Finite Group Databasebeta

← C127×#10035 #44573708

Subgroups — C127×#10035 #44573708

Order 32512.

498 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3135C211yesmaximal, characteristic
2C127×#3104C211yesmaximal, characteristic, complemented
3C127×#3103C211yesmaximal, characteristic
4C127×#1985C211yesmaximal, characteristic, complemented
5C127×#1481C211yesmaximal, characteristic, complemented
6C127×#1480C211yesmaximal, characteristic
7C127×#1275C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9#532×C127C2211yescharacteristic
10C2×C4×Q8×C127C2211yescharacteristic
11#491×C127—21no—
12#490×C127—21no—
13#489×C127—21no—
14#489×C127—21no—
15#484×C127—21no—
16#481×C127—21no—
17#477×C127—21no—
18#475×C127—21no—
19#462×C127—21no—
20#460×C127—21no—
21#451×C127—21no—
22#448×C127—21no—
23C4×Q16×C127—22no—
24C4×SD16×C127—22no—
25#431×C127C2211yescharacteristic
26#431×C127C2211yescharacteristic
27C2×C4⋊C8×C127C2211yescharacteristic
28#416×C127—22no—
29C2×#97×C127C2211yescharacteristic
30#336×C127—22no—
31Q8⋊C8×C127—22no—
32D4⋊C8×C127—22no—
33C2×#41×C127—21no—
34C22×Q8×C127D411yescharacteristic
35C2×Q16×C127—22no—
36C2×SD16×C127—22no—
37C22×C8×C127—21no—
38C22×C8×C127D412yes—
39C4⋊Q8×C127D411yescharacteristic
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42#127×C127D411yescharacteristic
43#125×C127—21no—
44#124×C127—21no—
45C22⋊Q8×C127—21no—
46C22⋊Q8×C127—21no—
47#121×C127—21no—
48#121×C127—21no—
49C4×Q8×C127—21no—
50C4×Q8×C127—21no—
51C4×Q8×C127—21no—
52C4×Q8×C127—21no—
53C4×Q8×C127—21no—
54C4×Q8×C127—21no—
55C4×D4×C127—21no—
56C4×D4×C127—21no—
57#117×C127—21no—
58C2×C4⋊C4×C127—21no—
59C2×C4⋊C4×C127D411yescharacteristic
60C2×C42×C127—21no—
61C2×C42×C127C2311yescharacteristic
62#107×C127—22no—
63#106×C127—22no—
64C4⋊C8×C127—21no—
65C4⋊C8×C127—21no—
66C4⋊C8×C127—21no—
67C4⋊C8×C127—21no—
68#103×C127—22no—
69#103×C127—22no—
70#103×C127—22no—
71#103×C127—22no—
72#103×C127—22no—
73#102×C127—22no—
74#102×C127—22no—
75#102×C127—22no—
76C22⋊C8×C127—21no—
77C22⋊C8×C127—21no—
78#97×C127—21no—
79#97×C127—21no—
80C4×C8×C127D412yes—
81C4×C8×C127D412yes—
82#41×C127—42no—
83#41×C127—42no—
84C2×Q8×C127—21no—
85C2×Q8×C127—21no—
86C2×Q8×C127—21no—
87C2×Q8×C127—21no—
88C2×Q8×C127—21no—
89C2×Q8×C127—42no—
90C2×D4×C127—21no—
91C2×D4×C127—21no—
92C2×D4×C127—21no—
93C2×D4×C127—41no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—41no—
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127#4111yescharacteristic
100Q16×C127—44no—
101SD16×C127—44no—
102C2×C8×C127—22no—
103C2×C8×C127—22no—
104C2×C8×C127—22no—
105C2×C8×C127—22no—
106C2×C8×C127—22no—
107C2×C8×C127—41no—
108C2×C8×C127—42no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C42×C127—41no—
125C42×C127—41no—
126C42×C127—41no—
127C42×C127C2×D411yescharacteristic
128C42×C127C2×D411yescharacteristic
129C42×C127C2×D411yescharacteristic
130C42×C127C2×D411yescharacteristic
131C23×C127—41no—
132C23×C127#12111yescharacteristic
133Q8×C127—22no—
134Q8×C127—22no—
135Q8×C127—41no—
136Q8×C127—41no—
137Q8×C127—42no—
138Q8×C127—42no—
139Q8×C127—42no—
140D4×C127—42no—
141D4×C127—42no—
142D4×C127—42no—
143D4×C127—82no—
144C2×C4×C127—22no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—42no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127#12011yescharacteristic
157C2×C4×C127#12011yescharacteristic
158C2×C4×C127#12011yescharacteristic
159C2×C4×C127#12111yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127#12711yescharacteristic
162C2×C4×C127#13512yes—
163C2×C4×C127#13712yes—
164C8×C127—42no—
165C8×C127—42no—
166C8×C127—42no—
167C8×C127—81no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127#39211yescharacteristic
174C22×C127#46412yes—
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—42no—
180C4×C127—81no—
181C4×C127—81no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127#45212yes—
185C4×C127#49511yescharacteristic
