Finite Group Databasebeta

← C127×#8402 #44572075

Subgroups — C127×#8402 #44572075

Order 32512.

716 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3461C211yesmaximal, characteristic
2C127×#1985C211yesmaximal, characteristic, complemented
3C4×#101×C127C211yesmaximal, characteristic, complemented
4C127×#1524C212yesmaximal, complemented
5C127×#1483C212yesmaximal, complemented
6#544×C127C411yescharacteristic
7#542×C127—22no—
8#541×C127—22no—
9#539×C127—21no—
10#539×C127C412yes—
11#537×C127C411yescharacteristic
12#536×C127—21no—
13#533×C127—22no—
14#529×C127—22no—
15#529×C127—21no—
16#529×C127C2212yes—
17C4×#41×C127—21no—
18C2×C4×Q8×C127C2211yescharacteristic
19C2×C4⋊C8×C127C2211yescharacteristic
20C2×#101×C127—21no—
21C4×M16×C127C2212yes—
22C2×#97×C127C2211yescharacteristic
23#343×C127—21no—
24#336×C127—21no—
25#336×C127—21no—
26#330×C127—22no—
27#329×C127—22no—
28Q8⋊C8×C127—22no—
29D4⋊C8×C127—22no—
30C2×#41×C127—21no—
31C22×Q8×C127D411yescharacteristic
32C2×M16×C127—22no—
33C22×C8×C127—21no—
34C22×C8×C127—21no—
35C4⋊Q8×C127—22no—
36C4⋊Q8×C127—22no—
37#126×C127—22no—
38#126×C127—22no—
39#126×C127—22no—
40#126×C127—22no—
41#125×C127—21no—
42#125×C127—22no—
43#125×C127—22no—
44#125×C127—22no—
45#125×C127D412yes—
46#124×C127—22no—
47#124×C127—21no—
48#124×C127D412yes—
49#123×C127—22no—
50#123×C127—22no—
51#123×C127—22no—
52#123×C127—22no—
53C22⋊Q8×C127—22no—
54C22⋊Q8×C127—22no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—22no—
57C22⋊Q8×C127—21no—
58C22⋊Q8×C127—22no—
59C22⋊Q8×C127C2×C412yes—
60#121×C127—22no—
61#121×C127—21no—
62#121×C127C2×C412yes—
63C4×Q8×C127—21no—
64C4×Q8×C127—21no—
65C4×Q8×C127—21no—
66C4×Q8×C127—22no—
67C4×Q8×C127—22no—
68C4×Q8×C127D412yes—
69C4×D4×C127—21no—
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127—22no—
73C4×D4×C127—22no—
74C4×D4×C127D412yes—
75#117×C127—22no—
76#117×C127—22no—
77#117×C127—21no—
78#117×C127—22no—
79C2×C4⋊C4×C127C2×C411yescharacteristic
80C2×C4⋊C4×C127C2×C411yescharacteristic
81C2×C4⋊C4×C127D411yescharacteristic
82C2×C42×C127—22no—
83C2×C42×C127D411yescharacteristic
84C2×C42×C127D411yescharacteristic
85C2×C42×C127C2311yescharacteristic
86C4⋊C8×C127—22no—
87#101×C127—24no—
88#97×C127—22no—
89#97×C127—22no—
90C4×C8×C127—22no—
91#41×C127—42no—
92#41×C127—42no—
93C2×Q8×C127—21no—
94C2×Q8×C127—21no—
95C2×Q8×C127—22no—
96C2×Q8×C127—22no—
97C2×Q8×C127—41no—
98C2×Q8×C127C22⋊C412yes—
99C2×D4×C127—21no—
100C2×D4×C127—22no—
101C2×D4×C127—21no—
102C2×D4×C127C22⋊C412yes—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127C22⋊C411yescharacteristic
107C22×C4×C127C22⋊C411yescharacteristic
108C22×C4×C127C22⋊C411yescharacteristic
109C22×C4×C127C22⋊C411yescharacteristic
110C22×C4×C127C22×C411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113M16×C127—24no—
114M16×C127—42no—
115C2×C8×C127—22no—
116C2×C8×C127—41no—
117C2×C8×C127—42no—
118C2×C8×C127—41no—
119C2×C8×C127—42no—
120C2×C8×C127—41no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—22no—
123C4⋊C4×C127—21no—
124C4⋊C4×C127—22no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—21no—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127C22⋊C412yes—
137C4⋊C4×C127C22⋊C412yes—
138C22⋊C4×C127—22no—
139C22⋊C4×C127—22no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—22no—
144C22⋊C4×C127—22no—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—22no—
147C42×C127—22no—
148C42×C127—22no—
149C42×C127—21no—
150C42×C127—21no—
151C42×C127—21no—
152C42×C127—22no—
153C42×C127—21no—
154C42×C127C2×D412yes—
155C42×C127C2×D412yes—
156C23×C127—22no—
157C23×C127C2×C22⋊C411yescharacteristic
158Q8×C127—44no—
159Q8×C127—42no—
160Q8×C127—42no—
161Q8×C127—81no—
162D4×C127—42no—
163D4×C127—42no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—81no—
167C2×C4×C127—21no—
168C2×C4×C127—21no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—21no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—22no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—41no—
182C2×C4×C127—44no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—82no—
188C2×C4×C127#10412yes—
189C2×C4×C127C2×C22⋊C412yes—
190C2×C4×C127#12011yescharacteristic
191C2×C4×C127#12012yes—
192C2×C4×C127#12011yescharacteristic
193C8×C127—42no—
194C8×C127—44no—
195C8×C127—81no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—42no—
199C22×C127—42no—
200C22×C127—42no—
201C22×C127#37911yescharacteristic
202C22×C127C2×#10411yescharacteristic
203C22×C127#42111yescharacteristic
204C4×C127—21no—
205C4×C127—22no—
