Finite Group Databasebeta

← C127×#11880 #44575553

Subgroups — C127×#11880 #44575553

Order 32512.

764 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2408C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic, complemented
3C127×#1459C211yesmaximal, characteristic, complemented
4C127×#1345C214yesmaximal, complemented
5C23×D4×C127C411yescharacteristic
6C2×#121×C127—21no—
7C2×#120×C127—21no—
8C2×C4×D4×C127C2211yescharacteristic
9#423×C127—21no—
10C2×#100×C127—21no—
11C2×C22⋊C8×C127—21no—
12#394×C127C2212yes—
13#392×C127C412yes—
14#390×C127—21no—
15#380×C127C411yescharacteristic
16#379×C127—21no—
17#343×C127C2212yescomplemented
18#324×C127C2212yescomplemented
19#323×C127—21no—
20C25×C127—21no—
21C22×D4×C127—22no—
22C22×D4×C127—21no—
23C22×D4×C127—41no—
24C22×D4×C127—41no—
25C22×D4×C127—44no—
26C22×D4×C127C2×C412yes—
27C22×D4×C127D411yescharacteristic
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C2×M16×C127—22no—
31C22×C8×C127—41no—
32#121×C127—44no—
33#120×C127—42no—
34#120×C127—42no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—41no—
47C4⋊C8×C127—41no—
48#100×C127—42no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—41no—
51#95×C127C2×C412yes—
52C24×C127—22no—
53C24×C127—42no—
54C24×C127—44no—
55C24×C127—42no—
56C24×C127—42no—
57C24×C127—82no—
58C24×C127C22⋊C411yescharacteristic
59C24×C127C22⋊C411yescharacteristic
60C2×D4×C127—24no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127—42no—
64C2×D4×C127—42no—
65C2×D4×C127—48no—
66C2×D4×C127—44no—
67C2×D4×C127—44no—
68C2×D4×C127—44no—
69C2×D4×C127—44no—
70C2×D4×C127—44no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—82no—
74C2×D4×C127D812yes—
75C2×D4×C127SD1612yes—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—22no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22×C411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88M16×C127—42no—
89M16×C127—42no—
90C2×C8×C127—42no—
91C2×C8×C127—42no—
92C2×C8×C127—82no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—42no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—44no—
98C22⋊C4×C127—42no—
99C22⋊C4×C127—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—82no—
102C42×C127—21no—
103C42×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—24no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—42no—
114C23×C127—42no—
115C23×C127—42no—
116C23×C127—48no—
117C23×C127—42no—
118C23×C127—42no—
119C23×C127—42no—
120C23×C127—84no—
121C23×C127—88no—
122C23×C127—88no—
123C23×C127—84no—
124C23×C127#10212yes—
125C23×C127#10212yes—
126C23×C127C2×C22⋊C411yescharacteristic
127D4×C127—42no—
128D4×C127—42no—
129D4×C127—44no—
130D4×C127—44no—
131D4×C127—44no—
132D4×C127—44no—
133D4×C127—88no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—22no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—81no—
150C2×C4×C127#9911yescharacteristic
151C2×C4×C127#9911yescharacteristic
152C2×C4×C127C2×D811yescharacteristic
153C2×C4×C127C2×SD1611yescharacteristic
154C8×C127—82no—
155C8×C127—82no—
156C22×C127—21no—
157C22×C127—21no—
158C22×C127—22no—
159C22×C127—22no—
160C22×C127—42no—
161C22×C127—42no—
162C22×C127—42no—
163C22×C127—44no—
164C22×C127—44no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127—44no—
170C22×C127—81no—
171C22×C127—82no—
172C22×C127—82no—
173C22×C127—816no—
174C22×C127—82no—
175C22×C127—82no—
176C22×C127C2×#9911yescharacteristic
177C22×C127C2×#10211yescharacteristic
178C22×C127#42111yescharacteristic
179C4×C127—21no—
180C4×C127—21no—
181C4×C127—21no—
182C4×C127—41no—
183C4×C127—41no—
184C4×C127—41no—
185C4×C127—82no—
186C4×C127AΣL(1,𝔽16)12yes—
187#11880C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—21no—
189C2×C127—21no—
190C2×C127—42no—
191C2×C127—42no—
192C2×C127—84no—
193C2×C127#151911yescharacteristic
