Finite Group Databasebeta

← C127×#10501 #44574174

Subgroups — C127×#10501 #44574174

Order 32512.

440 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3206C211yesmaximal, characteristic
2C127×#1997C211yesmaximal, characteristic, complemented
3C127×#1981C211yesmaximal, characteristic, complemented
4C127×#1980C211yesmaximal, characteristic
5C127×#1565C211yesmaximal, characteristic, complemented
6C127×#1547C211yesmaximal, characteristic
7C127×#1303C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#492×C127—21no—
11#487×C127—21no—
12#461×C127—21no—
13#461×C127—21no—
14#448×C127—22no—
15#431×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#104×C127—21no—
19C2×#104×C127—21no—
20C2×#103×C127—22no—
21C4×M16×C127C2211yescharacteristic
22C4×C4⋊C4×C127C2211yescharacteristic
23#343×C127—21no—
24#343×C127—21no—
25#335×C127—21no—
26#334×C127—21no—
27#332×C127—21no—
28#331×C127—21no—
29C2×#41×C127—21no—
30C22×Q8×C127D412yes—
31C2×SD16×C127—22no—
32C2×SD16×C127—22no—
33C2×M16×C127—21no—
34C2×M16×C127D411yescharacteristic
35C2×M16×C127D411yescharacteristic
36C22×C8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127—21no—
41C4⋊Q8×C127D411yescharacteristic
42#127×C127D411yescharacteristic
43#124×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59#104×C127—42no—
60#104×C127—42no—
61#103×C127—22no—
62#103×C127—22no—
63#103×C127—44no—
64C22⋊C8×C127—21no—
65#97×C127—21no—
66C4×C8×C127—21no—
67C4×C8×C127—21no—
68#95×C127—21no—
69#41×C127—41no—
70#41×C127—41no—
71#41×C127—41no—
72#41×C127—41no—
73C2×Q8×C127—22no—
74C2×Q8×C127—21no—
75C2×Q8×C127—22no—
76C2×Q8×C127—42no—
77C2×Q8×C127—42no—
78C2×D4×C127—21no—
79C2×D4×C127—21no—
80C2×D4×C127—21no—
81C2×D4×C127—41no—
82C22×C4×C127—22no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C22×C4×C127#4111yescharacteristic
88SD16×C127—82no—
89SD16×C127—82no—
90M16×C127—21no—
91M16×C127—21no—
92M16×C127—21no—
93M16×C127—41no—
94M16×C127—41no—
95M16×C127SD1612yescomplemented
96C2×C8×C127—21no—
97C2×C8×C127—21no—
98C2×C8×C127—21no—
99C2×C8×C127—21no—
100C2×C8×C127—42no—
101C2×C8×C127—41no—
102C2×C8×C127—41no—
103C4⋊C4×C127—22no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127—21no—
106C4⋊C4×C127—41no—
107C4⋊C4×C127—41no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C42×C127—41no—
114C42×C127—41no—
115C42×C127C2×D411yescharacteristic
116C42×C127C2×D411yescharacteristic
117C42×C127#4111yescharacteristic
118C42×C127#4111yescharacteristic
119C23×C127—41no—
120C23×C127#12111yescharacteristic
121Q8×C127—44no—
122Q8×C127—42no—
123Q8×C127—42no—
124Q8×C127—41no—
125Q8×C127—41no—
126D4×C127—41no—
127D4×C127—41no—
128D4×C127—41no—
129D4×C127—41no—
130D4×C127—81no—
131D4×C127—81no—
132D4×C127—81no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—41no—
136C2×C4×C127—42no—
137C2×C4×C127—41no—
138C2×C4×C127—42no—
139C2×C4×C127—81no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127—82no—
144C2×C4×C127#12011yescharacteristic
145C2×C4×C127#12111yescharacteristic
146C2×C4×C127#12111yescharacteristic
147C2×C4×C127#12311yescharacteristic
148C2×C4×C127#12311yescharacteristic
149C2×C4×C127#12411yescharacteristic
150C2×C4×C127C2×SD1611yescharacteristic
151C2×C4×C127#13511yescharacteristic
152C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C127#13711yescharacteristic
154C8×C127—22no—
155C8×C127—41no—
156C8×C127—41no—
157C8×C127—41no—
158C8×C127—81no—
159C8×C127—81no—
160C22×C127—21no—
161C22×C127—21no—
162C22×C127—81no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127#39411yescharacteristic
166C22×C127#46011yescharacteristic
167C22×C127#46411yescharacteristic
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—21no—
171C4×C127—82no—
172C4×C127—81no—
173C4×C127—82no—
174C4×C127#45311yescharacteristic
175C4×C127#45511yescharacteristic
176C4×C127#46111yescharacteristic
177C4×C127#46311yescharacteristic
