Finite Group Databasebeta

← C127×#20935 #44584608

Subgroups — C127×#20935 #44584608

Order 32512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q16×C127C211yesmaximal, characteristic
2C2×#519×C127C211yesmaximal, characteristic
3C2×#419×C127C211yesmaximal, characteristic
4C2×#419×C127C211yesmaximal, characteristic
5C127×#2310C211yesmaximal, characteristic
6C127×#1878C218yesmaximal, complemented
7C127×#1735C211yesmaximal, characteristic
8C127×#1729C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C23×Q8×C127C2211yescharacteristic
11C22×Q16×C127—24no—
12C22×Q16×C127—24no—
13C22×Q16×C127C418yescomplemented
14C22×Q16×C127C2214yes—
15C22×M16×C127C2211yescharacteristic
16C23×C8×C127C2211yescharacteristic
17#519×C127—24no—
18#519×C127—24no—
19C2×C4×Q8×C127—22no—
20C2×C4×Q8×C127C2214yes—
21C2×#117×C127—22no—
22C2×#117×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24C2×#117×C127C2211yescharacteristic
25#419×C127—24no—
26#419×C127—24no—
27C2×#103×C127C2214yes—
28C2×#103×C127C2214yes—
29#391×C127—22no—
30#391×C127C2214yes—
31#381×C127—22no—
32#340×C127C2214yes—
33#336×C127C2214yes—
34C22×Q8×C127—21no—
35C22×Q8×C127—22no—
36C22×Q8×C127—21no—
37C22×Q8×C127—22no—
38C22×Q8×C127—22no—
39C22×Q8×C127—22no—
40C22×Q8×C127—22no—
41C22×Q8×C127—22no—
42C22×Q8×C127—22no—
43C22×Q8×C127—22no—
44C22×Q8×C127C2×C414yes—
45C22×Q8×C127C2×C414yes—
46C22×Q8×C127D414yes—
47C22×Q8×C127D414yes—
48C22×Q8×C127C2312yes—
49C22×Q8×C127C2312yes—
50C23×C4×C127—21no—
51C23×C4×C127—21no—
52C23×C4×C127C2311yescharacteristic
53C2×Q16×C127—232no—
54C2×Q16×C127—28no—
55C2×Q16×C127—28no—
56C2×Q16×C127C2×C4116yes—
57C2×M16×C127—22no—
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C22×C8×C127—22no—
61C22×C8×C127—22no—
62C22×C8×C127C2×C414yes—
63C22×C8×C127C2312yes—
64C22×C8×C127C2312yes—
65C4×Q8×C127—216no—
66C4×Q8×C127—28no—
67C4×Q8×C127—28no—
68#117×C127—216no—
69#117×C127—22no—
70#117×C127—22no—
71#117×C127—22no—
72#117×C127—22no—
73#117×C127—22no—
74#117×C127D414yes—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127D412yes—
77C2×C4⋊C4×C127C2312yes—
78C2×C4⋊C4×C127C2312yes—
79C2×C22⋊C4×C127—21no—
80C2×C22⋊C4×C127—21no—
81C2×C22⋊C4×C127D412yes—
82C2×C42×C127—24no—
83C2×C42×C127—21no—
84C2×C42×C127—21no—
85C2×C42×C127C2312yes—
86#103×C127—28no—
87#103×C127—28no—
88#95×C127—28no—
89C24×C127C2×D411yescharacteristic
90C2×Q8×C127—24no—
91C2×Q8×C127—28no—
92C2×Q8×C127—24no—
93C2×Q8×C127—24no—
94C2×Q8×C127—24no—
95C2×Q8×C127—28no—
96C2×Q8×C127—28no—
97C2×Q8×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—22no—
100C2×Q8×C127—22no—
101C2×Q8×C127—28no—
102C2×Q8×C127—28no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—42no—
108C2×Q8×C127—42no—
109C2×Q8×C127—44no—
110C2×Q8×C127—44no—
111C2×Q8×C127C22⋊C4116yes—
112C2×Q8×C127C22×C414yes—
113C2×Q8×C127C22×C414yes—
114C2×Q8×C127C2×D414yes—
115C2×Q8×C127C2×D414yes—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—22no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—42no—
125C22×C4×C127—42no—
126C22×C4×C127C22×C412yes—
127C22×C4×C127C2×D414yes—
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D412yes—
132C22×C4×C127#4112yes—
133C22×C4×C127#4112yes—
134C22×C4×C127C2411yescharacteristic
135Q16×C127—232no—
136M16×C127—44no—
137C2×C8×C127—28no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127C22×C414yes—
