C127—22no—
139C8×C127—81no—
140C8×C127#12011yescharacteristic
141C8×C127#12311yescharacteristic
142C8×C127#12311yescharacteristic
143C8×C127#12411yescharacteristic
144C22×C127—41no—
145C22×C127—81no—
146C22×C127—82no—
147C22×C127—161no—
148C22×C127—162no—
149C22×C127—162no—
150C22×C127—162no—
151C22×C127#45911yescharacteristic
152C22×C127#46311yescharacteristic
153C22×C127#46911yescharacteristic
154C4×C127—81no—
155C4×C127—81no—
156C4×C127—161no—
157C4×C127#39411yescharacteristic
158C4×C127#45911yescharacteristic
159C4×C127#46311yescharacteristic
160C4×C127#46611yescharacteristic
161#13442C12711yesmaximal, characteristic, direct product factor, Sylow
162C2×C127—21no—
163C2×C127—21no—
164C2×C127—21no—
165C2×C127—161no—
166C2×C127—162no—
167C2×C127#205411yescharacteristic
168C2×#509C2×C12711yescharacteristic
169#2153C2×C12711yescharacteristic, complemented
170#2148C2×C12711yescharacteristic, complemented
171#2140C2×C12711yescharacteristic, complemented
172#1978C2×C12711yescharacteristic, complemented
173#1976C2×C12711yescharacteristic, complemented
174#1389C2×C12711yescharacteristic, complemented
175C127#1344211yescharacteristic, direct product factor, Sylow
176C2×#135C22×C12711yescharacteristic
177C22×D8C22×C12711yescharacteristic
178#509—22no—
179#509—22no—
180C2×SD32—21no—
181C2×D16—21no—
182C2×M32C22×C12711yescharacteristic
183C2×M32C22×C12711yescharacteristic
184C2×#108C22×C12711yescharacteristic
185#427C22×C12711yescharacteristic
186#421—21no—
187#418—21no—
188C2×#100—21no—
189#410—21no—
190#405C22×C12711yescharacteristic
191#364—22no—
192#362—21no—
193#361—21no—
194#357—22no—
195C2×#41—21no—
196C22×D4—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201C2×Q16D4×C12711yescharacteristic
202C2×SD16—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8D4×C12712yes—
209C2×D8D4×C12711yescharacteristic
210C2×M16—21no—
211C2×M16D4×C12711yescharacteristic
212C22×C8C23×C12711yescharacteristic
213#117—21no—
214#117D4×C12711yescharacteristic
215SD32—24no—
216D16—24no—
217M32—21no—
218M32—21no—
219M32—21no—
220M32D4×C12712yes—
221C2×C16—21no—
222C2×C16—21no—
223#108—21no—
224#108—21no—
225#107—21no—
226#106—21no—
227#104—42no—
228#102—42no—
229#100—42no—
230#99—42no—
231#97—21no—
232C4×C8—21no—
233C24—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4C2×D4×C12711yescharacteristic
249Q16—21no—
250Q16—21no—
251SD16—41no—
252SD16—41no—
253D8—21no—
254D8—22no—
255D8—22no—
256D8—21no—
257D8—41no—
258D8—41no—
259M16—21no—
260M16—41no—
261M16—41no—
262M16D8×C12712yes—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8C2×D4×C12711yescharacteristic
266C2×C8C2×D4×C12711yescharacteristic
267C2×C8C2×D4×C12711yescharacteristic
268C2×C8#41×C12711yescharacteristic
269C2×C8#41×C12711yescharacteristic
270C2×C8#41×C12711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—41no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C42—21no—
276C42—41no—
277C16—22no—
278C16—41no—
279C23—42no—
280C23—41no—
281C23—81no—
282C23—81no—
283C23—162no—
284C23AGL(1,ℤ/8)×C12711yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—42no—
288D4—41no—
289D4—41no—
290D4—42no—
291D4—81no—
292D4—81no—
293D4—81no—
294D4—81no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#121×C12711yescharacteristic
301C2×C4#121×C12711yescharacteristic
302C2×C4#121×C12711yescharacteristic
303C2×C4C2×D8×C12711yescharacteristic
304C2×C4#135×C12711yescharacteristic
305C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
306C8—22no—
307C8—81no—
308C8#120×C12711yescharacteristic
309C8#123×C12711yescharacteristic
310C8#123×C12711yescharacteristic
311C8#124×C12711yescharacteristic
312C22—41no—
313C22—81no—
314C22—82no—
315C22—162no—
316C22—161no—
317C22—162no—
318C22—162no—
319C22#459×C12711yescharacteristic
320C22#463×C12711yescharacteristic
321C22#469×C12711yescharacteristic
322C4—81no—
323C4—81no—
324C4—161no—
325C4#394×C12711yescharacteristic
326C4#459×C12711yescharacteristic
327C4#463×C12711yescharacteristic
328C4#466×C12711yescharacteristic
329C2—21no—
330C2—21no—
331C2—21no—
332C2—162no—
333C2—161no—
334C2C127×#205411yescharacteristic
subgroupG/H
center, socleC2×C127#2054
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
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
3. C127×#2148C2semidirect
4. C127×#2140C2semidirect
5. C127×#1978C2semidirect
6. C127×#1976C2semidirect
7. C127×#1389C2semidirect
161. #13442C127direct (N × H)
169. #2153C2×C127semidirect
170. #2148C2×C127semidirect
171. #2140C2×C127semidirect
172. #1978C2×C127semidirect
173. #1976C2×C127semidirect
174. #1389C2×C127semidirect
175. C127#13442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C127×#21532
C127×#21482
C127×#21402
C127×#19782
C127×#19762
C127×#13892
#13442127