Finite Group Databasebeta

← C127×#19560 #44583233

Subgroups — C127×#19560 #44583233

Order 32512.

602 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3254C211yesmaximal, characteristic
2C127×#3230C211yesmaximal, characteristic, complemented
3C127×#3206C211yesmaximal, characteristic
4C127×#2979C211yesmaximal, characteristic
5C127×#1699C212yesmaximal, complemented
6C127×#1693C212yesmaximal, complemented
7C127×#1679C212yesmaximal, complemented
8C127×#1673C212yesmaximal, complemented
9C127×#1574C211yesmaximal, characteristic, complemented
10C127×#1546C211yesmaximal, characteristic, complemented
11C127×#1544C211yesmaximal, characteristic, complemented
12#533×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4⋊Q8×C127C2211yescharacteristic
15#500×C127C2212yes—
16#492×C127—21no—
17#487×C127—21no—
18#487×C127C2212yes—
19#484×C127—22no—
20#477×C127—21no—
21#477×C127—21no—
22#477×C127—21no—
23#474×C127C2212yes—
24#468×C127—22no—
25#461×C127C2212yes—
26#461×C127C2212yes—
27#461×C127C2212yes—
28#460×C127—21no—
29#448×C127—22no—
30#436×C127—21no—
31#436×C127C2212yes—
32C8×D4×C127—21no—
33C8×D4×C127C2212yes—
34#431×C127C2211yescharacteristic
35#431×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#423×C127C2211yescharacteristic
38#408×C127—22no—
39#335×C127C2212yes—
40#334×C127C2212yes—
41#332×C127C2211yescharacteristic
42#332×C127C2211yescharacteristic
43#332×C127C2211yescharacteristic
44#332×C127C2211yescharacteristic
45#332×C127C2212yes—
46#332×C127C2212yes—
47C2×#41×C127—21no—
48C22×Q8×C127—21no—
49C2×SD16×C127—22no—
50C2×SD16×C127—22no—
51C2×SD16×C127—22no—
52C2×M16×C127—21no—
53C2×M16×C127—22no—
54C22×C8×C127—22no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127D411yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60C4⋊Q8×C127C2312yes—
61C4⋊Q8×C127C2311yescharacteristic
62#127×C127D411yescharacteristic
63#125×C127—21no—
64#124×C127—21no—
65C22⋊Q8×C127—21no—
66C22⋊Q8×C127—21no—
67#121×C127—21no—
68#121×C127D412yes—
69C4×Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127C2312yes—
73#117×C127—21no—
74C2×C4⋊C4×C127—21no—
75C2×C4⋊C4×C127—21no—
76C2×C42×C127C2311yescharacteristic
77#107×C127—22no—
78#107×C127—22no—
79#107×C127—22no—
80C4⋊C8×C127—21no—
81C4⋊C8×C127D411yescharacteristic
82C4⋊C8×C127D411yescharacteristic
83C4⋊C8×C127C2311yescharacteristic
84C4⋊C8×C127C2311yescharacteristic
85C4⋊C8×C127C2311yescharacteristic
86C4⋊C8×C127C2312yes—
87C4⋊C8×C127C2311yescharacteristic
88#103×C127—22no—
89#103×C127—22no—
90#103×C127—22no—
91#103×C127—22no—
92#103×C127—22no—
93#102×C127—22no—
94C22⋊C8×C127—21no—
95C22⋊C8×C127—21no—
96C22⋊C8×C127—22no—
97C22⋊C8×C127—22no—
98C22⋊C8×C127D412yes—
99C4×C8×C127—21no—
100C4×C8×C127—21no—
101C4×C8×C127C2312yes—
102#41×C127—81no—
103#41×C127—81no—
104C2×Q8×C127—21no—
105C2×Q8×C127—21no—
106C2×Q8×C127—21no—
107C2×Q8×C127—22no—
108C2×Q8×C127—41no—
109C2×Q8×C127—81no—
110C2×Q8×C127—81no—
111C2×D4×C127—22no—
112C2×D4×C127—21no—
113C2×D4×C127—21no—
114C2×D4×C127C2×D412yes—
115C22×C4×C127—22no—
116C22×C4×C127—41no—
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127#4111yescharacteristic
120SD16×C127—82no—
121SD16×C127—82no—
122SD16×C127—82no—
123M16×C127—82no—
124M16×C127—81no—
125C2×C8×C127—21no—
126C2×C8×C127—21no—
127C2×C8×C127—21no—
128C2×C8×C127—21no—
129C2×C8×C127—22no—
130C2×C8×C127—82no—
131C2×C8×C127C2×D412yes—
