Finite Group Databasebeta

← C127×#10503 #44574176

Subgroups — C127×#10503 #44574176

Order 32512.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3226C211yesmaximal, characteristic
2C127×#1988C211yesmaximal, characteristic, complemented
3C127×#1980C211yesmaximal, characteristic
4C127×#1966C211yesmaximal, characteristic, complemented
5C127×#1565C211yesmaximal, characteristic, complemented
6C127×#1547C211yesmaximal, characteristic
7C127×#1303C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#500×C127—21no—
11#486×C127—21no—
12#480×C127—22no—
13#474×C127—21no—
14#474×C127—21no—
15#431×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#104×C127—21no—
19C2×#104×C127—21no—
20C2×#101×C127—21no—
21C2×#101×C127—21no—
22C4×M16×C127C2211yescharacteristic
23C4×C4⋊C4×C127C2211yescharacteristic
24#340×C127—22no—
25#335×C127—21no—
26#334×C127—21no—
27#332×C127—21no—
28#331×C127—21no—
29C2×#41×C127—21no—
30C22×Q8×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127D411yescharacteristic
33C2×M16×C127D411yescharacteristic
34C22×C8×C127—21no—
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127D411yescharacteristic
40#127×C127D411yescharacteristic
41#124×C127—21no—
42#121×C127—21no—
43#121×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D412yes—
49C2×C42×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#107×C127—22no—
52#107×C127—22no—
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#102×C127—22no—
62#102×C127—22no—
63#101×C127—42no—
64#101×C127—42no—
65C22⋊C8×C127—21no—
66#97×C127—21no—
67C4×C8×C127—21no—
68C4×C8×C127—21no—
69#95×C127—21no—
70#41×C127—41no—
71#41×C127—41no—
72#41×C127—41no—
73#41×C127—41no—
74C2×Q8×C127—21no—
75C2×Q8×C127—41no—
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—21no—
83C2×D4×C127—21no—
84C2×D4×C127—41no—
85C22×C4×C127—22no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127#4111yescharacteristic
91M16×C127—21no—
92M16×C127—21no—
93M16×C127—21no—
94M16×C127—41no—
95M16×C127—41no—
96M16×C127D812yes—
97C2×C8×C127—21no—
98C2×C8×C127—21no—
99C2×C8×C127—21no—
100C2×C8×C127—21no—
101C2×C8×C127—42no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C4⋊C4×C127—22no—
105C4⋊C4×C127—22no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—22no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C42×C127—41no—
115C42×C127—41no—
116C42×C127C2×D411yescharacteristic
117C42×C127C2×D411yescharacteristic
118C42×C127#4111yescharacteristic
119C42×C127#4111yescharacteristic
120C23×C127—41no—
121C23×C127#12111yescharacteristic
122Q8×C127—41no—
123Q8×C127—41no—
124Q8×C127—81no—
125Q8×C127—81no—
126Q8×C127—81no—
127Q8×C127—81no—
128D4×C127—41no—
129D4×C127—41no—
130D4×C127—41no—
131D4×C127—41no—
132D4×C127—81no—
133D4×C127—81no—
134D4×C127—81no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—41no—
138C2×C4×C127—42no—
139C2×C4×C127—41no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127—81no—
146C2×C4×C127—81no—
147C2×C4×C127#12011yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127#12111yescharacteristic
150C2×C4×C127#12311yescharacteristic
151C2×C4×C127#12311yescharacteristic
152C2×C4×C127#12411yescharacteristic
153C2×C4×C127C2×D811yescharacteristic
154C2×C4×C127#13511yescharacteristic
155C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
157C8×C127—22no—
158C8×C127—41no—
159C8×C127—41no—
160C8×C127—41no—
161C8×C127—81no—
162C8×C127—81no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127#39411yescharacteristic
169C22×C127#45911yescharacteristic
170C22×C127#46311yescharacteristic
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—82no—
175C4×C127—82no—
176C4×C127—81no—
177C4×C127#45411yescharacteristic
178C4×C127#45611yescharacteristic
179C4×C127#45911yescharacteristic
180C4×C127#46311yescharacteristic
181C4×C127#46611yescharacteristic
182C4×C127#46911yescharacteristic
