Finite Group Databasebeta

← C127×#7634 #44571307

Subgroups — C127×#7634 #44571307

Order 32512.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C127C211yesmaximal, characteristic
2C127×#1749C211yesmaximal, characteristic
3C127×#1728C211yesmaximal, characteristic
4C127×#1272C212yesmaximal, complemented
5C127×#1271C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×C22⋊Q8×C127C411yescharacteristic
8C2×C4×Q8×C127C411yescharacteristic
9C22×C42×C127C2211yescharacteristic
10C2×C22⋊C8×C127—21no—
11C2×#97×C127—21no—
12#391×C127C2211yescharacteristic
13#389×C127C2211yescharacteristic
14#387×C127—21no—
15#385×C127—21no—
16#380×C127C411yescharacteristic
17C4×C4⋊C4×C127—21no—
18C4×C4⋊C4×C127C411yescharacteristic
19C4×C22⋊C4×C127—21no—
20#336×C127—21no—
21#336×C127C2212yes—
22#336×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—24no—
28C2×M16×C127—42no—
29C2×M16×C127—42no—
30C22×C8×C127—22no—
31C22×C8×C127—22no—
32C22⋊Q8×C127—22no—
33C22⋊Q8×C127—22no—
34C4×Q8×C127—42no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C42×C127—21no—
44C2×C42×C127—21no—
45C2×C42×C127—42no—
46C2×C42×C127C2×C411yescharacteristic
47C2×C42×C127D411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C2×C42×C127C2311yescharacteristic
50C22⋊C8×C127—24no—
51#97×C127—42no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57C24×C127C22⋊C411yescharacteristic
58C2×Q8×C127—21no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C2×Q8×C127M1612yescomplemented
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—22no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—41no—
75C22×C4×C127—41no—
76C22×C4×C127—41no—
77C22×C4×C127C22⋊C411yescharacteristic
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83M16×C127—48no—
84C2×C8×C127—24no—
85C2×C8×C127—24no—
86C2×C8×C127—42no—
87C2×C8×C127—42no—
88C2×C8×C127—42no—
89C2×C8×C127—42no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127M1612yescomplemented
98C22⋊C4×C127—24no—
99C22⋊C4×C127—42no—
100C42×C127—22no—
101C42×C127—22no—
102C42×C127—41no—
103C42×C127—41no—
104C42×C127—42no—
105C42×C127—42no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127#10412yes—
113C23×C127C2×C22⋊C411yescharacteristic
114Q8×C127—42no—
115Q8×C127—42no—
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—44no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127#9912yes—
147C2×C4×C127#10412yes—
148C2×C4×C127C2×M1611yescharacteristic
149C2×C4×C127C2×M1611yescharacteristic
150C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C127#13711yescharacteristic
152C2×C4×C127#13712yes—
153C8×C127—44no—
154C8×C127—44no—
155C22×C127—22no—
156C22×C127—22no—
157C22×C127—22no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127#40711yescharacteristic
163C22×C127C2×#9911yescharacteristic
164C22×C127#41311yescharacteristic
165C22×C127#41711yescharacteristic
166C22×C127#41911yescharacteristic
167C22×C127C2×#10411yescharacteristic
168C22×C127C2×#10411yescharacteristic
169C4×C127—21no—
170C4×C127—21no—
171C4×C127—21no—
172C4×C127—22no—
173C4×C127—21no—
174C4×C127—22no—
175C4×C127—22no—
176C4×C127—41no—
177C4×C127—42no—
178C4×C127—42no—
179C4×C127—81no—
180C4×C127—81no—
181#7634C12711yesmaximal, characteristic, direct product factor, Sylow
182C2×C127—42no—
183C2×C127#146511yescharacteristic
184C2×C127#148911yescharacteristic
185C2×C127#149111yescharacteristic
186C2×C127#150411yescharacteristic
187C2×C127#150811yescharacteristic
188C2×C127#152411yescharacteristic
189C2×C127#155911yescharacteristic
190C4×C22⋊Q8C2×C12711yescharacteristic
