Finite Group Databasebeta

← C127×#8380 #44572053

Subgroups — C127×#8380 #44572053

Order 32512.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C127C211yesmaximal, characteristic
2C127×#1824C212yesmaximal, complemented
3C127×#1799C211yesmaximal, characteristic
4C127×#1520C212yesmaximal, complemented
5C127×#1459C211yesmaximal, characteristic
6#554×C127—24no—
7#554×C127—24no—
8C2×C4⋊Q8×C127C411yescharacteristic, complemented
9C2×#125×C127—21no—
10C2×C22⋊Q8×C127—21no—
11C2×C22⋊Q8×C127—21no—
12C2×C22⋊Q8×C127C411yescharacteristic, complemented
13C2×C22⋊Q8×C127C2211yescharacteristic
14C2×C4×Q8×C127C411yescharacteristic, complemented
15C2×C4×D4×C127—21no—
16C2×C4×D4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C411yescharacteristic, complemented
18C22×C4⋊C4×C127C2211yescharacteristic
19C2×#99×C127—21no—
20C2×C22⋊C8×C127C2212yes—
21#380×C127C2212yes—
22#342×C127—21no—
23#340×C127—24no—
24#328×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C22×Q8×C127—21no—
28C22×Q8×C127C2×C411yescharacteristic
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—21no—
31C23×C4×C127—21no—
32C23×C4×C127C2×C411yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C22×C8×C127—22no—
35C4⋊Q8×C127—22no—
36C4⋊Q8×C127—22no—
37#125×C127—28no—
38C22⋊Q8×C127—28no—
39C22⋊Q8×C127—28no—
40C22⋊Q8×C127—22no—
41C22⋊Q8×C127—22no—
42C22⋊Q8×C127—22no—
43C22⋊Q8×C127D414yes—
44C4×Q8×C127—22no—
45C4×Q8×C127—22no—
46C4×D4×C127—28no—
47C4×D4×C127—22no—
48C4×D4×C127—22no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127C2×C411yescharacteristic
60C2×C4⋊C4×C127C2×C411yescharacteristic
61C2×C4⋊C4×C127C2×C411yescharacteristic
62C2×C4⋊C4×C127D411yescharacteristic
63C2×C4⋊C4×C127D414yes—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127D411yescharacteristic
68C2×C22⋊C4×C127D411yescharacteristic
69C2×C42×C127—21no—
70C2×C42×C127C2×C411yescharacteristic
71#99×C127—42no—
72C22⋊C8×C127—22no—
73C22⋊C8×C127—22no—
74#95×C127—22no—
75C24×C127C22⋊C411yescharacteristic
76C24×C127C2×D411yescharacteristic
77C2×Q8×C127—24no—
78C2×Q8×C127—21no—
79C2×Q8×C127—42no—
80C2×Q8×C127—82no—
81C2×Q8×C127C22⋊C412yes—
82C2×D4×C127—22no—
83C2×D4×C127—22no—
84C2×D4×C127SD1612yes—
85C2×D4×C127Q1612yes—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—42no—
95C22×C4×C127—42no—
96C22×C4×C127—42no—
97C22×C4×C127—82no—
98C22×C4×C127—82no—
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C411yescharacteristic
101C22×C4×C127C22⋊C411yescharacteristic
102C22×C4×C127C22×C411yescharacteristic
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D411yescharacteristic
106C2×C8×C127—44no—
107C2×C8×C127—42no—
108C4⋊C4×C127—24no—
109C4⋊C4×C127—24no—
110C4⋊C4×C127—24no—
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×C127—44no—
119C4⋊C4×C127C22⋊C412yes—
120C4⋊C4×C127C22⋊C412yes—
121C4⋊C4×C127C22⋊C412yes—
122C22⋊C4×C127—24no—
123C22⋊C4×C127—24no—
124C22⋊C4×C127—22no—
125C22⋊C4×C127—22no—
126C22⋊C4×C127—42no—
127C22⋊C4×C127—42no—
128C42×C127—24no—
129C42×C127—21no—
130C42×C127—21no—
131C23×C127—21no—
132C23×C127—21no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127#10312yes—
138C23×C127C2×C22⋊C411yescharacteristic
139C23×C127#12012yes—
140C23×C127C2×SD1611yescharacteristic
141C23×C127C2×Q1611yescharacteristic
142C23×C127#13712yes—
143Q8×C127—42no—
144Q8×C127—42no—
145Q8×C127—84no—
146D4×C127—24no—
147D4×C127—24no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—24no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—21no—
154C2×C4×C127—22no—
155C2×C4×C127—21no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—41no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—84no—
169C2×C4×C127—84no—
170C2×C4×C127—82no—
171C2×C4×C127—82no—
172C2×C4×C127—82no—
173C2×C4×C127#10312yes—
174C2×C4×C127C2×C22⋊C411yescharacteristic
175C2×C4×C127C2×C22⋊C411yescharacteristic
176C2×C4×C127#12012yes—
177C8×C127—82no—
178C22×C127—21no—
179C22×C127—22no—
180C22×C127—21no—
181C22×C127—22no—
182C22×C127—22no—
183C22×C127—41no—
184C22×C127—41no—
185C22×C127—42no—
186C22×C127—42no—
187C22×C127—42no—
188C22×C127—41no—
189C22×C127—41no—
190C22×C127#37911yescharacteristic
191C22×C127C2×#10311yescharacteristic
192C22×C127#41911yescharacteristic
193C22×C127#44812yes—
194C22×C127#45112yes—
195C4×C127—22no—
196C4×C127—21no—
197C4×C127—22no—
198C4×C127—42no—
199C4×C127—42no—
200C4×C127—42no—
201C4×C127—41no—
202C4×C127—41no—
203C4×C127—42no—
204C4×C127—162no—