206C4×C127—22no—
207C4×C127—22no—
208C4×C127—42no—
209C4×C127—41no—
210C4×C127—42no—
211C4×C127—41no—
212C4×C127—41no—
213C4×C127—42no—
214C4×C127#45411yescharacteristic
215C4×C127#45611yescharacteristic
216#8402C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127—21no—
218C2×C127—21no—
219C2×C127—82no—
220C2×C127#178911yescharacteristic
221C2×C127#179111yescharacteristic
222C2×C127#179311yescharacteristic
223#3461C2×C12711yescharacteristic
224#1985C2×C12711yescharacteristic, complemented
225C4×#101C2×C12711yescharacteristic, complemented
226#1524C2×C12712yescomplemented
227#1483C2×C12712yescomplemented
228C127#840211yescharacteristic, direct product factor, Sylow
229#544C4×C12711yescharacteristic
230#542—22no—
231#541—22no—
232#539—21no—
233#539C4×C12712yes—
234#537C4×C12711yescharacteristic
235#536—21no—
236#533—22no—
237#529—22no—
238#529—21no—
239#529C22×C12712yes—
240C4×#41—21no—
241C2×C4×Q8C22×C12711yescharacteristic
242C2×C4⋊C8C22×C12711yescharacteristic
243C2×#101—21no—
244C4×M16C22×C12712yes—
245C2×#97C22×C12711yescharacteristic
246#343—21no—
247#336—21no—
248#336—21no—
249#330—22no—
250#329—22no—
251Q8⋊C8—22no—
252D4⋊C8—22no—
253C2×#41—21no—
254C22×Q8D4×C12711yescharacteristic
255C2×M16—22no—
256C22×C8—21no—
257C22×C8—21no—
258C4⋊Q8—22no—
259C4⋊Q8—22no—
260#126—22no—
261#126—22no—
262#126—22no—
263#126—22no—
264#125—21no—
265#125—22no—
266#125—22no—
267#125—22no—
268#125D4×C12712yes—
269#124—22no—
270#124—21no—
271#124D4×C12712yes—
272#123—22no—
273#123—22no—
274#123—22no—
275#123—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—21no—
281C22⋊Q8—22no—
282C22⋊Q8C2×C4×C12712yes—
283#121—22no—
284#121—21no—
285#121C2×C4×C12712yes—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×Q8D4×C12712yes—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4D4×C12712yes—
298#117—22no—
299#117—22no—
300#117—21no—
301#117—22no—
302C2×C4⋊C4C2×C4×C12711yescharacteristic
303C2×C4⋊C4C2×C4×C12711yescharacteristic
304C2×C4⋊C4D4×C12711yescharacteristic
305C2×C42—22no—
306C2×C42D4×C12711yescharacteristic
307C2×C42D4×C12711yescharacteristic
308C2×C42C23×C12711yescharacteristic
309C4⋊C8—22no—
310#101—24no—
311#97—22no—
312#97—22no—
313C4×C8—22no—
314#41—42no—
315#41—42no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—41no—
321C2×Q8C22⋊C4×C12712yes—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—21no—
325C2×D4C22⋊C4×C12712yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4C22⋊C4×C12711yescharacteristic
330C22×C4C22⋊C4×C12711yescharacteristic
331C22×C4C22⋊C4×C12711yescharacteristic
332C22×C4C22⋊C4×C12711yescharacteristic
333C22×C4C22×C4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4C2×D4×C12711yescharacteristic
336M16—24no—
337M16—42no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—42no—
341C2×C8—41no—
342C2×C8—42no—
343C2×C8—41no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4C22⋊C4×C12712yes—
360C4⋊C4C22⋊C4×C12712yes—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C42—22no—
371C42—22no—
372C42—21no—
373C42—22no—
374C42—21no—
375C42—21no—
376C42—21no—
377C42C2×D4×C12712yes—
378C42C2×D4×C12712yes—
379C23—22no—
380C23C2×C22⋊C4×C12711yescharacteristic
381Q8—44no—
382Q8—42no—
383Q8—42no—
384Q8—81no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—81no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4#104×C12712yes—
412C2×C4C2×C22⋊C4×C12712yes—
413C2×C4#120×C12711yescharacteristic
414C2×C4#120×C12712yes—
415C2×C4#120×C12711yescharacteristic
416C8—42no—
417C8—44no—
418C8—81no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22#379×C12711yescharacteristic
425C22C2×#104×C12711yescharacteristic
426C22#421×C12711yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—21no—
431C4—41no—
432C4—42no—
433C4—41no—
434C4—41no—
435C4—42no—
436C4—42no—
437C4#454×C12711yescharacteristic
438C4#456×C12711yescharacteristic
439C2—21no—
440C2—21no—
441C2—82no—
442C2C127×#178911yescharacteristic
443C2C127×#179111yescharacteristic
444C2C127×#179311yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#379
prime radical#537×C127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1985C2semidirect
3. C4×#101×C127C2semidirect
4. C127×#1524C2semidirect
5. C127×#1483C2semidirect
216. #8402C127direct (N × H)
224. #1985C2×C127semidirect
225. C4×#101C2×C127semidirect
226. #1524C2×C127semidirect
227. #1483C2×C127semidirect
228. C127#8402direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34612
C127×#19852
C4×#101×C1272
C127×#15242
C127×#14832
#8402127