Finite Group Databasebeta

← C127×#13028 #44576701

Subgroups — C127×#13028 #44576701

Order 32512.

476 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C2×#443×C127C211yesmaximal, characteristic
3C2×#362×C127C211yesmaximal, characteristic, complemented
4C127×#2139C211yesmaximal, characteristic
5C127×#1969C211yesmaximal, characteristic, complemented
6C127×#1387C211yesmaximal, characteristic, complemented
7C127×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10C2×#131×C127—21no—
11#510×C127—22no—
12#510×C127C414yescomplemented
13C2×Q32×C127—21no—
14C2×SD32×C127—21no—
15C2×M32×C127C2211yescharacteristic
16C2×M32×C127C2211yescharacteristic
17#443×C127—22no—
18#443×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#107×C127C2211yescharacteristic
21C2×#104×C127—21no—
22C2×#103×C127—21no—
23C2×C4×C8×C127C2211yescharacteristic
24#391×C127—21no—
25#362×C127—22no—
26#358×C127—21no—
27#357×C127—21no—
28C2×#41×C127—21no—
29C22×Q8×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127C2×C412yes—
33#135×C127D412yes—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127C2×C412yes—
40C2×Q16×C127D411yescharacteristic
41C2×SD16×C127—21no—
42C2×D8×C127D411yescharacteristic
43#131×C127—24no—
44#131×C127—42no—
45C2×M16×C127—21no—
46C2×M16×C127—41no—
47C22×C8×C127—41no—
48C22×C8×C127D411yescharacteristic
49C22×C8×C127C2311yescharacteristic
50C2×C4⋊C4×C127—21no—
51C2×C42×C127D411yescharacteristic
52Q32×C127—24no—
53SD32×C127—24no—
54M32×C127—21no—
55M32×C127—21no—
56M32×C127—21no—
57M32×C127C2×C412yes—
58C2×C16×C127—21no—
59C2×C16×C127—21no—
60#108×C127—21no—
61#108×C127D412yes—
62#107×C127—21no—
63#107×C127—21no—
64#104×C127—24no—
65#103×C127—41no—
66#103×C127—41no—
67C4×C8×C127—21no—
68C4×C8×C127—21no—
69#95×C127—42no—
70#41×C127—22no—
71#41×C127—22no—
72#41×C127—41no—
73#41×C127—41no—
74C2×Q8×C127—22no—
75C2×Q8×C127—21no—
76C2×Q8×C127—41no—
77C2×Q8×C127—41no—
78C2×Q8×C127—41no—
79C2×Q8×C127—41no—
80C2×Q8×C127—41no—
81C2×D4×C127—21no—
82C2×D4×C127—41no—
83C22×C4×C127—21no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127C2×D411yescharacteristic
88Q16×C127—22no—
89Q16×C127—22no—
90Q16×C127—21no—
91Q16×C127—41no—
92Q16×C127—41no—
93Q16×C127C22⋊C412yes—
94SD16×C127—22no—
95SD16×C127—22no—
96D8×C127—21no—
97D8×C127C22⋊C412yes—
98M16×C127—22no—
99M16×C127—44no—
100M16×C127—41no—
101C2×C8×C127—21no—
102C2×C8×C127—21no—
103C2×C8×C127—44no—
104C2×C8×C127—41no—
105C2×C8×C127D811yescharacteristic
106C2×C8×C127D811yescharacteristic
107C2×C8×C127C22×C411yescharacteristic
108C2×C8×C127C2×D411yescharacteristic
109C2×C8×C127C2×D411yescharacteristic
110C2×C8×C127C2×D411yescharacteristic
111C2×C8×C127#4111yescharacteristic
112C2×C8×C127#4111yescharacteristic
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C42×C127—21no—
116C42×C127—21no—
117C16×C127—22no—
118C16×C127—41no—
119C23×C127—41no—
120C23×C127AGL(1,ℤ/8)11yescharacteristic
121Q8×C127—22no—
122Q8×C127—41no—
123Q8×C127—42no—
124Q8×C127—42no—
125Q8×C127—81no—
126Q8×C127—81no—
127D4×C127—22no—
128D4×C127—42no—
129D4×C127—42no—
130D4×C127—41no—
131C2×C4×C127—22no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127—82no—
141C2×C4×C127—81no—
142C2×C4×C127C4×D411yescharacteristic
143C2×C4×C127#12011yescharacteristic
144C2×C4×C127#12111yescharacteristic
145C2×C4×C127C2×D811yescharacteristic
146C2×C4×C127#13511yescharacteristic
147C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
148C8×C127—21no—
149C8×C127—21no—
150C8×C127—42no—
151C8×C127C2×C22⋊C411yescharacteristic
152C8×C127C4×D411yescharacteristic
153C8×C127#12111yescharacteristic
154C8×C127#12311yescharacteristic
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—42no—
158C22×C127—81no—
159C22×C127—81no—
160C22×C127#44211yescharacteristic
161C22×C127#44911yescharacteristic
162C22×C127#45911yescharacteristic
163C4×C127—42no—
164C4×C127—42no—
165C4×C127—82no—
166C4×C127—161no—
167C4×C127#38611yescharacteristic
168C4×C127C4×D811yescharacteristic
169C4×C127#44711yescharacteristic
