Finite Group Databasebeta

← C127×#11839 #44575512

Subgroups — C127×#11839 #44575512

Order 32512.

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

normal subgroups only

This group has 698 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×#2404C211yesmaximal, characteristic
2C127×#1819C211yesmaximal, characteristic, complemented
3C2×#323×C127C211yesmaximal, characteristic, complemented
4C127×#1351C212yesmaximal, complemented
5C127×#1343C212yesmaximal, complemented
6C22×#41×C127C411yescharacteristic, complemented
7C2×#120×C127—21no—
8C22×C22⋊C4×C127C2211yescharacteristic
9C2×C22⋊C8×C127—21no—
10#393×C127C411yescharacteristic, complemented
11#393×C127C2211yescharacteristic
12#392×C127C411yescharacteristic, complemented
13#392×C127C2211yescharacteristic
14#386×C127—21no—
15#386×C127—21no—
16#386×C127—21no—
17#381×C127C411yescharacteristic, complemented
18#379×C127—21no—
19#342×C127—21no—
20#342×C127C2212yes—
21#323×C127—21no—
22#323×C127C2212yes—
23C25×C127D411yescharacteristic
24C2×#41×C127—41no—
25C2×#41×C127—41no—
26C2×#41×C127—44no—
27C22×Q8×C127C2×C411yescharacteristic
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127—21no—
31C22×D4×C127C2×C411yescharacteristic
32C23×C4×C127—21no—
33C23×C4×C127C2×C411yescharacteristic
34C23×C4×C127D411yescharacteristic
35C22×C8×C127—41no—
36#120×C127—44no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—41no—
44C2×C22⋊C4×C127—41no—
45C2×C22⋊C4×C127—41no—
46C2×C22⋊C4×C127—41no—
47C2×C22⋊C4×C127C2×C411yescharacteristic
48C2×C22⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127D411yescharacteristic
50C2×C22⋊C4×C127C2311yescharacteristic
51C22⋊C8×C127—22no—
52C22⋊C8×C127—41no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127C2×C411yescharacteristic
57#95×C127C2×C411yescharacteristic
58C24×C127—21no—
59C24×C127—21no—
60C24×C127—21no—
61C24×C127—22no—
62C24×C127—41no—
63C24×C127—42no—
64C24×C127—81no—
65C24×C127C22⋊C411yescharacteristic
66C24×C127C22⋊C411yescharacteristic
67C24×C127C2×D411yescharacteristic
68#41×C127—44no—
69#41×C127—44no—
70#41×C127—44no—
71#41×C127—44no—
72C2×Q8×C127—42no—
73C2×Q8×C127—41no—
74C2×D4×C127—24no—
75C2×D4×C127—41no—
76C2×D4×C127—42no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—42no—
80C2×D4×C127—42no—
81C2×D4×C127—42no—
82C2×D4×C127—42no—
83C2×D4×C127—42no—
84C2×D4×C127—81no—
85C2×D4×C127—81no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—42no—
94C22×C4×C127—42no—
95C22×C4×C127—42no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127—81no—
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C411yescharacteristic
101C22×C4×C127C22×C411yescharacteristic
102C22×C4×C127C2×D411yescharacteristic
103C2×C8×C127—42no—
104C2×C8×C127—82no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—42no—
110C22⋊C4×C127—42no—
111C22⋊C4×C127—42no—
112C22⋊C4×C127—42no—
113C22⋊C4×C127—42no—
114C22⋊C4×C127—81no—
115C22⋊C4×C127—81no—
116C22⋊C4×C127—82no—
117C22⋊C4×C127—82no—
118C23×C127—22no—
119C23×C127—21no—
120C23×C127—21no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—22no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—41no—
128C23×C127—42no—
129C23×C127—42no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—41no—
138C23×C127—42no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—81no—
143C23×C127—81no—
144C23×C127—84no—
145C23×C127—84no—
146C23×C127#9911yescharacteristic
147C23×C127#9911yescharacteristic
148C23×C127C2×C22⋊C411yescharacteristic
149C23×C127#13512yes—
150Q8×C127—42no—
151Q8×C127—42no—
152D4×C127—44no—
153D4×C127—42no—
154D4×C127—42no—
155D4×C127—44no—
156D4×C127—84no—
157D4×C127—84no—
158C2×C4×C127—22no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—42no—
164C2×C4×C127—41no—
165C2×C4×C127—42no—
166C2×C4×C127—48no—
167C2×C4×C127—42no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—81no—
180C2×C4×C127—82no—
181C2×C4×C127—82no—
182C2×C4×C127—82no—
183C8×C127—82no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—22no—
191C22×C127—21no—
192C22×C127—42no—
193C22×C127—42no—
194C22×C127—42no—
195C22×C127—42no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—41no—
199C22×C127—41no—
200C22×C127—42no—
201C22×C127—41no—
202C22×C127—41no—
203C22×C127—41no—
204C22×C127—81no—
205C22×C127—84no—
206C22×C127—81no—
207C22×C127—81no—
208C22×C127—81no—
209C22×C127—84no—
210C22×C127—81no—
211C22×C127—81no—
212C22×C127AΣL(1,𝔽16)12yes—
213C22×C127C2×#9911yescharacteristic
214C22×C127#41611yescharacteristic
