Finite Group Databasebeta

← C127×#13040 #44576713

Subgroups — C127×#13040 #44576713

Order 32512.

508 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×#509×C127C211yesmaximal, characteristic
2C2×#444×C127C211yesmaximal, characteristic, complemented
3C2×#361×C127C211yesmaximal, characteristic, complemented
4C2×#360×C127C211yesmaximal, characteristic, complemented
5C127×#1972C211yesmaximal, characteristic, complemented
6C127×#1383C211yesmaximal, characteristic, complemented
7C127×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10C2×#131×C127—21no—
11#509×C127—22no—
12#509×C127—22no—
13C2×SD32×C127C412yescomplemented
14C2×D16×C127C412yescomplemented
15C2×M32×C127C2211yescharacteristic
16C2×M32×C127C2211yescharacteristic
17#444×C127—22no—
18#444×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#106×C127C2211yescharacteristic
21C2×#104×C127—21no—
22C2×#102×C127—21no—
23C2×#97×C127C2211yescharacteristic
24#390×C127—21no—
25#361×C127—22no—
26#360×C127—22no—
27C2×#41×C127—21no—
28C22×D4×C127—21no—
29#135×C127—21no—
30#135×C127—21no—
31#135×C127D412yes—
32#135×C127D412yes—
33C2×Q16×C127C2×C411yescharacteristic
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×C127C2×C412yes—
41C2×D8×C127C2×C411yescharacteristic
42#131×C127—24no—
43#131×C127—42no—
44C2×M16×C127—21no—
45C2×M16×C127—41no—
46C22×C8×C127—41no—
47C22×C8×C127D411yescharacteristic
48C22×C8×C127C2311yescharacteristic
49C2×C4⋊C4×C127—21no—
50C2×C22⋊C4×C127—42no—
51C2×C42×C127D411yescharacteristic
52SD32×C127—24no—
53D16×C127—24no—
54M32×C127—21no—
55M32×C127—21no—
56M32×C127—21no—
57M32×C127—21no—
58C2×C16×C127—21no—
59C2×C16×C127C2×C412yes—
60#108×C127—21no—
61#108×C127D412yes—
62#106×C127—21no—
63#106×C127—21no—
64#104×C127—24no—
65#102×C127—42no—
66#97×C127—21no—
67#97×C127—21no—
68C24×C127—41no—
69#41×C127—22no—
70#41×C127—22no—
71#41×C127—41no—
72#41×C127—41no—
73C2×Q8×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—22no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C22×C4×C127—21no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127C2×D411yescharacteristic
86Q16×C127—21no—
87Q16×C127C22⋊C412yescomplemented
88SD16×C127—22no—
89SD16×C127—22no—
90D8×C127—22no—
91D8×C127—21no—
92D8×C127—22no—
93D8×C127—41no—
94D8×C127—41no—
95D8×C127C22⋊C412yescomplemented
96M16×C127—22no—
97M16×C127—44no—
98M16×C127—41no—
99C2×C8×C127—21no—
100C2×C8×C127—21no—
101C2×C8×C127—44no—
102C2×C8×C127—41no—
103C2×C8×C127D812yes—
104C2×C8×C127C22×C411yescharacteristic
105C2×C8×C127C2×D411yescharacteristic
106C2×C8×C127C2×D411yescharacteristic
107C2×C8×C127C2×D411yescharacteristic
108C2×C8×C127#4111yescharacteristic
109C2×C8×C127#4111yescharacteristic
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C22⋊C4×C127—84no—
113C42×C127—21no—
114C42×C127—21no—
115C16×C127—22no—
116C16×C127—41no—
117C23×C127—41no—
118C23×C127—42no—
119C23×C127—82no—
120C23×C127—82no—
121C23×C127—81no—
122C23×C127—81no—
123C23×C127AGL(1,ℤ/8)11yescharacteristic
124Q8×C127—22no—
125Q8×C127—41no—
126D4×C127—22no—
127D4×C127—42no—
128D4×C127—42no—
129D4×C127—42no—
130D4×C127—41no—
131D4×C127—42no—
132D4×C127—81no—
133D4×C127—81no—
134C2×C4×C127—41no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—41no—
139C2×C4×C127—82no—
140C2×C4×C127—81no—
141C2×C4×C127C4×D411yescharacteristic
142C2×C4×C127#12011yescharacteristic
143C2×C4×C127#12111yescharacteristic
144C2×C4×C127C2×D811yescharacteristic
145C2×C4×C127#13511yescharacteristic
146C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
147C8×C127—22no—
148C8×C127—42no—
149C8×C127C2×C22⋊C411yescharacteristic
150C8×C127C4×D411yescharacteristic
151C8×C127#12111yescharacteristic
152C8×C127#12311yescharacteristic
153C22×C127—22no—
154C22×C127—42no—
155C22×C127—82no—
156C22×C127—82no—
157C22×C127—84no—
158C22×C127—162no—
159C22×C127—161no—
160C22×C127—161no—
161C22×C127#44211yescharacteristic
162C22×C127#44911yescharacteristic
163C22×C127#45911yescharacteristic
164C4×C127—42no—
165C4×C127—81no—
166C4×C127—161no—
167C4×C127#38611yescharacteristic
168C4×C127C4×D811yescharacteristic
169C4×C127#44711yescharacteristic
170C4×C127#46311yescharacteristic
171#13040C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127—21no—
173C2×C127—21no—
174C2×C127—82no—
175C2×C127—162no—
176C2×C127#187911yescharacteristic
177C2×C127AGL(1,ℤ/16)12yes—
178C2×#509C2×C12711yescharacteristic
