Finite Group Databasebeta

← C2×C127×#1921 #44584704

Subgroups — C2×C127×#1921 #44584704

Order 32512.

1086 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#107×C127C211yesmaximal, characteristic
2C2×#389×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
4C127×#1921C218yesmaximal, direct product factor
5C2×#340×C127C211yesmaximal, characteristic
6C2×#340×C127C211yesmaximal, characteristic
7C2×#340×C127C211yesmaximal, characteristic
8C2×#336×C127C211yesmaximal, characteristic
9C23×C8×C127C2211yescharacteristic
10C23×C8×C127C2211yescharacteristic
11C22×C4⋊C4×C127—21no—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C42×C127—21no—
17C22×C42×C127C2211yescharacteristic
18C2×#107×C127C418yescomplemented
19C2×#107×C127C2214yes—
20#389×C127—22no—
21#389×C127C2214yes—
22C4×C4⋊C4×C127—22no—
23C4×C4⋊C4×C127C2214yes—
24C2×#95×C127—21no—
25C2×#95×C127—21no—
26#340×C127C2214yes—
27#340×C127C2214yes—
28#340×C127C2214yes—
29#336×C127C2214yes—
30C23×C4×C127—21no—
31C23×C4×C127—21no—
32C23×C4×C127—21no—
33C23×C4×C127—21no—
34C23×C4×C127D411yescharacteristic
35C23×C4×C127D411yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C22×C8×C127—22no—
38C22×C8×C127—22no—
39C22×C8×C127—22no—
40C22×C8×C127—22no—
41C22×C8×C127—22no—
42C22×C8×C127C2×C414yes—
43C22×C8×C127C2312yes—
44C22×C8×C127C2312yes—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—44no—
56C2×C4⋊C4×C127C2×C414yes—
57C2×C4⋊C4×C127C2×C414yes—
58C2×C4⋊C4×C127Q814yes—
59C2×C4⋊C4×C127C2312yes—
60C2×C4⋊C4×C127C2312yes—
61C2×C4⋊C4×C127C2312yes—
62C2×C4⋊C4×C127C2312yes—
63C2×C42×C127—22no—
64C2×C42×C127—22no—
65C2×C42×C127—24no—
66C2×C42×C127—44no—
67C2×C42×C127D412yes—
68C2×C42×C127C2312yes—
69#107×C127C2×C4116yescomplemented
70#95×C127—24no—
71#95×C127—24no—
72C24×C127C2×D411yescharacteristic
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—42no—
86C22×C4×C127—42no—
87C22×C4×C127—42no—
88C22×C4×C127—42no—
89C22×C4×C127—42no—
90C22×C4×C127—42no—
91C22×C4×C127—42no—
92C22×C4×C127—42no—
93C22×C4×C127—42no—
94C22×C4×C127Q1614yes—
95C22×C4×C127C22×C412yes—
96C22×C4×C127C2×D412yes—
97C22×C4×C127C2×D412yes—
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×Q812yes—
100C22×C4×C127#4112yes—
101C22×C4×C127#4112yes—
102C22×C4×C127#4112yes—
103C22×C4×C127#4112yes—
104C22×C4×C127C2411yescharacteristic
105C2×C8×C127—28no—
106C2×C8×C127—22no—
107C2×C8×C127—22no—
108C2×C8×C127—22no—
109C2×C8×C127—22no—
110C2×C8×C127—22no—
111C2×C8×C127—44no—
112C2×C8×C127C22×C414yes—
113C4⋊C4×C127—24no—
114C4⋊C4×C127—24no—
115C4⋊C4×C127—24no—
116C4⋊C4×C127—22no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—22no—
120C4⋊C4×C127—22no—
121C4⋊C4×C127—48no—
122C4⋊C4×C127—42no—
123C4⋊C4×C127C22×C414yes—
124C4⋊C4×C127C22×C414yes—
125C4⋊C4×C127C2×Q814yes—
126C42×C127—24no—
127C42×C127—22no—
128C42×C127—22no—
129C42×C127—48no—
130C23×C127C4×D412yes—
131C23×C127C22⋊Q812yes—
132C23×C127#12312yes—
133C23×C127C2×Q1612yes—
134C23×C127#13512yes—
135C23×C127AGL(1,ℤ/8)12yes—
136C23×C127AGL(1,ℤ/8)12yes—
137C23×C127C22×D411yescharacteristic
138C2×C4×C127—22no—
139C2×C4×C127—22no—
140C2×C4×C127—28no—
141C2×C4×C127—24no—
142C2×C4×C127—24no—
143C2×C4×C127—24no—
144C2×C4×C127—22no—
145C2×C4×C127—22no—
146C2×C4×C127—22no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—42no—
