Finite Group Databasebeta

← C127×#8351 #44572024

Subgroups — C127×#8351 #44572024

Order 32512.

834 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3501C211yesmaximal, characteristic
2C127×#1892C212yesmaximal, complemented
3C127×#1869C211yesmaximal, characteristic
4C127×#1799C211yesmaximal, characteristic
5C127×#1520C212yesmaximal, complemented
6C23×C8×C127C2211yescharacteristic
7#554×C127—24no—
8#554×C127—22no—
9D4×Q8×C127—22no—
10#544×C127C412yescomplemented
11#543×C127—21no—
12#543×C127C412yescomplemented
13#533×C127—21no—
14C2×C22⋊Q8×C127—21no—
15C2×C22⋊Q8×C127C2212yes—
16#518×C127—21no—
17C2×C4×D4×C127C2211yescharacteristic
18C2×#103×C127—22no—
19C2×#99×C127—21no—
20C2×C22⋊C8×C127—21no—
21C2×C22⋊C8×C127C2211yescharacteristic
22#380×C127C2212yes—
23#342×C127—21no—
24#340×C127—22no—
25#336×C127—21no—
26#328×C127—24no—
27C22×Q8×C127—21no—
28C22×Q8×C127D412yes—
29C22×D4×C127D411yescharacteristic
30C23×C4×C127D411yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C22×C8×C127—21no—
33C22×C8×C127—22no—
34C22×C8×C127—21no—
35C22×C8×C127—42no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—24no—
39#125×C127—22no—
40#125×C127—24no—
41C22⋊Q8×C127—22no—
42C22⋊Q8×C127—22no—
43C22⋊Q8×C127—24no—
44C22⋊Q8×C127—24no—
45C22⋊Q8×C127—24no—
46C22⋊Q8×C127—22no—
47C22⋊Q8×C127—22no—
48C22⋊Q8×C127—22no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127—24no—
51C22⋊Q8×C127C2×C414yes—
52C22⋊Q8×C127D414yes—
53C4×Q8×C127—22no—
54C4×Q8×C127—22no—
55C4×D4×C127—24no—
56C4×D4×C127—24no—
57C4×D4×C127—22no—
58C4×D4×C127—22no—
59#117×C127—22no—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127C2×C411yescharacteristic
65C2×C4⋊C4×C127D412yes—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—22no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127C2×C411yescharacteristic
70C2×C22⋊C4×C127D411yescharacteristic
71C2×C42×C127D411yescharacteristic
72#103×C127—44no—
73#99×C127—42no—
74C22⋊C8×C127—22no—
75C22⋊C8×C127—42no—
76#95×C127—22no—
77C24×C127C22⋊C411yescharacteristic
78C24×C127C2×D411yescharacteristic
79C2×Q8×C127—22no—
80C2×Q8×C127—22no—
81C2×Q8×C127—22no—
82C2×Q8×C127—42no—
83C2×Q8×C127—42no—
84C2×Q8×C127—81no—
85C2×Q8×C127—81no—
86C2×Q8×C127C22⋊C414yes—
87C2×D4×C127—22no—
88C2×D4×C127—22no—
89C2×D4×C127SD1612yes—
90C2×D4×C127Q1612yes—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—41no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—42no—
102C22×C4×C127C22⋊C411yescharacteristic
103C22×C4×C127C22⋊C411yescharacteristic
104C22×C4×C127C22⋊C411yescharacteristic
105C22×C4×C127C22×C411yescharacteristic
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D412yes—
109C2×C8×C127—22no—
110C2×C8×C127—24no—
111C2×C8×C127—42no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—24no—
119C4⋊C4×C127—22no—
120C4⋊C4×C127—22no—
121C4⋊C4×C127—24no—
122C4⋊C4×C127—22no—
123C4⋊C4×C127—24no—
124C4⋊C4×C127—22no—
125C4⋊C4×C127—24no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—42no—
128C4⋊C4×C127—42no—
129C4⋊C4×C127C22⋊C414yes—
130C22⋊C4×C127—24no—
131C22⋊C4×C127—24no—
132C22⋊C4×C127—24no—
133C22⋊C4×C127—22no—
134C22⋊C4×C127—22no—
135C22⋊C4×C127—42no—
136C22⋊C4×C127—42no—
137C42×C127—24no—
138C42×C127—21no—
139C42×C127—21no—
140C23×C127—21no—
141C23×C127—21no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127—41no—
146C23×C127#10312yescomplemented
147C23×C127C2×C22⋊C411yescharacteristic
148C23×C127#12012yes—
149C23×C127C2×SD1611yescharacteristic
150C23×C127C2×Q1611yescharacteristic
151C23×C127#13712yes—
152Q8×C127—44no—
153Q8×C127—42no—
154Q8×C127—42no—
155Q8×C127—82no—
156Q8×C127—82no—
157D4×C127—24no—
158D4×C127—24no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—22no—
162C2×C4×C127—21no—
163C2×C4×C127—22no—
164C2×C4×C127—21no—
165C2×C4×C127—21no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—21no—
169C2×C4×C127—41no—
170C2×C4×C127—42no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—81no—
176C2×C4×C127—82no—
177C2×C4×C127—82no—
178C2×C4×C127—82no—
179C2×C4×C127—82no—
180C2×C4×C127—82no—
181C2×C4×C127—82no—
182C2×C4×C127—82no—
183C2×C4×C127#10312yescomplemented
184C2×C4×C127C2×C22⋊C412yes—
185C2×C4×C127#12011yescharacteristic
186C2×C4×C127#12011yescharacteristic
187C8×C127—42no—
188C8×C127—81no—
189C22×C127—21no—
190C22×C127—22no—
191C22×C127—21no—
192C22×C127—22no—
193C22×C127—22no—
194C22×C127—41no—
195C22×C127—41no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—41no—
199C22×C127—41no—
200C22×C127—81no—
201C22×C127#37911yescharacteristic
202C22×C127C2×#10311yescharacteristic
203C22×C127#41911yescharacteristic
