Finite Group Databasebeta

← C127×#11821 #44575494

Subgroups — C127×#11821 #44575494

Order 32512.

582 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2397C211yesmaximal, characteristic
2C127×#1799C211yesmaximal, characteristic, complemented
3C127×#1465C211yesmaximal, characteristic, complemented
4C127×#1352C212yesmaximal, complemented
5C127×#1343C212yesmaximal, complemented
6C2×C4×D4×C127—21no—
7C2×C4×D4×C127—21no—
8C2×C4×D4×C127C411yescharacteristic, complemented
9C2×C4×D4×C127C2211yescharacteristic
10C2×#99×C127—21no—
11#407×C127—21no—
12#399×C127—21no—
13#399×C127C411yescharacteristic, complemented
14#399×C127C2211yescharacteristic
15#392×C127—21no—
16#392×C127C411yescharacteristic, complemented
17#392×C127C2211yescharacteristic
18#380×C127—21no—
19#376×C127C411yescharacteristic, complemented
20#342×C127C2212yes—
21#324×C127—21no—
22#323×C127C2212yes—
23C22×D4×C127—21no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C22×D4×C127D411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C2×M16×C127—41no—
31C4×D4×C127—41no—
32C4×D4×C127—41no—
33C4×D4×C127—44no—
34C4×D4×C127—44no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—41no—
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127C2×C411yescharacteristic
49C2×C22⋊C4×C127C2311yescharacteristic
50C2×C42×C127—21no—
51C2×C42×C127C2×C411yescharacteristic
52#99×C127—42no—
53C22⋊C8×C127—22no—
54C22⋊C8×C127—41no—
55#95×C127—21no—
56#95×C127—41no—
57#95×C127C2×C411yescharacteristic
58#95×C127C2×C411yescharacteristic
59C24×C127—21no—
60C24×C127C22⋊C411yescharacteristic
61C24×C127C2×D411yescharacteristic
62C2×D4×C127—21no—
63C2×D4×C127—21no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
67C2×D4×C127—42no—
68C2×D4×C127—42no—
69C2×D4×C127—42no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—42no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—42no—
85C22×C4×C127—42no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127—42no—
89C22×C4×C127C22⋊C411yescharacteristic
90C22×C4×C127C22⋊C411yescharacteristic
91C22×C4×C127C22⋊C411yescharacteristic
92C22×C4×C127C22×C411yescharacteristic
93C22×C4×C127C2×D411yescharacteristic
94M16×C127—82no—
95C2×C8×C127—42no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—42no—
99C4⋊C4×C127—42no—
100C4⋊C4×C127—82no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—42no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—42no—
107C22⋊C4×C127—42no—
108C22⋊C4×C127—42no—
109C22⋊C4×C127—42no—
110C42×C127—24no—
111C42×C127—21no—
112C42×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—22no—
116C23×C127—21no—
117C23×C127—21no—
118C23×C127—21no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127—41no—
127C23×C127—41no—
128C23×C127—41no—
129C23×C127C2×C22⋊C411yescharacteristic
130C23×C127AGL(1,ℤ/8)11yescharacteristic
131C23×C127#13711yescharacteristic
132D4×C127—42no—
133D4×C127—42no—
134D4×C127—42no—
135D4×C127—44no—
136D4×C127—44no—
137D4×C127—48no—
138D4×C127—42no—
139C2×C4×C127—22no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
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—82no—
163C2×C4×C127—82no—
164C2×C4×C127—82no—
165C2×C4×C127—82no—
166C2×C4×C127—82no—
167C2×C4×C127#9911yescharacteristic
168C2×C4×C127#9911yescharacteristic
169C8×C127—82no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—42no—
177C22×C127—42no—
178C22×C127—42no—
179C22×C127—41no—
180C22×C127—41no—
181C22×C127—42no—
182C22×C127—41no—
183C22×C127—41no—
184C22×C127—41no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127—81no—
188C22×C127—81no—
189C22×C127—81no—
190C22×C127—81no—
191C22×C127C2×#9911yescharacteristic
192C22×C127#41711yescharacteristic
193C22×C127#42111yescharacteristic
194C4×C127—21no—
195C4×C127—42no—
196C4×C127—42no—