215C22×C127#42111yescharacteristic
216C4×C127—41no—
217C4×C127—42no—
218C4×C127—41no—
219C4×C127—41no—
220C4×C127—41no—
221C4×C127—81no—
222C4×C127—81no—
223C4×C127—162no—
224#11839C12711yesmaximal, characteristic, direct product factor, Sylow
225C2×C127—21no—
226C2×C127—21no—
227C2×C127—22no—
228C2×C127—42no—
229C2×C127—41no—
230C2×C127—81no—
231C2×C127—82no—
232C2×C127#151611yescharacteristic
233C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
234C2×C127#212711yescharacteristic
235#2404C2×C12711yescharacteristic
236#1819C2×C12711yescharacteristic, complemented
237C2×#323C2×C12711yescharacteristic, complemented
238#1351C2×C12712yescomplemented
239#1343C2×C12712yescomplemented
240C127#1183911yescharacteristic, direct product factor, Sylow
241C22×#41C4×C12711yescharacteristic, complemented
242C2×#120—21no—
243C22×C22⋊C4C22×C12711yescharacteristic
244C2×C22⋊C8—21no—
245#393C4×C12711yescharacteristic, complemented
246#393C22×C12711yescharacteristic
247#392C4×C12711yescharacteristic, complemented
248#392C22×C12711yescharacteristic
249#386—21no—
250#386—21no—
251#386—21no—
252#381C4×C12711yescharacteristic, complemented
253#379—21no—
254#342—21no—
255#342C22×C12712yes—
256#323—21no—
257#323C22×C12712yes—
258C25D4×C12711yescharacteristic
259C2×#41—41no—
260C2×#41—41no—
261C2×#41—44no—
262C22×Q8C2×C4×C12711yescharacteristic
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4C2×C4×C12711yescharacteristic
267C23×C4—21no—
268C23×C4C2×C4×C12711yescharacteristic
269C23×C4D4×C12711yescharacteristic
270C22×C8—41no—
271#120—44no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4—41no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4C2×C4×C12711yescharacteristic
283C2×C22⋊C4D4×C12711yescharacteristic
284C2×C22⋊C4D4×C12711yescharacteristic
285C2×C22⋊C4C23×C12711yescharacteristic
286C22⋊C8—22no—
287C22⋊C8—41no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95C2×C4×C12711yescharacteristic
292#95C2×C4×C12711yescharacteristic
293C24—21no—
294C24—21no—
295C24—21no—
296C24—22no—
297C24—41no—
298C24—42no—
299C24—81no—
300C24C22⋊C4×C12711yescharacteristic
301C24C22⋊C4×C12711yescharacteristic
302C24C2×D4×C12711yescharacteristic
303#41—44no—
304#41—44no—
305#41—44no—
306#41—44no—
307C2×Q8—42no—
308C2×Q8—41no—
309C2×D4—24no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—81no—
320C2×D4—81no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—81no—
334C22×C4C22⋊C4×C12711yescharacteristic
335C22×C4C22⋊C4×C12711yescharacteristic
336C22×C4C22×C4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C2×C8—42no—
339C2×C8—82no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—81no—
350C22⋊C4—81no—
351C22⋊C4—82no—
352C22⋊C4—82no—
353C23—22no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—41no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—81no—
378C23—81no—
379C23—84no—
380C23—84no—
381C23#99×C12711yescharacteristic
382C23#99×C12711yescharacteristic
383C23C2×C22⋊C4×C12711yescharacteristic
384C23#135×C12712yes—
385Q8—42no—
386Q8—42no—
387D4—44no—
388D4—42no—
389D4—42no—
390D4—44no—
391D4—84no—
392D4—84no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—48no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C8—82no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22—84no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—84no—
445C22—81no—
446C22—81no—
447C22AΣL(1,𝔽16)×C12712yes—
448C22C2×#99×C12711yescharacteristic
449C22#416×C12711yescharacteristic
450C22#421×C12711yescharacteristic
451C4—41no—
452C4—42no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—162no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2—41no—
464C2—81no—
465C2—82no—
466C2C127×#151611yescharacteristic
467C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
468C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC127×#2404C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1819C2semidirect
3. C2×#323×C127C2semidirect
4. C127×#1351C2semidirect
5. C127×#1343C2semidirect
6. C22×#41×C127C4semidirect
10. #393×C127C4semidirect
12. #392×C127C4semidirect
17. #381×C127C4semidirect
224. #11839C127direct (N × H)
236. #1819C2×C127semidirect
237. C2×#323C2×C127semidirect
238. #1351C2×C127semidirect
239. #1343C2×C127semidirect
240. C127#11839direct (N × H)
241. C22×#41C4×C127semidirect
245. #393C4×C127semidirect
247. #392C4×C127semidirect
252. #381C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24042
C127×#18192
C2×#323×C1272
C127×#13512
C127×#13432
#11839127