144C4⋊C4×C127—216no—
145C4⋊C4×C127—24no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127C2×D414yes—
150C22⋊C4×C127—24no—
151C22⋊C4×C127—24no—
152C22⋊C4×C127—42no—
153C42×C127—216no—
154C42×C127—24no—
155C42×C127—22no—
156C42×C127—22no—
157C42×C127—42no—
158C23×C127—24no—
159C23×C127C4×D412yes—
160C23×C127#12012yes—
161C23×C127#12112yes—
162C23×C127C22×D411yescharacteristic
163Q8×C127—24no—
164Q8×C127—24no—
165Q8×C127—24no—
166Q8×C127—216no—
167Q8×C127—24no—
168Q8×C127—24no—
169Q8×C127—42no—
170Q8×C127—42no—
171Q8×C127—48no—
172Q8×C127C2×C22⋊C418yes—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—216no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—28no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—44no—
184C2×C4×C127—48no—
185C2×C4×C127—42no—
186C2×C4×C127—44no—
187C2×C4×C127C2×C22⋊C414yes—
188C2×C4×C127C4×D414yes—
189C2×C4×C127C4×D412yes—
190C2×C4×C127#12012yes—
191C2×C4×C127#12114yes—
192C2×C4×C127#12112yes—
193C2×C4×C127#12314yes—
194C2×C4×C127C23×C411yescharacteristic
195C2×C4×C127C22×D411yescharacteristic
196C2×C4×C127C22×D411yescharacteristic
197C2×C4×C127C22×D411yescharacteristic
198C2×C4×C127C2×#4111yescharacteristic
199C2×C4×C127C2×#4111yescharacteristic
200C8×C127—24no—
201C8×C127—42no—
202C22×C127—24no—
203C22×C127—24no—
204C22×C127—24no—
205C22×C127#38614yes—
206C22×C127C2×C4×D411yescharacteristic
207C22×C127C2×#12011yescharacteristic
208C22×C127C2×#12111yescharacteristic
209C22×C127#57814yes—
210C4×C127—28no—
211C4×C127—44no—
212C4×C127—44no—
213C4×C127—44no—
214C4×C127—82no—
215C4×C127#38614yes—
216C4×C127C22×C22⋊C411yescharacteristic
217C4×C127C2×C4×D411yescharacteristic
218C4×C127C2×#12111yescharacteristic
219C4×C127C2×#12311yescharacteristic
220#20935C12711yesmaximal, characteristic, direct product factor, Sylow
221C2×C127—24no—
222C2×C127C2×#38611yescharacteristic
223C2×C127#295012yes—
224C2×C127#301112yes—
225C2×C127#304412yes—
226C23×Q16C2×C12711yescharacteristic
227C2×#519C2×C12711yescharacteristic
228C2×#419C2×C12711yescharacteristic
229C2×#419C2×C12711yescharacteristic
230#2310C2×C12711yescharacteristic
231#1878C2×C12718yescomplemented
232#1735C2×C12711yescharacteristic
233#1729C2×C12711yescharacteristic
234C127#2093511yescharacteristic, direct product factor, Sylow
235C23×Q8C22×C12711yescharacteristic
236C23×Q8C22×C12711yescharacteristic
237C22×Q16—24no—
238C22×Q16—24no—
239C22×Q16C4×C12718yescomplemented
240C22×Q16C22×C12714yes—
241C22×M16C22×C12711yescharacteristic
242C23×C8C22×C12711yescharacteristic
243#519—24no—
244#519—24no—
245C2×C4×Q8—22no—
246C2×C4×Q8C22×C12714yes—
247C2×#117—22no—
248C2×#117C22×C12711yescharacteristic
249C2×#117C22×C12711yescharacteristic
250C2×#117C22×C12711yescharacteristic
251#419—24no—
252#419—24no—
253C2×#103C22×C12714yes—
254C2×#103C22×C12714yes—
255#391—22no—
256#391C22×C12714yes—
257#381—22no—
258#340C22×C12714yes—
259#336C22×C12714yes—
260C22×Q8—21no—
261C22×Q8—22no—
262C22×Q8—21no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8C2×C4×C12714yes—
271C22×Q8C2×C4×C12714yes—
272C22×Q8D4×C12714yes—
273C22×Q8D4×C12714yes—
274C22×Q8C23×C12712yes—
275C22×Q8C23×C12712yes—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4C23×C12711yescharacteristic
279C2×Q16—232no—
280C2×Q16—28no—
281C2×Q16—28no—
