Finite Group Databasebeta

← C127×#10976 #44574649

Subgroups — C127×#10976 #44574649

Order 32512.

1462 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
1C22×#124×C127C211yesmaximal, characteristic
2C2×#418×C127C212yesmaximal
3C22×#101×C127C211yesmaximal, characteristic, complemented
4C127×#2310C211yesmaximal, characteristic, complemented
5C2×#339×C127C212yesmaximal, complemented
6C23×Q8×C127C2211yescharacteristic
7C23×D4×C127C2211yescharacteristic
8C22×M16×C127C2212yes—
9C2×#124×C127—22no—
10C2×#124×C127—24no—
11C2×#124×C127—24no—
12C2×#124×C127C414yescomplemented
13C2×#117×C127C2212yes—
14C22×C22⋊C4×C127—22no—
15C22×C42×C127C2211yescharacteristic
16#418×C127—24no—
17#418×C127—24no—
18C2×#102×C127—24no—
19C2×#101×C127—22no—
20C2×#101×C127—24no—
21#391×C127—24no—
22#381×C127—22no—
23#339×C127—24no—
24C25×C127—21no—
25C22×Q8×C127—22no—
26C22×Q8×C127—22no—
27C22×Q8×C127—22no—
28C22×Q8×C127—22no—
29C22×Q8×C127—22no—
30C22×Q8×C127—22no—
31C22×Q8×C127C2×C412yes—
32C22×Q8×C127D412yes—
33C22×D4×C127—22no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C412yes—
40C22×D4×C127D414yes—
41C23×C4×C127—21no—
42C23×C4×C127D412yes—
43C23×C4×C127C2311yescharacteristic
44C2×M16×C127—22no—
45C2×M16×C127—22no—
46C2×M16×C127—22no—
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127D414yes—
50C22×C8×C127—22no—
51#124×C127—216no—
52#124×C127—28no—
53#124×C127—28no—
54#117×C127—22no—
55#117×C127—22no—
56#117×C127—22no—
57#117×C127—22no—
58C2×C4⋊C4×C127D414yes—
59C2×C22⋊C4×C127—216no—
60C2×C22⋊C4×C127—28no—
61C2×C22⋊C4×C127—22no—
62C2×C42×C127—22no—
63C2×C42×C127—21no—
64C2×C42×C127—22no—
65C2×C42×C127C2×C412yes—
66C2×C42×C127D414yes—
67#102×C127—216no—
68#101×C127—28no—
69#95×C127—28no—
70C24×C127—22no—
71C24×C127—24no—
72C24×C127—48no—
73C24×C127—41no—
74C24×C127—42no—
75C24×C127—41no—
76C24×C127C2×D411yescharacteristic
77C2×Q8×C127—22no—
78C2×Q8×C127—22no—
79C2×Q8×C127—24no—
80C2×Q8×C127—24no—
81C2×Q8×C127—22no—
82C2×Q8×C127—24no—
83C2×Q8×C127—24no—
84C2×Q8×C127—22no—
85C2×Q8×C127—42no—
86C2×Q8×C127—42no—
87C2×Q8×C127—42no—
88C2×Q8×C127—42no—
89C2×Q8×C127—42no—
90C2×Q8×C127—42no—
91C2×Q8×C127—42no—
92C2×Q8×C127—42no—
93C2×D4×C127—22no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—24no—
99C2×D4×C127—24no—
100C2×D4×C127—24no—
101C2×D4×C127—41no—
102C2×D4×C127—42no—
103C2×D4×C127—42no—
104C2×D4×C127—42no—
105C2×D4×C127—41no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127C22⋊C414yes—
109C22×C4×C127—22no—
110C22×C4×C127—24no—
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—24no—
114C22×C4×C127—22no—
115C22×C4×C127—24no—
116C22×C4×C127—44no—
117C22×C4×C127C22⋊C414yes—
118C22×C4×C127C22×C411yescharacteristic
119C22×C4×C127C2×D412yes—
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127#4112yes—
125C22×C4×C127#4112yes—
126M16×C127—24no—
127M16×C127—24no—
128M16×C127—42no—
129M16×C127—42no—
130C2×C8×C127—24no—
131C2×C8×C127—42no—
132C2×C8×C127—42no—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—24no—
135C22⋊C4×C127—232no—
136C22⋊C4×C127—42no—
137C22⋊C4×C127—42no—
138C42×C127—22no—
139C42×C127—24no—
140C42×C127—42no—
141C42×C127—42no—
142C42×C127C22⋊C414yes—
143C23×C127—24no—