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—41no—
200C4×C127—41no—
201C4×C127—81no—
202C4×C127—162no—
203C4×C127#35312yes—
204#11821C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—21no—
206C2×C127—21no—
207C2×C127—41no—
208C2×C127—41no—
209C2×C127—81no—
210C2×C127—82no—
211C2×C127#151311yescharacteristic
212C2×C127#212011yescharacteristic
213C2×C127C2×#35311yescharacteristic
214#2397C2×C12711yescharacteristic
215#1799C2×C12711yescharacteristic, complemented
216#1465C2×C12711yescharacteristic, complemented
217#1352C2×C12712yescomplemented
218#1343C2×C12712yescomplemented
219C127#1182111yescharacteristic, direct product factor, Sylow
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4C4×C12711yescharacteristic, complemented
223C2×C4×D4C22×C12711yescharacteristic
224C2×#99—21no—
225#407—21no—
226#399—21no—
227#399C4×C12711yescharacteristic, complemented
228#399C22×C12711yescharacteristic
229#392—21no—
230#392C4×C12711yescharacteristic, complemented
231#392C22×C12711yescharacteristic
232#380—21no—
233#376C4×C12711yescharacteristic, complemented
234#342C22×C12712yes—
235#324—21no—
236#323C22×C12712yes—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C2×C4×C12711yescharacteristic
240C22×D4D4×C12711yescharacteristic
241C23×C4—21no—
242C23×C4D4×C12711yescharacteristic
243C23×C4D4×C12711yescharacteristic
244C2×M16—41no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—41no—
250C4×D4—41no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4C2×C4×C12711yescharacteristic
255C2×C4⋊C4D4×C12711yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4C2×C4×C12711yescharacteristic
263C2×C22⋊C4C23×C12711yescharacteristic
264C2×C42—21no—
265C2×C42C2×C4×C12711yescharacteristic
266#99—42no—
267C22⋊C8—22no—
268C22⋊C8—41no—
269#95—21no—
270#95—41no—
271#95C2×C4×C12711yescharacteristic
272#95C2×C4×C12711yescharacteristic
273C24—21no—
274C24C22⋊C4×C12711yescharacteristic
275C24C2×D4×C12711yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4C22⋊C4×C12711yescharacteristic
304C22×C4C22⋊C4×C12711yescharacteristic
305C22×C4C22⋊C4×C12711yescharacteristic
306C22×C4C22×C4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308M16—82no—
309C2×C8—42no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—82no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C42—24no—
325C42—21no—
326C42—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23C2×C22⋊C4×C12711yescharacteristic
344C23AGL(1,ℤ/8)×C12711yescharacteristic
345C23#137×C12711yescharacteristic
346D4—42no—
347D4—42no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—42no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4#99×C12711yescharacteristic
382C2×C4#99×C12711yescharacteristic
383C8—82no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C2×#99×C12711yescharacteristic
406C22#417×C12711yescharacteristic
407C22#421×C12711yescharacteristic
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—162no—
417C4#353×C12712yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—82no—
424C2C127×#151311yescharacteristic
425C2C127×#212011yescharacteristic
426C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC127×#2397C2
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×#1465C2semidirect
4. C127×#1352C2semidirect
5. C127×#1343C2semidirect
8. C2×C4×D4×C127C4semidirect
13. #399×C127C4semidirect
16. #392×C127C4semidirect
19. #376×C127C4semidirect
204. #11821C127direct (N × H)
215. #1799C2×C127semidirect
216. #1465C2×C127semidirect
217. #1352C2×C127semidirect
218. #1343C2×C127semidirect
219. C127#11821direct (N × H)
222. C2×C4×D4C4×C127semidirect
227. #399C4×C127semidirect
230. #392C4×C127semidirect
233. #376C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23972
C127×#17992
C127×#14652
C127×#13522
C127×#13432
#11821127