153C2×C4×C127—48no—
154C2×C4×C127—48no—
155C2×C4×C127—48no—
156C2×C4×C127—44no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—84no—
161C2×C4×C127#11714yes—
162C2×C4×C127C4×D412yes—
163C2×C4×C127C4×Q814yes—
164C2×C4×C127C22⋊Q812yes—
165C2×C4×C127#12312yes—
166C2×C4×C127#12514yes—
167C2×C4×C127#12614yes—
168C2×C4×C127C2×Q1614yes—
169C2×C4×C127C23×C411yescharacteristic
170C2×C4×C127C22×Q811yescharacteristic
171C2×C4×C127C2×#4111yescharacteristic
172C2×C4×C127C2×#4111yescharacteristic
173C2×C4×C127C2×#4111yescharacteristic
174C2×C4×C127C2×#4111yescharacteristic
175C8×C127—24no—
176C8×C127—42no—
177C22×C127#38714yes—
178C22×C127C4×Q1614yes—
179C22×C127#44214yes—
180C22×C127#47714yes—
181C22×C127#47814yes—
182C22×C127#48214yes—
183C22×C127#48414yes—
184C22×C127C2×C4×D411yescharacteristic
185C22×C127C2×C22⋊Q811yescharacteristic
186C22×C127C2×#12311yescharacteristic
187C22×C127C22×Q1611yescharacteristic
188C22×C127C2×#13511yescharacteristic
189C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
190C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
191C4×C127—24no—
192C4×C127—44no—
193C4×C127—42no—
194C4×C127—44no—
195C4×C127—44no—
196C4×C127—82no—
197C4×C127#38714yes—
198C4×C127C2×#11711yescharacteristic
199C4×C127C2×C4×Q811yescharacteristic
200C4×C127C2×#12511yescharacteristic
201C4×C127C2×#12611yescharacteristic
202C2×#1921C12711yesmaximal, characteristic, direct product factor, Sylow
203C2×C127#192118yesdirect product factor
204C2×C127C2×#38711yescharacteristic
205C2×C127C2×C4×Q1611yescharacteristic
206C2×C127C2×#44211yescharacteristic
207C2×C127C2×#47811yescharacteristic
208C2×C127C2×#47711yescharacteristic
209C2×C127C2×#48211yescharacteristic
210C2×C127C2×#48411yescharacteristic
211C22×#107C2×C12711yescharacteristic
212C2×#389C2×C12711yescharacteristic
213C2×C4×C4⋊C4C2×C12711yescharacteristic
214#1921C2×C12718yesdirect product factor
215C2×#340C2×C12711yescharacteristic
216C2×#340C2×C12711yescharacteristic
217C2×#340C2×C12711yescharacteristic
218C2×#336C2×C12711yescharacteristic
219C127C2×#192111yescharacteristic, direct product factor, Sylow
220C23×C8C22×C12711yescharacteristic
221C23×C8C22×C12711yescharacteristic
222C22×C4⋊C4—21no—
223C22×C4⋊C4C22×C12711yescharacteristic
224C22×C4⋊C4C22×C12711yescharacteristic
225C22×C4⋊C4C22×C12711yescharacteristic
226C22×C4⋊C4C22×C12711yescharacteristic
227C22×C42—21no—
228C22×C42C22×C12711yescharacteristic
229C2×#107C4×C12718yescomplemented
230C2×#107C22×C12714yes—
231#389—22no—
232#389C22×C12714yes—
233C4×C4⋊C4—22no—
234C4×C4⋊C4C22×C12714yes—
235C2×#95—21no—
236C2×#95—21no—
237#340C22×C12714yes—
238#340C22×C12714yes—
239#340C22×C12714yes—
240#336C22×C12714yes—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4D4×C12711yescharacteristic
246C23×C4D4×C12711yescharacteristic
247C23×C4C23×C12711yescharacteristic
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8C2×C4×C12714yes—
254C22×C8C23×C12712yes—
255C22×C8C23×C12712yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—44no—
267C2×C4⋊C4C2×C4×C12714yes—
268C2×C4⋊C4C2×C4×C12714yes—
269C2×C4⋊C4Q8×C12714yes—
270C2×C4⋊C4C23×C12712yes—
271C2×C4⋊C4C23×C12712yes—
272C2×C4⋊C4C23×C12712yes—
