Finite Group Databasebeta

← C127×#10320 #44573993

Subgroups — C127×#10320 #44573993

Order 32512.

1066 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3186C211yesmaximal, characteristic, complemented
2C127×#2847C212yesmaximal, complemented
3C127×#1779C211yesmaximal, characteristic, complemented
4C127×#1519C212yesmaximal, complemented
5C127×#1289C211yesmaximal, characteristic, complemented
6C24×C4×C127C2211yescharacteristic
7C2×#121×C127—22no—
8C2×#121×C127C2212yes—
9C2×#120×C127—22no—
10#480×C127—22no—
11#466×C127—22no—
12#447×C127—22no—
13C2×C22⋊C8×C127—22no—
14C2×C22⋊C8×C127C2211yescharacteristic
15C2×C22⋊C8×C127C2211yescharacteristic
16#386×C127—22no—
17#386×C127—24no—
18#380×C127—22no—
19#380×C127C2212yes—
20#327×C127—24no—
21C25×C127D411yescharacteristic
22C22×D4×C127—24no—
23C22×D4×C127—22no—
24C22×D4×C127D412yescomplemented
25C23×C4×C127—22no—
26C23×C4×C127—21no—
27C23×C4×C127—22no—
28C23×C4×C127—21no—
29C23×C4×C127—44no—
30C23×C4×C127D411yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C2×D8×C127—22no—
33C22×C8×C127—21no—
34C22×C8×C127D412yescomplemented
35#121×C127—22no—
36#121×C127—22no—
37#121×C127—22no—
38#121×C127—22no—
39#121×C127—48no—
40#120×C127—44no—
41#120×C127—44no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127D412yescomplemented
44C2×C22⋊C4×C127—24no—
45C2×C22⋊C4×C127—24no—
46C2×C22⋊C4×C127—22no—
47C2×C22⋊C4×C127—22no—
48#107×C127—22no—
49#102×C127—24no—
50C22⋊C8×C127—22no—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—44no—
53#95×C127—24no—
54#95×C127D414yescomplemented
55C24×C127—22no—
56C24×C127—21no—
57C24×C127—21no—
58C24×C127—22no—
59C24×C127—22no—
60C24×C127—42no—
61C24×C127—42no—
62C24×C127D812yescomplemented
63C24×C127C2×D411yescharacteristic
64C2×D4×C127—22no—
65C2×D4×C127—22no—
66C2×D4×C127—44no—
67C2×D4×C127—48no—
68C2×D4×C127—48no—
69C2×D4×C127—48no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127—42no—
73C2×D4×C127—42no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C22×C4×C127—24no—
77C22×C4×C127—28no—
78C22×C4×C127—22no—
79C22×C4×C127—21no—
80C22×C4×C127—22no—
81C22×C4×C127—24no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—44no—
85C22×C4×C127—42no—
86C22×C4×C127—44no—
87C22×C4×C127—42no—
88C22×C4×C127—44no—
89C22×C4×C127—42no—
90C22×C4×C127—41no—
91C22×C4×C127—42no—
92C22×C4×C127—41no—
93C22×C4×C127C2×D412yes—
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D412yes—
96C22×C4×C127#4111yescharacteristic
97D8×C127—82no—
98C2×C8×C127—22no—
99C2×C8×C127—42no—
100C2×C8×C127—42no—
101C2×C8×C127—41no—
102C4⋊C4×C127—22no—
103C4⋊C4×C127—22no—
104C4⋊C4×C127—44no—
105C22⋊C4×C127—48no—
106C22⋊C4×C127—48no—
107C22⋊C4×C127—42no—
108C22⋊C4×C127—42no—
109C22⋊C4×C127—42no—
110C22⋊C4×C127—42no—
111C23×C127—24no—
112C23×C127—22no—
113C23×C127—24no—
114C23×C127—22no—
115C23×C127—24no—
116C23×C127—22no—
117C23×C127—41no—
118C23×C127—44no—
119C23×C127—41no—
120C23×C127—42no—
121C23×C127—41no—
122C23×C127—42no—
123C23×C127—41no—
124C23×C127—48no—
125C23×C127—44no—
126C23×C127—44no—
127C23×C127—44no—
128C23×C127—41no—
129C23×C127—42no—
130C23×C127—41no—
131C23×C127—42no—
132C23×C127—42no—
133C23×C127—42no—
134C23×C127#12012yes—
135C23×C127#12111yescharacteristic
136C23×C127C2×D811yescharacteristic
137C23×C127#13511yescharacteristic
138C23×C127AGL(1,ℤ/8)12yes—
139D4×C127—44no—
140D4×C127—82no—
141D4×C127—816no—
142D4×C127—82no—
143D4×C127—82no—
144D4×C127—82no—
145D4×C127—82no—
146C2×C4×C127—24no—
147C2×C4×C127—22no—
148C2×C4×C127—24no—
149C2×C4×C127—22no—
150C2×C4×C127—42no—
151C2×C4×C127—41no—
152C2×C4×C127—44no—
153C2×C4×C127—48no—
154C2×C4×C127—42no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—44no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—42no—
161C2×C4×C127—44no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127#12011yescharacteristic
165C2×C4×C127#12112yes—
166C2×C4×C127#12711yescharacteristic
167C8×C127—42no—
168C8×C127—81no—
169C22×C127—22no—
170C22×C127—21no—
171C22×C127—22no—
172C22×C127—21no—
173C22×C127—28no—
174C22×C127—24no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127—42no—
178C22×C127—44no—
179C22×C127—42no—
180C22×C127—44no—
181C22×C127—44no—
182C22×C127—42no—
183C22×C127—42no—
184C22×C127—42no—
185C22×C127—42no—
186C22×C127—42no—
187C22×C127—84no—
188C22×C127—84no—
189C22×C127—82no—
190C22×C127—82no—
191C22×C127—82no—
192C22×C127#39211yescharacteristic
193C22×C127#44712yes—
194C22×C127#44912yes—
195C22×C127#46611yescharacteristic
196C22×C127#46911yescharacteristic
197C4×C127—21no—
198C4×C127—22no—
199C4×C127—42no—
200C4×C127—84no—
201C4×C127—82no—
202C4×C127B(4,𝔽2)12yes—
203#10320C12711yesmaximal, characteristic, direct product factor, Sylow