170C4×C127#46311yescharacteristic
171#13028C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127—21no—
173C2×C127—21no—
174C2×C127—82no—
175C2×C127#187911yescharacteristic
176C2×C127#221211yescharacteristic
177C2×C127#221411yescharacteristic
178C2×#510C2×C12711yescharacteristic
179C2×#443C2×C12711yescharacteristic
180C2×#362C2×C12711yescharacteristic, complemented
181#2139C2×C12711yescharacteristic
182#1969C2×C12711yescharacteristic, complemented
183#1387C2×C12711yescharacteristic, complemented
184#1376C2×C12711yescharacteristic, complemented
185C127#1302811yescharacteristic, direct product factor, Sylow
186C2×#135C22×C12711yescharacteristic
187C22×Q16C22×C12711yescharacteristic
188C2×#131—21no—
189#510—22no—
190#510C4×C12714yescomplemented
191C2×Q32—21no—
192C2×SD32—21no—
193C2×M32C22×C12711yescharacteristic
194C2×M32C22×C12711yescharacteristic
195#443—22no—
196#443—22no—
197C2×#108C22×C12711yescharacteristic
198C2×#107C22×C12711yescharacteristic
199C2×#104—21no—
200C2×#103—21no—
201C2×C4×C8C22×C12711yescharacteristic
202#391—21no—
203#362—22no—
204#358—21no—
205#357—21no—
206C2×#41—21no—
207C22×Q8—21no—
208#135—21no—
209#135—21no—
210#135C2×C4×C12712yes—
211#135D4×C12712yes—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16C2×C4×C12712yes—
218C2×Q16D4×C12711yescharacteristic
219C2×SD16—21no—
220C2×D8D4×C12711yescharacteristic
221#131—24no—
222#131—42no—
223C2×M16—21no—
224C2×M16—41no—
225C22×C8—41no—
226C22×C8D4×C12711yescharacteristic
227C22×C8C23×C12711yescharacteristic
228C2×C4⋊C4—21no—
229C2×C42D4×C12711yescharacteristic
230Q32—24no—
231SD32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32C2×C4×C12712yes—
236C2×C16—21no—
237C2×C16—21no—
238#108—21no—
239#108D4×C12712yes—
240#107—21no—
241#107—21no—
242#104—24no—
243#103—41no—
244#103—41no—
245C4×C8—21no—
246C4×C8—21no—
247#95—42no—
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C12711yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—21no—
269Q16—41no—
270Q16—41no—
271Q16C22⋊C4×C12712yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C22⋊C4×C12712yes—
276M16—22no—
277M16—44no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8D8×C12711yescharacteristic
284C2×C8D8×C12711yescharacteristic
285C2×C8C22×C4×C12711yescharacteristic
286C2×C8C2×D4×C12711yescharacteristic
287C2×C8C2×D4×C12711yescharacteristic
288C2×C8C2×D4×C12711yescharacteristic
289C2×C8#41×C12711yescharacteristic
290C2×C8#41×C12711yescharacteristic
291C4⋊C4—41no—
292C4⋊C4—41no—
293C42—21no—
294C42—21no—
295C16—22no—
296C16—41no—
297C23—41no—
298C23AGL(1,ℤ/8)×C12711yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4C4×D4×C12711yescharacteristic
321C2×C4#120×C12711yescharacteristic
322C2×C4#121×C12711yescharacteristic
323C2×C4C2×D8×C12711yescharacteristic
324C2×C4#135×C12711yescharacteristic
325C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×C22⋊C4×C12711yescharacteristic
330C8C4×D4×C12711yescharacteristic
331C8#121×C12711yescharacteristic
332C8#123×C12711yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22#442×C12711yescharacteristic
339C22#449×C12711yescharacteristic
340C22#459×C12711yescharacteristic
341C4—42no—
342C4—42no—
343C4—82no—
344C4—161no—
345C4#386×C12711yescharacteristic
346C4C4×D8×C12711yescharacteristic
347C4#447×C12711yescharacteristic
348C4#463×C12711yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2C127×#187911yescharacteristic
353C2C127×#221211yescharacteristic
354C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C2×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
3. C2×#362×C127C2semidirect
5. C127×#1969C2semidirect
6. C127×#1387C2semidirect
7. C127×#1376C2semidirect
12. #510×C127C4semidirect
171. #13028C127direct (N × H)
180. C2×#362C2×C127semidirect
182. #1969C2×C127semidirect
183. #1387C2×C127semidirect
184. #1376C2×C127semidirect
185. C127#13028direct (N × H)
190. #510C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C2×#443×C1272
C2×#362×C1272
C127×#21392
C127×#19692
C127×#13872
C127×#13762
#13028127