204C22×C127#44812yes—
205C22×C127#45112yes—
206C4×C127—22no—
207C4×C127—21no—
208C4×C127—22no—
209C4×C127—41no—
210C4×C127—44no—
211C4×C127—41no—
212C4×C127—44no—
213C4×C127—162no—
214C4×C127B(4,𝔽2)11yescharacteristic
215C4×C127#45811yescharacteristic
216#8351C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127—22no—
218C2×C127—21no—
219C2×C127—21no—
220C2×C127—22no—
221C2×C127—42no—
222C2×C127#178711yescharacteristic
223C2×C127#179011yescharacteristic
224C2×C127#179411yescharacteristic
225#3501C2×C12711yescharacteristic
226#1892C2×C12712yescomplemented
227#1869C2×C12711yescharacteristic
228#1799C2×C12711yescharacteristic
229#1520C2×C12712yescomplemented
230C127#835111yescharacteristic, direct product factor, Sylow
231C23×C8C22×C12711yescharacteristic
232#554—24no—
233#554—22no—
234D4×Q8—22no—
235#544C4×C12712yescomplemented
236#543—21no—
237#543C4×C12712yescomplemented
238#533—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C22×C12712yes—
241#518—21no—
242C2×C4×D4C22×C12711yescharacteristic
243C2×#103—22no—
244C2×#99—21no—
245C2×C22⋊C8—21no—
246C2×C22⋊C8C22×C12711yescharacteristic
247#380C22×C12712yes—
248#342—21no—
249#340—22no—
250#336—21no—
251#328—24no—
252C22×Q8—21no—
253C22×Q8D4×C12712yes—
254C22×D4D4×C12711yescharacteristic
255C23×C4D4×C12711yescharacteristic
256C23×C4C23×C12711yescharacteristic
257C22×C8—21no—
258C22×C8—22no—
259C22×C8—21no—
260C22×C8—42no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—24no—
264#125—22no—
265#125—24no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C22⋊Q8—24no—
269C22⋊Q8—24no—
270C22⋊Q8—24no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—24no—
276C22⋊Q8C2×C4×C12714yes—
277C22⋊Q8D4×C12714yes—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×D4—24no—
281C4×D4—24no—
282C4×D4—22no—
283C4×D4—22no—
284#117—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4C2×C4×C12711yescharacteristic
290C2×C4⋊C4D4×C12712yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4C2×C4×C12711yescharacteristic
295C2×C22⋊C4D4×C12711yescharacteristic
296C2×C42D4×C12711yescharacteristic
297#103—44no—
298#99—42no—
299C22⋊C8—22no—
300C22⋊C8—42no—
301#95—22no—
302C24C22⋊C4×C12711yescharacteristic
303C24C2×D4×C12711yescharacteristic
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—42no—
308C2×Q8—42no—
309C2×Q8—81no—
310C2×Q8—81no—
311C2×Q8C22⋊C4×C12714yes—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4SD16×C12712yes—
315C2×D4Q16×C12712yes—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4C22⋊C4×C12711yescharacteristic
328C22×C4C22⋊C4×C12711yescharacteristic
329C22×C4C22⋊C4×C12711yescharacteristic
330C22×C4C22×C4×C12711yescharacteristic
331C22×C4C2×D4×C12712yes—
332C22×C4C2×D4×C12711yescharacteristic
333C22×C4C2×D4×C12712yes—
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4C22⋊C4×C12714yes—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C42—24no—
363C42—21no—
364C42—21no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23#103×C12712yescomplemented
372C23C2×C22⋊C4×C12711yescharacteristic
373C23#120×C12712yes—
374C23C2×SD16×C12711yescharacteristic
375C23C2×Q16×C12711yescharacteristic
376C23#137×C12712yes—
377Q8—44no—
378Q8—42no—
379Q8—42no—
380Q8—82no—
381Q8—82no—
382D4—24no—
383D4—24no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4#103×C12712yescomplemented
409C2×C4C2×C22⋊C4×C12712yes—
410C2×C4#120×C12711yescharacteristic
411C2×C4#120×C12711yescharacteristic
412C8—42no—
413C8—81no—
414C22—21no—
415C22—22no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22#379×C12711yescharacteristic
427C22C2×#103×C12711yescharacteristic
428C22#419×C12711yescharacteristic
429C22#448×C12712yes—
430C22#451×C12712yes—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—44no—
436C4—41no—
437C4—44no—
438C4—162no—
439C4B(4,𝔽2)×C12711yescharacteristic
440C4#458×C12711yescharacteristic
441C2—22no—
442C2—21no—
443C2—21no—
444C2—22no—
445C2—42no—
446C2C127×#178711yescharacteristic
447C2C127×#179011yescharacteristic
448C2C127×#179411yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1892C2semidirect
5. C127×#1520C2semidirect
10. #544×C127C4semidirect
12. #543×C127C4semidirect
146. C23×C127#103semidirect
183. C2×C4×C127#103semidirect
216. #8351C127direct (N × H)
226. #1892C2×C127semidirect
229. #1520C2×C127semidirect
230. C127#8351direct (N × H)
235. #544C4×C127semidirect
237. #543C4×C127semidirect
371. C23#103×C127semidirect
408. C2×C4#103×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35012
C127×#18922
C127×#18692
C127×#17992
C127×#15202
#8351127