132C2×C8×C127C2×D412yes—
133C4⋊C4×C127—21no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—41no—
141C4⋊C4×C127—41no—
142C4⋊C4×C127—41no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127C2×D412yes—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—41no—
148C42×C127—41no—
149C42×C127C2×D411yescharacteristic
150C42×C127C2×D411yescharacteristic
151C42×C127#4111yescharacteristic
152C42×C127C2411yescharacteristic
153C23×C127—22no—
154C23×C127#12111yescharacteristic
155Q8×C127—41no—
156Q8×C127—42no—
157Q8×C127—42no—
158Q8×C127—41no—
159Q8×C127—41no—
160Q8×C127—41no—
161Q8×C127—81no—
162Q8×C127—82no—
163D4×C127—22no—
164D4×C127—22no—
165D4×C127—42no—
166D4×C127—81no—
167D4×C127—82no—
168C2×C4×C127—21no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—21no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—42no—
179C2×C4×C127—82no—
180C2×C4×C127#12111yescharacteristic
181C2×C4×C127#12111yescharacteristic
182C2×C4×C127#12111yescharacteristic
183C2×C4×C127C22×D411yescharacteristic
184C2×C4×C127C22×D411yescharacteristic
185C2×C4×C127C2×#4111yescharacteristic
186C8×C127—22no—
187C8×C127—22no—
188C8×C127—42no—
189C8×C127—41no—
190C8×C127—41no—
191C8×C127—41no—
192C8×C127—41no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127C2×#12111yescharacteristic
200C4×C127—21no—
201C4×C127—21no—
202C4×C127—21no—
203C4×C127—42no—
204C4×C127—81no—
205C4×C127—82no—
206C4×C127—81no—
207C4×C127#47312yes—
208C4×C127#57611yescharacteristic
209C4×C127#57711yescharacteristic
210C4×C127#57711yescharacteristic
211C4×C127#57711yescharacteristic
212#19560C12711yesmaximal, characteristic, direct product factor, Sylow
213C2×C127—41no—
214C2×C127—82no—
215C2×C127#304211yescharacteristic
216C2×C127#306211yescharacteristic
217C2×C127C2×#47311yescharacteristic
218#3254C2×C12711yescharacteristic
219#3230C2×C12711yescharacteristic, complemented
220#3206C2×C12711yescharacteristic
221#2979C2×C12711yescharacteristic
222#1699C2×C12712yescomplemented
223#1693C2×C12712yescomplemented
224#1679C2×C12712yescomplemented
225#1673C2×C12712yescomplemented
226#1574C2×C12711yescharacteristic, complemented
227#1546C2×C12711yescharacteristic, complemented
228#1544C2×C12711yescharacteristic, complemented
229C127#1956011yescharacteristic, direct product factor, Sylow
230#533C22×C12711yescharacteristic
231#532C22×C12711yescharacteristic
232C2×C4⋊Q8C22×C12711yescharacteristic
233#500C22×C12712yes—
234#492—21no—
235#487—21no—
236#487C22×C12712yes—
237#484—22no—
238#477—21no—
239#477—21no—
240#477—21no—
241#474C22×C12712yes—
242#468—22no—
243#461C22×C12712yes—
244#461C22×C12712yes—
245#461C22×C12712yes—
246#460—21no—
247#448—22no—
248#436—21no—
249#436C22×C12712yes—
250C8×D4—21no—
251C8×D4C22×C12712yes—
252#431C22×C12711yescharacteristic
253#431C22×C12711yescharacteristic
254#431C22×C12711yescharacteristic
255#423C22×C12711yescharacteristic
256#408—22no—
257#335C22×C12712yes—
258#334C22×C12712yes—
259#332C22×C12711yescharacteristic
260#332C22×C12711yescharacteristic
261#332C22×C12711yescharacteristic
262#332C22×C12711yescharacteristic
263#332C22×C12712yes—
264#332C22×C12712yes—
265C2×#41—21no—
266C22×Q8—21no—
267C2×SD16—22no—
268C2×SD16—22no—
269C2×SD16—22no—
270C2×M16—21no—
271C2×M16—22no—
272C22×C8—22no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8D4×C12711yescharacteristic
277C4⋊Q8C23×C12712yes—
278C4⋊Q8C23×C12711yescharacteristic