273C2×C4⋊C4C23×C12712yes—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—24no—
277C2×C42—44no—
278C2×C42D4×C12712yes—
279C2×C42C23×C12712yes—
280#107C2×C4×C127116yescomplemented
281#95—24no—
282#95—24no—
283C24C2×D4×C12711yescharacteristic
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4Q16×C12714yes—
306C22×C4C22×C4×C12712yes—
307C22×C4C2×D4×C12712yes—
308C22×C4C2×D4×C12712yes—
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4C2×Q8×C12712yes—
311C22×C4#41×C12712yes—
312C22×C4#41×C12712yes—
313C22×C4#41×C12712yes—
314C22×C4#41×C12712yes—
315C22×C4C24×C12711yescharacteristic
316C2×C8—28no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—44no—
323C2×C8C22×C4×C12714yes—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—48no—
333C4⋊C4—42no—
334C4⋊C4C22×C4×C12714yes—
335C4⋊C4C22×C4×C12714yes—
336C4⋊C4C2×Q8×C12714yes—
337C42—24no—
338C42—22no—
339C42—22no—
340C42—48no—
341C23C4×D4×C12712yes—
342C23C22⋊Q8×C12712yes—
343C23#123×C12712yes—
344C23C2×Q16×C12712yes—
345C23#135×C12712yes—
346C23AGL(1,ℤ/8)×C12712yes—
347C23AGL(1,ℤ/8)×C12712yes—
348C23C22×D4×C12711yescharacteristic
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—28no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—48no—
365C2×C4—48no—
366C2×C4—48no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—84no—
372C2×C4#117×C12714yes—
373C2×C4C4×D4×C12712yes—
374C2×C4C4×Q8×C12714yes—
375C2×C4C22⋊Q8×C12712yes—
376C2×C4#123×C12712yes—
377C2×C4#125×C12714yes—
378C2×C4#126×C12714yes—
379C2×C4C2×Q16×C12714yes—
380C2×C4C23×C4×C12711yescharacteristic
381C2×C4C22×Q8×C12711yescharacteristic
382C2×C4C2×#41×C12711yescharacteristic
383C2×C4C2×#41×C12711yescharacteristic
384C2×C4C2×#41×C12711yescharacteristic
385C2×C4C2×#41×C12711yescharacteristic
386C8—24no—
387C8—42no—
388C22#387×C12714yes—
389C22C4×Q16×C12714yes—
390C22#442×C12714yes—
391C22#477×C12714yes—
392C22#478×C12714yes—
393C22#482×C12714yes—
394C22#484×C12714yes—
395C22C2×C4×D4×C12711yescharacteristic
396C22C2×C22⋊Q8×C12711yescharacteristic
397C22C2×#123×C12711yescharacteristic
398C22C22×Q16×C12711yescharacteristic
399C22C2×#135×C12711yescharacteristic
400C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
401C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
402C4—24no—
403C4—42no—
404C4—44no—
405C4—44no—
406C4—44no—
407C4—82no—
408C4#387×C12714yes—
409C4C2×#117×C12711yescharacteristic
410C4C2×C4×Q8×C12711yescharacteristic
411C4C2×#125×C12711yescharacteristic
412C4C2×#126×C12711yescharacteristic
413C2C127×#192118yesdirect product factor
414C2C2×#387×C12711yescharacteristic
415C2C2×C4×Q16×C12711yescharacteristic
416C2C2×#442×C12711yescharacteristic
417C2C2×#478×C12711yescharacteristic
418C2C2×#477×C12711yescharacteristic
419C2C2×#482×C12711yescharacteristic
420C2C2×#484×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1921C2direct (N × H)
18. C2×#107×C127C4semidirect
69. #107×C127C2×C4semidirect
202. C2×#1921C127direct (N × H)
203. C2×C127#1921direct (N × H)
214. #1921C2×C127direct (N × H)
219. C127C2×#1921direct (N × H)
229. C2×#107C4×C127semidirect
280. #107C2×C4×C127semidirect
413. C2C127×#1921direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#107×C1272
C2×#389×C1272
C2×C4×C4⋊C4×C1272
C127×#19212
C2×#340×C1272
C2×#336×C1272
C2×#1921127