Finite Group Databasebeta

← C127×#18293 #44581966

Subgroups — C127×#18293 #44581966

Order 32512.

1220 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C127C211yesmaximal, characteristic
2C127×#3187C212yesmaximal, complemented
3C127×#2627C211yesmaximal, characteristic, complemented
4C127×#1616C214yesmaximal, complemented
5C127×#1604C214yesmaximal, complemented
6C127×#1519C212yesmaximal, complemented
7C2×#324×C127C211yesmaximal, characteristic, complemented
8C22×#41×C127—21no—
9#537×C127—24no—
10#537×C127—22no—
11#537×C127C2214yes—
12C2×C22⋊Q8×C127—22no—
13C2×C22⋊Q8×C127C2211yescharacteristic
14C2×#121×C127—22no—
15C2×#121×C127—21no—
16C2×#121×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18#483×C127—22no—
19#481×C127C2214yescomplemented
20#465×C127—24no—
21#450×C127—22no—
22#448×C127C2214yescomplemented
23C2×C22⋊C8×C127C2212yes—
24#400×C127C2212yescomplemented
25#398×C127—22no—
26#395×C127C2212yescomplemented
27#385×C127—21no—
28#381×C127—21no—
29#380×C127C2211yescharacteristic
30#327×C127C2218yescomplemented
31#324×C127C2214yescomplemented
32C2×#41×C127—24no—
33C2×#41×C127—24no—
34C2×#41×C127—44no—
35C2×#41×C127—44no—
36C22×Q8×C127—21no—
37C22×Q8×C127C2311yescharacteristic
38C22×D4×C127—21no—
39C22×D4×C127—22no—
40C22×D4×C127—21no—
41C22×D4×C127D412yes—
42C23×C4×C127—22no—
43C23×C4×C127D411yescharacteristic
44C23×C4×C127D411yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C2×SD16×C127—24no—
47C22×C8×C127—22no—
48C22⋊Q8×C127—28no—
49C22⋊Q8×C127—28no—
50C22⋊Q8×C127—22no—
51C22⋊Q8×C127—22no—
52#121×C127—24no—
53#121×C127—28no—
54#121×C127—28no—
55#121×C127—24no—
56#121×C127—22no—
57#121×C127—22no—
58#121×C127D414yes—
59#121×C127C2314yes—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127D412yes—
67C2×C4⋊C4×C127D412yes—
68C2×C4⋊C4×C127C2311yescharacteristic
69C2×C4⋊C4×C127C2312yes—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—21no—
73C2×C22⋊C4×C127—21no—
74#106×C127—24no—
75#103×C127—24no—
76#102×C127—24no—
77C22⋊C8×C127—22no—
78C22⋊C8×C127C2314yes—
79#95×C127—22no—
80#95×C127—22no—
81#95×C127—22no—
82#95×C127C2312yes—
83C24×C127—22no—
84C24×C127C2×D411yescharacteristic
85#41×C127—48no—
86#41×C127—416no—
87#41×C127—48no—
88C2×Q8×C127—24no—
89C2×Q8×C127—22no—
90C2×Q8×C127—44no—
91C2×Q8×C127—81no—
92C2×D4×C127—24no—
93C2×D4×C127—24no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—22no—
97C2×D4×C127—44no—
98C2×D4×C127—44no—
99C2×D4×C127—44no—
100C2×D4×C127—82no—
101C2×D4×C127—82no—
102C2×D4×C127C2×D414yes—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—28no—
107C22×C4×C127—21no—
108C22×C4×C127—22no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—21no—
113C22×C4×C127—48no—
114C22×C4×C127—81no—
115C22×C4×C127—81no—
116C22×C4×C127SD1614yescomplemented
117C22×C4×C127C2×D412yes—
118C22×C4×C127C2×D412yes—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2411yescharacteristic
123SD16×C127—84no—
124C2×C8×C127—24no—
125C2×C8×C127—82no—
126C4⋊C4×C127—24no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—42no—
132C4⋊C4×C127—81no—
133C4⋊C4×C127—82no—
134C4⋊C4×C127C2×D414yes—
135C22⋊C4×C127—28no—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—24no—
138C22⋊C4×C127—41no—
139C22⋊C4×C127—41no—