183#10503C12711yesmaximal, characteristic, direct product factor, Sylow
184C2×C127—21no—
185C2×C127—21no—
186C2×C127—161no—
187C2×C127#203811yescharacteristic
188C2×C127#204911yescharacteristic
189C2×C127#205411yescharacteristic
190#3226C2×C12711yescharacteristic
191#1988C2×C12711yescharacteristic, complemented
192#1980C2×C12711yescharacteristic
193#1966C2×C12711yescharacteristic, complemented
194#1565C2×C12711yescharacteristic, complemented
195#1547C2×C12711yescharacteristic
196#1303C2×C12711yescharacteristic, complemented
197C127#1050311yescharacteristic, direct product factor, Sylow
198#532C22×C12711yescharacteristic
199C2×C4⋊Q8C22×C12711yescharacteristic
200#500—21no—
201#486—21no—
202#480—22no—
203#474—21no—
204#474—21no—
205#431C22×C12711yescharacteristic
206#423C22×C12711yescharacteristic
207C2×C4⋊C8C22×C12711yescharacteristic
208C2×#104—21no—
209C2×#104—21no—
210C2×#101—21no—
211C2×#101—21no—
212C4×M16C22×C12711yescharacteristic
213C4×C4⋊C4C22×C12711yescharacteristic
214#340—22no—
215#335—21no—
216#334—21no—
217#332—21no—
218#331—21no—
219C2×#41—21no—
220C22×Q8—21no—
221C2×M16—21no—
222C2×M16D4×C12711yescharacteristic
223C2×M16D4×C12711yescharacteristic
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C12711yescharacteristic
230#127D4×C12711yescharacteristic
231#124—21no—
232#121—21no—
233#121—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C12712yes—
239C2×C42—21no—
240C2×C42C23×C12711yescharacteristic
241#107—22no—
242#107—22no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C12711yescharacteristic
248C4⋊C8D4×C12711yescharacteristic
249#104—42no—
250#104—42no—
251#102—22no—
252#102—22no—
253#101—42no—
254#101—42no—
255C22⋊C8—21no—
256#97—21no—
257C4×C8—21no—
258C4×C8—21no—
259#95—21no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C12711yescharacteristic
279C22×C4C2×D4×C12711yescharacteristic
280C22×C4#41×C12711yescharacteristic
281M16—21no—
282M16—21no—
283M16—21no—
284M16—41no—
285M16—41no—
286M16D8×C12712yes—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—42no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C42—41no—
305C42—41no—
306C42C2×D4×C12711yescharacteristic
307C42C2×D4×C12711yescharacteristic
308C42#41×C12711yescharacteristic
309C42#41×C12711yescharacteristic
310C23—41no—
311C23#121×C12711yescharacteristic
312Q8—41no—
313Q8—41no—
314Q8—81no—
315Q8—81no—
316Q8—81no—
317Q8—81no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#120×C12711yescharacteristic
338C2×C4#121×C12711yescharacteristic
339C2×C4#121×C12711yescharacteristic
340C2×C4#123×C12711yescharacteristic
341C2×C4#123×C12711yescharacteristic
342C2×C4#124×C12711yescharacteristic
343C2×C4C2×D8×C12711yescharacteristic
344C2×C4#135×C12711yescharacteristic
345C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
346C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
347C8—22no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22#394×C12711yescharacteristic
359C22#459×C12711yescharacteristic
360C22#463×C12711yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—82no—
366C4—81no—
367C4#454×C12711yescharacteristic
368C4#456×C12711yescharacteristic
369C4#459×C12711yescharacteristic
370C4#463×C12711yescharacteristic
371C4#466×C12711yescharacteristic
372C4#469×C12711yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C127×#203811yescharacteristic
377C2C127×#204911yescharacteristic
378C2C127×#205411yescharacteristic
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×#1988C2semidirect
4. C127×#1966C2semidirect
5. C127×#1565C2semidirect
7. C127×#1303C2semidirect
183. #10503C127direct (N × H)
191. #1988C2×C127semidirect
193. #1966C2×C127semidirect
194. #1565C2×C127semidirect
196. #1303C2×C127semidirect
197. C127#10503direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32262
C127×#19882
C127×#19802
C127×#19662
C127×#15652
C127×#15472
C127×#13032
#10503127