Finite Group Databasebeta

← C127×#8473 #44572146

Subgroups — C127×#8473 #44572146

Order 32512.

732 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3503C211yesmaximal, characteristic
2C127×#1997C211yesmaximal, characteristic, complemented
3C127×#1966C211yesmaximal, characteristic, complemented
4C127×#1561C211yesmaximal, characteristic, complemented
5C127×#1526C211yesmaximal, characteristic, complemented
6C127×#1489C211yesmaximal, characteristic
7C127×#1489C211yesmaximal, characteristic
8Q82×C127—21no—
9#557×C127—21no—
10#554×C127—21no—
11#554×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127—21no—
14#544×C127—22no—
15#544×C127C412yes—
16#533×C127—21no—
17#533×C127C2211yescharacteristic
18C2×C4⋊Q8×C127—21no—
19C2×C4⋊Q8×C127C2211yescharacteristic
20#520×C127C412yes—
21C4×#41×C127C2211yescharacteristic
22#423×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24C2×#101×C127—22no—
25C4×M16×C127C2211yescharacteristic
26C4×M16×C127C2211yescharacteristic
27#343×C127—22no—
28#332×C127—21no—
29#332×C127—21no—
30#330×C127—22no—
31Q8⋊C8×C127—21no—
32Q8⋊C8×C127—21no—
33D4⋊C8×C127—21no—
34D4⋊C8×C127—21no—
35C2×#41×C127C2×C411yescharacteristic
36C22×Q8×C127—22no—
37C22×Q8×C127D412yes—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C2×M16×C127—21no—
42C4⋊Q8×C127—22no—
43C4⋊Q8×C127—22no—
44C4⋊Q8×C127—24no—
45C4⋊Q8×C127—22no—
46C4⋊Q8×C127—22no—
47C4⋊Q8×C127—21no—
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127D411yescharacteristic
52C4⋊Q8×C127D411yescharacteristic
53#125×C127—24no—
54#125×C127—22no—
55#125×C127—22no—
56#125×C127D412yes—
57C22⋊Q8×C127—22no—
58C22⋊Q8×C127—22no—
59C22⋊Q8×C127—24no—
60C22⋊Q8×C127—24no—
61C22⋊Q8×C127—24no—
62C22⋊Q8×C127—21no—
63C22⋊Q8×C127—21no—
64C4×Q8×C127—22no—
65C4×Q8×C127—22no—
66C4×Q8×C127—22no—
67C4×Q8×C127—21no—
68C4×Q8×C127—21no—
69C4×Q8×C127D411yescharacteristic
70C4×Q8×C127D411yescharacteristic
71C4×D4×C127—22no—
72C4×D4×C127—24no—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127D411yescharacteristic
76C4×D4×C127D411yescharacteristic
77#117×C127—22no—
78#117×C127—21no—
79#117×C127C2×C411yescharacteristic
80#117×C127C2×C412yes—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127C2×C412yes—
84C2×C4⋊C4×C127D412yes—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91#101×C127—44no—
92#97×C127—21no—
93#97×C127—21no—
94C4×C8×C127—21no—
95C4×C8×C127—21no—
96#41×C127—22no—
97#41×C127—22no—
98C2×Q8×C127—24no—
99C2×Q8×C127—21no—
100C2×Q8×C127—22no—
101C2×Q8×C127—21no—
102C2×Q8×C127—22no—
103C2×Q8×C127—42no—
104C2×Q8×C127—42no—
105C2×Q8×C127—82no—
106C2×Q8×C127—82no—
107C2×Q8×C127C22⋊C411yescharacteristic
108C2×D4×C127—21no—
109C2×D4×C127C22⋊C411yescharacteristic
110C22×C4×C127—21no—
111C22×C4×C127—24no—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127C22⋊C414yes—
115C22×C4×C127C22×C411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118M16×C127—22no—
119M16×C127—22no—
120M16×C127—41no—
121M16×C127—41no—
122M16×C127—42no—
123M16×C127—42no—
124C2×C8×C127—41no—
125C2×C8×C127—41no—
126C2×C8×C127—41no—
127C2×C8×C127—41no—
128C4⋊C4×C127—24no—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—24no—
131C4⋊C4×C127—24no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127C22⋊C412yes—
143C4⋊C4×C127C22⋊C412yes—
144C4⋊C4×C127C22⋊C411yescharacteristic
