Finite Group Databasebeta

← C127×#13036 #44576709

Subgroups — C127×#13036 #44576709

Order 32512.

476 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic
2C127×#2957C211yesmaximal, characteristic, complemented
3C2×#361×C127C211yesmaximal, characteristic, complemented
4C127×#2143C211yesmaximal, characteristic, complemented
5C127×#1978C211yesmaximal, characteristic, complemented
6C127×#1385C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10#568×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#443×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#108×C127C2211yescharacteristic
21#421×C127—21no—
22#418×C127—21no—
23C2×#100×C127—21no—
24#405×C127C2211yescharacteristic
25#361×C127—22no—
26#359×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—21no—
46C2×M16×C127—42no—
47C2×M16×C127D411yescharacteristic
48C22×C8×C127C2311yescharacteristic
49#117×C127D411yescharacteristic
50SD32×C127—24no—
51D16×C127—24no—
52M32×C127—21no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56C2×C16×C127—21no—
57C2×C16×C127C2×C412yes—
58#108×C127—21no—
59#108×C127—21no—
60#108×C127—21no—
61#108×C127D412yes—
62#104×C127—24no—
63#102×C127—42no—
64#100×C127—42no—
65#97×C127—21no—
66C4×C8×C127—21no—
67C24×C127—41no—
68#41×C127—22no—
69#41×C127—22no—
70#41×C127—41no—
71#41×C127—41no—
72C2×Q8×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—22no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127C2×D411yescharacteristic
83Q16×C127—21no—
84Q16×C127C22⋊C412yes—
85SD16×C127—22no—
86SD16×C127—22no—
87D8×C127—22no—
88D8×C127—21no—
89D8×C127—22no—
90D8×C127—41no—
91D8×C127—41no—
92D8×C127C22⋊C412yes—
93M16×C127—21no—
94M16×C127—22no—
95M16×C127—44no—
96M16×C127—41no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127D812yes—
100C2×C8×C127—21no—
101C2×C8×C127—44no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
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—21no—
111C22⋊C4×C127—21no—
112C42×C127—21no—
113C16×C127—22no—
114C16×C127—41no—
115C23×C127—41no—
116C23×C127—42no—
117C23×C127—81no—
118C23×C127—81no—
119C23×C127—162no—
120C23×C127#13511yescharacteristic
121Q8×C127—22no—
122Q8×C127—41no—
123D4×C127—22no—
124D4×C127—42no—
125D4×C127—42no—
126D4×C127—42no—
127D4×C127—41no—
128D4×C127—42no—
129D4×C127—81no—
130D4×C127—81no—
131C2×C4×C127—41no—
132C2×C4×C127—42no—
133C2×C4×C127—42no—
134C2×C4×C127—41no—
135C2×C4×C127C4×D411yescharacteristic
136C2×C4×C127#12011yescharacteristic
137C2×C4×C127#12111yescharacteristic
138C2×C4×C127C2×D811yescharacteristic
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
141C8×C127—22no—
142C8×C127—42no—
143C8×C127—81no—
144C8×C127C2×C22⋊C411yescharacteristic
145C8×C127C4×D411yescharacteristic
146C8×C127#12111yescharacteristic
147C8×C127#12311yescharacteristic
148C22×C127—41no—
149C22×C127—42no—
150C22×C127—82no—
151C22×C127—161no—
152C22×C127—162no—
153C22×C127—162no—
154C22×C127—162no—
155C22×C127C4×D811yescharacteristic
156C22×C127#44911yescharacteristic
157C22×C127#46311yescharacteristic
158C4×C127—42no—
159C4×C127—81no—
160C4×C127#38611yescharacteristic
161C4×C127#44211yescharacteristic
162C4×C127#44711yescharacteristic
163C4×C127#45911yescharacteristic
164#13036C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127—21no—
168C2×C127—82no—
169C2×C127—162no—
170C2×C127#187911yescharacteristic
171C2×#509C2×C12711yescharacteristic
172#2957C2×C12711yescharacteristic, complemented
173C2×#361C2×C12711yescharacteristic, complemented
174#2143C2×C12711yescharacteristic, complemented
175#1978C2×C12711yescharacteristic, complemented
176#1385C2×C12711yescharacteristic, complemented
177#1378C2×C12711yescharacteristic, complemented
178C127#1303611yescharacteristic, direct product factor, Sylow
179C2×#135C22×C12711yescharacteristic
180C22×D8C22×C12711yescharacteristic
181#568—21no—
182#509—22no—
183#509—22no—
