Finite Group Databasebeta

← C127×#8373 #44572046

Subgroups — C127×#8373 #44572046

Order 32512.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C127C211yesmaximal, characteristic
2C4×#100×C127C211yesmaximal, characteristic, complemented
3C127×#1528C212yesmaximal, complemented
4C127×#1490C212yesmaximal, complemented
5C127×#1466C211yesmaximal, characteristic, complemented
6#553×C127—24no—
7#553×C127—24no—
8C2×#126×C127—21no—
9C2×#125×C127C2211yescharacteristic
10C2×#123×C127—21no—
11C2×#121×C127—21no—
12C2×#121×C127C411yescharacteristic
13C2×#121×C127C411yescharacteristic
14C2×C4×D4×C127—21no—
15C2×C4×D4×C127C2211yescharacteristic
16C2×C4×D4×C127C2211yescharacteristic
17C2×#117×C127C411yescharacteristic
18C22×C4⋊C4×C127C411yescharacteristic
19#432×C127C2212yes—
20C2×#100×C127—21no—
21C4×M16×C127C2212yes—
22#343×C127—21no—
23#330×C127—24no—
24D4⋊C8×C127—24no—
25#323×C127—21no—
26#323×C127—21no—
27C22×D4×C127—21no—
28C22×D4×C127—21no—
29C22×D4×C127C2×C411yescharacteristic
30C22×D4×C127D411yescharacteristic
31C23×C4×C127—21no—
32C23×C4×C127—21no—
33C23×C4×C127C2×C411yescharacteristic
34C23×C4×C127C2×C411yescharacteristic
35C2×M16×C127—22no—
36#126×C127—28no—
37#125×C127—22no—
38#125×C127D414yes—
39#123×C127—28no—
40#121×C127—28no—
41#121×C127—22no—
42#121×C127—22no—
43#121×C127—22no—
44#121×C127—22no—
45C4×D4×C127—28no—
46C4×D4×C127—22no—
47C4×D4×C127—22no—
48C4×D4×C127—22no—
49C4×D4×C127D414yes—
50#117×C127—22no—
51#117×C127—22no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127C2×C411yescharacteristic
58C2×C4⋊C4×C127C2×C411yescharacteristic
59C2×C4⋊C4×C127C2×C411yescharacteristic
60C2×C4⋊C4×C127D411yescharacteristic
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127D411yescharacteristic
66C2×C22⋊C4×C127D411yescharacteristic
67C2×C42×C127—21no—
68C2×C42×C127C2311yescharacteristic
69C4⋊C8×C127—22no—
70#100×C127—24no—
71C22⋊C8×C127—22no—
72#97×C127—22no—
73#97×C127—22no—
74C4×C8×C127—22no—
75C24×C127—21no—
76C24×C127C22⋊C411yescharacteristic
77C24×C127C22⋊C411yescharacteristic
78C2×D4×C127—24no—
79C2×D4×C127—22no—
80C2×D4×C127—24no—
81C2×D4×C127—21no—
82C2×D4×C127—22no—
83C2×D4×C127—42no—
84C2×D4×C127—41no—
85C2×D4×C127—42no—
86C2×D4×C127—42no—
87C2×D4×C127—82no—
88C2×D4×C127C22⋊C412yes—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—24no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—24no—
98C22×C4×C127—42no—
99C22×C4×C127—42no—
100C22×C4×C127—82no—
101C22×C4×C127—82no—
102C22×C4×C127C22⋊C411yescharacteristic
103C22×C4×C127C22⋊C411yescharacteristic
104C22×C4×C127C22×C411yescharacteristic
105C22×C4×C127C2×D411yescharacteristic
106C22×C4×C127C2×D411yescharacteristic
107M16×C127—24no—
108M16×C127—42no—
109C2×C8×C127—42no—
110C2×C8×C127—42no—
111C4⋊C4×C127—24no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—24no—
116C4⋊C4×C127—24no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127C22⋊C412yes—
119C4⋊C4×C127C22⋊C412yes—
120C4⋊C4×C127C22⋊C412yes—
121C22⋊C4×C127—24no—
122C22⋊C4×C127—24no—
123C22⋊C4×C127—24no—
124C22⋊C4×C127—24no—
125C22⋊C4×C127—22no—
126C22⋊C4×C127—22no—
127C42×C127—24no—
128C42×C127C2×D412yes—
129C42×C127C2×D412yes—
130C23×C127—21no—
131C23×C127—21no—
132C23×C127—21no—
133C23×C127—22no—
134C23×C127—21no—
135C23×C127—21no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127#10412yes—
145C23×C127C2×C22⋊C411yescharacteristic
146D4×C127—24no—
147D4×C127—44no—
148D4×C127—42no—
149D4×C127—48no—
150D4×C127—84no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—22no—
154C2×C4×C127—21no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—21no—
158C2×C4×C127—22no—
159C2×C4×C127—41no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—84no—
171C2×C4×C127—84no—
172C2×C4×C127C2×C22⋊C411yescharacteristic
173C2×C4×C127C2×C22⋊C411yescharacteristic
174C2×C4×C127#12012yes—
175C2×C4×C127#12012yes—
176C8×C127—44no—
177C8×C127—82no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—22no—
181C22×C127—42no—
182C22×C127—42no—
183C22×C127—41no—
184C22×C127—41no—
185C22×C127—42no—
186C22×C127—41no—
187C22×C127—41no—
188C22×C127—42no—
189C22×C127—41no—
190C22×C127—42no—
191C22×C127—81no—
192C22×C127—81no—
193C22×C127—82no—
194C22×C127—82no—
195C22×C127#37911yescharacteristic