191#1749C2×C12711yescharacteristic
192#1728C2×C12711yescharacteristic
193#1272C2×C12712yescomplemented
194#1271C2×C12712yescomplemented
195C127#763411yescharacteristic, direct product factor, Sylow
196C22×M16—21no—
197C2×C22⋊Q8C4×C12711yescharacteristic
198C2×C4×Q8C4×C12711yescharacteristic
199C22×C42C22×C12711yescharacteristic
200C2×C22⋊C8—21no—
201C2×#97—21no—
202#391C22×C12711yescharacteristic
203#389C22×C12711yescharacteristic
204#387—21no—
205#385—21no—
206#380C4×C12711yescharacteristic
207C4×C4⋊C4—21no—
208C4×C4⋊C4C4×C12711yescharacteristic
209C4×C22⋊C4—21no—
210#336—21no—
211#336C22×C12712yes—
212#336C22×C12712yes—
213C22×Q8C2×C4×C12711yescharacteristic
214C23×C4C2×C4×C12711yescharacteristic
215C23×C4D4×C12711yescharacteristic
216C23×C4D4×C12711yescharacteristic
217C2×M16—24no—
218C2×M16—42no—
219C2×M16—42no—
220C22×C8—22no—
221C22×C8—22no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C4×Q8—42no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C12711yescharacteristic
229C2×C4⋊C4C2×C4×C12711yescharacteristic
230C2×C4⋊C4C2×C4×C12711yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42—42no—
236C2×C42C2×C4×C12711yescharacteristic
237C2×C42D4×C12711yescharacteristic
238C2×C42D4×C12711yescharacteristic
239C2×C42C23×C12711yescharacteristic
240C22⋊C8—24no—
241#97—42no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247C24C22⋊C4×C12711yescharacteristic
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8M16×C12712yescomplemented
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C22⋊C4×C12711yescharacteristic
268C22×C4C22⋊C4×C12711yescharacteristic
269C22×C4C22⋊C4×C12711yescharacteristic
270C22×C4C22×C4×C12711yescharacteristic
271C22×C4C2×D4×C12711yescharacteristic
272C22×C4C2×D4×C12711yescharacteristic
273M16—48no—
274C2×C8—24no—
275C2×C8—24no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C4⋊C4—24no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4M16×C12712yescomplemented
288C22⋊C4—24no—
289C22⋊C4—42no—
290C42—22no—
291C42—22no—
292C42—41no—
293C42—41no—
294C42—42no—
295C42—42no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#104×C12712yes—
303C23C2×C22⋊C4×C12711yescharacteristic
304Q8—42no—
305Q8—42no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#99×C12712yes—
337C2×C4#104×C12712yes—
338C2×C4C2×M16×C12711yescharacteristic
339C2×C4C2×M16×C12711yescharacteristic
340C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
341C2×C4#137×C12711yescharacteristic
342C2×C4#137×C12712yes—
343C8—44no—
344C8—44no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22#407×C12711yescharacteristic
353C22C2×#99×C12711yescharacteristic
354C22#413×C12711yescharacteristic
355C22#417×C12711yescharacteristic
356C22#419×C12711yescharacteristic
357C22C2×#104×C12711yescharacteristic
358C22C2×#104×C12711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—42no—
368C4—42no—
369C4—81no—
370C4—81no—
371C2—42no—
372C2C127×#146511yescharacteristic
373C2C127×#148911yescharacteristic
374C2C127×#149111yescharacteristic
375C2C127×#150411yescharacteristic
376C2C127×#150811yescharacteristic
377C2C127×#152411yescharacteristic
378C2C127×#155911yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1272C2semidirect
5. C127×#1271C2semidirect
61. C2×Q8×C127M16semidirect
97. C4⋊C4×C127M16semidirect
181. #7634C127direct (N × H)
193. #1272C2×C127semidirect
194. #1271C2×C127semidirect
195. C127#7634direct (N × H)
251. C2×Q8M16×C127semidirect
287. C4⋊C4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C1272
C127×#17492
C127×#17282
C127×#12722
C127×#12712
#7634127