205C4×C127#41012yes—
206#8380C12711yesmaximal, characteristic, direct product factor, Sylow
207C2×C127—22no—
208C2×C127—21no—
209C2×C127—21no—
210C2×C127—22no—
211C2×C127—42no—
212C2×C127#178211yescharacteristic
213C2×C127#178711yescharacteristic
214C2×C127#179511yescharacteristic
215C2×#554C2×C12711yescharacteristic
216#1824C2×C12712yescomplemented
217#1799C2×C12711yescharacteristic
218#1520C2×C12712yescomplemented
219#1459C2×C12711yescharacteristic
220C127#838011yescharacteristic, direct product factor, Sylow
221#554—24no—
222#554—24no—
223C2×C4⋊Q8C4×C12711yescharacteristic, complemented
224C2×#125—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C4×C12711yescharacteristic, complemented
228C2×C22⋊Q8C22×C12711yescharacteristic
229C2×C4×Q8C4×C12711yescharacteristic, complemented
230C2×C4×D4—21no—
231C2×C4×D4C22×C12711yescharacteristic
232C22×C4⋊C4C4×C12711yescharacteristic, complemented
233C22×C4⋊C4C22×C12711yescharacteristic
234C2×#99—21no—
235C2×C22⋊C8C22×C12712yes—
236#380C22×C12712yes—
237#342—21no—
238#340—24no—
239#328—24no—
240#324—21no—
241#323—21no—
242C22×Q8—21no—
243C22×Q8C2×C4×C12711yescharacteristic
244C22×D4D4×C12711yescharacteristic
245C23×C4—21no—
246C23×C4—21no—
247C23×C4C2×C4×C12711yescharacteristic
248C23×C4C23×C12711yescharacteristic
249C22×C8—22no—
250C4⋊Q8—22no—
251C4⋊Q8—22no—
252#125—28no—
253C22⋊Q8—28no—
254C22⋊Q8—28no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8D4×C12714yes—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×D4—28no—
262C4×D4—22no—
263C4×D4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4C2×C4×C12711yescharacteristic
275C2×C4⋊C4C2×C4×C12711yescharacteristic
276C2×C4⋊C4C2×C4×C12711yescharacteristic
277C2×C4⋊C4D4×C12711yescharacteristic
278C2×C4⋊C4D4×C12714yes—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4D4×C12711yescharacteristic
283C2×C22⋊C4D4×C12711yescharacteristic
284C2×C42—21no—
285C2×C42C2×C4×C12711yescharacteristic
286#99—42no—
287C22⋊C8—22no—
288C22⋊C8—22no—
289#95—22no—
290C24C22⋊C4×C12711yescharacteristic
291C24C2×D4×C12711yescharacteristic
292C2×Q8—24no—
293C2×Q8—21no—
294C2×Q8—42no—
295C2×Q8—82no—
296C2×Q8C22⋊C4×C12712yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4SD16×C12712yes—
300C2×D4Q16×C12712yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—82no—
313C22×C4—82no—
314C22×C4C22⋊C4×C12711yescharacteristic
315C22×C4C22⋊C4×C12711yescharacteristic
316C22×C4C22⋊C4×C12711yescharacteristic
317C22×C4C22×C4×C12711yescharacteristic
318C22×C4C2×D4×C12712yes—
319C22×C4C2×D4×C12712yes—
320C22×C4C2×D4×C12711yescharacteristic
321C2×C8—44no—
322C2×C8—42no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—44no—
334C4⋊C4C22⋊C4×C12712yes—
335C4⋊C4C22⋊C4×C12712yes—
336C4⋊C4C22⋊C4×C12712yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C42—24no—
344C42—21no—
345C42—21no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#103×C12712yes—
353C23C2×C22⋊C4×C12711yescharacteristic
354C23#120×C12712yes—
355C23C2×SD16×C12711yescharacteristic
356C23C2×Q16×C12711yescharacteristic
357C23#137×C12712yes—
358Q8—42no—
359Q8—42no—
360Q8—84no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—84no—
384C2×C4—84no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4#103×C12712yes—
389C2×C4C2×C22⋊C4×C12711yescharacteristic
390C2×C4C2×C22⋊C4×C12711yescharacteristic
391C2×C4#120×C12712yes—
392C8—82no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22#379×C12711yescharacteristic
406C22C2×#103×C12711yescharacteristic
407C22#419×C12711yescharacteristic
408C22#448×C12712yes—
409C22#451×C12712yes—
410C4—22no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4—41no—
419C4—162no—
420C4#410×C12712yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2C127×#178211yescharacteristic
427C2C127×#178711yescharacteristic
428C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×D4×C127D4
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×#1824C2semidirect
4. C127×#1520C2semidirect
8. C2×C4⋊Q8×C127C4semidirect
12. C2×C22⋊Q8×C127C4semidirect
14. C2×C4×Q8×C127C4semidirect
17. C22×C4⋊C4×C127C4semidirect
206. #8380C127direct (N × H)
216. #1824C2×C127semidirect
218. #1520C2×C127semidirect
220. C127#8380direct (N × H)
223. C2×C4⋊Q8C4×C127semidirect
227. C2×C22⋊Q8C4×C127semidirect
229. C2×C4×Q8C4×C127semidirect
232. C22×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1272
C127×#18242
C127×#17992
C127×#15202
C127×#14592
#8380127