145C4⋊C4×C127C22⋊C411yescharacteristic
146C22⋊C4×C127—24no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—21no—
149C22⋊C4×C127—21no—
150C22⋊C4×C127—21no—
151C42×C127—24no—
152C42×C127—21no—
153C42×C127—22no—
154C42×C127—21no—
155C42×C127—21no—
156C42×C127C2×D411yescharacteristic
157C42×C127C2×D411yescharacteristic
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C23×C127—21no—
161C23×C127C2×C22⋊C411yescharacteristic
162Q8×C127—21no—
163Q8×C127—42no—
164Q8×C127—41no—
165Q8×C127—41no—
166Q8×C127—42no—
167Q8×C127—41no—
168Q8×C127—41no—
169Q8×C127—82no—
170Q8×C127—84no—
171Q8×C127#10112yescomplemented
172D4×C127—24no—
173D4×C127—21no—
174D4×C127#10112yescomplemented
175C2×C4×C127—24no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
183C2×C4×C127—22no—
184C2×C4×C127—21no—
185C2×C4×C127—21no—
186C2×C4×C127—24no—
187C2×C4×C127—22no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—41no—
192C2×C4×C127—44no—
193C2×C4×C127—84no—
194C2×C4×C127C2×C22⋊C411yescharacteristic
195C2×C4×C127C2×C22⋊C411yescharacteristic
196C2×C4×C127#12011yescharacteristic
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127#12011yescharacteristic
200C8×C127—42no—
201C8×C127—42no—
202C8×C127—81no—
203C8×C127—81no—
204C22×C127—21no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—22no—
208C22×C127—41no—
209C22×C127—41no—
210C22×C127#37911yescharacteristic
211C4×C127—21no—
212C4×C127—21no—
213C4×C127—21no—
214C4×C127—22no—
215C4×C127—41no—
216C4×C127—44no—
217C4×C127—42no—
218C4×C127—41no—
219C4×C127—42no—
220C4×C127C2×#10111yescharacteristic
221C4×C127C2×#10111yescharacteristic
222C4×C127#45311yescharacteristic
223C4×C127#45411yescharacteristic
224C4×C127#45511yescharacteristic
225C4×C127#45611yescharacteristic
226#8473C12711yesmaximal, characteristic, direct product factor, Sylow
227C2×C127—41no—
228C2×C127—42no—
229C2×C127#178411yescharacteristic
230C2×C127#179211yescharacteristic
231C2×C127#179311yescharacteristic
232#3503C2×C12711yescharacteristic
233#1997C2×C12711yescharacteristic, complemented
234#1966C2×C12711yescharacteristic, complemented
235#1561C2×C12711yescharacteristic, complemented
236#1526C2×C12711yescharacteristic, complemented
237#1489C2×C12711yescharacteristic
238#1489C2×C12711yescharacteristic
239C127#847311yescharacteristic, direct product factor, Sylow
240Q82—21no—
241#557—21no—
242#554—21no—
243#554—22no—
244D4×Q8—22no—
245D4×Q8—21no—
246#544—22no—
247#544C4×C12712yes—
248#533—21no—
249#533C22×C12711yescharacteristic
250C2×C4⋊Q8—21no—
251C2×C4⋊Q8C22×C12711yescharacteristic
252#520C4×C12712yes—
253C4×#41C22×C12711yescharacteristic
254#423C22×C12711yescharacteristic
255#423C22×C12711yescharacteristic
256C2×#101—22no—
257C4×M16C22×C12711yescharacteristic
258C4×M16C22×C12711yescharacteristic
259#343—22no—
260#332—21no—
261#332—21no—
262#330—22no—
263Q8⋊C8—21no—
264Q8⋊C8—21no—
265D4⋊C8—21no—
266D4⋊C8—21no—
267C2×#41C2×C4×C12711yescharacteristic
268C22×Q8—22no—
269C22×Q8D4×C12712yes—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C4⋊Q8—22no—
275C4⋊Q8—22no—
276C4⋊Q8—24no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8D4×C12711yescharacteristic
284C4⋊Q8D4×C12711yescharacteristic
285#125—24no—
286#125—22no—
287#125—22no—
288#125D4×C12712yes—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—24no—
292C22⋊Q8—24no—