194C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
195C2×C127#213411yescharacteristic
196#2408C2×C12711yescharacteristic
197#1800C2×C12711yescharacteristic, complemented
198#1459C2×C12711yescharacteristic, complemented
199#1345C2×C12714yescomplemented
200C127#1188011yescharacteristic, direct product factor, Sylow
201C23×D4C4×C12711yescharacteristic
202C2×#121—21no—
203C2×#120—21no—
204C2×C4×D4C22×C12711yescharacteristic
205#423—21no—
206C2×#100—21no—
207C2×C22⋊C8—21no—
208#394C22×C12712yes—
209#392C4×C12712yes—
210#390—21no—
211#380C4×C12711yescharacteristic
212#379—21no—
213#343C22×C12712yescomplemented
214#324C22×C12712yescomplemented
215#323—21no—
216C25—21no—
217C22×D4—22no—
218C22×D4—21no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—44no—
222C22×D4C2×C4×C12712yes—
223C22×D4D4×C12711yescharacteristic
224C23×C4C2×C4×C12711yescharacteristic
225C23×C4D4×C12711yescharacteristic
226C2×M16—22no—
227C22×C8—41no—
228#121—44no—
229#120—42no—
230#120—42no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C23×C12711yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4C2×C4×C12711yescharacteristic
240C2×C22⋊C4D4×C12711yescharacteristic
241C2×C42D4×C12711yescharacteristic
242C4⋊C8—41no—
243C4⋊C8—41no—
244#100—42no—
245C22⋊C8—22no—
246C22⋊C8—41no—
247#95C2×C4×C12712yes—
248C24—22no—
249C24—42no—
250C24—44no—
251C24—42no—
252C24—42no—
253C24—82no—
254C24C22⋊C4×C12711yescharacteristic
255C24C22⋊C4×C12711yescharacteristic
256C2×D4—24no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—48no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—82no—
270C2×D4D8×C12712yes—
271C2×D4SD16×C12712yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C22⋊C4×C12711yescharacteristic
280C22×C4C22⋊C4×C12711yescharacteristic
281C22×C4C22×C4×C12711yescharacteristic
282C22×C4C2×D4×C12711yescharacteristic
283C22×C4C2×D4×C12711yescharacteristic
284M16—42no—
285M16—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—82no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—44no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—82no—
298C42—21no—
299C42—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—48no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—84no—
317C23—88no—
318C23—88no—
319C23—84no—
320C23#102×C12712yes—
321C23#102×C12712yes—
322C23C2×C22⋊C4×C12711yescharacteristic
323D4—42no—
324D4—42no—
325D4—44no—
326D4—44no—
327D4—44no—
328D4—44no—
329D4—88no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4#99×C12711yescharacteristic
347C2×C4#99×C12711yescharacteristic
348C2×C4C2×D8×C12711yescharacteristic
349C2×C4C2×SD16×C12711yescharacteristic
350C8—82no—
351C8—82no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—44no—
360C22—44no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—44no—
366C22—81no—
367C22—82no—
368C22—82no—
369C22—816no—
370C22—82no—
371C22—82no—
372C22C2×#99×C12711yescharacteristic
373C22C2×#102×C12711yescharacteristic
374C22#421×C12711yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4AΣL(1,𝔽16)×C12712yes—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—42no—
387C2—84no—
388C2C127×#151911yescharacteristic
389C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
390C2C127×#213411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#2408C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1800C2semidirect
3. C127×#1459C2semidirect
4. C127×#1345C2semidirect
17. #343×C127C22semidirect
18. #324×C127C22semidirect
187. #11880C127direct (N × H)
197. #1800C2×C127semidirect
198. #1459C2×C127semidirect
199. #1345C2×C127semidirect
200. C127#11880direct (N × H)
213. #343C22×C127semidirect
214. #324C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24082
C127×#18002
C127×#14592
C127×#13452
#11880127