282C2×Q16C2×C4×C127116yes—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8C2×C4×C12714yes—
289C22×C8C23×C12712yes—
290C22×C8C23×C12712yes—
291C4×Q8—216no—
292C4×Q8—28no—
293C4×Q8—28no—
294#117—216no—
295#117—22no—
296#117—22no—
297#117—22no—
298#117—22no—
299#117—22no—
300#117D4×C12714yes—
301C2×C4⋊C4—24no—
302C2×C4⋊C4D4×C12712yes—
303C2×C4⋊C4C23×C12712yes—
304C2×C4⋊C4C23×C12712yes—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4D4×C12712yes—
308C2×C42—24no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42C23×C12712yes—
312#103—28no—
313#103—28no—
314#95—28no—
315C24C2×D4×C12711yescharacteristic
316C2×Q8—24no—
317C2×Q8—28no—
318C2×Q8—24no—
319C2×Q8—24no—
320C2×Q8—24no—
321C2×Q8—28no—
322C2×Q8—28no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—28no—
328C2×Q8—28no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8C22⋊C4×C127116yes—
338C2×Q8C22×C4×C12714yes—
339C2×Q8C22×C4×C12714yes—
340C2×Q8C2×D4×C12714yes—
341C2×Q8C2×D4×C12714yes—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4C22×C4×C12712yes—
353C22×C4C2×D4×C12714yes—
354C22×C4C2×D4×C12712yes—
355C22×C4C2×D4×C12712yes—
356C22×C4C2×D4×C12711yescharacteristic
357C22×C4C2×D4×C12712yes—
358C22×C4#41×C12712yes—
359C22×C4#41×C12712yes—
360C22×C4C24×C12711yescharacteristic
361Q16—232no—
362M16—44no—
363C2×C8—28no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8C22×C4×C12714yes—
370C4⋊C4—216no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4C2×D4×C12714yes—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—42no—
379C42—216no—
380C42—24no—
381C42—22no—
382C42—22no—
383C42—42no—
384C23—24no—
385C23C4×D4×C12712yes—
386C23#120×C12712yes—
387C23#121×C12712yes—
388C23C22×D4×C12711yescharacteristic
389Q8—24no—
390Q8—24no—
391Q8—24no—
392Q8—216no—
393Q8—24no—
394Q8—24no—
395Q8—42no—
396Q8—42no—
397Q8—48no—
398Q8C2×C22⋊C4×C12718yes—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—216no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—48no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4C2×C22⋊C4×C12714yes—
414C2×C4C4×D4×C12714yes—
415C2×C4C4×D4×C12712yes—
416C2×C4#120×C12712yes—
417C2×C4#121×C12714yes—
418C2×C4#121×C12712yes—
419C2×C4#123×C12714yes—
420C2×C4C23×C4×C12711yescharacteristic
421C2×C4C22×D4×C12711yescharacteristic
422C2×C4C22×D4×C12711yescharacteristic
423C2×C4C22×D4×C12711yescharacteristic
424C2×C4C2×#41×C12711yescharacteristic
425C2×C4C2×#41×C12711yescharacteristic
426C8—24no—
427C8—42no—
428C22—24no—
429C22—24no—
430C22—24no—
431C22#386×C12714yes—
432C22C2×C4×D4×C12711yescharacteristic
433C22C2×#120×C12711yescharacteristic
434C22C2×#121×C12711yescharacteristic
435C22#578×C12714yes—
436C4—28no—
437C4—44no—
438C4—44no—
439C4—44no—
440C4—82no—
441C4#386×C12714yes—
442C4C22×C22⋊C4×C12711yescharacteristic
443C4C2×C4×D4×C12711yescharacteristic
444C4C2×#121×C12711yescharacteristic
445C4C2×#123×C12711yescharacteristic
446C2—24no—
447C2C2×#386×C12711yescharacteristic
448C2C127×#295012yes—
449C2C127×#301112yes—
450C2C127×#304412yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C127×#1878C2semidirect
13. C22×Q16×C127C4semidirect
220. #20935C127direct (N × H)
231. #1878C2×C127semidirect
234. C127#20935direct (N × H)
239. C22×Q16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×Q16×C1272
C2×#519×C1272
C2×#419×C1272
C127×#23102
C127×#18782
C127×#17352
C127×#17292
#20935127