178C4×C127#46511yescharacteristic
179C4×C127#46811yescharacteristic
180#10501C12711yesmaximal, characteristic, direct product factor, Sylow
181C2×C127—21no—
182C2×C127—21no—
183C2×C127—161no—
184C2×C127#203711yescharacteristic
185C2×C127#204911yescharacteristic
186C2×C127#205511yescharacteristic
187#3206C2×C12711yescharacteristic
188#1997C2×C12711yescharacteristic, complemented
189#1981C2×C12711yescharacteristic, complemented
190#1980C2×C12711yescharacteristic
191#1565C2×C12711yescharacteristic, complemented
192#1547C2×C12711yescharacteristic
193#1303C2×C12711yescharacteristic, complemented
194C127#1050111yescharacteristic, direct product factor, Sylow
195#532C22×C12711yescharacteristic
196C2×C4⋊Q8C22×C12711yescharacteristic
197#492—21no—
198#487—21no—
199#461—21no—
200#461—21no—
201#448—22no—
202#431C22×C12711yescharacteristic
203#423C22×C12711yescharacteristic
204C2×C4⋊C8C22×C12711yescharacteristic
205C2×#104—21no—
206C2×#104—21no—
207C2×#103—22no—
208C4×M16C22×C12711yescharacteristic
209C4×C4⋊C4C22×C12711yescharacteristic
210#343—21no—
211#343—21no—
212#335—21no—
213#334—21no—
214#332—21no—
215#331—21no—
216C2×#41—21no—
217C22×Q8D4×C12712yes—
218C2×SD16—22no—
219C2×SD16—22no—
220C2×M16—21no—
221C2×M16D4×C12711yescharacteristic
222C2×M16D4×C12711yescharacteristic
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C12711yescharacteristic
229#127D4×C12711yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42C23×C12711yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8D4×C12711yescharacteristic
245C4⋊C8D4×C12711yescharacteristic
246#104—42no—
247#104—42no—
248#103—22no—
249#103—22no—
250#103—44no—
251C22⋊C8—21no—
252#97—21no—
253C4×C8—21no—
254C4×C8—21no—
255#95—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×D4×C12711yescharacteristic
273C22×C4C2×D4×C12711yescharacteristic
274C22×C4#41×C12711yescharacteristic
275SD16—82no—
276SD16—82no—
277M16—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16SD16×C12712yescomplemented
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—42no—
288C2×C8—41no—
289C2×C8—41no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—41no—
301C42—41no—
302C42C2×D4×C12711yescharacteristic
303C42C2×D4×C12711yescharacteristic
304C42#41×C12711yescharacteristic
305C42#41×C12711yescharacteristic
306C23—41no—
307C23#121×C12711yescharacteristic
308Q8—44no—
309Q8—42no—
310Q8—42no—
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4#120×C12711yescharacteristic
332C2×C4#121×C12711yescharacteristic
333C2×C4#121×C12711yescharacteristic
334C2×C4#123×C12711yescharacteristic
335C2×C4#123×C12711yescharacteristic
336C2×C4#124×C12711yescharacteristic
337C2×C4C2×SD16×C12711yescharacteristic
338C2×C4#135×C12711yescharacteristic
339C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
340C2×C4#137×C12711yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#394×C12711yescharacteristic
353C22#460×C12711yescharacteristic
354C22#464×C12711yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—81no—
361C4#453×C12711yescharacteristic
362C4#455×C12711yescharacteristic
363C4#461×C12711yescharacteristic
364C4#463×C12711yescharacteristic
365C4#465×C12711yescharacteristic
366C4#468×C12711yescharacteristic
367C2—21no—
368C2—21no—
369C2—161no—
370C2C127×#203711yescharacteristic
371C2C127×#204911yescharacteristic
372C2C127×#205511yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1997C2semidirect
3. C127×#1981C2semidirect
5. C127×#1565C2semidirect
7. C127×#1303C2semidirect
95. M16×C127SD16semidirect
180. #10501C127direct (N × H)
188. #1997C2×C127semidirect
189. #1981C2×C127semidirect
191. #1565C2×C127semidirect
193. #1303C2×C127semidirect
194. C127#10501direct (N × H)
282. M16SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32062
C127×#19972
C127×#19812
C127×#19802
C127×#15652
C127×#15472
C127×#13032
#10501127