293C22⋊Q8—24no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8D4×C12711yescharacteristic
302C4×Q8D4×C12711yescharacteristic
303C4×D4—22no—
304C4×D4—24no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4D4×C12711yescharacteristic
308C4×D4D4×C12711yescharacteristic
309#117—22no—
310#117—21no—
311#117C2×C4×C12711yescharacteristic
312#117C2×C4×C12712yes—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4C2×C4×C12712yes—
316C2×C4⋊C4D4×C12712yes—
317C2×C42—21no—
318C2×C42C23×C12711yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323#101—44no—
324#97—21no—
325#97—21no—
326C4×C8—21no—
327C4×C8—21no—
328#41—22no—
329#41—22no—
330C2×Q8—24no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—82no—
338C2×Q8—82no—
339C2×Q8C22⋊C4×C12711yescharacteristic
340C2×D4—21no—
341C2×D4C22⋊C4×C12711yescharacteristic
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4C22⋊C4×C12714yes—
347C22×C4C22×C4×C12711yescharacteristic
348C22×C4C2×D4×C12711yescharacteristic
349C22×C4C2×D4×C12711yescharacteristic
350M16—22no—
351M16—22no—
352M16—41no—
353M16—41no—
354M16—42no—
355M16—42no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4C22⋊C4×C12712yes—
375C4⋊C4C22⋊C4×C12712yes—
376C4⋊C4C22⋊C4×C12711yescharacteristic
377C4⋊C4C22⋊C4×C12711yescharacteristic
378C22⋊C4—24no—
379C22⋊C4—22no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C42—24no—
384C42—21no—
385C42—22no—
386C42—21no—
387C42—21no—
388C42C2×D4×C12711yescharacteristic
389C42C2×D4×C12711yescharacteristic
390C42C2×D4×C12711yescharacteristic
391C42C2×D4×C12711yescharacteristic
392C23—21no—
393C23C2×C22⋊C4×C12711yescharacteristic
394Q8—21no—
395Q8—42no—
396Q8—41no—
397Q8—41no—
398Q8—42no—
399Q8—41no—
400Q8—41no—
401Q8—82no—
402Q8—84no—
403Q8#101×C12712yescomplemented
404D4—24no—
405D4—21no—
406D4#101×C12712yescomplemented
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—44no—
425C2×C4—84no—
426C2×C4C2×C22⋊C4×C12711yescharacteristic
427C2×C4C2×C22⋊C4×C12711yescharacteristic
428C2×C4#120×C12711yescharacteristic
429C2×C4#120×C12711yescharacteristic
430C2×C4#120×C12711yescharacteristic
431C2×C4#120×C12711yescharacteristic
432C8—42no—
433C8—42no—
434C8—81no—
435C8—81no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22#379×C12711yescharacteristic
443C4—21no—
444C4—22no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—44no—
449C4—42no—
450C4—41no—
451C4—42no—
452C4C2×#101×C12711yescharacteristic
453C4C2×#101×C12711yescharacteristic
454C4#453×C12711yescharacteristic
455C4#454×C12711yescharacteristic
456C4#455×C12711yescharacteristic
457C4#456×C12711yescharacteristic
458C2—41no—
459C2—42no—
460C2C127×#178411yescharacteristic
461C2C127×#179211yescharacteristic
462C2C127×#179311yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#41×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1997C2semidirect
3. C127×#1966C2semidirect
4. C127×#1561C2semidirect
5. C127×#1526C2semidirect
171. Q8×C127#101semidirect
174. D4×C127#101semidirect
226. #8473C127direct (N × H)
233. #1997C2×C127semidirect
234. #1966C2×C127semidirect
235. #1561C2×C127semidirect
236. #1526C2×C127semidirect
239. C127#8473direct (N × H)
403. Q8#101×C127semidirect
406. D4#101×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35032
C127×#19972
C127×#19662
C127×#15612
C127×#15262
C127×#14892
#8473127