204C2×C127—22no—
205C2×C127—21no—
206C2×C127—22no—
207C2×C127—21no—
208C2×C127—44no—
209C2×C127—162no—
210C2×C127#199911yescharacteristic
211C2×C127#201011yescharacteristic
212C2×C127#202111yescharacteristic
213#3186C2×C12711yescharacteristic, complemented
214#2847C2×C12712yescomplemented
215#1779C2×C12711yescharacteristic, complemented
216#1519C2×C12712yescomplemented
217#1289C2×C12711yescharacteristic, complemented
218C127#1032011yescharacteristic, direct product factor, Sylow
219C24×C4C22×C12711yescharacteristic
220C2×#121—22no—
221C2×#121C22×C12712yes—
222C2×#120—22no—
223#480—22no—
224#466—22no—
225#447—22no—
226C2×C22⋊C8—22no—
227C2×C22⋊C8C22×C12711yescharacteristic
228C2×C22⋊C8C22×C12711yescharacteristic
229#386—22no—
230#386—24no—
231#380—22no—
232#380C22×C12712yes—
233#327—24no—
234C25D4×C12711yescharacteristic
235C22×D4—24no—
236C22×D4—22no—
237C22×D4D4×C12712yescomplemented
238C23×C4—22no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—44no—
243C23×C4D4×C12711yescharacteristic
244C23×C4C23×C12711yescharacteristic
245C2×D8—22no—
246C22×C8—21no—
247C22×C8D4×C12712yescomplemented
248#121—22no—
249#121—22no—
250#121—22no—
251#121—22no—
252#121—48no—
253#120—44no—
254#120—44no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4D4×C12712yescomplemented
257C2×C22⋊C4—24no—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261#107—22no—
262#102—24no—
263C22⋊C8—22no—
264C22⋊C8—22no—
265C22⋊C8—44no—
266#95—24no—
267#95D4×C12714yescomplemented
268C24—22no—
269C24—21no—
270C24—21no—
271C24—22no—
272C24—22no—
273C24—42no—
274C24—42no—
275C24D8×C12712yescomplemented
276C24C2×D4×C12711yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—44no—
280C2×D4—48no—
281C2×D4—48no—
282C2×D4—48no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C22×C4—24no—
290C22×C4—28no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—44no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—42no—
301C22×C4—44no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4C2×D4×C12712yes—
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4C2×D4×C12712yes—
309C22×C4#41×C12711yescharacteristic
310D8—82no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—41no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—44no—
318C22⋊C4—48no—
319C22⋊C4—48no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C23—24no—
325C23—22no—
326C23—24no—
327C23—22no—
328C23—24no—
329C23—22no—
330C23—41no—
331C23—44no—
332C23—41no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—48no—
338C23—44no—
339C23—44no—
340C23—44no—
341C23—41no—
342C23—42no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23#120×C12712yes—
348C23#121×C12711yescharacteristic
349C23C2×D8×C12711yescharacteristic
350C23#135×C12711yescharacteristic
351C23AGL(1,ℤ/8)×C12712yes—
352D4—44no—
353D4—82no—
354D4—816no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—82no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—48no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4#120×C12711yescharacteristic
378C2×C4#121×C12712yes—
379C2×C4#127×C12711yescharacteristic
380C8—42no—
381C8—81no—
382C22—22no—
383C22—21no—
384C22—22no—
385C22—21no—
386C22—28no—
387C22—24no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—44no—
392C22—42no—
393C22—44no—
394C22—44no—
395C22—42no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—84no—
401C22—84no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22#392×C12711yescharacteristic
406C22#447×C12712yes—
407C22#449×C12712yes—
408C22#466×C12711yescharacteristic
409C22#469×C12711yescharacteristic
410C4—21no—
411C4—22no—
412C4—42no—
413C4—84no—
414C4—82no—
415C4B(4,𝔽2)×C12712yes—
416C2—22no—
417C2—21no—
418C2—22no—
419C2—21no—
420C2—44no—
421C2—162no—
422C2C127×#199911yescharacteristic
423C2C127×#201011yescharacteristic
424C2C127×#202111yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC23×C4C23×C127
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3186C2semidirect
2. C127×#2847C2semidirect
3. C127×#1779C2semidirect
4. C127×#1519C2semidirect
5. C127×#1289C2semidirect
24. C22×D4×C127D4semidirect
34. C22×C8×C127D4semidirect
43. C2×C4⋊C4×C127D4semidirect
54. #95×C127D4semidirect
62. C24×C127D8semidirect
203. #10320C127direct (N × H)
213. #3186C2×C127semidirect
214. #2847C2×C127semidirect
215. #1779C2×C127semidirect
216. #1519C2×C127semidirect
217. #1289C2×C127semidirect
218. C127#10320direct (N × H)
237. C22×D4D4×C127semidirect
247. C22×C8D4×C127semidirect
256. C2×C4⋊C4D4×C127semidirect
267. #95D4×C127semidirect
275. C24D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31862
C127×#28472
C127×#17792
C127×#15192
C127×#12892
#10320127