Finite Group Databasebeta

← C127×#11873 #44575546

Subgroups — C127×#11873 #44575546

Order 32512.

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

normal subgroups only

This group has 776 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×#1799C211yesmaximal, characteristic, complemented
3C127×#1460C211yesmaximal, characteristic, complemented
4C127×#1343C214yesmaximal, complemented
5C23×D4×C127C411yescharacteristic, complemented
6C2×#121×C127—21no—
7C2×#120×C127—21no—
8C2×C4×D4×C127C2211yescharacteristic
9#431×C127—21no—
10C2×#99×C127—21no—
11#394×C127C412yescomplemented
12#392×C127C2212yes—
13#390×C127—21no—
14#380×C127—21no—
15#380×C127C411yescharacteristic, complemented
16#379×C127—21no—
17#342×C127C2212yescomplemented
18#323×C127—21no—
19#323×C127C2212yescomplemented
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
30#121×C127—44no—
31#120×C127—42no—
32#120×C127—42no—
33C4×D4×C127—41no—
34C4×D4×C127—41no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C22⋊C4×C127C2311yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—41no—
47#99×C127—42no—
48C22⋊C8×C127—22no—
49C4×C8×C127—41no—
50#95×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×C127C2×D411yescharacteristic
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—42no—
71C2×D4×C127—42no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—82no—
75C2×D4×C127D812yes—
76C2×D4×C127SD1612yes—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—22no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—42no—
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22⋊C411yescharacteristic
88C22×C4×C127C22×C411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C2×C8×C127—42no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—82no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—44no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—44no—
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×C127C2×C22⋊C411yescharacteristic
126C23×C127C2×D811yescharacteristic
127C23×C127C2×SD1611yescharacteristic
128D4×C127—42no—
129D4×C127—42no—
130D4×C127—44no—
131D4×C127—44no—
132D4×C127—44no—
133D4×C127—44no—
134D4×C127—84no—
135D4×C127—84no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—22no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—81no—
152C2×C4×C127—82no—
153C2×C4×C127—82no—
154C2×C4×C127—82no—
155C2×C4×C127#9911yescharacteristic
156C2×C4×C127#9911yescharacteristic
157C2×C4×C127#10212yes—
158C8×C127—82no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—21no—
162C22×C127—22no—
163C22×C127—21no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—42no—
167C22×C127—42no—
168C22×C127—44no—
169C22×C127—44no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—44no—
175C22×C127—81no—
176C22×C127—82no—
177C22×C127—82no—
178C22×C127—816no—
179C22×C127—82no—
180C22×C127—82no—
181C22×C127C2×#9911yescharacteristic
182C22×C127C2×#10211yescharacteristic
183C22×C127#42111yescharacteristic
184C4×C127—21no—
185C4×C127—22no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—41no—
189C4×C127—82no—
190C4×C127—162no—
191C4×C127AΣL(1,𝔽16)12yes—
192#11873C12711yesmaximal, characteristic, direct product factor, Sylow
193C2×C127—21no—
194C2×C127—21no—
195C2×C127—41no—
196C2×C127—42no—
197C2×C127—41no—
198C2×C127—84no—
199C2×C127#151911yescharacteristic
200C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
201C2×C127#212811yescharacteristic
202#2408C2×C12711yescharacteristic
203#1799C2×C12711yescharacteristic, complemented
204#1460C2×C12711yescharacteristic, complemented
205#1343C2×C12714yescomplemented
206C127#1187311yescharacteristic, direct product factor, Sylow
207C23×D4C4×C12711yescharacteristic, complemented
208C2×#121—21no—
209C2×#120—21no—
210C2×C4×D4C22×C12711yescharacteristic
211#431—21no—
212C2×#99—21no—
213#394C4×C12712yescomplemented
214#392C22×C12712yes—
215#390—21no—
216#380—21no—
217#380C4×C12711yescharacteristic, complemented
218#379—21no—
219#342C22×C12712yescomplemented
220#323—21no—
221#323C22×C12712yescomplemented
222C25—21no—
223C22×D4—22no—
224C22×D4—21no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—44no—
228C22×D4C2×C4×C12712yes—
229C22×D4D4×C12711yescharacteristic
230C23×C4C2×C4×C12711yescharacteristic
231C23×C4D4×C12711yescharacteristic
232#121—44no—
233#120—42no—
234#120—42no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4C2×C4×C12711yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4D4×C12711yescharacteristic
246C2×C22⋊C4C23×C12711yescharacteristic
247C2×C42D4×C12711yescharacteristic
248C4⋊C8—41no—
249#99—42no—
250C22⋊C8—22no—
251C4×C8—41no—
252#95—41no—
253#95C2×C4×C12712yes—
254C24—22no—
255C24—42no—
256C24—44no—
257C24—42no—
258C24—42no—
259C24—82no—
260C24C22⋊C4×C12711yescharacteristic
261C24C2×D4×C12711yescharacteristic
262C2×D4—24no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—48no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—82no—
277C2×D4D8×C12712yes—
278C2×D4SD16×C12712yes—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C22⋊C4×C12711yescharacteristic
288C22×C4C22⋊C4×C12711yescharacteristic
289C22×C4C22⋊C4×C12711yescharacteristic
290C22×C4C22×C4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292C2×C8—42no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—82no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C22⋊C4—44no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—82no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—24no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—48no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—84no—
323C23—88no—
324C23—88no—
325C23—84no—
326C23#102×C12712yes—
327C23C2×C22⋊C4×C12711yescharacteristic
328C23C2×D8×C12711yescharacteristic
329C23C2×SD16×C12711yescharacteristic
330D4—42no—
331D4—42no—
332D4—44no—
333D4—44no—
334D4—44no—
335D4—44no—
336D4—84no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4#99×C12711yescharacteristic
358C2×C4#99×C12711yescharacteristic
359C2×C4#102×C12712yes—
360C8—82no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—44no—
371C22—44no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—44no—
377C22—81no—
378C22—82no—
379C22—82no—
380C22—816no—
381C22—82no—
382C22—82no—
383C22C2×#99×C12711yescharacteristic
384C22C2×#102×C12711yescharacteristic
385C22#421×C12711yescharacteristic
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—82no—
392C4—162no—
393C4AΣL(1,𝔽16)×C12712yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—42no—
398C2—41no—
399C2—84no—
400C2C127×#151911yescharacteristic
401C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
402C2C127×#212811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊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×#1799C2semidirect
3. C127×#1460C2semidirect
4. C127×#1343C2semidirect
5. C23×D4×C127C4semidirect
11. #394×C127C4semidirect
15. #380×C127C4semidirect
17. #342×C127C22semidirect
19. #323×C127C22semidirect
192. #11873C127direct (N × H)
203. #1799C2×C127semidirect
204. #1460C2×C127semidirect
205. #1343C2×C127semidirect
206. C127#11873direct (N × H)
207. C23×D4C4×C127semidirect
213. #394C4×C127semidirect
217. #380C4×C127semidirect
219. #342C22×C127semidirect
221. #323C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24082
C127×#17992
C127×#14602
C127×#13432
#11873127