179C2×#444C2×C12711yescharacteristic, complemented
180C2×#361C2×C12711yescharacteristic, complemented
181C2×#360C2×C12711yescharacteristic, complemented
182#1972C2×C12711yescharacteristic, complemented
183#1383C2×C12711yescharacteristic, complemented
184#1375C2×C12711yescharacteristic, complemented
185C127#1304011yescharacteristic, direct product factor, Sylow
186C2×#135C22×C12711yescharacteristic
187C22×D8C22×C12711yescharacteristic
188C2×#131—21no—
189#509—22no—
190#509—22no—
191C2×SD32C4×C12712yescomplemented
192C2×D16C4×C12712yescomplemented
193C2×M32C22×C12711yescharacteristic
194C2×M32C22×C12711yescharacteristic
195#444—22no—
196#444—22no—
197C2×#108C22×C12711yescharacteristic
198C2×#106C22×C12711yescharacteristic
199C2×#104—21no—
200C2×#102—21no—
201C2×#97C22×C12711yescharacteristic
202#390—21no—
203#361—22no—
204#360—22no—
205C2×#41—21no—
206C22×D4—21no—
207#135—21no—
208#135—21no—
209#135D4×C12712yes—
210#135D4×C12712yes—
211C2×Q16C2×C4×C12711yescharacteristic
212C2×SD16—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8C2×C4×C12712yes—
219C2×D8C2×C4×C12711yescharacteristic
220#131—24no—
221#131—42no—
222C2×M16—21no—
223C2×M16—41no—
224C22×C8—41no—
225C22×C8D4×C12711yescharacteristic
226C22×C8C23×C12711yescharacteristic
227C2×C4⋊C4—21no—
228C2×C22⋊C4—42no—
229C2×C42D4×C12711yescharacteristic
230SD32—24no—
231D16—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32—21no—
236C2×C16—21no—
237C2×C16C2×C4×C12712yes—
238#108—21no—
239#108D4×C12712yes—
240#106—21no—
241#106—21no—
242#104—24no—
243#102—42no—
244#97—21no—
245#97—21no—
246C24—41no—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C2×D4×C12711yescharacteristic
264Q16—21no—
265Q16C22⋊C4×C12712yescomplemented
266SD16—22no—
267SD16—22no—
268D8—22no—
269D8—21no—
270D8—22no—
271D8—41no—
272D8—41no—
273D8C22⋊C4×C12712yescomplemented
274M16—22no—
275M16—44no—
276M16—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—44no—
280C2×C8—41no—
281C2×C8D8×C12712yes—
282C2×C8C22×C4×C12711yescharacteristic
283C2×C8C2×D4×C12711yescharacteristic
284C2×C8C2×D4×C12711yescharacteristic
285C2×C8C2×D4×C12711yescharacteristic
286C2×C8#41×C12711yescharacteristic
287C2×C8#41×C12711yescharacteristic
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—84no—
291C42—21no—
292C42—21no—
293C16—22no—
294C16—41no—
295C23—41no—
296C23—42no—
297C23—82no—
298C23—82no—
299C23—81no—
300C23—81no—
301C23AGL(1,ℤ/8)×C12711yescharacteristic
302Q8—22no—
303Q8—41no—
304D4—22no—
305D4—42no—
306D4—42no—
307D4—42no—
308D4—41no—
309D4—42no—
310D4—81no—
311D4—81no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—82no—
318C2×C4—81no—
319C2×C4C4×D4×C12711yescharacteristic
320C2×C4#120×C12711yescharacteristic
321C2×C4#121×C12711yescharacteristic
322C2×C4C2×D8×C12711yescharacteristic
323C2×C4#135×C12711yescharacteristic
324C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
325C8—22no—
326C8—42no—
327C8C2×C22⋊C4×C12711yescharacteristic
328C8C4×D4×C12711yescharacteristic
329C8#121×C12711yescharacteristic
330C8#123×C12711yescharacteristic
331C22—22no—
332C22—42no—
333C22—82no—
334C22—82no—
335C22—84no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22#442×C12711yescharacteristic
340C22#449×C12711yescharacteristic
341C22#459×C12711yescharacteristic
342C4—42no—
343C4—81no—
344C4—161no—
345C4#386×C12711yescharacteristic
346C4C4×D8×C12711yescharacteristic
347C4#447×C12711yescharacteristic
348C4#463×C12711yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2—162no—
353C2C127×#187911yescharacteristic
354C2C127×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C127#442
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#444×C127C2semidirect
3. C2×#361×C127C2semidirect
4. C2×#360×C127C2semidirect
5. C127×#1972C2semidirect
6. C127×#1383C2semidirect
7. C127×#1375C2semidirect
13. C2×SD32×C127C4semidirect
14. C2×D16×C127C4semidirect
87. Q16×C127C22⋊C4semidirect
95. D8×C127C22⋊C4semidirect
171. #13040C127direct (N × H)
179. C2×#444C2×C127semidirect
180. C2×#361C2×C127semidirect
181. C2×#360C2×C127semidirect
182. #1972C2×C127semidirect
183. #1383C2×C127semidirect
184. #1375C2×C127semidirect
185. C127#13040direct (N × H)
191. C2×SD32C4×C127semidirect
192. C2×D16C4×C127semidirect
265. Q16C22⋊C4×C127semidirect
273. D8C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C2×#444×C1272
C2×#361×C1272
C2×#360×C1272
C127×#19722
C127×#13832
C127×#13752
#13040127