184C2×SD32C4×C12712yescomplemented
185C2×D16C4×C12712yescomplemented
186C2×M32C22×C12711yescharacteristic
187C2×M32C22×C12711yescharacteristic
188#444—22no—
189#443—22no—
190C2×#108C22×C12711yescharacteristic
191C2×#108C22×C12711yescharacteristic
192#421—21no—
193#418—21no—
194C2×#100—21no—
195#405C22×C12711yescharacteristic
196#361—22no—
197#359—22no—
198C2×#41—21no—
199C22×D4—21no—
200#135—21no—
201#135—21no—
202#135D4×C12712yes—
203#135D4×C12712yes—
204C2×Q16C2×C4×C12711yescharacteristic
205C2×SD16—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8C2×C4×C12712yes—
212C2×D8C2×C4×C12711yescharacteristic
213#131—24no—
214#131—42no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—42no—
218C2×M16D4×C12711yescharacteristic
219C22×C8C23×C12711yescharacteristic
220#117D4×C12711yescharacteristic
221SD32—24no—
222D16—24no—
223M32—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227C2×C16—21no—
228C2×C16C2×C4×C12712yes—
229#108—21no—
230#108—21no—
231#108—21no—
232#108D4×C12712yes—
233#104—24no—
234#102—42no—
235#100—42no—
236#97—21no—
237C4×C8—21no—
238C24—41no—
239#41—22no—
240#41—22no—
241#41—41no—
242#41—41no—
243C2×Q8—21no—
244C2×D4—21no—
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C22×C4—41no—
253C22×C4C2×D4×C12711yescharacteristic
254Q16—21no—
255Q16C22⋊C4×C12712yes—
256SD16—22no—
257SD16—22no—
258D8—22no—
259D8—21no—
260D8—22no—
261D8—41no—
262D8—41no—
263D8C22⋊C4×C12712yes—
264M16—21no—
265M16—22no—
266M16—44no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16D8×C12712yes—
271C2×C8—21no—
272C2×C8—44no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8C22×C4×C12711yescharacteristic
276C2×C8C2×D4×C12711yescharacteristic
277C2×C8C2×D4×C12711yescharacteristic
278C2×C8C2×D4×C12711yescharacteristic
279C2×C8#41×C12711yescharacteristic
280C2×C8#41×C12711yescharacteristic
281C4⋊C4—21no—
282C22⋊C4—21no—
283C42—21no—
284C16—22no—
285C16—41no—
286C23—41no—
287C23—42no—
288C23—81no—
289C23—81no—
290C23—162no—
291C23#135×C12711yescharacteristic
292Q8—22no—
293Q8—41no—
294D4—22no—
295D4—42no—
296D4—42no—
297D4—42no—
298D4—41no—
299D4—42no—
300D4—81no—
301D4—81no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4C4×D4×C12711yescharacteristic
307C2×C4#120×C12711yescharacteristic
308C2×C4#121×C12711yescharacteristic
309C2×C4C2×D8×C12711yescharacteristic
310C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
311C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
312C8—22no—
313C8—42no—
314C8—81no—
315C8C2×C22⋊C4×C12711yescharacteristic
316C8C4×D4×C12711yescharacteristic
317C8#121×C12711yescharacteristic
318C8#123×C12711yescharacteristic
319C22—41no—
320C22—42no—
321C22—82no—
322C22—161no—
323C22—162no—
324C22—162no—
325C22—162no—
326C22C4×D8×C12711yescharacteristic
327C22#449×C12711yescharacteristic
328C22#463×C12711yescharacteristic
329C4—42no—
330C4—81no—
331C4#386×C12711yescharacteristic
332C4#442×C12711yescharacteristic
333C4#447×C12711yescharacteristic
334C4#459×C12711yescharacteristic
335C2—21no—
336C2—21no—
337C2—21no—
338C2—82no—
339C2—162no—
340C2C127×#187911yescharacteristic
subgroupG/H
center, socleC2×C127#1879
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C2×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×#2957C2semidirect
3. C2×#361×C127C2semidirect
4. C127×#2143C2semidirect
5. C127×#1978C2semidirect
6. C127×#1385C2semidirect
7. C127×#1378C2semidirect
13. C2×SD32×C127C4semidirect
14. C2×D16×C127C4semidirect
164. #13036C127direct (N × H)
172. #2957C2×C127semidirect
173. C2×#361C2×C127semidirect
174. #2143C2×C127semidirect
175. #1978C2×C127semidirect
176. #1385C2×C127semidirect
177. #1378C2×C127semidirect
178. C127#13036direct (N × H)
184. C2×SD32C4×C127semidirect
185. C2×D16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C127×#29572
C2×#361×C1272
C127×#21432
C127×#19782
C127×#13852
C127×#13782
#13036127