279C4⋊Q8C23×C12711yescharacteristic
280#127D4×C12711yescharacteristic
281#125—21no—
282#124—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285#121—21no—
286#121D4×C12712yes—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×D4—21no—
290C4×D4C23×C12712yes—
291#117—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C42C23×C12711yescharacteristic
295#107—22no—
296#107—22no—
297#107—22no—
298C4⋊C8—21no—
299C4⋊C8D4×C12711yescharacteristic
300C4⋊C8D4×C12711yescharacteristic
301C4⋊C8C23×C12711yescharacteristic
302C4⋊C8C23×C12711yescharacteristic
303C4⋊C8C23×C12711yescharacteristic
304C4⋊C8C23×C12712yes—
305C4⋊C8C23×C12711yescharacteristic
306#103—22no—
307#103—22no—
308#103—22no—
309#103—22no—
310#103—22no—
311#102—22no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8D4×C12712yes—
317C4×C8—21no—
318C4×C8—21no—
319C4×C8C23×C12712yes—
320#41—81no—
321#41—81no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4C2×D4×C12712yes—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4C2×D4×C12711yescharacteristic
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4#41×C12711yescharacteristic
338SD16—82no—
339SD16—82no—
340SD16—82no—
341M16—82no—
342M16—81no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—82no—
349C2×C8C2×D4×C12712yes—
350C2×C8C2×D4×C12712yes—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4C2×D4×C12712yes—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C42—41no—
367C42C2×D4×C12711yescharacteristic
368C42C2×D4×C12711yescharacteristic
369C42#41×C12711yescharacteristic
370C42C24×C12711yescharacteristic
371C23—22no—
372C23#121×C12711yescharacteristic
373Q8—41no—
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—41no—
378Q8—41no—
379Q8—81no—
380Q8—82no—
381D4—22no—
382D4—22no—
383D4—42no—
384D4—81no—
385D4—82no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—82no—
398C2×C4#121×C12711yescharacteristic
399C2×C4#121×C12711yescharacteristic
400C2×C4#121×C12711yescharacteristic
401C2×C4C22×D4×C12711yescharacteristic
402C2×C4C22×D4×C12711yescharacteristic
403C2×C4C2×#41×C12711yescharacteristic
404C8—22no—
405C8—22no—
406C8—42no—
407C8—41no—
408C8—41no—
409C8—41no—
410C8—41no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22C2×#121×C12711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—82no—
424C4—81no—
425C4#473×C12712yes—
426C4#576×C12711yescharacteristic
427C4#577×C12711yescharacteristic
428C4#577×C12711yescharacteristic
429C4#577×C12711yescharacteristic
430C2—41no—
431C2—82no—
432C2C127×#304211yescharacteristic
433C2C127×#306211yescharacteristic
434C2C2×#473×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ 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×#3230C2semidirect
5. C127×#1699C2semidirect
6. C127×#1693C2semidirect
7. C127×#1679C2semidirect
8. C127×#1673C2semidirect
9. C127×#1574C2semidirect
10. C127×#1546C2semidirect
11. C127×#1544C2semidirect
212. #19560C127direct (N × H)
219. #3230C2×C127semidirect
222. #1699C2×C127semidirect
223. #1693C2×C127semidirect
224. #1679C2×C127semidirect
225. #1673C2×C127semidirect
226. #1574C2×C127semidirect
227. #1546C2×C127semidirect
228. #1544C2×C127semidirect
229. C127#19560direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32542
C127×#32302
C127×#32062
C127×#29792
C127×#16992
C127×#16932
C127×#16792
C127×#16732
C127×#15742
C127×#15462
C127×#15442
#19560127