Finite Group Databasebeta

← C127×#12140 #44575813

Subgroups — C127×#12140 #44575813

Order 32512.

478 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2680C211yesmaximal, characteristic, complemented
2C127×#2039C211yesmaximal, characteristic, complemented
3C127×#1604C211yesmaximal, characteristic, complemented
4C127×#1598C211yesmaximal, characteristic
5C127×#1354C211yesmaximal, characteristic, complemented
6C127×#1345C211yesmaximal, characteristic, complemented
7C127×#1325C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9C2×#123×C127—21no—
10C2×C22⋊Q8×C127—21no—
11#448×C127—21no—
12#447×C127—21no—
13C2×#104×C127—21no—
14#417×C127—21no—
15#398×C127—21no—
16#397×C127—21no—
17#395×C127C2211yescharacteristic
18#394×C127C2211yescharacteristic
19#388×C127—21no—
20#385×C127—21no—
21#384×C127C2211yescharacteristic
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C22×Q8×C127D411yescharacteristic
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—21no—
31C2×SD16×C127—41no—
32C2×D8×C127—41no—
33C2×M16×C127—21no—
34#123×C127—44no—
35C22⋊Q8×C127—44no—
36C22⋊Q8×C127—41no—
37#121×C127—21no—
38#121×C127—21no—
39#121×C127—41no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127D411yescharacteristic
46C2×C4⋊C4×C127C2311yescharacteristic
47C2×C22⋊C4×C127—21no—
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C42×C127D411yescharacteristic
53#104×C127—42no—
54#103×C127—41no—
55#103×C127—41no—
56#102×C127—41no—
57#102×C127—41no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127—21no—
63#95×C127D411yescharacteristic
64#95×C127D411yescharacteristic
65C24×C127—21no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70C2×Q8×C127—21no—
71C2×Q8×C127—42no—
72C2×Q8×C127—41no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—41no—
77C2×D4×C127—42no—
78C2×D4×C127—41no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—41no—
85C22×C4×C127—42no—
86C22×C4×C127—42no—
87C22×C4×C127—81no—
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127C2×D411yescharacteristic
91SD16×C127—82no—
92D8×C127—82no—
93M16×C127—41no—
94M16×C127—41no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—42no—
103C4⋊C4×C127—42no—
104C4⋊C4×C127—42no—
105C4⋊C4×C127—42no—
106C4⋊C4×C127—42no—
107C22⋊C4×C127—24no—
108C22⋊C4×C127—42no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—42no—
112C22⋊C4×C127—42no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C42×C127—21no—
116C42×C127—21no—
117C23×C127—22no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127#12011yescharacteristic
126Q8×C127—41no—
127Q8×C127—41no—
128Q8×C127—42no—
129Q8×C127—81no—
130D4×C127—41no—
131D4×C127—41no—
132D4×C127—42no—
133D4×C127—81no—
134D4×C127—81no—
135D4×C127—81no—
136D4×C127—81no—
137D4×C127—81no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—81no—
161C2×C4×C127—81no—
162C2×C4×C127—84no—
163C2×C4×C127#13511yescharacteristic
164C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
165C8×C127—81no—
166C8×C127—81no—
167C8×C127—81no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—42no—
171C22×C127—42no—
172C22×C127—42no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127#44911yescharacteristic
181C22×C127#45411yescharacteristic
182C22×C127B(4,𝔽2)11yescharacteristic
183C4×C127—21no—
184C4×C127—21no—
185C4×C127—42no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—42no—
189C4×C127—81no—
190C4×C127—81no—
191C4×C127—81no—
192C4×C127—81no—
193#12140C12711yesmaximal, characteristic, direct product factor, Sylow
194C2×C127—21no—
195C2×C127—21no—
196C2×C127—82no—
197C2×C127—161no—
198C2×C127#159711yescharacteristic
199C2×C127#219611yescharacteristic
200C2×C127#220311yescharacteristic
201#2680C2×C12711yescharacteristic, complemented
202#2039C2×C12711yescharacteristic, complemented
203#1604C2×C12711yescharacteristic, complemented
204#1598C2×C12711yescharacteristic
205#1354C2×C12711yescharacteristic, complemented
206#1345C2×C12711yescharacteristic, complemented
207#1325C2×C12711yescharacteristic, complemented
208C127#1214011yescharacteristic, direct product factor, Sylow
209#537C22×C12711yescharacteristic
210C2×#123—21no—
211C2×C22⋊Q8—21no—
212#448—21no—
213#447—21no—
214C2×#104—21no—
215#417—21no—
216#398—21no—
217#397—21no—
218#395C22×C12711yescharacteristic
219#394C22×C12711yescharacteristic
220#388—21no—
221#385—21no—
222#384C22×C12711yescharacteristic
223#343C22×C12711yescharacteristic
224#327—21no—
225#327—21no—
226#324C22×C12711yescharacteristic
227#324C22×C12711yescharacteristic
228C2×#41—21no—
229C22×Q8D4×C12711yescharacteristic
230C22×D4D4×C12711yescharacteristic
231C23×C4—21no—
232C2×SD16—41no—
233C2×D8—41no—
234C2×M16—21no—
235#123—44no—
236C22⋊Q8—44no—
237C22⋊Q8—41no—
238#121—21no—
239#121—21no—
240#121—41no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C12711yescharacteristic
247C2×C4⋊C4C23×C12711yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42D4×C12711yescharacteristic
254#104—42no—
255#103—41no—
256#103—41no—
257#102—41no—
258#102—41no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95D4×C12711yescharacteristic
265#95D4×C12711yescharacteristic
266C24—21no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—81no—
289C22×C4C2×D4×C12711yescharacteristic
290C22×C4C2×D4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292SD16—82no—
293D8—82no—
294M16—41no—
295M16—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C22⋊C4—24no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—21no—
317C42—21no—
318C23—22no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23#120×C12711yescharacteristic
327Q8—41no—
328Q8—41no—
329Q8—42no—
330Q8—81no—
331D4—41no—
332D4—41no—
333D4—42no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—84no—
364C2×C4#135×C12711yescharacteristic
365C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
366C8—81no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22#449×C12711yescharacteristic
382C22#454×C12711yescharacteristic
383C22B(4,𝔽2)×C12711yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2C127×#159711yescharacteristic
399C2C127×#219611yescharacteristic
400C2C127×#220311yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2680C2semidirect
2. C127×#2039C2semidirect
3. C127×#1604C2semidirect
5. C127×#1354C2semidirect
6. C127×#1345C2semidirect
7. C127×#1325C2semidirect
193. #12140C127direct (N × H)
201. #2680C2×C127semidirect
202. #2039C2×C127semidirect
203. #1604C2×C127semidirect
205. #1354C2×C127semidirect
206. #1345C2×C127semidirect
207. #1325C2×C127semidirect
208. C127#12140direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26802
C127×#20392
C127×#16042
C127×#15982
C127×#13542
C127×#13452
C127×#13252
#12140127