196C22×C127C2×#10411yescharacteristic
197C22×C127#42111yescharacteristic
198C4×C127—22no—
199C4×C127—21no—
200C4×C127—22no—
201C4×C127—42no—
202C4×C127—42no—
203C4×C127—41no—
204C4×C127—41no—
205C4×C127—42no—
206C4×C127#41312yes—
207#8373C12711yesmaximal, characteristic, direct product factor, Sylow
208C2×C127—21no—
209C2×C127—21no—
210C2×C127—42no—
211C2×C127—81no—
212C2×C127—82no—
213C2×C127#178511yescharacteristic
214C2×C127#178911yescharacteristic
215C2×C127#179511yescharacteristic
216C2×#553C2×C12711yescharacteristic
217C4×#100C2×C12711yescharacteristic, complemented
218#1528C2×C12712yescomplemented
219#1490C2×C12712yescomplemented
220#1466C2×C12711yescharacteristic, complemented
221C127#837311yescharacteristic, direct product factor, Sylow
222#553—24no—
223#553—24no—
224C2×#126—21no—
225C2×#125C22×C12711yescharacteristic
226C2×#123—21no—
227C2×#121—21no—
228C2×#121C4×C12711yescharacteristic
229C2×#121C4×C12711yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4C22×C12711yescharacteristic
232C2×C4×D4C22×C12711yescharacteristic
233C2×#117C4×C12711yescharacteristic
234C22×C4⋊C4C4×C12711yescharacteristic
235#432C22×C12712yes—
236C2×#100—21no—
237C4×M16C22×C12712yes—
238#343—21no—
239#330—24no—
240D4⋊C8—24no—
241#323—21no—
242#323—21no—
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C2×C4×C12711yescharacteristic
246C22×D4D4×C12711yescharacteristic
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C2×C4×C12711yescharacteristic
250C23×C4C2×C4×C12711yescharacteristic
251C2×M16—22no—
252#126—28no—
253#125—22no—
254#125D4×C12714yes—
255#123—28no—
256#121—28no—
257#121—22no—
258#121—22no—
259#121—22no—
260#121—22no—
261C4×D4—28no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4D4×C12714yes—
266#117—22no—
267#117—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4C2×C4×C12711yescharacteristic
274C2×C4⋊C4C2×C4×C12711yescharacteristic
275C2×C4⋊C4C2×C4×C12711yescharacteristic
276C2×C4⋊C4D4×C12711yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4D4×C12711yescharacteristic
282C2×C22⋊C4D4×C12711yescharacteristic
283C2×C42—21no—
284C2×C42C23×C12711yescharacteristic
285C4⋊C8—22no—
286#100—24no—
287C22⋊C8—22no—
288#97—22no—
289#97—22no—
290C4×C8—22no—
291C24—21no—
292C24C22⋊C4×C12711yescharacteristic
293C24C22⋊C4×C12711yescharacteristic
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4C22⋊C4×C12712yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C22⋊C4×C12711yescharacteristic
319C22×C4C22⋊C4×C12711yescharacteristic
320C22×C4C22×C4×C12711yescharacteristic
321C22×C4C2×D4×C12711yescharacteristic
322C22×C4C2×D4×C12711yescharacteristic
323M16—24no—
324M16—42no—
325C2×C8—42no—
326C2×C8—42no—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4C22⋊C4×C12712yes—
335C4⋊C4C22⋊C4×C12712yes—
336C4⋊C4C22⋊C4×C12712yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C42—24no—
344C42C2×D4×C12712yes—
345C42C2×D4×C12712yes—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23#104×C12712yes—
361C23C2×C22⋊C4×C12711yescharacteristic
362D4—24no—
363D4—44no—
364D4—42no—
365D4—48no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4—84no—
388C2×C4C2×C22⋊C4×C12711yescharacteristic
389C2×C4C2×C22⋊C4×C12711yescharacteristic
390C2×C4#120×C12712yes—
391C2×C4#120×C12712yes—
392C8—44no—
393C8—82no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—41no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22#379×C12711yescharacteristic
412C22C2×#104×C12711yescharacteristic
413C22#421×C12711yescharacteristic
414C4—21no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4#413×C12712yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—82no—
427C2—81no—
428C2C127×#178511yescharacteristic
429C2C127×#178911yescharacteristic
430C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#553×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#100×C127C2semidirect
3. C127×#1528C2semidirect
4. C127×#1490C2semidirect
5. C127×#1466C2semidirect
207. #8373C127direct (N × H)
217. C4×#100C2×C127semidirect
218. #1528C2×C127semidirect
219. #1490C2×C127semidirect
220. #1466C2×C127semidirect
221. C127#8373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#553×C1272
C4×#100×C1272
C127×#15282
C127×#14902
C127×#14662
#8373127