140C22⋊C4×C127—42no—
141C23×C127—24no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—44no—
145C23×C127—44no—
146C23×C127—44no—
147C23×C127#12011yescharacteristic
148C23×C127#12011yescharacteristic
149C23×C127C2×SD1612yes—
150C23×C127AGL(1,ℤ/8)12yes—
151C23×C127C22×D411yescharacteristic
152Q8×C127—48no—
153Q8×C127—44no—
154D4×C127—44no—
155D4×C127—48no—
156D4×C127—44no—
157D4×C127—44no—
158D4×C127—48no—
159D4×C127—82no—
160D4×C127—84no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—22no—
166C2×C4×C127—24no—
167C2×C4×C127—41no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
170C2×C4×C127—41no—
171C2×C4×C127—416no—
172C2×C4×C127—42no—
173C2×C4×C127—44no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—42no—
182C2×C4×C127—81no—
183C2×C4×C127#12012yes—
184C2×C4×C127C2×SD1614yes—
185C2×C4×C127C22×D412yes—
186C8×C127—44no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—42no—
194C22×C127—42no—
195C22×C127—44no—
196C22×C127—44no—
197C22×C127—44no—
198C22×C127—88no—
199C22×C127#45012yes—
200C22×C127#45012yes—
201C22×C127C2×#12011yescharacteristic
202C22×C127C22×SD1611yescharacteristic
203C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
204C4×C127—24no—
205C4×C127—22no—
206C4×C127—22no—
207C4×C127—44no—
208C4×C127—42no—
209C4×C127—82no—
210C4×C127—81no—
211C4×C127—81no—
212#18293C12711yesmaximal, characteristic, direct product factor, Sylow
213C2×C127—21no—
214C2×C127—22no—
215C2×C127—21no—
216C2×C127—22no—
217C2×C127—84no—
218C2×C127C2×#45011yescharacteristic
219C2×C127#302011yescharacteristic
220C2×C127#302611yescharacteristic
221C2×#537C2×C12711yescharacteristic
222#3187C2×C12712yescomplemented
223#2627C2×C12711yescharacteristic, complemented
224#1616C2×C12714yescomplemented
225#1604C2×C12714yescomplemented
226#1519C2×C12712yescomplemented
227C2×#324C2×C12711yescharacteristic, complemented
228C127#1829311yescharacteristic, direct product factor, Sylow
229C22×#41—21no—
230#537—24no—
231#537—22no—
232#537C22×C12714yes—
233C2×C22⋊Q8—22no—
234C2×C22⋊Q8C22×C12711yescharacteristic
235C2×#121—22no—
236C2×#121—21no—
237C2×#121C22×C12712yes—
238C22×C4⋊C4C22×C12711yescharacteristic
239#483—22no—
240#481C22×C12714yescomplemented
241#465—24no—
242#450—22no—
243#448C22×C12714yescomplemented
244C2×C22⋊C8C22×C12712yes—
245#400C22×C12712yescomplemented
246#398—22no—
247#395C22×C12712yescomplemented
248#385—21no—
249#381—21no—
250#380C22×C12711yescharacteristic
251#327C22×C12718yescomplemented
252#324C22×C12714yescomplemented
253C2×#41—24no—
254C2×#41—24no—
255C2×#41—44no—
256C2×#41—44no—
257C22×Q8—21no—
258C22×Q8C23×C12711yescharacteristic
259C22×D4—21no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4D4×C12712yes—
263C23×C4—22no—
264C23×C4D4×C12711yescharacteristic
265C23×C4D4×C12711yescharacteristic
266C23×C4C23×C12711yescharacteristic
267C2×SD16—24no—
268C22×C8—22no—
269C22⋊Q8—28no—
270C22⋊Q8—28no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273#121—24no—
274#121—28no—
275#121—28no—
276#121—24no—
277#121—22no—
278#121—22no—
279#121D4×C12714yes—
280#121C23×C12714yes—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4D4×C12712yes—
288C2×C4⋊C4D4×C12712yes—
289C2×C4⋊C4C23×C12711yescharacteristic