144C23×C127—24no—
145C23×C127—48no—
146C23×C127—416no—
147C23×C127—42no—
148C23×C127—42no—
149C23×C127—44no—
150C23×C127—44no—
151C23×C127—84no—
152C23×C127—88no—
153C23×C127—84no—
154C23×C127C2×C22⋊C411yescharacteristic
155C23×C127#12012yes—
156C23×C127#12011yescharacteristic
157C23×C127#12112yes—
158C23×C127#12311yescharacteristic
159Q8×C127—44no—
160Q8×C127—44no—
161Q8×C127—44no—
162Q8×C127—44no—
163D4×C127—28no—
164D4×C127—44no—
165D4×C127—44no—
166D4×C127—44no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—44no—
172C2×C4×C127—48no—
173C2×C4×C127—44no—
174C2×C4×C127—44no—
175C2×C4×C127—44no—
176C2×C4×C127—48no—
177C2×C4×C127C2×C22⋊C411yescharacteristic
178C2×C4×C127C2×C22⋊C411yescharacteristic
179C2×C4×C127C4×D412yes—
180C2×C4×C127C4×D412yes—
181C2×C4×C127#12012yes—
182C2×C4×C127#12011yescharacteristic
183C2×C4×C127#12012yes—
184C2×C4×C127#12112yes—
185C2×C4×C127#12112yes—
186C2×C4×C127#12112yes—
187C2×C4×C127#12112yes—
188C2×C4×C127#12112yes—
189C2×C4×C127#12312yes—
190C2×C4×C127#12311yescharacteristic
191C2×C4×C127#12412yes—
192C2×C4×C127#12712yes—
193C8×C127—44no—
194C22×C127—22no—
195C22×C127—22no—
196C22×C127—24no—
197C22×C127—24no—
198C22×C127—48no—
199C22×C127—44no—
200C22×C127—84no—
201C22×C127—88no—
202C22×C127—84no—
203C22×C127—88no—
204C22×C127#37911yescharacteristic
205C22×C127#38611yescharacteristic
206C22×C127#38611yescharacteristic
207C22×C127#39212yes—
208C22×C127#39412yes—
209C22×C127#45414yes—
210C4×C127—44no—
211C4×C127—44no—
212C4×C127—84no—
213C4×C127#38612yes—
214C4×C127#39012yes—
215C4×C127#39212yes—
216C4×C127#39412yes—
217#10976C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—21no—
219C2×C127—21no—
220C2×C127—22no—
221C2×C127—84no—
222C2×C127#143811yescharacteristic
223C2×C127#188812yes—
224C2×C127#200314yes—
225C22×#124C2×C12711yescharacteristic
226C2×#418C2×C12712yes—
227C22×#101C2×C12711yescharacteristic, complemented
228#2310C2×C12711yescharacteristic, complemented
229C2×#339C2×C12712yescomplemented
230C127#1097611yescharacteristic, direct product factor, Sylow
231C23×Q8C22×C12711yescharacteristic
232C23×D4C22×C12711yescharacteristic
233C22×M16C22×C12712yes—
234C2×#124—22no—
235C2×#124—24no—
236C2×#124—24no—
237C2×#124C4×C12714yescomplemented
238C2×#117C22×C12712yes—
239C22×C22⋊C4—22no—
240C22×C42C22×C12711yescharacteristic
241#418—24no—
242#418—24no—
243C2×#102—24no—
244C2×#101—22no—
245C2×#101—24no—
246#391—24no—
247#381—22no—
248#339—24no—
249C25—21no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8C2×C4×C12712yes—
257C22×Q8D4×C12712yes—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4C2×C4×C12712yes—
265C22×D4D4×C12714yes—
266C23×C4—21no—
267C23×C4D4×C12712yes—
268C23×C4C23×C12711yescharacteristic
269C2×M16—22no—
270C2×M16—22no—
271C2×M16—22no—
272C2×M16—22no—
273C2×M16—22no—
274C2×M16D4×C12714yes—
275C22×C8—22no—
276#124—216no—
277#124—28no—
278#124—28no—
279#117—22no—
280#117—22no—
281#117—22no—
282#117—22no—
283C2×C4⋊C4D4×C12714yes—
284C2×C22⋊C4—216no—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—22no—
287C2×C42—22no—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42C2×C4×C12712yes—
291C2×C42D4×C12714yes—
292#102—216no—
293#101—28no—