186C4×C127#49711yescharacteristic
187#10035C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—22no—
189C2×C127—161no—
190C2×C127#201011yescharacteristic
191C2×C127#201511yescharacteristic
192C2×C127#201711yescharacteristic
193#3135C2×C12711yescharacteristic
194#3104C2×C12711yescharacteristic, complemented
195#3103C2×C12711yescharacteristic
196#1985C2×C12711yescharacteristic, complemented
197#1481C2×C12711yescharacteristic, complemented
198#1480C2×C12711yescharacteristic
199#1275C2×C12711yescharacteristic, complemented
200C127#1003511yescharacteristic, direct product factor, Sylow
201#533C22×C12711yescharacteristic
202#532C22×C12711yescharacteristic
203C2×C4×Q8C22×C12711yescharacteristic
204#491—21no—
205#490—21no—
206#489—21no—
207#489—21no—
208#484—21no—
209#481—21no—
210#477—21no—
211#475—21no—
212#462—21no—
213#460—21no—
214#451—21no—
215#448—21no—
216C4×Q16—22no—
217C4×SD16—22no—
218#431C22×C12711yescharacteristic
219#431C22×C12711yescharacteristic
220C2×C4⋊C8C22×C12711yescharacteristic
221#416—22no—
222C2×#97C22×C12711yescharacteristic
223#336—22no—
224Q8⋊C8—22no—
225D4⋊C8—22no—
226C2×#41—21no—
227C22×Q8D4×C12711yescharacteristic
228C2×Q16—22no—
229C2×SD16—22no—
230C22×C8—21no—
231C22×C8D4×C12712yes—
232C4⋊Q8D4×C12711yescharacteristic
233C4⋊Q8D4×C12711yescharacteristic
234C4⋊Q8D4×C12711yescharacteristic
235#127D4×C12711yescharacteristic
236#125—21no—
237#124—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240#121—21no—
241#121—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×D4—21no—
249C4×D4—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C12711yescharacteristic
253C2×C42—21no—
254C2×C42C23×C12711yescharacteristic
255#107—22no—
256#106—22no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261#103—22no—
262#103—22no—
263#103—22no—
264#103—22no—
265#103—22no—
266#102—22no—
267#102—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271#97—21no—
272#97—21no—
273C4×C8D4×C12712yes—
274C4×C8D4×C12712yes—
275#41—42no—
276#41—42no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4C2×D4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292C22×C4#41×C12711yescharacteristic
293Q16—44no—
294SD16—44no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—42no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—41no—
318C42—41no—
319C42—41no—
320C42C2×D4×C12711yescharacteristic
321C42C2×D4×C12711yescharacteristic
322C42C2×D4×C12711yescharacteristic
323C42C2×D4×C12711yescharacteristic
324C23—41no—
325C23#121×C12711yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—41no—
329Q8—41no—
330Q8—42no—
331Q8—42no—
332Q8—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—82no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4#120×C12711yescharacteristic
350C2×C4#120×C12711yescharacteristic
351C2×C4#120×C12711yescharacteristic
352C2×C4#121×C12711yescharacteristic
353C2×C4#121×C12711yescharacteristic
354C2×C4#127×C12711yescharacteristic
355C2×C4#135×C12712yes—
356C2×C4#137×C12712yes—
357C8—42no—
358C8—42no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22#392×C12711yescharacteristic
367C22#464×C12712yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4#452×C12712yes—
378C4#495×C12711yescharacteristic
379C4#497×C12711yescharacteristic
380C2—22no—
381C2—161no—
382C2C127×#201011yescharacteristic
383C2C127×#201511yescharacteristic
384C2C127×#201711yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#392
prime radical#532×C127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3104C2semidirect
4. C127×#1985C2semidirect
5. C127×#1481C2semidirect
7. C127×#1275C2semidirect
187. #10035C127direct (N × H)
194. #3104C2×C127semidirect
196. #1985C2×C127semidirect
197. #1481C2×C127semidirect
199. #1275C2×C127semidirect
200. C127#10035direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31352
C127×#31042
C127×#31032
C127×#19852
C127×#14812
C127×#14802
C127×#12752
#10035127