290C2×C4⋊C4C23×C12712yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295#106—24no—
296#103—24no—
297#102—24no—
298C22⋊C8—22no—
299C22⋊C8C23×C12714yes—
300#95—22no—
301#95—22no—
302#95—22no—
303#95C23×C12712yes—
304C24—22no—
305C24C2×D4×C12711yescharacteristic
306#41—48no—
307#41—416no—
308#41—48no—
309C2×Q8—24no—
310C2×Q8—22no—
311C2×Q8—44no—
312C2×Q8—81no—
313C2×D4—24no—
314C2×D4—24no—
315C2×D4—24no—
316C2×D4—24no—
317C2×D4—22no—
318C2×D4—44no—
319C2×D4—44no—
320C2×D4—44no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4C2×D4×C12714yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—28no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—48no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4SD16×C12714yescomplemented
338C22×C4C2×D4×C12712yes—
339C22×C4C2×D4×C12712yes—
340C22×C4C2×D4×C12711yescharacteristic
341C22×C4C2×D4×C12712yes—
342C22×C4C2×D4×C12712yes—
343C22×C4C24×C12711yescharacteristic
344SD16—84no—
345C2×C8—24no—
346C2×C8—82no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4—81no—
354C4⋊C4—82no—
355C4⋊C4C2×D4×C12714yes—
356C22⋊C4—28no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—42no—
362C23—24no—
363C23—41no—
364C23—41no—
365C23—44no—
366C23—44no—
367C23—44no—
368C23#120×C12711yescharacteristic
369C23#120×C12711yescharacteristic
370C23C2×SD16×C12712yes—
371C23AGL(1,ℤ/8)×C12712yes—
372C23C22×D4×C12711yescharacteristic
373Q8—48no—
374Q8—44no—
375D4—44no—
376D4—48no—
377D4—44no—
378D4—44no—
379D4—48no—
380D4—82no—
381D4—84no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—416no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—81no—
404C2×C4#120×C12712yes—
405C2×C4C2×SD16×C12714yes—
406C2×C4C22×D4×C12712yes—
407C8—44no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—88no—
420C22#450×C12712yes—
421C22#450×C12712yes—
422C22C2×#120×C12711yescharacteristic
423C22C22×SD16×C12711yescharacteristic
424C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
425C4—24no—
426C4—22no—
427C4—22no—
428C4—44no—
429C4—42no—
430C4—82no—
431C4—81no—
432C4—81no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—84no—
438C2C2×#450×C12711yescharacteristic
439C2C127×#302011yescharacteristic
440C2C127×#302611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC2×#537×C127C2
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×#3187C2semidirect
3. C127×#2627C2semidirect
4. C127×#1616C2semidirect
5. C127×#1604C2semidirect
6. C127×#1519C2semidirect
7. C2×#324×C127C2semidirect
19. #481×C127C22semidirect
22. #448×C127C22semidirect
24. #400×C127C22semidirect
26. #395×C127C22semidirect
30. #327×C127C22semidirect
31. #324×C127C22semidirect
116. C22×C4×C127SD16semidirect
212. #18293C127direct (N × H)
222. #3187C2×C127semidirect
223. #2627C2×C127semidirect
224. #1616C2×C127semidirect
225. #1604C2×C127semidirect
226. #1519C2×C127semidirect
227. C2×#324C2×C127semidirect
228. C127#18293direct (N × H)
240. #481C22×C127semidirect
243. #448C22×C127semidirect
245. #400C22×C127semidirect
247. #395C22×C127semidirect
251. #327C22×C127semidirect
252. #324C22×C127semidirect
337. C22×C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1272
C127×#31872
C127×#26272
C127×#16162
C127×#16042
C127×#15192
C2×#324×C1272
#18293127