294#95—28no—
295C24—22no—
296C24—24no—
297C24—48no—
298C24—41no—
299C24—42no—
300C24—41no—
301C24C2×D4×C12711yescharacteristic
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—24no—
305C2×Q8—24no—
306C2×Q8—22no—
307C2×Q8—24no—
308C2×Q8—24no—
309C2×Q8—22no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—42no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×Q8—42no—
318C2×D4—22no—
319C2×D4—24no—
320C2×D4—24no—
321C2×D4—24no—
322C2×D4—24no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—41no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4C22⋊C4×C12714yes—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—44no—
342C22×C4C22⋊C4×C12714yes—
343C22×C4C22×C4×C12711yescharacteristic
344C22×C4C2×D4×C12712yes—
345C22×C4C2×D4×C12712yes—
346C22×C4C2×D4×C12712yes—
347C22×C4C2×D4×C12712yes—
348C22×C4C2×D4×C12711yescharacteristic
349C22×C4#41×C12712yes—
350C22×C4#41×C12712yes—
351M16—24no—
352M16—24no—
353M16—42no—
354M16—42no—
355C2×C8—24no—
356C2×C8—42no—
357C2×C8—42no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C22⋊C4—232no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—22no—
364C42—24no—
365C42—42no—
366C42—42no—
367C42C22⋊C4×C12714yes—
368C23—24no—
369C23—24no—
370C23—48no—
371C23—416no—
372C23—42no—
373C23—42no—
374C23—44no—
375C23—44no—
376C23—84no—
377C23—88no—
378C23—84no—
379C23C2×C22⋊C4×C12711yescharacteristic
380C23#120×C12712yes—
381C23#120×C12711yescharacteristic
382C23#121×C12712yes—
383C23#123×C12711yescharacteristic
384Q8—44no—
385Q8—44no—
386Q8—44no—
387Q8—44no—
388D4—28no—
389D4—44no—
390D4—44no—
391D4—44no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—44no—
397C2×C4—48no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—48no—
402C2×C4C2×C22⋊C4×C12711yescharacteristic
403C2×C4C2×C22⋊C4×C12711yescharacteristic
404C2×C4C4×D4×C12712yes—
405C2×C4C4×D4×C12712yes—
406C2×C4#120×C12712yes—
407C2×C4#120×C12711yescharacteristic
408C2×C4#120×C12712yes—
409C2×C4#121×C12712yes—
410C2×C4#121×C12712yes—
411C2×C4#121×C12712yes—
412C2×C4#121×C12712yes—
413C2×C4#121×C12712yes—
414C2×C4#123×C12712yes—
415C2×C4#123×C12711yescharacteristic
416C2×C4#124×C12712yes—
417C2×C4#127×C12712yes—
418C8—44no—
419C22—22no—
420C22—22no—
421C22—24no—
422C22—24no—
423C22—48no—
424C22—44no—
425C22—84no—
426C22—88no—
427C22—84no—
428C22—88no—
429C22#379×C12711yescharacteristic
430C22#386×C12711yescharacteristic
431C22#386×C12711yescharacteristic
432C22#392×C12712yes—
433C22#394×C12712yes—
434C22#454×C12714yes—
435C4—44no—
436C4—44no—
437C4—84no—
438C4#386×C12712yes—
439C4#390×C12712yes—
440C4#392×C12712yes—
441C4#394×C12712yes—
442C2—21no—
443C2—21no—
444C2—22no—
445C2—84no—
446C2C127×#143811yescharacteristic
447C2C127×#188812yes—
448C2C127×#200314yes—
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×#101×C127C2semidirect
4. C127×#2310C2semidirect
5. C2×#339×C127C2semidirect
12. C2×#124×C127C4semidirect
217. #10976C127direct (N × H)
227. C22×#101C2×C127semidirect
228. #2310C2×C127semidirect
229. C2×#339C2×C127semidirect
230. C127#10976direct (N × H)
237. C2×#124C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C2×#418×C1272
C22×#101×C1272
C127×#23102
C2×#339×C1272
#10976127